1 Culex nigripalpus (DIPTERA: CULICIDAE) POPULATION AGE STRUCTURE UNDER HETEROGENEOUS ENVIRO NMENTS AND SOURCES OF ERROR ON THE ESTIMATION OF MOSQUI TO INFECTION RATES By DULCE MARIA BUSTAMANTE ZAMORA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009
2 Dulce Maria Bustamante Zamora
3 With love for my mother, Clelia; my brother, Jose Maria; and my grandmother, Felicita.
4 ACKNOWLEDGMENTS I would like to acknowledge my advisory co mmittee Dr. Cynthia Lord, Dr. Jonathan Day, Dr. Philip Lounibos, and Dr. Benjamin Bolker. I am thankful to Dr. Lord for supporting my work through her NIH grant and for her guidance. I want to thank Dr. Day for helping me better understand the ecology of mosquitoes and arboviruses in Florida. I want to thank Dr. Lounibos and Dr. Bolker for their re visions to my work. Thank you to all the friends and colleagues at FMEL that have helped me in various tasks during this process, but especia lly to Dr. George OMeara, w ho always gave me good advice about field work. He also allowed me to use his minivan to travel to the collecting sites and he let me use his compound microscope for parity determinations. To Mr. Gregory Ross, who always helped me in technical aspects, to obtain climate data, and reviewed my modeling protocol. I thank Sara Lynn, who helped me na vigate through the lab, taught me how to make traps, and helped count mosquito samples. I wa nt to thank Carol Thomas for making editorial revisions to the dissertation. I want to thank Dr. Volker Grimm (UFZ Ce nter for Environmental Research LeipzigHalle) who reviewed my modeling protocol. I also want to thank Mrs. Hilda Lynn, the Department of Recreation of the city of Vero Beach, and the Florida Fish and Wildlife Conservation Commission for allowing me access to the field collections sites. To my friends Sara Lynn, Kendra Pesko, Da vid Melius, Veronica Manrique, and Rodrigo Diaz, thank you because your friendship and suppor t have been extremely important for me, you are the ones who made me feel at home in Vero Beach. To Kyle Beucke, thank you for your love, support and company during this time.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ............................................................................................................... 4LIST OF TABLES ...........................................................................................................................8LIST OF FIGURES .......................................................................................................................10ABSTRACT ...................................................................................................................... .............14 CHAP TER 1 GENERAL INTRODUCTION .............................................................................................. 162 Culex nigripalpus AND MOSQUIT O AGE STRUCTURE: REVIEW OF THE LITERATURE AND PROBLEM STATEMENT .................................................................19Culex nigripalpus Taxonomy and Distribution ......................................................................19Culex nigripalpus in Florida ................................................................................................... 19Biology ....................................................................................................................... .....19Culex nigripalpus Population Structure and its Relation to Rainfall ..............................24Culex nigripalpus as a Disease Vector ............................................................................ 25Rainfall-Driven Population Dynamics of Culex nigripalpus in Florida and its Relation to Arbovirus Epidemics ................................................................................. 26Mosquito Age, Survival, and Population Ag e Structure: Epidemiological Relevance ..........29Methods to Measure Adult Female Mosquito Age ......................................................... 33Methods to Estimate Survival Rates ................................................................................ 37Methods based on age determination ....................................................................... 37Methods independent of age determination ............................................................. 39Factors Affecting Physiological and Chronological Age St ructure in Mosquitoes ................ 40Modeling Population Age Structure .......................................................................................45Leslie Matrix Population Models .................................................................................... 45Age Structure in Continuous Time Models ..................................................................... 47Individual-Based Models ................................................................................................. 49Problem Statement ............................................................................................................. .....523 RELATIVE ABUNDANCE AND PHYS IOL OGICAL AGE STRUCTURE OF Culex nigripalpus AS A FUNCTION OF ENVI RONMENTAL VARIABLES ............................. 57Introduction .................................................................................................................. ...........57Materials and Methods ...........................................................................................................64Collection Sites ................................................................................................................64Mosquito Collections ....................................................................................................... 65Mosquito Identification ................................................................................................... 67Parity Determinations ...................................................................................................... 67Data Analysis ...................................................................................................................68
6 Model selection using the Akaike Inf ormation Criteria (AIC) ................................71Model selection of a GLM for the prediction of the average number of Culex nigripalpus females collected per trap night ........................................................74Model selection of a GLM for prediction of the estimated proportion of parous females ..................................................................................................................75Model selection of a GLM for prediction of the estimated average number of nulliparous Culex nigripalpus females collected per trap night ........................... 76Adequacy of linear model and goodness of fit ......................................................... 77Results .....................................................................................................................................78Mosquito Collections and Weather .................................................................................78Model Results ..................................................................................................................79Linearity and Goodness of Fit .........................................................................................82Discussion .................................................................................................................... ...........834 A SPATIALLY EXPLICIT INDIVIDUAL -BASE D MODEL TO STUDY THE EMERGENCE OF AGE STRUCTURE IN Culex nigripalpus POPULATIONS ...............126Introduction .................................................................................................................. .........126Dispersal and Foraging in Heterogeneous Environments ............................................. 128An Individual-Based Model for Culex nigripalpus .......................................................133Materials and Methods .........................................................................................................134The ODD Protocol ......................................................................................................... 134Overview ...................................................................................................................... .135Statement of model purpose ................................................................................... 135State variables and scales .......................................................................................135Process overview and scheduling ........................................................................... 136Design Concepts ............................................................................................................137Details ....................................................................................................................... .....138Initialization ........................................................................................................... 138Input ....................................................................................................................... 138Submodels .............................................................................................................. 144Simulation Experiments ................................................................................................ 152Sensitivity An alysis ....................................................................................................... 153Results ...................................................................................................................................155Simulation Experiments ................................................................................................ 155Population size and spatial spread with MM resource finding efficiency ............. 155Physiological age structure: percenta ge of parous females with MM resource finding efficiency ................................................................................................157Chronological age structure: the age of unfed parous 1 and parous 2 females with MM resource finding efficiency .................................................................158Simulation experiments results summary .............................................................. 162Sensitivity An alysis ....................................................................................................... 163Population size and spatial spread .......................................................................... 163Physiological age structure .....................................................................................165Chronological age structure ................................................................................... 166Sensitivity analysis results summary ...................................................................... 167
7 Discussion .................................................................................................................... .........167Discussion Summary ............................................................................................................ 1765 SOURCES OF ERROR IN THE ESTIMA TION OF AR BOVIRUS INFECTION RATES IN MOSQUITOES .................................................................................................. 216Introduction .................................................................................................................. .........216Methods and Results .............................................................................................................223Model I: Relationship between Mos quito Infection and Infectiousness ......................223Results for Model I ........................................................................................................ 227Model II: Relationship between Populat ion Infection Prevalence and Estimated Infection Rate .............................................................................................................228Results for Model II ....................................................................................................... 232Discussion .................................................................................................................... .........2336 GENERAL DISCUSSION ................................................................................................... 250APPENDIX: INPUTS FOR THE Culex nigripalpus SPATIALLY EXPLICIT INDIVIDUAL BASED MODEL ......................................................................................... 263 LIST OF REFERENCES .............................................................................................................273BIOGRAPHICAL SKETCH .......................................................................................................288
8 LIST OF TABLES Table page 2-1 Vectorial capacity at different values of p ......................................................................... 563-1 Species of mosquitoes and total numb er of mosquitoes collected during 2007 and 2008....................................................................................................................................993-2 Culex nigripalpus collected in the year 2007 and nu mbers of mosquitoes dissected for parity determination. .................................................................................................. 1003-3 Culex nigripalpus collected in the year 2008 and nu mbers of mosquitoes dissected for parity determination. .................................................................................................. 1023-4 Model selection results for a predictive m odel on the average number of mosquitoes collected per trap night..................................................................................................... 1043-5 Parameter estimates and their confidence intervals for the predictive models ................ 1053-6 Simple correlations among environmental variables. ...................................................... 1063-7 Model selection results for a predic tive model of the proportion of parous mosquitoes .................................................................................................................... ...1073-8 Model selection results for a predictive model on the average number of nulliparous mosquitoes collected per trap night. ................................................................................ 1084-1 Mosquito population sizes after init ialization under different resource finding efficiency conditions fo r the two landscapes ................................................................... 1784-2 Weather conditions by month fo r weather patterns W1 and W2. .................................... 1794-3 Description of the rela tive humidity and oviposition site availability in the landscapes for each simulated weather condition. ........................................................... 1804-4 Probabilities of flight initiation during th e night hours as a func tion of the fraction of the moon illuminated. ...................................................................................................... 1814-5 Total mosquito production and average spatial spread for each of the 10 runs with the MM foraging probability functions ............................................................................ 1814-6 Numbers of extinctions observed under different resource finding efficiency conditions. ................................................................................................................... .....1825-1 Duration of the gonotrophic cycle and da ily survival rates obtained from the literature for Cx. tarsalis and Cx. p. quinquefasciatus .................................................... 240
9 5-2 Results of Model I for mosquito populat ions with vir al tite r distribution 1 (101.5-104 PFU/mosquito). ................................................................................................................ 2415-3 Results of Model I for mosquito populat ions with viral tite r distribution 2 (102-106 PFU/mosquito) ................................................................................................................. 2425-4 Results of the Kolmogorov-Smirnov test comparing MLE frequency distributions from Model II ................................................................................................................. ..243A-1 Relative humidity and temperature inputs for the Culex nigripalpus SEIBM. ................ 264
10 LIST OF FIGURES Figure page 3-1 Collection sites in Indi an River County, Florida ............................................................. 1093-2 Geographical overview of the Park Site ..........................................................................1103-3 Details of the Park Site. ...................................................................................................1113-4 Geographical overview of the Yard Site .......................................................................... 1123-5 Details of the Yard Site .................................................................................................. ..1133-6 Geographical overview of the Groves Site.. .................................................................... 1143-7 Details of the Groves Site. ............................................................................................... 1153-8 The lard can trap. ........................................................................................................ .....1163-9 The classification of ovaries in Culex nigripalpus females based on the status of the tracheal coiling. ................................................................................................................1173-10 Location of the reportin g sites from which the KBDI and MWTD data were obtained. ..................................................................................................................... ......1183-11 Weather conditions 2007. ................................................................................................1193-12 Weather conditions 2008 .................................................................................................1203-13 Observed and predicted average numb er of mosquitoes per trap night. .......................... 1213-14 Comparison of the average and the single models for the average number of mosquitoes per trap night ................................................................................................. 1223-15 Observed and predicted estimated pr oportion of female parous mosquitoes ..................1233-16 Observed and predicted estimated number of nulliparous mosquitoes collected per trap night ..........................................................................................................................1243-17 Graphical evaluation of re siduals to evaluate the ade quacy of the linear model ............. 1254-1 Simplified life cycle of an individual Culex nigripalpus used in the modeling study .....1834-2 The favorable landscape ..................................................................................................1844-3 The unfavorable landscape .............................................................................................. 1854-4 Discrete changes in the area availa ble for oviposition for each treatment ...................... 186
11 4-5 Changes in the attractiveness scores of ce lls on the basis of their vegetation type as a function of relative hum idity. ........................................................................................ 1874-6 Example of the process to select a cell during mosquito dispersal, on the basis of vegetation type and number of hosts. .............................................................................. 1884-7 Daily changes in the size of the mosquito population for each treatment ....................... 1894-8 Daily changes in the spatial spread of the mosquito population for each treatment. ....... 1904-9 Differences in mosquito production and sp atial spread among the treatments with the MM resource finding efficiency. ..................................................................................... 1914-10 Daily changes in the percentage of pa rous females of the mosquito population for each treatment with the MM resource finding efficiency ................................................ 1924-11 Maximum percentage of parous female s per month on each treatment with the MM resource finding efficiency ..............................................................................................1934-12 Daily changes in the average age in days of unfed parous 1 females for each treatment with the MM resource finding efficiency ........................................................ 1944-13 Daily changes in the average age in days of unfed parous 2 females for each treatment with the MM resource finding efficiency ........................................................ 1954-14 Daily changes in average age of unfed parous 1 females for one population per treatment with the MM resource finding efficiency ........................................................ 1964-15 Daily changes in average age of unfed parous 2 females for one population per treatment with the MM resource finding efficiency ........................................................ 1974-16 Differences on age structures of unfed pa rous 1 females among treatments with the MM resource finding efficiency. ..................................................................................... 1984-17 Differences on age structures of unfed pa rous 2 females among treatments with the MM resource finding efficiency.. ....................................................................................1994-18 Averages per month of the proportion of parous 1 females over the age of 12.5 days for each treatment with the MM resource finding efficiency. ......................................... 2004-19 Sensitivity of the total mosquito production to changes in the resource finding efficiency .................................................................................................................... ......2014-20 Sensitivity of the average spatial sp read to changes in the resource finding efficiency. ................................................................................................................... ......2024-21 Sensitivity of the maximum percentage of parous females per month to changes in the resource finding efficiency in the unfavorable landscape. ......................................... 203
12 4-22 Sensitivity of the maximum percentage of paro us females per month to changes in the resource finding efficiency in the favorable landscape .............................................. 2044-23 Sensitivity of the age structures of parous 1 females to changes in resource finding efficiency in the unfavorable:W1 treatment. ................................................................... 2054-24 Sensitivity of the age structures of parous 1 females to changes in resource finding efficiency in the unfavorable:W2 treatment .................................................................... 2064-25 Sensitivity of the age structures of parous 1 females to changes in resource finding efficiency in the favorable:W1 treatment ........................................................................ 2074-26 Sensitivity of the age structures of parous 1 females to changes in resource finding efficiency in the favorable:W2 treatment. ....................................................................... 2084-27 Sensitivity of the age structures of parous 2 females to changes in resource finding efficiency in the unfavorable:W1 treatment. ................................................................... 2094-28 Sensitivity of the age structures of parous 2 females to changes in resource finding efficiency in the unfavorable:W2 treatment. ................................................................... 2104-29 Sensitivity of the age structures of parous 2 females to changes in resource finding efficiency in the favorable:W1 treatment. ....................................................................... 2114-30 Sensitivity of the age structures of parous 2 females to changes in resource finding efficiency in the favorable:W2 treatment). ...................................................................... 2124-31 Sensitivity of the monthly average of the proportion of parous 1 females over 12.5 days of age to changes in resource finding efficiency in the unfavorable landscape. ..... 2134-32 Sensitivity of the monthly average of the proportion of parous 1 females over 12.5 days of age to changes in resource findi ng efficiency in the favorable landscape. ......... 2144-33 Changes over time in the absolute number of gravid females in four simulated populations in the favorable landscape. ........................................................................... 2155-1 Relationships studied with Model I and Model II. ..........................................................2445-2 Dissemination of virus in mosqu itoes at different temperatures ..................................... 2455-3 Relationship between infection and infec tiousness, modified by incubation time and temperature on two mosquito-virus systems studied with Model I. ................................ 2465-4 Design for the simulations of Model II to study the relationship between proportion of infected mosquitoes in a popul ation and the infection rate. ........................................2475-5 Results of Model II for the population with 15 infected mosquitoes per 1000 and virus titer distribution 2 ....................................................................................................248
13 5-6 Median outcomes of the estim ated infection rates (MLE) resulting from Model II ........ 249A-1 Vegetation types per cell for the favorable landscape. ................................................... 265A-2 Vegetation types per cell fo r the unfavorable landscape. ................................................ 266A-3 Percentage of the cells area with wa ter for ovipositon under dry conditions for the favorable landscape. .........................................................................................................267A-4 Percentage of the cells area with wa ter for ovipositon under dry conditions for the unfavorable landscape. ..................................................................................................... 268A-5 Percentage of the cells area with wa ter for ovipositon under average conditions for the favorable landscape. ...................................................................................................269A-6 Percentage of the cells area with wa ter for ovipositon under average conditions for the unfavorable landscape. ...............................................................................................270A-7 Percentage of the cells area with wa ter for ovipositon under wet conditions for the favorable landscape. .........................................................................................................271A-8 Percentage of the cells area with wa ter for ovipositon under wet conditions for the unfavorable landscape. ..................................................................................................... 272
14 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Culex nigripalpus (DIPTERA: CULICIDAE) POPULATION AGE STRUCTURE UNDER HETEROGENEOUS ENVIRO NMENTS AND SOURCES OF ERROR ON THE ESTIMATION OF MOSQUI TO INFECTION RATES By Dulce Maria Bustamante Zamora December 2009 Chair: Cynthia Lord Major: Entomology and Nematology The monitoring of mosquito popul ations within an arbovirus surveillance program relies on a good understanding of the processes that drive the dynamics of the population. The main goals of this study were to help improve our und erstanding of the causes of variation in the age structure of mosquitoes and study the factors that affect our abili ty to estimate and interpret mosquito infection rates in the field. The mosquito Culex nigripalpus is one of the most important vectors of arboviruses in Florida. The results of a field and a modeling study that investigated environmental causes of variation in the age structure of Cx. nigripalpus are presented here. Age structure is of epidemio logical importance because only a subset of mosquitoes will be capable of transmitting viru s and this depends on an interaction between physiological and calendar age. The field study results supported that dry periods followed by heavy rains could cause important increases in the propor tion of parous females that could be potentially infected and looking for a bloodmeal. In contrast, th e proportion of parous females declines 7-14 days after hea vy rains due to the emergence of young mosquitoes. The modeling study suggested that mosquito behavior, weathe r, and landscape complexity are all important factors that introduce variability in the chronologi cal age distribution of unfed parous females.
15 There was more variability in age and olde r ages became more common, when weather conditions were dry or cool, when mosquitoes were assume d to be less efficient in finding resources, and when the landscape was more complex. Environmental changes have the potential to modify Cx. nigripalpus age structure, but more resear ch is needed on how mosquito behavior affects age distribution. Biological factors such as daily mosquito survival and virus titer variation in mosquitoes in troduce errors in estimates of in fection and hinder their use as surveillance indicators. Methodolog ical aspects such as sample si ze and type of viral assay also introduce biases that result in frequent underestim ation of the true arbovira l infection rate in a mosquito population. Age variability in mosqu itoes has environmental and behavioral causes which deserve further study.
16 CHAPTER 1 GENERAL INTRODUCTION The State of Florida has a considerable networ k of agencies dedicated to mosquito control and to the surveillance of mosquito-borne arbov iruses (Florida Department of Health 2009). There are at least three mosquito -borne arboviruses that can cause human and animal disease in Florida: St. Louis encephalitis virus, eastern equine encephalitis virus, and West Nile virus (Rutledge 2004). The surveillance of these arboviruses in the stat e is conducted in an integrated program that includes monitoring of arboviral se roconversions in sentinel chickens, weather patterns, mosquito abundance, mosquito populati on age structure, and th e incidence of human and animal disease (Florida Department of Health 2009). The surveillance of arboviral diseases is based on an unde rstanding of the factors that interact to create conditions that increase the risk of arbovirus transmission to humans and domestic animals. The primary objective of a su rveillance program is to predict when and where arbovirus transmission is likely to occur at epidemic levels and then use this information for the implementation of prevention and control activitie s (Florida Department of Health 2009). In Florida, extensive studies of the St. Louis encephalitis outb reak of 1990 have led to a good understanding of environmental and biological f actors that can increase arbovirus transmission (Day and Curtis 1999, Shaman et al. 2003, Shaman et al. 2004, Day and Shaman 2008). The present work addressed topics that are rele vant to mosquito surveillance. The goals of this work were to (a) study the external causes of variation in the age structure of mosquito populations and (b) provide insight s into how biological factors (s uch as mosquito survival and the variability of virus titers in mosquitoes of different ages) inte ract with methodological aspects which affect our ability to estimate mosquito infection rates in the field.
17 Variation in mosquito age is epidemiologica lly important because older mosquitoes are more likely to have completed the virus extr insic incubation period (time from acquiring the virus to become infectious) rendering them capab le of viral transmission. The chronological age of an adult mosquito is the le ngth of time sin ce emergence from the last immature stage (Lehane 1985). The physiological age of an adult female mosquito is the number of gonotrophic cycles (time from bloodfeeding to egg lying) it has undergone (Detinova 1962). The chronological age and the number of gonotrophic cycles are difficult to determine in field collected mosquitoes. Therefore, the proportion of mosquitoes that have completed at least one gonotrophic cycle (proportion parous) is used as a pr oxy for mosquito age calculations. Chapters 2, 3, and 4 of this dissertation report the results of studies on the age structure of Culex nigripalpus populations in Florida. This mosquito has been identified as the main vector of St. Louis encephalitis and West Nile viruses in Florida, and a br idge vector of eastern equine encephalitis virus (Florida Department of Health 2009). A review of the literature (Chapter 2) was conducted to highlight releva nt aspects of the biology of Cx. nigripalpus and the importance of mosquito age and population age structure in arbovirus epidemiology. A review of methods used to determine mosquito ag e and of modeling approaches fo r studying age structure are also included. A field and a modeling study of the age structure of Cx. nigripalpus were conducted. The goal of the field study (Chapter 3) was to examin e if environmental factor s such as water table depth, drought index, rainfall, and temperature could help explai n the observed variation in the proportion of parous Cx. nigripalpus in the field study. Multivariate regression model to forecast changes in Cx. nigripalpus relative abundance and in the pro portion of parous females were developed using field data.
18 The goal of the modeling study (Chapter 4) was to improve our understanding of the mechanisms behind variation in th e chronological age structure of Cx. nigripalpus field populations. An individual-based model was us ed to simulate the dispersal and foraging behavior of individual mosquitoes in heterogeneous environments. Factors such as changes in relative humidity conditions and oviposition site ava ilability were studied as possible causes of variation in the age distribution of unfed par ous 1 and unfed parous 2 mosquitoes in the simulated populations. Chapter 5 is a theoretical study addressing how ce rtain biological factors, such as mosquito survival and the variability of virus titers in mosquitoes of different ages, can affect the estimation of the proportion of mosquitoes in a popul ation that are infected with a virus. These biological factors, together with methodological limitations, of ten introduce biases in our estimates of infection rates in mosquito populations. This may l ead to an underestimation of the true infection rate in a mosqu ito population, reducing the applicability of estimated infection rates in surveillance. The final Chapter 6, is a discussion of how ne w knowledge of the causes of mosquito age variability, and the sources of erro r in the estimation of virus infection rates, can contribute to the surveillance of arboviral diseases Possible directions for future studies are also suggested.
19 CHAPTER 2 Culex nigripalpus AND MOSQUITO AGE STRUCTURE: REVIEW OF THE LITERATURE AND PROBLEM STATEMENT Culex nigripalpus Taxonomy and Distribution Culex nigripalpus Theobald is a Neotropical m osquito species. It belongs to the insect order Diptera, the family Culic idae, subfamily Culicinae, genus Culex, subgenus Culex and species nigripalpus (Darsie and Ward 2005). In the United States this species has been found in the southeaste rn states and Texas. It has been recorded in the following countries: Mexi co, Guatemala, Belize, El Salvador, Honduras, Nicaragua, Costa Rica, Panama, Colombia, Venezu ela, Guiana, Ecuador, Brazil, and Paraguay. In the Caribbean it has been recorded in the Greater and Lesser Antilles, the Bahamas, and Trinidad (Provost 1969, Nayar 1982). Culex nigripalpus in Florida Biology Culex nigripalpus is an abundant m osquito in Florida. It is present throughout the year but its populations have a defined seas onality in the state. Repro duction is low from January to March and the populations slowly build from April to June. Rapid population increases typically occur with the onset of rainfall from July to October followed by a gradual decline from November to December (Provost 1969, Nayar 1982, Day and Curtis 1994). Culex nigripalpus is known for the opportunistic nature of its oviposition behavior. The immature stages of this species have been found in numerous types of natural and artificial aquatic habitats, from lakes, grassy pools and ditches to artificial c ontainers (Provost 1969, Nayar 1982). During the rainy season in south Flor ida, this species often oviposits in the furrows and ditches of citrus groves, wh ich provide a large-scale aquatic habitat thereby contributing to a rapid population increase during the summer and fall (Day and Curtis 1994).
20 The mean fecundity on a si ngle reproductive cycle of Cx. nigripalpus females from laboratory colonies was estimated at 160 eggs (Nayar and Sauerman 1977) and 175 eggs in a different study (Edman and Lynn 1975). Field caught females that were later fed and reared in the laboratory produced a higher mean fecundity of 273 eggs with a standard deviation of 57.13 eggs (McCann 2006). The eggs of this species do not undergo qui escence or diapause and hatch immediately upon completing embryogenesis. The time to egg ha tch decreases as temper ature increases, with times ranging from 122 to 126 hours at 15C, down to 18 to 20 hours at 35C (Nayar 1982). The duration of the immature stages of Cx. nigripalpus has been studied using Florida strains of this species. Under laboratory condi tions, it has been observed that it takes longer for these mosquitoes to complete the time from egg hatch to adult emergence when temperatures are low and larval crowding is high. Even when larv ae are crowded, increases in temperature and in food supply can reduce the time from egg hatch to adult emergence (Nayar 1968a). For instance, at 27C the time from egg hatch to adult emergence was 192 hours with 75 larvae per pan. When the temperature was increased to 32C the time decreased to 177 hours. When the food was doubled the emergence time was 149 hours (Nayar 1968a). The longevity of this species in nature is determined by physiological and environmental factors (Provost 1969). In the laboratory, newl y emerged females that were not offered carbohydrate nutritional resources survived until 8090% of their glycogen reserves had been depleted, which occurred after 3 to 4 days (Nayar 1968b). Female mosquito life span increased when nectar nourishment was provided (Provost 1 969). In a laboratory study, 50% of unmated Cx. nigripalpus females (kept at 27C with unlimited s ugar) survived 65 days (Nayar and Sauerman 1973). More recent studies of first generation (F1) Culex nigripalpus in the laboratory
21 showed that mortality increased with temperature and decelerated at older ages. Mosquitoes maintained at 35C lived up to 20 days while mosquitoes maintained at 15C lived up to 140 days (Lord and LeFevre, unpublished data). The physiological basis of ag ing in mosquitoes is not yet known (Styer et al. 2006). Mosquito lifespan is also affected by hazards associated with daily events including: oviposition, host de fensiveness, bloodfeedi ng, searching flights, predation, rainfall, humidity, and the quality of resting sites (Provost 1969, Day and Edman 1984, Day and Curtis 1994, Charlwood 2003). Adult Cx. nigripalpus have been described as woodland mosquitoes because they tend to fly and rest in densely vege tated areas like hardwood hammocks or swamps where relative humidity remains high (Bidlingmayer 1971). The mo squitoes rest close to the ground or in the leaf litter where rain and dew accumulate, keep ing the microhabitat saturated during the day. They will go into deeper concealment if the conditions are dry and hot during the day (Provost 1969, Day and Curtis 1994). Culex nigripalpus does commute into other areas in search of blood meals or oviposition sites and adul ts can be found flying in most environments including fields, agricultural sites, housing developments, trailer parks, and pine forests (Bidlingmayer and Hem 1981). Culex nigripalpus numbers dramatically increase in these open areas when rainfall and rising humidity make conditions more suitable fo r flight (Day and Carlson 1985, Day and Curtis 1994). Preferred mosquito resting sites might be those that provide the grea test amount of shade and are not necessarily closer to vertebrate hosts (Servi ce 1971). In California, Culex tarsalis females congregated at specific landscape features including citrus orchards and elevated patches of vegetation. These resting site s were not necessarily associated with large concentrations of potential vertebrate hosts such as avian roosting sites or human dwellings (Lothrop and Reisen
22 2001). Although this has not been studied in the field, evidence suggests that Cx. nigripalpus might not rest and bloodfeed in the sa me locations (Day and Curtis 1994). Culex nigripalpus is an opportunistic feeder and will take blood from any available vertebrate host. Birds and mamm als are usually preferred, but frogs snakes, or turtles can also serve as hosts (Provost 1969, Nayar 1982, Day and Cu rtis 1994). During the winter and spring in Florida, host selection favors birds, but w ith the onset of summer ra infalls (May-June) the proportion of mosquitoes that feeds on mammal s increases (Edman and Taylor 1968, Edman 1974). The decrease in avian feedin g is not associated with a decrea se in the abundance of birds. One possible cause of this shift is a seasonal cha nge in the availability of habitats into which mosquitoes can fly. During the rainy season, an increasing number of mosquitoes fly into open grassy habitats where mammalian hosts such as cattle, horses, and rabbits are found (Edman 1974). Culex nigripalpus is active during the night, with activ ity (flight) peaks during the evening twilight period up to 3 hours after sunset and just before sunrise (Provost 1969, Nayar and Sauerman 1973, Day and Curtis 1994). Lunar illumination has a noticeable effect on the number of this species collected using truck, animal baite d and suction traps, with more collected during the full moon than during the new moon (Bidlingmayer 1974). The collections in open spaces are more affected by moonlight than collectio ns under the forest canopy (Bidlingmayer 1971). Visual cues appear to be very important during navigation in flight and this species seems to be attracted to the presence of masses of vegetation: more mosquitoes can be collected in forested areas than in open areas (Bidlingmayer and Hem 1980, 1981). A reduction in the number of Cx. nigripalpus collected has been observed when the temperature falls below 17-18C (Bidlingmayer 1971, 1974). As with other mosquito species,
23 trap collections of this species decrease with increasing wind ve locity. However, it is not known if the species could minimize wind effects by modifying the height at which it flies (Bidlingmayer 1974). Numbers of Culex nigripalpus in traps have shown a positive relationship with day-to-day changes in relative humidity during days without ra infall (Dow and Gerrish 1970). Other studies have shown that these positive responses to humidity are best observed when using a New Jersey light-trap (Bidlingm ayer 1974). Wind tunnel laboratory experiments have also demonstrated that Cx. nigripalpus females prefer to oviposit at high humidity above 90%, with reduced oviposition as humi dity declines (Day et al. 1990). A laboratory study of the flight performance of Florida mosquito species showed that Cx. nigripalpus mosquitoes are strong-flyers (Nayar and Sauerman 1973). In flight mill studies, Cx. nigripalpus flew at an approximate speed of 1000 m/h and, unlike other species, its flight speed was fairly consistent throughout the duration of each trial (4.5 h long). This speed was maintained by some mosquitoes in subseque nt weekly trials for up to 7 weeks. Culex nigripalpus flew from 3 to 5 km during the first hour of a trial (Nayar and Sauerman 1973). The total area that a given mosquito will fly while looking for a specific resource is unknown, but in a mark-release-reca pture study, the majority of Cx. nigripalpus mosquitoes that were released (82.4%) were recaptured within a 0.4 km radius from the release site (Nayar 1982). Weather conditions, wind direction and speed, the availa bility of nutritional sources, resting places and oviposition sites, will determin e the extent to which a brood of mosquitoes will disperse after emergence (Nayar 1982). There is field evidence suggesting that Cx. nigripalpus mosquitoes will disperse away from pr ime resting or oviposition sites during the summer and fall months and might not return during their life span (Day and Curtis 1994). The
24 causes of this behavior are unknown but it can be sp eculated that mosquitoes disperse to exploit blood sources and oviposition sites in other areas. Culex nigripalpus mosquitoes respond positively to humidity and rainfall, and consequentially the populations grow during the summer and fall seasons in southern Florida. Laboratory experiments showed that this species is a strong flyer with long dispersal potential, and a long lifespan in compar ison to other local species. Culex nigripalpus Population Structure and its Relation to Rainfall Culex nigripalpus abundance and the feeding and parity status of individual fem ales were studied in Indian River County, Flor ida. Periodical collections of resting mosquitoes were made in a cabbage palm-southern live oak hammock during the years 1985, 1986 and 1987 (Day et al. 1990). Mosquitoes were rare during the dry se ason, but abundant during the wet season (July through December). During the rainy season, gr een (recently emerged) nulliparous mosquitoes were more commonly collected after an increase in the number of parous females. This was reflected in a time series analysis where the abundance of green nulliparous was positively associated with the abundance of parous mosqu itoes in the previous days. The abundance of gravid Cx. nigripalpus peaked during dry period s between rainfall events. A time series analysis confirmed the trend showing a negative correlat ion between gravid female abundance and daily rainfall 0-7 days prior to the day of collection (Day et al. 199 0). Previous laboratory studies showed that gravid Cx. nigripalpus females can retain eggs for long periods of time until oviposition sites become avai lable (Day and Edman 1988). Bloodfed females were more abundant in the hammock during 1985, the year when populations were highest. The number of recently bloodfed females was positively associated with rainfall, presumably because increased rainfall and humidity produce condi tions that favor host-seeking fli ghts. Thus, more mosquitoes had taken a bloodmeal prior to the aspira tor collection (Day and Curtis 1989).
25 Rainfall affects the population structure of Cx. nigripalpus populations with respect to physiological status. We could expect that the conditions of humidity and the availability of oviposition sites created by rainfall influence the time required by a female mosquito to complete a gonotrophic cycle (the time from taking a bl oodmeal to laying eggs). Environmental conditions could have an impact on the number and duration of these cycles. Culex nigripalpus as a Disease Vector After a St. Louis encephalitis virus (SLEV) epid em ic started in Pinellas County, Florida in August 1962, mosquito surveillance studies incriminated Cx. nigripalpus as the primary epidemic vector. This was due to its high abunda nce and relatively high overall infection rate during the epidemic: 1.06 infected mosquitoes per 1000 (Chamberlain et al. 1964, Dow et al. 1964, Taylor et al. 1969). Subsequent laboratory studies demonstrated the competence of this species to acquire and transmit SLEV (Sudia and Chamberlain 1964). Similarly, during the 1990 SLE epidemic in Indian River County, Florida, emergency mosquito collections estimated an infection rate during the epidemic of 1.1 in fected mosquitoes per 1000 (Shroyer 1991). Culex nigripalpus has also been recently identified as a vect or of West Nile virus (WNV) in Florida (Blackmore et al. 2003, Rutledge et al. 2003, Vitek et al. 2008). Other viruses, includi ng eastern equine encepha litis virus (EEEV) and Tensaw virus, have been isolated from Florida populations of Cx. nigripalpus (Taylor et al. 1968). In addition to viruses, Florida Cx. nigripalpus have been found infected with Plasmodium hermani (wild turkey malaria), dog heartworm Dirofilaria immitis and an avian poxvirus (Nayar 1982). Culex nigripalpus is a capable arbovirus vector in Fl orida due to its opp ortunistic bloodfeeding behavior and its ability to forage in di verse habitats (Day and Edman 1988). This species could maintain virus circulation among wildlife, domestic animals, and humans. The association between Cx. nigripalpus and resident wild birds is of particular significan ce given that resident
26 passerine birds are the most important avian am plification hosts of S LE virus due to their competence and abundance (Day 2001, Shaman et al. 2003). The shift in Cx. nigripalpus feeding behavior to mamma ls during the summer and fall (Edman and Taylor 1968) might also significantly contribute to an increased risk of transmission of arboviruses such as SLEV, WNV, and EEEV in Fl orida. Shifts in host feeding behavior are considered an important factor contributing to arbovirus epidemics in North America. For Culex pipiens, a reduction in the propor tion of mosquitoes feeding on birds, and an increase in the proportion of mosquitoes feeding on humans, coinci des with an increase in the number of WNV human infections (Kilpatrick et al. 2005). Culex nigripalpus is also capable of retaining eggs for long periods until suitable oviposition sites become availa ble (Day and Edman 1988). This behavior and the species longevity could allow viruses to complete their extrinsic incubation periods and be transmitted to susceptible hosts before the mosquitos death. Rainfall-Driven Population Dynamics of Culex nigripalpus in Florida and its Relation to Arbovirus Epidemics Florida Cx. nigripalpus populations have marked abunda nce cycles that are strongly correlated with seasonal changes such as temp erature and rainfall (Provost 1969, Day et al. 1990, Shaman et al. 2003). Rainfall has a strong effect on host feeding behavior oviposition behavior, longevity, and population size of Cx. nigripalpus mosquitoes. Temperature affects mosquito longevity, behavior, and the time for virus incubation. All of those factors are important for virus transmission and therefore seasonal population dynamics of th e vector species are crucial to understand epizootic and epidemic events. Culex nigripalpus abundance is associated with the expansion of aquatic habitats due to rainfall (Provost 1969, Shaman and Day 2005). Heavy rainfall events of 50 mm within 3 days
27 have been found to correlate positively with increases in the abundance of Cx. nigripalpus 5-8 days and 12-15 days after later (D ay and Curtis 1993). This amount of rainfall is the minimum necessary to produce temporary larval habitats that will last at le ast 7 days, allowing mosquitoes to complete their immature life cycle (Day et al. 1990). As mentioned before, rainfall also increases near-surface humidity enhancing flight activity and host-seeking behavior, consequentially accelerating the reproductive cycl e of the mosquito and increasing its abundance (Dow and Gerrish 1970, Day and Curtis 1989, Day et al. 1990, Shaman and Day 2005). Hydrological models have recently shown that high transmission rates of SLEV and WNV in south-central Florida are more likely to take place after a spring drought followed by constant summer rainfall (Shaman and Day 2005). During droughts, especially those that occur during the Florida avian nesti ng season (April-June), Cx. nigripalpus populations become restricted to hammock habitats where many species of birds nest. This overlap of vectors and avian amplification hosts makes an ideal environment for rapid epizootic amplification of arboviruses (Shaman et al. 2002a, 2003, 2005, Shaman 2007). When the drought ends, usually in June, infected mosquitoes disperse and initiate secondary transmission foci away from the original amplification sites (Shaman and Day 2005). The 1990 Indian River County, Florida SLE ep idemic provides evidence for the weather mediated mosquito-bird dynamics previously describe d. It is believed that different bird species likely played dissimilar roles prior to the epidem ic. Their distribution in the landscape made them differentially available to Cx. nigripalpus for feeding. Nesting northern cardinals ( Cardinalis cardinalis ) and blue jays ( Cyanocitta cristata ) were abundant within hammocks and were likely the avian species that initiated th e amplification of SLEV during the epidemic. When wetter conditions allowed Cx. nigripalpus to disperse to the areas surrounding the
28 hammocks, they fed upon a population of susceptible mourning doves ( Zenaida macroura ) and common grackles (Quiscalus quiscula ) that were nesting primaril y in open habitats and were likely secondary amplificati on hosts (Shaman et al. 2003). Studies of mosquitoes in California have suggested that their populations will expand when conditions are favorable for dispersal and oviposition, but will contr act into refuges (such as densely vegetated hammock habitats) during unfavorable conditions (Reisen et al. 1995). Rainfall patterns during the summer and fall mont hs in south-central Florida determine the periodicity of the expansion and contraction cycles of Cx. nigripalpus populations. During wet years, rainfall events ar e continuous and mosquito popul ations remain elevated and widespread because oviposition sites are abund ant and available throughout the mosquito reproductive season (Day and Curtis 1989, 1994; Day et al. 1990). During wet years, Cx. nigripalpus females can oviposit as soon as 4 days af ter a bloodmeal. If oviposition sites are available these females can oviposit and seek a second bloodmeal in less than a week. This means that during wet years when oviposition sites abound, female mosquitoes can go through up to three gonotrophic cycles during the 10-14 da y virus extrinsic incubation period (Day 1997) required for a mosquito to become infective. It is unlikely that many female mosquitoes can survive this rapid-fire reproducti ve schedule due to increased st ress associated with flight, predator avoidance, and the location of suitable daytime resting sites and oviposition sites. Many females will die before the virus extrinsic inc ubation period is complete and before they are capable of transmitting the virus. Therefore higher mosquito abundance during wet years will not necessary yield higher arboviral transmission rates (Day and Curtis 1994). When rainfall events are intermittent, ovipos ition sites may persist long enough for the emergence of one mosquito brood, but dry up befo re newly gravid females can oviposit, forcing
29 them to wait for the next rainfall event. If the dry period lasts betw een 10-20 days the viral incubation could be completed by females during a single gonotrophic cycle. Intermittent epic rainfall events will synchronize Cx. nigripalpus oviposition, blood feeding, and virus transmission (Day et al. 1990, Day and Curtis 1994). Mosquito Age, Survival, and Population Age Structure: Epidemiological Relevan ce The chronological age of an adult female mo squito is the amount of time since adult eclosion (Lehane 1985). The physiological age of an adult female mosquito is the number of gonotrophic cycles it has undergone (Detinova 1962). A gonotrophic cycle is the time period between a bloodmeal and oviposition (Clements 2000). Physiological age does not correspond to chronological age (Klowden and Lea 1980). Fo r instance by this definition, a three week old nulliparous mosquito would be categorized as physiologically young by this definition, while a 1 week old parous mosquito will be physiologically old. In spite of this, the determination of physiological age is the most widely used met hodology to age adult female mosquitoes collected in the field, given that chronological age is di fficult to establish with certainty (methods are explained in the next section). Measuring the age of insects is important to estimate ra tes of population increase, to understand age-dependent changes in behavior, to estimate the proporti on of potential insect vectors that have completed the extrinsic inc ubation period of a pathoge n, and to estimate the expected mean duration of the infective life of the insect (Lehane 1985, Milby and Reisen 1989, Hayes and Wall 1999). In the case of mosquitoes, the estimation of physiological age remains the most widely used method to study the age structure of populat ions and to estimate mosquito survival. Survival is an important parameter that influenc es vectorial capacity b ecause it determines the duration of the infective life of a mosquito. Vectorial capacit y is defined as the daily rate at
30 which future infections arise from a currently infective case (Dye 1986, Milby and Reisen 1989). The expression and term vectoria l capacity were developed for malaria epidemiology by GarrettJones (1964), based on the work of Ronald Ro ss and George Macdonald (Dye 1986) and it can be expressed as follows: (2-1) where C is the vectorial capacity, m is the number of female mosquitoes per person, a is the daily biting rate of female mosquitoes on humans, b is th e fraction of infectious females, p is the daily survival rate of female mosquito es, and n is the time in days from acquiring the parasite until the parasite reaches the salivary glands and the mosquito is cap able of transmission. This time period (n) is known as the ex trinsic incubation period. The duration of the gonotrophic cycle can impact the magnitude of the vectorial capacity in a multiplicative way. The daily biting rate a can be expressed as the ratio between the proportion of bloodmeals taken on humans also known as the Human Blood I ndex (HBI), and the duration of the gonotrophic cycle g (Lardeux et al. 2008): (2-2) Thus C can be rewritten as: (2-3) The value of C decreases by the square of the length of the gonotrophic cycle. The vectorial capacity is related to the basic reproductive number, R0, which is the expected number of people that will become inf ected after one generation of the parasite by a single infectious person introduced to a susceptible populati on (see review by Smith et al. 2007). The R0 includes both host and vector factors a nd is expressed as follows:
31 (2-4) where C is the vectorial capacity, t is the probabi lity that a human becomes infected from a bite by an infectious mosquito, u is the probability th at a mosquito becomes infected from a bite on an infected human, and 1/r is the time necessary to clear an infection (Smith et al. 2007). Gordon-Smith (1987) provided modi fications to the expression of the basic reproductive number for mosquito-borne arboviruses and called it the reproduction rate of the infection (R). An important consideration about arboviruses such as SLEV, WNV, and EEEV is that these viruses infect various species of vertebrate host. However, only a few species serve as reservoirs for the long-term maintenance of the virus and these are known as main tenance hosts (Edman 2004). The reproduction rate of the infection (R) is defi ned as the average number of vertebrate maintenance hosts infe cted by mosquitoes that became infected on a single vertebrate maintenance host (Gordon-Smith 1987). The R take s into consideration the fraction of meals taken exclusively on maintenance hosts by mosquitoes: (2-5) where m is the average daily number of mosquito es per vertebrate maintenance hosts, a is the average daily biting rate of mosquitoes on ve rtebrate maintenance hosts, h is the average proportion of mosquitoes biting vertebrate maintenance hosts, sm is the proportion of mosquitoes susceptible to infection, v is th e average duration in days of in fective viremia in vertebrate maintenance hosts, sv is the proportion of vertebrate mainte nance hosts susceptible to infection, p is the mosquito daily survivorship, and n is the time that it takes a mosquito to become infectious. The parameters a and p in Equations 2-1 and 2-4, are both related to mosquito age. The daily biting rate (a) could be estimated as the inverse of the average number of days between
32 bloodmeals, which is the duration of one gonotrophic cycle. Mosquito survival p is usually estimated from the proportion of parous females in the population (as it will be explained below), which is the proportion of females that have completed at least one gonotrophic cycle. The vectorial capacity is highly sensitive to the mosquito daily survival rate p (GarrettJones 1964). The term pn/-ln(p) has been called the longevity factor because it summarizes the aspects of vector survival (r eviewed by Dye 1986, 1994). This fact or increases e xponentially as p increases, thus a high increase in the magnitude of C occurs at the highest values of p (Table 21). This indicates that reductions in mosquito su rvival have an important impact in reducing the daily infection rates of a pathogen. The physiological age structure of a mosquito population can be defi ned as the frequency of female mosquitoes at differe nt physiological stages. A phys iological stage is defined by the number of reproductive cycles completed by th e female: a nulliparous females have completed no cycles, a parous 1 female has completed one cy cle, etc. (Detinova 1968). On the other hand, chronological age structure could be defined as the frequency distribution of age groups (e.g., 0-2 days old, >2-5 days old, etc.) in the population. Age structure has epidemiological significan ce. The risk of pathogen or parasite transmission increases as the mosquito populatio n increases and becomes widespread. However, this must be accompanied with an increase in th e number of females that have lived long enough to become infective (Detinova 1968, Day 2001, Eldri dge 2004). Age structure is also important for practical applications. Reductions in the pr oportion of parous mosquitoes can provide some indication if the older mosquitoes in the population were successfu lly targeted during insecticide applications (Bown et al. 1991). Similarly, the presen ce of parous mosquito es in insecticide treated areas can indicate areas that were not covered by insecticide treatm ents or avoidance of
33 the treated areas by mosquitoes (Detinova 1968). Recently developed mosquito control methods aim to change the age structure of the mosquito population with the introduction of some strains of the bacteria Wolbachia that can shorten the life span of individual mosquitoes (Cook et al. 2008). A better understanding of ag e structure and improved methods for age determination are necessary to evaluate the success of su ch novel mosquito control strategies. Wolbachia infected mosquitoes are also being considered as transgenic drivers fo r the introduction of genes that block parasite transmission. Modeling studies have suggested that mosquito age structure in the field should dictate the number and the stage at which the Wolbachia transgenic mosquitoes should be released to improve the probability of a successful introduction (Rasgon and Scott 2004). Methods to Measure Adult Female Mosquito Age The m ajority of techniques to measure th e age of adult insect s rely on the study of physiological changes in the body (fat bodies, repr oductive organs), observation of wear in the cuticle, or observation of cuticular grow th bands (Lehane 1985, Hayes and Wall 1999). Biochemical techniques such as measurement of the accumulation of pteridines in the head capsule (Lehane 1985, Hayes and Wall 1999), the te mporal changes in the concentration of cuticular hydrocarbons (Desena et al. 1999), and more recently, changes in the expression of certain age dependent genes have also been used to quantify the physiologi cal age of mosquitoes (Cook et al. 2006). After age grad ing the insects, different models and assumptions exist to estimate survival rates for a particular population. The following is a review of some of the techniques used to age adult female mosquitoes and to calculate their su rvival rates. These methodologies have been helpful to parameterize mathematical models of mosquito population dynamics and pathogen transmission, to understand mosquito population structure in the field, and to monitor the success of vector cont rol campaigns (Lehane 1985, Hayes and Wall 1999).
34 Detinova (1962) offers a review of methods to determine the physiological age of female Anopheles mosquitoes in a monograph that is considered a classical reference on the subject. Among the many methods available, the most wide ly used are based on the observation of the irreversible changes that occur to the ovari es after the completion of a gonotrophic cycle (Detinova 1962, Lehane 1985, Hayes and Wall 1999). The method developed by Povolodova (1949, cited by Detinova 1962) observes the stretching of the ovariole sheath resulting from egg growth which subsequently leaves behind dilatations in the sheath after the egg is shed. These dilatations are permanent and can be counted, and there is some correlation between the number of ovarian cycles completed and the number of dilatations (Detinova 1962, Lehane 1985, Hayes and Wall 1999). However, variation in the numbers of dilatations is in troduced due to other factors, such as follicle degeneration and egg resorption making the method unreliable for physiological age determinati on (Nayar and Knight 1981, Lehane 1985, Hugo et al. 2008). Another method is the observation of changes in the tracheal system of the ovaries, which can be used to classify female mosquitoes as nulliparous or par ous. In nulliparous females, the tracheoles that supply the ovaries with oxygen are tightly coiled (skeins), but they become distended after the first batch of eggs is developed (Detinov a 1962, Lehane 1985). This method has the disadvantage that some ovaries can show an intermediate status with coiled and uncoiled tracheoles found in the same ovary making the cl assification difficult a nd subject to biases introduced by the examiner (Hugo et al. 2008). Other recent methods have been developed to estimate chronological age, such as the analysis of proportional changes of two or more cu ticular hydrocarbons in the legs of a mosquito as it ages. The relative abundances of hydrocarb ons are modeled as a function of mosquito age to produce age predictive models (Desena et al 1999). Laboratory studie s of this technique
35 (Desena et al. 1999) as well as fi eld validation studies (Gerade et al. 2004), have shown that the age of Aedes aegypti females can be predicted only up to 12-15 calendar days. The age of mosquitoes older than 15 days cannot yet be determined with this method as hydrocarbon contents are less variable. This prediction threshold can vary with the mosquito species under study and some species, like Aedes vigilax do not show any relationship between hydrocarbons and age (Hugo et al. 2008). The use of gene-transcript abundance profiles to estimate mosquito chronological age was possible after identificati on of genes that show age-dependent expression in Ae. aegypti (Cook et al. 2006). These genes are not influenced by th e mosquitoes digestive status, reproductive status, or environmental conditions. Information collected from eight Ae. aegypti genes showed a strong relationship between transcriptional profiles and age with 87.03% of the variance explained by age and with age estimates from bli nd samples falling within days of the actual age. The performance of this method was an improvement from cuticular hydrocarbons whose quantitative profiles had only 68.97% of their variance explained by age and estimates from blind samples falling within da ys of actual age (Cook et al. 2006). Nelson (1966) compared two methods (Povolodo vas sheath dilatation presence/absence and Detinovas tracheal coiling presence/abse nce) to determine parity status of Cx. tarsalis The study did not attempt to determine the number of gonotrophic cycles, citing that it had previously been determined that the number of sheath dilatations in Cx. tarsalis did not correspond to the number of oviposition events. The study showed that both methods allowed a good identification of nulliparous and parous mosquitoes (96-99% correct classification), although there was an advantage in using dilatation when there was yol k deposition in the ovarioles that obscured the tracheal coiling.
36 Nayar and Knight (1981) compared the Povolodova and the Detinova methods to study their reliability to verify the nul liparous status of recently emerged Cx. nigripalpus mosquitoes. They observed that within 4 days of emergence there were no dilatations in the ovariaole, but after one week, 50% of colony reared nulliparous females had developed one dilatation in the ovariole, and that the number of dilatations in nulliparous mosquitoes increased with time. When they compared both methods in the same mosquitoes using one ovary for each method, they found that they provided similar results within a 4 day period after emergence, but the Detinova method provided more reli able results beyond that period. Hugo et al. (2008) compared various met hods to determine physiological age in Ae. vigilax and Cx. annulirostris Among the methods used were the Detinova method for ovarian tracheal coiling and the Povolodova method for the numbe r of dilatations in the sheath (up to 3 dilatations). For Ae. vigilax more than 80% of females were correctly classified into the nulliparous and parous categories by the Detinova method. A large percentage of samples was classified as indeterminate (more than 30%), and so me could not be classified at all (8%) due to residues that obscured the tracheoles. The use of the Povolodova method was more difficult and time consuming and only about 58% of the sample s were correctly classi fied in the categories nulliparous, parous 1, parous 2, and parous 3 (Hugo et al. 2008). Culex annulirostris was only evaluated using the Povolodova method. As with Ae. vigilax, this method was found time consuming and only a small percentage of ovarioles could be detached intact for observation. Almost all ovarioles from nulliparous females lacked sheath dilatations. Only 40% of the ovarioles from parous 1 females showed 1 dilatati on (the rest showed from 0 to 3 dilatations), 29% of ovariaoles from parous 2 females show ed 2 dilatations, and 16% of ovarioles from
37 parous 3 females showed 3 dilatations. The method was considered extremely difficult to implement and with low discriminatory value. Ovary dissections to differentia te between parous and nullipar ous stages remains the more practical and inexpensive method to estimate the physiological age of mosquitoes. The Detinova method has been found to have a good classification rate for Culex mosquitoes (Nelson 1966, Nayar and Knight 1981, Reisen et al. 1986). Until the newly de veloped methods to determine chronological age (cutic ular hydrocarbons, age-specific gene expression) become more refined and less costly (Hugo et al. 2008), ovary dissectio ns will continue to be used for coarse determinations of mosqu itoes physiological age. Methods to Estimate Survival Rates The survival rate is an important param eter of mosquito populations that can give an indication of the expected duration of the infec tive life of mosquitoes. Survival rates can be estimated based on mosquito age or by direct m easurements of the proportion of mosquitoes in a cohort that survive over successive days. Methods based on age determination The survival rate can be calculated from the estimates of the proportion of parous females in a population at a particular locatio n and time. If the survival rate (p) is assumed to be constant (not age dependent), survival can be calculated as the gth root of the parous proportion, where g is the length of the gonotr ophic cycle (Davidson 1954): (2-6) Prior knowledge of the duration of the gonotro phic cycle is necessary. This method assumes a stationary age structure for the population (birth or immigration ra tes equal to death or emigration rates), accurate identification of th e nulliparous versus parous individuals, equal
38 probability of sampling all physiological age gr oups in the population, transition between age groups occurs synchronously, the time between age groups is re latively constant and can be determined (Milby and Reisen 1989), and that g is constant over the relative time period and between individuals. Survival rates can also be estimated from the analysis of daily collections of mosquitoes classified as nulliparous or parous (Birley and Rajagopalan 1981, Holmes and Birley 1987, Lord and Baylis 1999). The number of parous females at time t (Pt) is the product of the total number of mosquitoes alive in the previous gonotrophic cycle (Tt-g, where g is the length of the gonotrophic cycle), multiplied by the proportion that survived the cycle (S) (Holmes and Birley 1987): (2-7) (2-8) where Nt is the number of parous females at time t. S can be estimated by regression of Pt on Tt-g (Lord and Baylis 1999). Assumptions of the model include equal probability of sampling all physiological age groups in the popu lation, a constant survival rate minimal loss of individuals due to emigration, and little va riation in the length of the gonot rophic cycle between individuals (Lord and Baylis 1999). Simulation models were used to determine that the accuracy of the survival rate estimate is high fo r time series of 10-100 days and that sampling biases for different age groups reduce the accuracy of th e estimate (Lord and Baylis 1999). Clements and Paterson (1981) presented a tabular method to calculate the mortality rate at different physiological ages estimated using the Povolodova method. However, given the inaccuracies of the Povolodova method, the calc ulation of survival rates at different physiological age groups is probably unreliable. Clements and Paterson (1981) calculated the
39 mortality rate () for an intermediate physiologi cal age group (parous .5 for instance), as the difference between the logarithm of the number of individuals of the previous age group (parous 1) minus the logarithm of the number of individuals in the next age group (parous 2): (2-9) Methods independent of age determination One field based method to estimate mosquito survival that does not depend on age estimation uses the mark, release, and recapture of individual mosquitoes in a cohort. Survival is estimated using the number of recaptures on successi ve days. If the daily survival rate (p) is assumed to be constant, the number of ma rked mosquitoes recaptured on each day (mt) is a function of the number of released mosquitoes (M0), recapture rate (r) an d time since release (t) (Milby and Reisen 1989): (2-10) The daily survival rate can be calculated with a least squares regressi on of the logarithm of the previous function: (2-11) Assumptions of this method include that the ma rking does not affect survival and behavior of the mosquitoes, the mark is visible throughout the mosquitos lifetime, the mosquitoes have the same likelihood of being sampled on each day of their life, and that loss of individuals due to emigration is minimal (Milby and Reisen 1989). All methods for survival rate estimation rely on assumptions which are perhaps difficult to meet, such as stationary age structure and minimal emigration. The method chosen should be selected based on the biology of the species under study. For a species like Cx. nigripalpus, known for its dispersal behavior, mark-release-re capture methods have proven challenging (Day
40 and Carlson 1994). Yet methods based on daily collections, which assume minimal emigration, might not be appropriate. Parity ra tes can be practically estimated for Culex mosquitoes using the Detinova method. Therefore the Davidson (1 954) method to estimate survival could be applied. However, little is known about the va riation of the duration of the gonotrophic cycle under different conditions or if the age structure is stationary. If the age structure is not stationary we cannot assume that individuals in different age groups have the same probability of being sampled in consecutive days. This would ma ke our estimates of survival not comparable from time to time. Variations over time on th e duration of gonotrophic cycles could contribute to non-stationary age structure, thus we need more information on the conditions that would introduce more variability in the duration of mosquito gonotrophic cycles. In spite of these difficulties, the method based on parity proportions could provide an insight into the survival rates for this species. Factors Affecting Physiological and Chro nological Age Structure in Mosquitoes Physiological age structure could be primarily influenced by the time it takes for female mosquitoes to complete a gonotrophic cycle, by their daily survival, and by the timing of emergence of new individuals (Detinova 1968). Similarly, chronological age structure could be influenced by mosquito survival and varia tions in the emergence of larval cohorts. Some environmental factors have been found to be correlated with temporal variations in physiological age structure for some mosquito sp ecies. Changes in parity rates of female Culex tarsalis were correlated positively with temperature (Reisen et al. 1983). A negative correlation between parity and rainfall was observed for Anopheles stephensi, and a negative correlation between parity and temperature was found for Culex tritaeniorhynchus (Reisen et al. 1986). Weather conditions could be associated with fa vorable (or unfavorable) conditions for mosquito flight, which might influence the proportion of females ovipositing and becoming parous. For
41 example, warmer temperatures could stimulate flight in gravid fe males while cooler temperatures can reduce mosquito activity. Th is could result in less gravid females ovipositing and becoming parous during periods of cool temperatures. Mosquito daily survival can decrease with incr easing mosquito age. A laboratory study of Ae. aegypti (Styer et al. 2006) found that mosquitoes 10 days or older have higher mortality than younger mosquitoes, but mortality decelerates for th e oldest individuals (a ge range studied was 0 to ~60 days). The mortality of Cx. nigripalpus also shows a deceleration at older ages, with the rate being dependent on temperature: mosquitoes reared at 35C lived up to 20 days while mosquitoes reared at 15C lived up to 140 da ys (Lord and LeFevre, unpublished data). Activities will expose the mosquito to differe nt mortality hazards (Provost 1969, Day and Edman 1984, Day and Curtis 1994, Charlwood 2003). Increases in daily mortality will decreased the lifespan of mosquito es and affect the chronological age structure of the population. It could also affect the physiological age stru cture by decreasing the proportion of females that complete reproductive cycles. Host-seeking mo squitoes are exposed to predators, weather hazards (wind and rain), and host defensive behavi or. Similarly, gravid mosquitoes may have a higher mortality rate than resting mosquitoes due to the risks posed by search flight and oviposition. Resting mosquitoes also face such hazards as predators and desiccation (Charlwood 2003). If the frequency of activity (flying, bi ting, and oviposition) of the mosquitoes is increased, their exposure to hazards might also increase. The duration of the gonotrophic cycle will determine how often mosquitoes would need to be active, and the heterogeneous distribution of resources probably dictates how long it would take mo squitoes to find a bloodmeal or oviposit.
42 One of the best known factor s that affects the duration of the gonotrophic cycle is temperature. This is because blood digestion rate and the time for egg development are both influenced by temperature (Clements 2000). The mean length of the gonotrophic cycle of Anopheles albimanus was shown to be significantly shorter for mosquitoes reared at 30C (2.88 d) versus 24C (3.68 d) (Rua et al. 2005). The mean duration of the gonotrophic cycle for Aedes albopictus was also temperature dependent, with signifi cant reductions in leng th from 20C (8.1 d), to 25C (4.5 d), and to 30C (3.5 d), and an incr ease at 35C (4.4 d) (Del atte et al 2009). The non-linear relationship could be due to a negative impact of higher temperatures on egg development. In a field study in Kenya (Afrane et al. 2005), the duration of the first and second gonotrophic cycle of Anopheles gambiae was studied using caged, bloodfed mosquitoes placed inside houses of a highland villag e in a forested area and compared to mosquitoes placed inside houses of a lowland village of a deforested area. The temperatures were monitored inside the houses and it was determined that microclima tic differences affected the duration of the gonotrophic cycle. Higher temperatures were observed indoors in the deforested areas (1.8C higher in the dry season and 1.2C hi gher in the rainy season) than in the forested areas. These differences led to gonotrophic cycles that were betw een 1-1.5 days shorter in the deforested areas (Afrane et al. 2005). Environmental factors such as temperature infl uence mosquito survival and the duration of the gonotrophic cycle. Less is known about how th e distribution of resour ces in space and their abundance affects the time to complete a gonotrophi c cycle, the time needed to search for a vertebrate host, or an ovipositi on site. There is little informa tion on how efficient mosquitoes are in searching for these resources.
43 Mosquitoes will become active and try to find resources only under certain environmental conditions. In the case of Cx. nigripalpus flight activity, blood fe eding and oviposition are stimulated by high relative humidity 90% (Dow and Gerrish 1970, Day and Curtis 1989, Day et al. 1990). Flight activity decreases in temperatures belo w 17-18C (Bidlingmayer 1974). Culex nigripalpus collections have been found to decrea se by 23% for each 0.1 mps increase in wind velocity, and they increase by 1.6-1.8% ab ove new moon catches as the moon illumination progresses to full moon in a 14 day period (Bidlingmayer 1985). When the conditions are favorable for mosquito flight, mosquitoes locate resources with a combination of visual and chemical cues (Alla n et al. 1987, Day 2005). Some mosquito species use vegetation patterns for flight orientation (Bidlingmayer and Hem 1980, 1981). Vertebrate host odor plumes (CO2 and other chemicals such as lactic acid), host movement, size, temperature, and color are all important for hos t location (Day 2005). Li ght reflectance over the water surface, chemical and organic composition of the water, and size and shape of artificial containers have been found as relevant factors fo r oviposition site identifi cation and selection for certain mosquito species (OMeara et al. 1989, Allan et al. 2005, Day 2005). We do not know much about the functional relationship between resource abundance and the rates at which mosquitoes find resources in the field. With respect to mosquito feeding success, laboratory studies have found that some mosquito species can experience high mortal ity and low feeding success depending on the vertebrate host species on which they try to feed. Experiments where a single host was exposed to mosquitoes in a cage showed that vertebra te hosts can potentially inflict high mortality on mosquitoes (Day and Edman 1984). Among f our vertebrate hosts used in a study ( Mus musculus Peromyscus maniculatus, hamster, and domestic chicken) hamsters generally inflicted
44 less mortality when left unrestrained in the cage s with the mosquitoes. The recovery rates of mosquitoes ranged from 0% (100% mortality for Anopheles stephensi in trials with unrestrained M. musculus and P. maniculatus ) to 93% (7% mortality for Culex quinquefasciatus mosquitoes exposed to unrestrained hamsters). When testing Cx. nigripalpus using unrestrained vertebrate hosts, the recovery rates ranged from 30-70%, but feeding was only achieved on chickens by 20% of the surviving mosquitoes. Mosquito bi ting persistence can dec line as hosts become defensive, as was observed for Aedes triseriatus biting a human hand (Walker and Edman 1985). In a different study, a negative relationship was observed between mo squito density and feeding success: the percentage of Cx. nigripalpus females feeding on avian species decreased as the number of mosquitoes in the cage increased (Edman et al. 1972). Some avian species showed a more aggressive defensive behavior (w hite ibis and cattle egret) allowing only ~50% of mosquitoes to feed at the lowest mosqu ito densities (25 mosquitoes/cage with <80% mosquitoes recovered) while the less defensiv e avian species (black crowned night heron and green heron) allowed ~90% of mo squitoes to feed at the lowest densities (25 mosquitoes/cage with >90% mosquitoes recovered). Bloodfeeding success declined steadily as mosquito density increased (Edman et al. 1972). In summary, the time to complete a gonotrophic cycle is not only a function of temperature. The availability of resources and the rate at which mosquitoes find and use those resources, will affect the durati on of the gonotrophic cycle. Additionally, mosquitoes have to survive the hazards in their environment. The interrelations between mortality (age dependent and age independent), resource search behavior, and environmental variability have rarely been explored. The interaction among those factors could a ffect the proportion of females completing gonotrophic cycles and the time that it takes to co mplete each cycle. A field study (Chapter 3)
45 was conducted to determine if variation in rainfa ll patterns influences the proportion of parous Cx. nigripalpus in the population. If rainfall influences th e age structure, this could support that changes in resource availability (such as oviposition sites) and the effects of humidity on mosquito activity, affects how many females ar e completing gonotrophic cycles. In addition, a modeling study (Chapter 4) addr essed how mortality, search behavior, and environmental conditions could affect the age structure (chr onological and physiological) of a simulated Cx. nigripalpus population. Modeling Population Age Structure The reproductive status of a population, birth and death rates, and the persistence of the population in the future are influenced by the ages of the individuals that com pose the populations (Yazdani and Agarwal 1997). There ar e various approaches to the study of age structure. Life table studies emphasize the disc overy of the patterns of growth, survival, death, and movement of organisms. On the other hand, population dynamics st udy the causes of these patterns (environmental, biologi cal) (Price 1997). Following is a review of some population dynamics modeling approaches that incorporate age structure using insect examples with emphasis on mosquitoes. Models are a simplificati on of the real systems they are attempting to represent and their stru cture depends on the questions of interest about the system. In the following review, we emphasize how models can be used to study dynamic changes in populations, taking age struct ure into consideration. Leslie Matrix Population Models Leslie m atrix population models are often used to include the effects of age structure to study the growth and age distri bution of a population over time (C aswell 2001). Leslie matrix population models use discrete time steps and discrete ag e classes, as opposed to continuous time and age. Age classes are defined using the same width as the projection ti me step. Projections
46 of the number of individu als in each age class (ni) are made on the basis of the probability that an individual on age class i su rvives to age class i+1 (Pi), and the per capita fertility of each age class (Fi) (Caswell 2001). The following is the simplest form of the model for a population with three age classes (Caswell 2001): (2-12) There are many modifications to the Leslie ma trix model; one of the most important ones is the use of stages inst ead of discrete classes of calendar age. For arth ropods, the use of stageage models is common, given that it allows the incorporation of temper ature effects into the probabilities of transition from one stage of deve lopment to the next. For example, a stage-age model of the cabbage root fly in Europe (S ndgerath and Mller-Pietr alla 1996) divided the population into four developmental stages (egg, larva, pupa, and adult), and for each of these stages an age structure was assumed. Each stage had up to 120 age classes depending on the temperature. A similar stage-age model exists for the citrus rust mite in Florida (Yang et al. 1997). Both the cabbage root fly and the citr us mite models, predicted the temperature dependent population growth of the organisms fa irly well, and their use for pest management was suggested. A model of the population dynamics of the mosquito Ae. aegypti used an approach similar to a matrix model called dynamic life table simu lation (Focks et al. 1993). This model used information on weather and aquatic habitats to simulate the population dynamics of container inhabiting mosquitoes. The model divided the population into stages (egg, larva, pupa and adult). The transition to the ne xt stage was defined by a threshol d of cumulative developmental units, which were a function of temperature (in the case of larvae, the transition to the pupal
47 stage was also a function of weight). In this mode l, daily survival rates we re calculated based on functions for each stage of development, and th e fecundity of the fema les was a function of body weight (Focks et al. 1993). The Ae. aegypti model provided predicti ons of the changes in immature mosquito abundance with relatively good agreement between observed and predicted data. Matrix models such as the one for Ae. aegypti provide a framework to study changes in the number of individuals in pre-spec ified age or stage classes. However, they do not allow for the investigation of changes in ag e structure that might arise due to individual differences in behavior as a response to envir onmental changes. Also, indivi dual variability in chronological age cannot be taken in consideration. Age Structure in Continuous Time Models The population dynam ics of insects can be modeled using compartmental models of differential equations that describe the cha nges in the numbers of individuals in each developmental stage (egg, larva, pupa, and adult) in continuous time. Adult stages are usually not compartmentalized further in terms of age, bu t for some model applications the adult stage is structured in different compartments related to stat us (i.e., feeding status, in fection status, etc.). A recent differential equation model of th e dynamics of malaria mosquito vectors, incorporated developmental stage compartments and structured the female adult population on the basis of infection with the malaria parasite (susceptible, exposed, a nd infectious) (Hancock and Godfray 2007). A lumped-age class techniqu e was used and a single differential equation was used to describe the dynamics of the immature stages. For the adult stage, the number of susceptible females was a function of the numbe r of eggs laid in a previous time and the probability that those eggs survived the three imma ture stages; susceptible mosquitoes were lost due to density independent mortality and to infection with the malaria parasite. Female
48 mosquitoes in the exposed class were lost due to density independent mortality and maturation into the infectious class at a fixed rate. Mosquitoes in the infectious class were lost only due to density independent mortality (Hancock and G odfray 2007). This model incorporated dynamics of both immature and adult mosqu ito stages, with the intention to use the model to study the effects of integrated control strategies against larvae and adults of malaria vectors. Authors acknowledged that the weaknesses of the model are that it considers constant demographic parameters within a stage, and that it is not pos sible to categorize adult mosquitoes according to their physiological stage w ithin a gonotrophic cycle. More deta ils in the adult mosquito stages could make this model more useful because some control interventions target adult mosquitoes at specific stages (e.g., impregnated bedne ts target host-seeking females). In a different model of malaria transmi ssion, the adult female population was also structured into susceptible and infected classes with new female mosquitoes being recruited at a fixed rate (Smith et al. 2004). Another model ha d a fixed emergence rate of females and divided the adult population into fed and unfed susceptible, latent, and infectious classes (Le Menach et al. 2005). Both of these models were spatially structured and the change in the number of females in each class was modeled for different pa tches in the simulated environment. Mosquito gains and losses were defined by birth into the susceptible class, deaths, migration, and in the case of the second model, the duration of the resting period before oviposition (transition from fed to unfed). These two models (Smith et al. 2004, Le Menach et al. 2005) studied how the behavior of adult females, depending on their phy siological stage, affect ed the distribution of human malaria cases over space. These models us ed constant demographic parameters and thus, did not consider all the i ndividual variability that could exist in age and infectious status. This variability could definitely affect transmission rates.
49 Although the age structure of the adult mosquito population is acknowledged as an important factor for disease transmission, models in continuous time rare ly incorporate detailed descriptions of adult chronologica l or physiological age. This w ould require keeping track of the age of each individual in the population or at least following the age of different cohorts. Individual-Based Models Individual-based m odels (IBMs) are simulati on models based on the assumption that the dynamics of an ecosystem, community or popul ation, emerge from the variability among individuals and their inte ractions with other individuals of the same species, different species, and with their environment (DeAngelis and Mooij 2005, Grimm and Railsback 2005). Individual-based models are unlike other models in the sense that instead of dealing with populations that have different birt h and death rates at different stag e-age classes, they deal with individuals whose growth, repr oduction, and survival depends on their behavior and their interactions with their internal and external environment, as modified by their age or state (Grimm and Railsback 2005). In order to design an IBM, a higher level pattern from the population or community (such as migration or population dynamics) is usually chosen, and the functions, processes, and entities that are believed to cause the pattern are then included in the model. DeAngelis and Mooij (2005) provide a review of variat ion among individuals that can ge nerate higher level patterns. They classify the types of indivi dual variations in: (a) spatial processes and movement, (b) life cycle and development, (c) phenotypic variability plasticity and behavi or, (d) differences in experience and learning, and (e) genetic variability and evolut ion (DeAngelis and Mooij 2005). These causes of variation would be differentia lly addressed in a model, depending on the particular patterns under study. For example, if a model is to address migration or dispersal of organisms through space, it needs to take into consideration individual movement behavior
50 depending on age or status. If th e objective of the model is to a ddress predator-prey interactions, adaptive defensive or avoidance behaviors might n eed to be explicitly represented in the model. Grimm and Railsback (2005) a nd Grimm et al. (2006) indicate that IBMs have lacked a common language like calculus in classical models which could allow scientists to communicate and compare the concepts exposed in their models They proposed a standard protocol and a series of concepts to describe IBMs, and they advocate the adoption of this framework to help in the design, development, description, classificat ion and evaluation of IB Ms. Here, the main conceptual framework will be briefly discussed; for a description of the protocol consult Grimm et al. (2006). The conceptual framework for IBMs includes 10 concepts that the model could potentially address. These concepts are (Gri mm and Railsback 2005, Grimm et al. 2006): Emergence: description of what particular sy stem pattern emerges from individual traits. Adaptation: this refers to the description of how individuals res pond to changes in their internal (growth, change of stat us) and external environment. These adaptive traits could directly or indirectly influe nce the fitness of individuals. Fitness: fitness-seeking traits could be mode led explicitly or implicitly. If explicit (the individuals adaptive behavior has a direct impact on fitness), the model requires each individual to know how the environment and decisions made affect its own fitness. Prediction: if fitness is explicit in the model, this requires simulating how individuals predict how the choices availa ble to them affect a meas ure of their fitness. Sensing: this concept refe rs to the amount and quality of knowledge that an individual will have about its surroundings. Sensing information includes both information from the internal (energy reserves, disease status) and external environments (knowledge of habitats of high predation risk, resource availabi lity, distance to resour ces, etc.). The way sensing is represented in the model will have an impact on the decisions made by individuals and on the emergence of higher level patterns. Interaction: the model could represent indi viduals interacting directly (information is exchanged among individuals affecting their d ecisions) or indirectly, through the effects of indirect competition for resources.
51 Stochasticity: this refers to the use of random numbers and probabilities to represent certain processes in the IBM. Stochasticity can be introduced into the input variables (weather) or into the individuals behavior (mak ing a decision with certain probability). Scheduling: description of the time step (d iscrete, continuous, a combination) and how the processes are updated (s ynchronously, asynchronously). Collectives: collectives refer to aggregations of individuals. In some models, modeling the behavior of collectives (like fish schools) takes the place of individuals. Observation: definition of the model outco mes that will be used to test IBMs and compare among model outputs. Individual-based models are widely used tools to explore the emergence of population characteristics under environmental heterogeneit y (Breckling et al. 2005, Breckling et al. 2006). These types of models are used to study indivi dual dispersal behavior in fragmented landscapes and its effects on colonization probabilities and spatial distribution (Vuilleumier and Metzger 2006), and population persistence over time (Popp et al. 2007, Eldred and Nott 2008). Other examples of emergent population characteristics studied include age structure (Charles et al. 2008), and body size and mass distribution (Hol ker and Breckling 2005, Ch arles et al. 2008). Some of these models incorporate changes in th e environment over time, such as prey mobility in predator-prey models (McCauley et al. 1993 ) or the effects of the timing of pesticide applications on the density and disper sal of pests (Parry et al. 2006). Individual-based models with spatial component s (spatially explicit IB Ms or SEIBM) have been recently used to study the emergence of characteristics relating to disease transmission by mosquitoes. The effects of heterogeneous spatia l distribution of resources in the likelihood of viral amplification in a mos quito-bird-arbovirus system (Shaman 2007) and the impact of oviposition site reduction on the population dynamics of An. gambiae and malaria transmission (Gu and Novak 2009) have been studied using SEIBMs. In these models the female mosquito population was subdivided by physiological stag e (host-seeking, bloodfed, and gravid) and
52 infection status. Mosquito disp ersal behavior was an important component of both models. In the first model mosquitoes moved in a grid and ma de the decision to move to a different cell with a certain probability based on detecting an ovipositi on site or host within their sensory range (9 grid cells) (Shaman 2007). In the second model the spa tial configuration represented a typical village in Africa with oviposition sites surrounding the houses, and the female flight behavior involved two parameters, the sensory range and th e maximal flight length (Gu and Novak 2009). These model structures allowed for the consid eration of mosquito be havior at different physiological stages within the gonotrophic cycle and its consequences in arbovirus amplification (Shaman 2007) and malaria prevalence (Gu and Novak 2009). The challenging aspects of these models are the sensitivity anal yses, given that they in clude a large number of parameters including not only the biology of the or ganism, but its behavior and its environment. For the purposes of the modeling study in this Dissertation, IBMs appear as a good option to study the changes in age structure in a mo squito population over time in a heterogeneous space. Both the Leslie Matrix models and co mpartmental differential equation models can be used to study population dynamics over space and tim e. However, IBMs provide a framework in which the chronological and physiological age of each individual adult female could be traced. Variability in the chronological age structure of the population would not only be a result of mortality and fecundity rates, but a result of individual variation in mortality. The physiological age structure of the population woul d be influenced by the resources available for females in the environment to complete their gonotrophic cycles. Problem Statement The changes in abundance of Cx. nigripalpus in south Florida ar e largely driven by changes in r elative humidity and the availability of oviposition sites associated with rainfall. More information is needed on how these envi ronmental changes affect the physiological and
53 chronological age structure of the populations of this mosquito. Ch anges in parity rates in other species have been found to be associated with temperature and rainfa ll (Reisen et al. 1983, Reisen et al. 1986). The abundance of gravid Culex nigripalpus mosquitoes has been found to be negatively associated with daily ra infall 0-7 days prior to the day of collection (Day et al. 1990). Thus it could be expected that the age structur e of this species is affected by environmental conditions, particularly rainfall and increases in humidity. It is important to understand the changes in age structure of a mosquito vector population because age structure is a determinant of the size of the infectiv e population (Detinova 1968). There has been recent interest in understanding the effects of heterogeneities on the risk of pathogen or parasite transmission by mosquito es. These heterogeneities could include patchy distribution of resources such as hosts and oviposition sites (Smith et al. 2004, LeMenach et al. 2005) and the effects of differential biting pr eferences by mosquitoes (Kelly and Thompson 2000). Modeling studies have shown that these environmental heterogeneities could have an impact on the spatial distribution of older, pote ntially infectious mosquitoes (Smith et al. 2004, LeMenach et al. 2005). The overall goal of this part of the study was to gain knowledge of the effects that environmental heterogeneity could have on the p hysiological and chronologi cal age structure of the Cx. nigripalpus population. Here, environmental heteroge neity refers to variations in both the availability of oviposition sites and hosts over space and time and variation in humidity conditions, both due partly to rainfa ll patterns. Variations in the female mosquito efficiency in locating resources in a heterogeneous environment were also considered. Culex nigripalpus in Florida is a mosquito vector of St. Louis encephalitis and West Nile viruses, and a bridge vector for eastern equine encephalitis virus (Florida Department of Health
54 2009), and a better understanding of the environmental factors that affect the age structure of its populations could help in survei llance programs. There is ev idence supporting that certain environmental conditions can incr ease the probability of arbovirus epidemics in Florida where Cx. nigripalpus is most likely the primary vector implicated (Day 2001, Shaman and Day 2005, Day and Shaman 2008). Drought conditions in la te spring, wet events in early summer, drought in late summer, and wet events in the fall incr ease the likelihood of epidemics (Day and Shaman 2008). The probability of human arbovirus infec tions in south Florida increases with drought conditions 4 months prior and wett ing conditions one and half mont hs prior to the onset of the human cases (Shaman et al. 2004). The results from this study can complement that evidence and can help to improve our knowledge of one of the mechanisms behind ep izootics and epidemics: the aging of the mosquito population. A field study was conducted in Indian River County, Florida. The goal was to study examine if environmental factor s such as water table depth, rainfall, and temperature, among others, could help explain th e variation in physiological age structure of Cx. nigripalpus populations observed in the field. The phys iological age structure was approximated by the proportion of parous mosquitoes and a multivariate statistical regression model was developed to predict changes in this proportion. Models to expl ain changes in total mosquito relative abundance and nulliparous mosquito re lative abundance using environmental variables were also developed. Multivariate models to examine the relationships between Cx. nigripalpus abundance and parity and environmental f actors were not prev iously available. Given that it is difficult to determine the chr onological age of mosqu itoes collected in the field, an IBM was used to study how changing envi ronments could introduce variations in the chronological age structure of mosquito populations. Individual-based models were selected
55 because they allowed tracking the chronological age and parity status of individual mosquitoes. The model simulated the mosquitoes searching behavior for hosts and oviposition sites in hypothetical landscapes. These lands capes had heterogeneous distribut ions of water sources that changed with weather. Weather cha nges also affected relative humidity. The first objective of the modeling experiment was to determine if spatial and temporal variation in resource availability (oviposition sites) and humidity conditions could have an impact on the chronological age of parous females, the percentage of parous females, and on the size and spatial spread of the population. The se cond objective was to determine how variations in the efficiency of mosquitoes to find resources could impact the age structure, size, and spatial spread of the population. More information is needed regarding Cx. nigripalpus movement patterns, searching behavior, and other behavioral aspects relevant to the pr oblem at hand. However, the information available on the biology of the speci es was used to design a model that included hypothesized functions describing dispersal activity and the probability that mosquitoes will find host or oviposition sites as a function of resource density.
56 Table 2-1. Vectorial capacity (E quation 2-1) at different values of p with all other parameters held constant (m = 1000, a = 0.1, b = 0.25, n = 12). ma2b p pn C 2.50 0.90 2.68 6.70 2.50 0.80 0.31 0.77 2.50 0.70 0.04 0.10 2.50 0.60 4.24 x10-3 0.01 2.50 0.50 3.52 x10-4 8.81 x10-4
57 CHAPTER 3 RELATIVE ABUNDANCE AND PHYS IOLOGICAL AGE STRUCTURE OF Culex nigripalpus AS A FUNCTION OF ENVIRONMENTAL VARIABLES Introduction The abundance and age structure of adult fem a les in a mosquito population are important parameters for the epidemiological surveillance of mosquito-borne diseases (Dye 1986, Moore et al. 1993, Eldridge 2004). This is because the size of the infectious mosquito population is often related to mosquito abundance a nd age structure. The risk of pathogen or parasite transmission increases as mosquitoes increase in numbers and disperse, but this must be accompanied by an increase in the number of females that have su rvived long enough to become infective (Detinova 1968, Day 2001, Eldridge 2004). The relative abundance of mosquitoes is infl uenced by intrinsic popul ation characteristics (e.g., birth and death rates) and by external biolog ical factors (e.g., predation, competition), but it is also influenced by environmental factors su ch as precipitation and temperature (Eldridge 2004). The relationship between the age structure of a mosqu ito population and environmental factors has been studied less than the effects of the envi ronment on relative abundance. Traps or backpack aspirators are commonly us ed to collect mosquitoes and to obtain a measure of their relative abundance, expressed as the number of mosquitoes collected per trap night or mosquitoes per unit area. Traps vary in their efficacy for different species and most are designed to target particular phys iological stages (Moore et al. 1993). For example, light traps collect all female physiological st ages and male mosquitoes. Traps baited with carbon dioxide sample the unfed host-seeking female mosquitoes and gravid traps collect females that have digested a bloodmeal and hold eggs (California Department of P ublic Health 2009). Backpack aspirators can be used to collect adult mosquitoes in their resting places: female mosquitoes of
58 all physiological stages (green or recently emerged, unfed, bloodfed, and gravid) and males (Moore et al. 1993). The environmental factors which are major drivers of the changes in the relative abundance of a mosquito population depend on th e mosquito species and its biology. For example, tidal patterns have been found to be important to explain the dynamics of salt marsh mosquitoes such as Aedes sollicitans in the northeastern United States (Shone et al. 2006) and Aedes vigilax in northern Australia (Yang et al. 2008). The water content of the snow in the Sierra Nevada is a good predictor of river runoff, which is dir ectly related to the relative abundance of Culex tarsalis during the summer months in Ke rn County, California (Wegbreit and Reisen 2000). The age of an adult female mosquito can be defined in two ways. Chronological age is the time since adult eclosion, and phys iological age is the number gonotrophic cycles a female has completed. The gonotrophic cycle is the time elapsed from taking a bloodmeal to oviposition (Clements 2000). The chronological age structure can be defined as the frequency distribution of groups of ages (e.g., 0-2 d, >2-5 d, etc.) in the population. Physiological age structure can be defined as the proportion of female mosquitoes that are at different physiological stages (nulliparous, parous 1, etc.) in the population (Detinova 1968). The chronological age of female mosquitoes can be approximated using chemical (Gerade et al. 2004) or gene transcrip tion methods (Cook et al. 2006), but these methods are expensive and need further calibration (Hugo et al. 2008). Th e physiological age of female mosquitoes can be determined by observing changes in the ovari es that occur after ovi position. The Detinova method is a practical way to determine parity status It is based on the observation of changes in the tracheal system of the mosquito ovaries. Nulliparous mosquitoes show tightly coiled
59 tracheoles (skeins), but after laying the first batc h of eggs the tracheoles become distended. Thus, parous mosquitoes usually lack coiled tracheoles (Detinova 1962). The Detinova method has been successfully used to determine the physi ological age of Culex mosquitoes (Nelson 1966, Reisen et al. 1983, Reisen et al 1986) and other genera such as Anopheles (Reisen et al. 1986, Atieli 2007) and Aedes (Hugo et al. 2008). The Detin ova method can only separate between nulliparous and parous mosquitoes so it only provides an approximation for age structure. The physiological age structure of females in a mosquito population is partly determined by the time it takes for the mosquitoes to comple te a gonotrophic cycle, by their daily survival (Detinova 1968), and by the times of nulliparous mosquito emergence. The time to complete a gonotrophic cycle is influenced by complex inte ractions among factors such as mosquito searching behavior for hosts and oviposition si tes, host preferences, host abundance, and host defensive behavior. Environmental inputs such as availability of oviposition sites, rainfall, temperature, and relative humidity also affect the duration of the gonotrophic cycle because they could induce mortality (e.g., mortality resulting from rainfall or changes in temperature) or affect mosquito activity. While searching, mosquitoes might be exposed to predators or, when attempting to feed, to the host defensive behavi or (Charlwood 2003). Daily survival is also influenced by mosquito age (Styer et al. 2006, Lord and LeFevre unpublished data). Previous studies have found that environm ental factors can help explain temporal variations in physiological age structure for some mosquito species. Changes in parity rates of female Cx. tarsalis collected in resting boxes in Kern County, California, correlated positively with the air temperature (Reisen et al. 1983). The relationship be tween monthly averages of the proportion of parous females and monthly averages of rainfall and temperature was studied for
60 three mosquito species in Pakistan (Reisen et al. 1986). No relati onships were found for Anopheles culicifacies a negative correlation between pari ty and rainfall was observed for Anopheles stephensi, and a negative correlation between parity and temperature was found for Culex tritaeniorhynchus The authors did not speculate on th e causes of these relationships, but weather conditions could be associated with fa vorable (or unfavorable) conditions for mosquito flight and oviposition thus influencing the pr oportion of females completing gonotrophic cycles. Culex nigripalpus is a vector of various pathogens a nd parasites in Florida (Nayar 1982), where it was implicated as the main vector of St. Louis encephalitis virus (SLEV) in various epidemics (Day 2001). It has been identified as a vector of West Nile virus (WNV) (Blackmore et al. 2003), and a bridge vector for easter n equine encephalitis virus (EEEV) (Florida Department of Health 2009). In southern Florida, changes in the abundance of Cx. nigripalpus are probably associated with changes in the gr ound water levels due to rainfall leading to the expansion of aquatic habitats (Provost 1969, Shaman and Day 2005). Rainfall events of 50 mm within 3 days have been found to be correlate d positively with increases in the abundance of Cx. nigripalpus (Day and Curtis 1993). It has been specula ted that this amount of rainfall is the minimum necessary to provide te mporary larval habitats that will last at least 7 d, allowing mosquitoes to complete their immature st ages during the summer and fall months when temperatures are warm (Day et al. 1990). Increas es in the number of mosquitoes collected with aspirators 5-8 days and 12-15 days after heavy rain were observed in Indian River County, Florida (Day and Curtis 1993). The authors cons idered that the first mosquito emergence was related to eggs deposited by gravid females during the rainfall event, and to the adults emerging from these eggs 5-8 days later. The second abundance peak could have been due to females that
61 bloodfed during the rainfall ev ent, laid eggs 3-4 days later, and to the adults emerging from these eggs 12-15 days after the rainfall event (Day and Curtis 1993). In the case of Cx. nigripalpus a species whose dynamics are linked to rainfall patterns, parity rates could be influenced by changes in oviposition site availability. The proportion of parous females at time t (Pt) could be viewed as function of the proportion of unfed (both parous and nulliparous) females at a previous time t-g (Ut-g) that took a bloodmeal, developed eggs, laid eggs, and survived to time t: Pt = Ut-g*S, where S is the probabil ity of survival through a gonotrophic cycle. Thus the pr oportion of females that comple tes a gonotrophic cycle could be some function of the number of suitable water sources. Howeve r, this relationship should be modified by weather conditions that could either facilitate or impede searching flights to find hosts to take bloodmeals and aqua tic habitats for oviposition. It is known that increases in temperature, relative humidity and rainfall stimulate Cx. nigripalpus to bloodfeed and oviposit (Dow and Gerrish 1970, Bidlingmayer 1974, Day and Curtis 1989, Day et al. 1990). Culex nigripalpus activity is also affected by moon illumination and wind speed. Bidlingmayer (1964, 1974) extensively studied the effects of moon illumination on mosquito trap collecti ons in Florida. He reported that for some local species, including Cx. nigripalpus larger collections were obtained with tr uck traps, baited traps, and suction traps during twilight and whenever the full or quarter moon was visible. This was not true for light traps, which yielded reduced collections duri ng full moon nights (Bidlingmayer 1974). This was probably due to weakened attractiveness of the artificial light when moon illumination was strong. Bidlingmayer (1974) considered that tr uck traps were the most appropriate traps to detect changes in mosquito activity due to moon illumination. Culex nigripalpus mosquitoes are attracted to tall vegetation and it is believed that their navigation improves when moon light is
62 present (Bidlingmayer and Hem 1980, 1981) be cause moon illumination provides a better contrast between vegetated areas an open fields Bidlingmayer (1974) also reported smaller collections when wind velocities in creased to 1-2 miles per hour comp ared to collections made at <1 mph. However, he acknowledged that his co llections were made at 1.25 m above ground, and it is unknown if wind could modify the behavior of mosquitoes that could fly closer to the ground under higher wind velocities. In the present study, the changes in the rela tive abundance and physiolo gical age structure of populations of the mosquito Cx. nigripalpus were studied at three sites in Indian River County, Florida. The goal was to study examine if environmental factors such as water table depth, rainfall, and temperature, drought inde x, moon illumination, and wind, could help explain the variation in physiolo gical age structure of Cx. nigripalpus populations observed in the field. The physiological age structure was approximated by the proportion of parous mosquitoes and a multivariate statistical regressi on model was developed to predict changes of this proportion. Models to explain changes in total mosquito relative abunda nce and nulliparous mosquito relative abundance using environmental variables were also developed. Multivariate models to examine the relationships between Cx. nigripalpus abundance and parity with environmental factors were not previously available. Models of the relationships between envi ronmental variables and mosquito relative abundance can be simple linear regressions wh ich consider the relationships with each environmental variable separately (examples can be found in Shaman et al. 2002b and Wegbreit and Reisen 2000). When many variables are considered at once, there is always the question of what variables to include in the model. Two of the variable selection te chniques that have been used in the past for models of mosquito abunda nce include multivariate linear regression with
63 backward elimination of vari ables (DeGaetano 2005), and genera lized linear models with a priori selection of explanatory variables based on cross-correlation analysis (Shone et al. 2006). Burnham and Anderson (1998) stated that when there are many possible explanatory variables, the selecti on of a model with a certain combin ation of variables using hypothesis testing (only significant va riables are included in the model) can lead to over fitted models with spurious correlations. Models bui lt in this manner can also be uns table, meaning that they would probably vary considerably if another sample of the same process was used. According to Burnham and Anderson (1998) data analysis for observational st udies like the one conducted here should be viewed as a problem of mode l selection and parameter estimation, and that hypothesis testing should be reserved for formal experiments in which the effects of treatments, controls, and random assignments ove r the mean can be hypothesized a priori They propose the use of the Akaike Information Cr iteria (AIC) and model weights fo r model selection. The use of AIC and model weights for model selection is detailed in the ma terials and methods section. Here we build multivariate statistical linear models to predict changes in relative abundance and parity rates in Cx. nigripalpus, using different combinations of eleven explanatory environmental variables that descri be weather conditions, collection site, and moon illumination. We use the AIC and model weights to select the model that could best predict the changes in relative abundance and parity rates of Cx. nigripalpus populations observed in the field. This type of predictive model could be important in epidemiological assessments to predict changes in the size of the infectious mosquito populati on which is related to increases in the proportion of parous females.
64 Materials and Methods Collection Sites Mosquitoes were collected at three sites in Indian River County, Flor ida (Figure 3-1) from June to November, 2007 and from June to Octobe r, 2008. A description of the land uses in an area of 5.7 km2 centered on each collection site is in cluded. An aerial image from the free software Google Earth 4.3 ( http://earth.google.com ) dated Decem ber 2005 and knowledge of the areas provided support for the descriptions. The Park Site was located in Charles Park in downtown Vero Beach (27.627802,80.409773), 2 km west of US Highway 1 (US-1). The park is open daily from 7 am to 10 am and is heavily used by local residents for recrea tional activities and exercise. It has typical southern Florida vegetation with pine trees ( Pinus sp.), oaks ( Quercus sp.) and cabbage palms ( Sabal palmetto ) and is surrounded by a small wooded area with a lush understory and residential neighborhoods (Figure 3-2, Figure 3-3). The Park Site had an area of 0.04 km2 which corresponded to 0.70% of the selected 5.7 km2 area. Other land uses included the local high school and commercial buildings which occupied 22.81% of the area and re sidences which made up the other 76.49%. A survey of potential ovipos ition sites was not conducted as part of this study but according to information in OMeara et al. (2003), natu ral and artificial containers, storm water drainage, and retention swales might be potential oviposition sites for Cx. nigripalpus in the area. The Yard Site was located in the yard of a private residence in western Vero Beach, 5.6 km west of US-1 (27.602463,-80.438260). It is a suburban environment with houses intermixed with open land with vegetation that includes oaks ( Quercus sp.), grasses, and invasive plants such as the Brazilian pepper ( Schinus terebinthifolius ) (Figure 3-4, Figure 3-5). The Yard Site had an area of 0.003 km2 which corresponded to 0.05% of the 5.7 km2 surrounding area.
65 Other land uses in the surrounding area included large grassy fields with scattered or no trees (14.91%) and residences (85.04%). Potential ovipositi on sites in this area could include natural and artificial containers storm water drainage, and retenti on swales (OMeara et al. 2003). There were many gated residential communities with water retention ponds within the area surrounding the Yard Site but it is unclear if th ese could function as aquatic habitats for this species given that they might be tr eated to prevent mosquito reproduction. The Groves Site was located in an ope n field with multiple cypress domes ( Taxodium sp.) surrounded by citrus groves, 25 km west of US-1 (27.605853,-80.632225) (Figure 3-6, Figure 3-7). The oviposition sites in these areas might include natural containers, ponds with emergent vegetation, and drainage and irrigation furrows in the citrus groves (OMeara et al. 2003). The Groves Site was located in an open fi eld with cypress domes that had an area of 0.64 km2, 11.23% of the 5.7km2 surrounding area; the remainder was occupied by citrus groves (88.77%). These three sites lay on an east to west gradient across Indian River County that encompasses typical landscape features of the area. Mosquito Collections Mosquitoes were collected using lard can tr aps b aited with carbon dioxide. A recent study in south Florida collected predominantly Cx. nigripalpus with this type of trap baited with chickens, with more than 95% of the specimens belonging to this spec ies (Vitek et al. 2008). Four traps were placed at each site. The traps were suspended by string on a double-hooked garden pole of ~1.80 m in height. A 1 gallon co oler filled with dry ice was hung on the opposite hook from the trap and a hose dispensed the carbon dioxide into the trap (Figure 3-8). Traps were placed at irregular distances on each site but were at least 5 meters apart, usually hidden behind trees (Figure 3-2 B, Figur e 3-4 B, and Figure 3-6 B). Th is was done to prevent possible
66 disturbances from pedestrians especially at the Park and Yard Sites. At the Groves Site, traps were placed 10 meters outside from th e one of the edges of a cypress dome. Traps were set 0.5 to1 hour before sunset to guarantee that the dry ice would last throughout the night. They next morning they were picked up between 7 and 8 am, following sunrise, when most Cx. nigripalpus activity had ceased. Depending on the month, sunrise was between 6:30 and 7:30 am. The collection dates were selected according to the moon phases. The moon phases were classified on the basis of the fraction of moon illuminated (FMI) published by the Astronomical Applications Department of the U.S. Naval Observatory ( http://aa.usno.navy.mil/data/docs/MoonFraction.php ). Inform ation on the FMI for each night of the years 2007 and 2008 was used to plan coll ections on the nights before, during, and after a full moon (FMI = 1), the new moon (FMI = 0), and the first and last quarter moon (FMI ~ 0.5). The only exceptions were the firs t three collecting night s of 2007 that were made during June 1012 (FMI of 0.31, 0.21, and 0.12, respectively). Collect ions were made during three consecutive nights (before, during, and after the moon phase) by placing traps at a different site each night. The order in which the sites were sampled on each three-night collecting period was randomly chosen. Mosquitoes were collected around moon pha ses because previous st udies reported that moon illumination can have an important effect on the size of Cx. nigripalpus collections (Bidlingmayer 1974). There were a total of 126 collection nights (21 per site per year), with one additional night for the Park Site in 2008. Mosquitoes were transported from the collect ion sites to the laboratory where they were anesthetized using triethylamine. They were rem oved from the traps, placed in labeled vials, and stored at -80C for later identification and counting.
67 Mosquito Identification Mosquito samples were sorted to species a nd cou nted to determine the abundance of each. Species determinations were made with the aid of the adult female mosquito identification key by Darsie and Ward (2005). A sample of up to 100 Cx. nigripalpus mosquitoes from each trap was kept after sorting and stored at -80C for parity determination. Parity Determinations Nullipa rous and parous Cx. nigripalpus female mosquitoes were classified by examining the condition of the tracheal sy stem of the ovaries (Detinova 1962). Dissections were conducted following a technique similar to Atieli (2007), dissecting only those females with visibly empty abdomens. Briefly, a mosquito and a drop of distil led water were placed on a microscope slide. Using a stereoscope, the abdomen was removed from the rest of the body with a pair of forceps and placed in the drop distilled water. The 7t h and 8th abdominal segments were removed by pulling them with forceps. The ovaries were isolated from ot her tissues and transferred to another slide with a drop of dis tilled water and were allowed to ai r dry. After drying, the ovaries were observed under 200X magnification using a compound microscope. Nulliparous specimens had tightly coiled tracheoles (Figure 3-9 A a nd C), while parous specimens had loose or distended tracheoles (Figure 3-9 B and D). Ovarie s were classified as indeterminate when the parity status was unclear s howing both coiled and distended trachea (Figure 3-9 E). Additionally, some ovaries did not preserve co rrectly making tracheoles difficult to visualize under the microscope. These were classifi ed as undetermined (Figure 3-9 F). A minimum of 10 mosquitoes per trap was dissected for a total of 40 per site per night. After scoring some samples it was determined that many of the ovaries in the sample had tracheoles that were difficult to visualize (pos sibly due to bad preser vation), and additional
68 mosquitoes from that trap were dissected. This resulted in variable numbers of mosquitoes dissected per site per night. Five collection nights had less than 40 mosq uitoes to dissect. Parity data for the first three weeks of collect ing in 2007 are not available. This is because parity determination was initially attempted usi ng a 40X dissecting microscope. That proved to be unsuccessful for examining the tracheal coiling. Thus, no samples were available for parity evaluation with the 200X compoun d microscope. An average of 44.85.13 mosquitoes per site per night were dissected for collections from 2007 and an average of 38.32.68 for 2008. Data Analysis The two response variab les of interest define d for each site where the average number of Cx. nigripalpus females collected per trap night (rel ative abundance) and the estimated proportion of parous mosquitoes pe r night (physiological age structure) of this species. The proportion of parous mosquitoes was calculated over the total number of mosquitoes dissected. An alternative was to calculate the proportion over the total number of mosquitoes that were clearly classified as either parous or nulliparous. Both alternatives were explored and provided very similar results. Only the results for form er are presented here. Only proportions obtained from collection dates for which 20 or more parous females were dissected per site were included in the analysis. Environmental variables and the collection site were used as expl anatory variables in generalized linear models (GLM) to pr edict relative abundanc e and parity of Cx. nigripalpus in Indian River County. All models were fitted in the statistical package R 2.7.0 (R Development Core Team 2008). The explanatory variables used were: daily total pr ecipitation (mm), daily minimum temperature (C), daily Keetch Byram Drought Index (KBDI), daily modeled water table depth (MWTD), daily average wind speed (kph), the FMI, and collection site.
69 The environmental variables used here were se lected on the basis that they can influence the availability of oviposition sites (rainfall, wate r table depth, location), they can be indicators of conditions at which mosquitoes are active and flying during a particular night (temperature, drought, moon illumination, wind), or they can infl uence the developmental time of immature mosquitoes (temperature). The time from egg hatch to adult eclosion in Cx. nigripalpus is reduced as temperature increases (Nayar 1982). Culex nigripalpus females prefer to oviposit under high relative humidity 90% (Day et al. 1990); their flight activity decreases when temperatures are below 17-18C (Bidlingmayer 1974) and increases when relative humidity is high (Dow and Gerrish 1970). Bloodfeeding increas es following heavy rainfall events (Day and Curtis 1989). The KBDI is a measurement that indicates moisture deficiency in the soil and duff layers resulting from the net effect of evotranspiration and precipitation. It give s an indication of the flammability of organic material in the ground and is used in fore stry to monitor the risk of wildfires (Keetch and Byram 1968). The KBDI wa s used here as an indicator of humidity changes that can greatly affect Cx. nigripalpus behavior: dry conditions can decrease mosquito activity and reduce the number of mosquitoes that search for hos ts or oviposition sites. The KBDI measures values from 0 to 800; hi gh KBDI values corres pond to dry conditions. Modeled water table depth (MWTD) was used here as an indicator of ground water accumulations which are related to the creation of potential Cx. nigripalpus oviposition habitats. Modeled water table depth data are obtained by modeling surface wetn ess as a function of precipitation, temperature, topography, soil prop erties, vegetation, and prior wetness conditions (Shaman et al. 2002b). Modeled wa ter table depth data have been used to develop predictive models of mosquito abundance (Shaman et al. 2002b), and a wate r table depth model developed
70 for peninsular Florida is currently being used for real time forecasting of the risk arbovirus epidemics (Day and Shaman 2008). The MWTD tracks values between ~ -1.6 to 0 meters and is an indicator of the depth of the water table below the ground surface. Wind was included as an expl anatory variable because increases in wind speed are associated with decreases in the size of mosquito collections (Bidlingmayer 1974). Moon phase also has an important e ffect in the size of Cx. nigripalpus collections. This was observed in previous studies using suction, truck, and baited traps (Bid lingmayer 1964, 1974) and it was of interest to evaluate if moon phase could help predict the collections ma de with stationary CO2 baited lard can traps. The daily total precipitation, minimum temperat ure, and average wind speed data for Vero Beach, FL were obtained from the National Clim atological Data Center, National Environmental Satellite, Data and Information Service, from the National Oceanic and Atmospheric Administration. Files (ASCII format) containing information on the daily weather data for the Vero Beach Municipal Airport Station (Figure 31) for the months from May to November 2007 and from May to October 2008 were downloaded from http://www.ncdc.noaa.gov/oa/ncdc.html The data f or FMI were obtained from the Astron omical Applications Department of the U.S. Naval Observatory website (see above). Mr Gregory Ross, from the Florida Medical Entomology Laboratory, provide d the daily KBDI for 9 reporti ng sites and the MWTD from 4 reporting sites located west of Vero Beach (Fig ure 3-1 and Figure 3-10). Data for the KBDI reporting sites were made available to him by th e Division of Forestry, Florida Department of Agriculture and Consumer Services ( http://www.fl-dif.con/fire_w eather/infor mation/kbdi.html ). The MWTD data were generated at FMEL usi ng a previously developed algorithm (Shaman 2002b). Additional information about model deve lopment and implementation can be found at
71 http://mosquito.ifas.ufl. edu/MW TD_Risk_Model.htm and in Day and Shaman (2008). The daily KBDI data from the 9 reporting sites and the daily MWTD data fo r the 4 reporting sites were averaged to obtain a single da ily value to use in the analysis. Previous studies have shown that temporal changes in mosquito abundance can be explained by lagged meteorological data (Day et al. 1990, Shaman et al. 2002b, Shone et al. 2006). For this study, the mean values for daily precipitation 0-6 days (prcp06) and 7-14 days (prcp14) prior to the collection night were calculated and tested as explanatory variables. These time intervals were selected based on our understanding of Cx. nigripalpus ecology during the summer months: the development of an egg to the adult stage takes a bout 10 days at 27C and about 7 days at 32C (Nayar 1982). If it takes between 7-10 days for mosquitoes to emerge, rainfall events 7-14 days and 0-6 days before the collecti on could encompass one or two generations of mosquitoes that would become active, take bloodmeals, and oviposit thus affecting the size of the catch dur ing summer trap collections. The following variables were also averaged ove r the periods 0-6 days and 7-14 days prior to collections: mean daily minimum temperature (tmin06, tmin714), mean daily KBDI (kbdi06, kbdi714), and mean MWTD (mwtd06, mwtd714). The FMI (moon) and the daily average wind speed (wind) on the day of the collection were also tested as explanatory variables. Precipitation data were missing for 11 dates in 2007 and 21 dates in 2008, mostly on non consecutive days. Averages were calculated over five or six days instead of seven in those cases. There were also a few missing observations in the KBDI data set for 2008. Model selection using the Akaike Information Criteria (AIC) The AIC wa s derived by the mathematician Hirotugu Akaike and is an approximation of the Kullback-Liebler (KL) distance. The KL dist ance measures the amount of information that is lost when a model is used to represent the full re ality that generated the obs erved data or the full
72 truth ( f ), for which the number of parameters is unknown but it could encompass a large number of them (Burnham and Anderson 1998). The calcul ation of the KL distance requires knowledge of f thus it cannot be used for model selection. Ak aike demonstrated that the relative expected KL distance can be approximated by the actual log-likelihood of a model given the data. A model is defined as a set of parameter values ( ). He also showed that the log-likelihood is a biased estimator of the relative expected KL distance by a factor approximately equal to the number of the estimable parameters (K) in the model (Burnham and Anderson 1998). Akaike then proposed an approximately unbiased estimat or of the relative expected KL distance: (3-1) where L( |Y) is the likelihood of the model ( ) given the data set (Y). The AIC can be viewed as an estimator of the relative distance between the fitted model and the unknown true mechanism that generated the observed data (Burnham and Anderson 1998). By estimating and comparing the likelihood of various different models ( i) given the data one could evaluate the relative support of the da ta for each model. It would not be possible to evaluate a model without comparing its ability to represent the data versus other models (Hobbs and Hilborn 2006). The model that yields the smallest AIC should be considered closest to the reality that generated the data (Burnham and Anderson 1998). Howe ver, uncertainty arises when there are small differences in the AIC values among the candidate models. A measure of model selection uncertainty is provi ded by the Akaike weights (wi), which can be interpreted as the probability that a particular m odel i is selected as the best m odel after many repetitions of the model selection exercise (Hobbs and Hilborn 2006). The values of the weights range from 0 to 1. The weights can be calculated as follows: (3-2)
73 where i is the difference between the smalle st AIC from all models and the AIC for model i. The expression exp(i) is an estimate of the relative likelihood of the m odel (given the parameter values i fitted with the data). exp(r) is the summation of the i values for the total number (R) of mode ls under consideration. When there is not a single model that emerges as the best among the candidates (defined by the smallest AIC and highest weight closer to 1), model selection uncertainty can be introduced to parameter estimation through model averaging (Burnham and Anderson 1998). The number of models to average can be selected based on certain criteria One could select a set of models whose weights are larger or equal to a certain probability defined as the confidence set. Hobbs and Hilborn (2006) recomme nd selecting the models with weights 0.05 for the confidence set. The level 0.05 is arbitrary but is necessary to have a cut off point for decision making. With this threshold the models in th e confidence set could be interpreted as those models that would be selected at least 5 out of 100 times if th e model selection exercise is repeated many times. Model averaging should be conducted over the models in these sets and not over all candidate mode ls (Hobbs and Hilborn 2006). The parameter estimates and their respective stan dard errors are averaged across all models where a parameter is included. Parameters estim ates are averaged by multiplying the parameter estimate i for model i by a rescaled wi based only on the models containing the parameter of interest, and then summed over all the m odels (R) that contain that parameter: (3-3) The standard error of the parameters is recalculated using the following equation: (3-4)
74 where var( i|Mi) is the variance of the parameter estimat e of model i and the sum is over all the models (R) that contain that parameter. Model selection of a GLM for the p rediction of the average number of Culex nigripalpus females co llected per trap night A global model for the predicti on of the average number of Cx. nigripalpus females per trap night was set up as a linear model that in cluded eleven explanatory variables as fixed effects. The response variable was the square root of the average number of Cx. nigripalpus females collected per trap night. The response variable was square root transformed to assure positive predicted values and to stabilize the variance. The global model was as follows: (3-5) where sqrt(mosquitoes per trap ni ght) is assumed to be normally distributed. The collection site is a categorical variab le that affects the va lue of the intercept. The multi-model inference package MuMIn v.0.12.2 for R (R Development Core Team 2008) was used to fit candidate models, conduc t model selection, and model averaging. The dredge function in MuMIn fits all the possible models from all combinations of the explanatory variables in the global model, without including interactions. In this case the candidate models included all possible models from the combinati ons that can be constr ucted by taking 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10 variables at a time and the full model. This totaled 2048 candidate models. The dredge function calculates the following fit measures for each model: number of parameters (K), Deviance, AIC, AICc (which is a correction of the AI C for small samples), difference between the smallest AIC and the model AICi ( i), and the Akaike weight for each model (wi). Because the sample size here wa s small (ratio between the sample size including all data and the
75 number of parameters was usually <40, Burnham and Anderson 1998) the AICc was used to calculate i and wi. The global model (Equation 3-5) was used as input for the dredge function in MuMIn. Based on the output it was possible to determine if there was support for a single best model (largest weight) or if there was model uncertain ty (no clear best model). If there was no support for a single best model, and uncertainty was hi gh, model averaging was to be conducted over a confidence set including those models with weights equal to or above 0.01. This value is smaller than the 0.05 recommended by Hobbs and Hilbor n (2006) to build conf idence sets but if uncertainty was high it was considered important to evaluate parameters averaged across a large set of models. The model.avg function in MuMIn was used to av erage over all models in this confidence set and to estimate parameter values ( ) and their confidence intervals. The results from the averaged model were compared to the results from the single model with the highest weight value. The goal of this analysis was to build a linear function to generate predicted values of the average number of mosquitoes collec ted per trap night by using the AICc to select the best model. Given that hypothesis te sting was not conducted to select variables to include in the model, the possible effects of multicollinearity in the standard errors of parameters were not relevant to generate the model with the best expe cted predictive capability. The predicted values obtained were squared to back tr ansform to the original scale. Model selection of a GLM for prediction of the estimate d proportion of parous females The MuMIn package v.0.12.2 for R (R Developm ent Core Team 2008) was also used to conduct model selection and averaging for the phys iological age structure model. The global model was a generalized linear mode l including 11 explanatory vari ables as fixed effects and the proportion of parous females as the response variable:
76 (3-6) where the proportion parous has a binomial distri bution and the collection site is a categorical variable that affects the value of the intercept. A generalized linear model with a binomial di stribution for the response variable was used in this case because it was known a priori that the response variable consisted of proportions. When variables are bounded as in a proportion (fo r example, when x out of y animals have a certain condition) their predicted values should follow the same distribution. If a normal distribution for continuous variab les is used to predict proporti ons, the predicted values might fall outside of the expected range (Agresti 1996) When the response variable takes values between 0 and 1 a logit link function (f(z)=log(z/(1 -z)) is appropriate to provide the relationship between the linear predictor and the mean of the distribution func tion (Agresti 1996). Thus, a logit link was used here. The global model was input into the dredge function of MuMIn to obtain m odel weights (wi). If there was no support for a single model, a ll models with weights e qual to or higher than 0.01 were to be selected as a confidence set. The function model.avg was then be used to obtain parameter estimates ( ) and their variance using model averaging over that set. The predictions from parameter estimates obtained through averagi ng were to be compared to the predictions from the single model with highest weight. Model selection of a GLM for prediction of t he estimated average number of nulliparous Culex nigripalpus females collected per trap night The number of empty nulliparous mosquitoes in a population might be more directly related to recent weather due to their depe ndence on freshly flooded oviposition sites.
77 Nulliparous Cx. nigripalpus females emerge from an oviposition site 7-14 days after oviposition depending on the conditions of temperature, food availability, crowding, etc. (Nayar 1982). For each collection site, the average number of nulliparous Cx. nigripalpus collected per trap night was estimated here by multiplying the proporti on of nulliparous mosquitoes (1-proportion parous) by the total number of mo squitoes collected in the trap s and dividing by the number of traps. A model to predict changes in the num ber of nulliparous mosquitoes was fitted in the same way as the two previous models. The same eleven explanatory variables were used in the global model and the MuMIn package v.0.12.2 for R (R Development Core Team 2008) was also used to conduct model selection and averaging. It was decided to use nulliparous numbers, and not only proportions, to determine if the model could explain the magnitude of emergences of new mosquitoes into the population. Adequacy of linear model and goodness of fit Burnham and Anderson (1998) recommend checking the fit of the global model and if the fit is acceptable, all the candida te models are probably also ac ceptable to describe the data. Graphical analysis was used to evaluate the linearity of the relati onship between response and explanatory variables and the possible presence of serial correlation over time. Plots of the observed versus predicted values, predicted valu es versus Pearson residuals, and time (days) versus Pearson residuals were generated for global models and visually evaluated for patterns When linearity is appropriate, points are symmet rically distributed around a diagonal line in the observed versus predicted values plots and symmetrically distributed around a horizontal line in the predicted values versus Pears on residuals plots. Patterns in the plots of time versus Pearson residuals would indicate if there is a time effect or serial correlations among observations that should be included in the model stru cture (Zuur et al. 2009). In a ddition to the graphical analysis a Tukeys Test for Nonadditivity or Curvature was performed using the residual.plots function of
78 the alr3 v.1.1.8 package for R (R Developmen t Core Team 2008). A simple measure of goodness of fit called the explained deviance (Zuur et al. 2009) was used to give a description of the percentage of variation in the response variable e xplained by the model. Values closer to 100% indicate more explained variance. The ex plained deviance is calc ulated as follows: (3-7) Results Mosquito Collections and Weather A total of 210,095 m osquitoes was collect ed during this study. Of these, 124,728 (59.37%) were collected during 2007 (Table 3-1). Culex nigripalpus was consistently the most abundant species collected (65.51%). Culex nigripalpus constituted 98.84% of the mosquitoes collected at the Park Site and 92.40% of the mo squitoes collected at the Yard Site, but only 45.70% of the mosquitoes collected at th e Groves Site. At the Groves Site, Psorophora columbiae was also collected in high numbers while Mansonia titillans and Mansonia dyari were also relatively abundant. The number of Cx. nigripalpus collected per date and site ar e shown in Table 3-2 (2007) and Table 3-3 (2008). A total of 2,422 mosquitoes collected in 2007 were dissected for parity determination. Of those dissected 1,899 ( 78.41%) were in good condition and had clearly identifiable ovaries for parity determination (T able 3-2). A total of 2,177 mosquitoes were dissected for 2008 and 2,051 (94.21%) of those had unambiguous ovaries for parity determinations (Table 3-3). The higher propor tion of mosquitoes with indeterminate parity status in 2007 was due mostly to ovaries with tracheal coiling that were difficult to observe, likely as a result of poor preser vation (Figure 3-9 E). It was common during 2007 to find the mosquitoes wet and in poor condition. Many we re dead and maybe already decomposing when
79 they were frozen. The rainfall frequency duri ng 2008 was reduced compared with 2007 and this may have contributed to a lower proporti on of ovaries with pa rtially decomposing. The year 2007 had frequent rainfall events of 50 mm or more within 3 days, between July and August and in late September (Figure 3-11 B) Those periods of frequent rainfall produced two clear periods of low KBDI (Figure 3-11 C) The year 2008 had an exceptional period of more than 100 mm of rain in 3 days in Augus t (Figure 3-12 B). This period coincided with a clear period of low KBDI in August (Figure 3-12 C). Both years showed increased daily average wind speeds from August to November and clear declines in the daily minimum temperatures starting in October (Figure 3-11A and D, Figure 3-12 A and D). Model Results A total of 2048 m odels that included all possi ble combinations of explanatory variables (excluding interactions) were fitted and compared using the MuMIn package for R to select the model that could best predict the average number of mosquitoes collected per trap night (column Average per trap in Tables 3-2 and 3-3). However, model weights did not support a single model as the best among the candidates. The highest weight observed was only 0.05 and a total of 23 models had weights equal to or above 0.01 (Table 3-4); models w ith weight 0.01 are only five times less likely to be selected as the best model than models with weight equal to 0.05. The variables kbdi06, tmin06, and collection site were always included in these 23 models. Wind, prcp06, tmin714 were only included in 3 of those 23 models, prcp714 was in 4/23 models, kbdi714 was in 7/23 models, mwtd74 was in 11/23 models, moon was in 13/23 models, and mwtd06 was in 14/23 models. The 23 models with weights equal or above 0.01 (Table 3-4) were selected as the confidence set, and model averaging was applied over them to obtain parameter estimates. The averaged parameters for a predictive linear model for Cx. nigripalpus relative abundance are
80 shown in Table 3-5. The predicted abundance va lues obtained from the averaged linear model showed good agreement with the observed abundan ce values (Figure 3-13). The averaged model predicted the times when cha nges in mosquito relative a bundance occurred. However, the magnitude of rapid increases was poorly predicted especi ally for the year 2007. The first peak of abundance in 2007 was not predicted by the averaged model. The predictions from the averaged model were compared to the predictions obtained from the single model with weight 0.05. The variables in the single model were kbdi06, mwtd06, tmin06, moon and collection site and the parameters estimates are in Table 3-5. The predictions from the single model are nearly identical to those from the averaged model (Figure 3-14) which suggests that the variables in that single model can explain much of the variation in the observed Cx. nigripalpus relative abundance. It is possible that the variable s absent from the single model were redundant. The variable prcp06 was highly correlated with mwtd06 (Table 3-5). The variables kbdi714, mwtd714, and tmin714 were highly correlated with kbdi06, mwtd06, and tmin06, respectively (Table 3-5). Some of these variables can be expect ed to be correlated since they were derived from others, for instance the KBDI and the MWTD are calculated using informati on on rainfall and temperature, among others. The variable wind was probably ex cluded from the model due to its lack of explanatory power. The variables moon and collec tion site were always included in the models with best predictive ability. The variable collection site is a categor ical variable that affected the value of the intercept by taking differe nt values, depending on the site. The default value of the intercept corresponded to the intercept for the Groves Site (the program R uses an alphabetical order to report results). The differences between the Park Site and Groves Site intercept values and between the Yard Site an d Groves Site intercept values
81 (Table 3-5) show that given the magnitude a nd sign of the difference between intercepts the Groves Site produced slightly larger colle ctions than the other two sites. Another 2048 models were fitted to select th e best predictive model for changes in the proportion parous Cx. nigripalpus females (column Proportion parous in Tables 3-2 and 3-3). Similarly, there was no support for a single best model among the candidates and a total of 28 models had weights of 0.01 or more (Tab le 3-7). The variables moon, wind, prcp06, and prcp714 were included in all of the 28 models. The variables tmin06 and mwtd714 were also common and were in 25 and 23 of the m odels, respectively. The kbdi714 was in 7/28 models, kbdi06 was in 10/28 models, mwtd06 was in 13/28 models, tmin714 was in 17/28 models, and collection site was in 18/28 models. Model averaging was applied ove r the 28 models with weights of 0.01 or more and their predictions compared to the predictions obtained from the single model with weight of 0.09. Similar to what was observed with the mode l of mosquito abundance, the predictions from the averaged and the single model were nearly identical. Given these observations, only the parameter estimates (Table 3-7) and the predictio ns from the single model for parity (Figure 315) are shown. Predicted values from the single model with the highest weight show moderate agreement with the observed proportion parous values (Figure 3-15) and the magnitude of increments in the proportion parous was not al ways well explained. For example, the times when parity reached above 0.5 were underestim ated by the model. The times at which the proportion of parous mosquitoes declined were us ually well predicted. For example, the times when the proportion parous fell to zero in 2008 we re accurately predicted in the Park and Yard sites. The variables that appear to influence reductions in parity were prcp714, tmin714, and mwtd714. Increases in rainfa ll and temperature and decreases in the water table depth the second
82 week before collections reduced parity. Parity changes in the Groves Site were generally poorly predicted. Model selection for the prediction of changes in the average number of nulliparous females proceeded similarly to the previous two models From the 2048 candidate models only 25 had weights equal to or above 0.01 (Table 3-8). Collection site and tmin06 were included in all 25 of those models. Kbdi06 was in 24/25 models while moon and prcp714 were in 23/25 models. Other variables were less frequent with wind, prcp06, and tmin714 in 5/25 models; mwtd06 and mwtd714 in 7/25 models; and kbdi714 in 8/25 models. Model parameters were obtained by averaging across the 25 models with higher weights and the predictions were compared to the results from the single model with the highest weight. As before, the results were very similar and only the parameter estimates (Table 3-5) and the predic tions from the single model (Figure 3-16) are shown. Observed and predicted values of the average number of nulliparous mosquitoes per trap night (Figure 3-16) show good agreement for the year 2008. However, the predictions of the number of nulliparous females for 2007 were less accurate, especially during the emergence peak early that year. Linearity and Goodness of Fit Graphical analysis of the residuals f rom th e full models revealed that the observed and predicted values were linearly re lated. No strong patterns were observed when residuals were plotted against predicted values (Figure 3-17), indicating that linear models were appropriate. Thus, it was not necessary to include non-linear relationships. Additionally, there were no patterns observed between residuals and time, suggesting that including serial correlations might not improve model fit. Linearity was also s upported by the non-additivit y test which indicated lack of curvature for the rela tive abundance (T = -0.98, p = 0.33) parity (T = 1.48, p = 0.14), and nulliparous relative abundance (T = -0.04, p = 0.96) global models.
83 The explained deviance for the global m odels was 61.11% for the relative abundance model, 45.33% for the parity model, and 56.85% fo r the nulliparous relative abundance model. This is an indicator of how much of the respons e variable variation was explained by the model. The explained deviance was calculated also for the single model with highest weight and the results were very similar: 60.26% for the re lative abundance model, 44.67% for the parity model, and 56.01% for the nulliparo us relative abundance model. Th ese results supp ort that the simplest models have a similar pred ictive ability to the global model. Discussion The results of this study suppor t previous observations that C x. nigripalpus relative abundance is influenced by the environmental conditions on the days preceding mosquito collections. This is likely due to the effect s of environmental factors on mosquito activity, foraging behavior, oviposition beha vior, and developmental rates. This study shows that we can make approximate predictions a bout the times when changes in Cx. nigripalpus abundance and physiological age structure can take place, using multiple regression models. According to the Florida Department of Health ( 2009) guidelines for mosquito survei llance, it is very important to know when changes in the mosquito population size and structure could happen because this determines changes in the risk of arbovirus transmission. The flight activity, bloodf eeding, and oviposition of Cx. nigripalpus are stimulated by high relative humidity 90% (Dow and Gerrish 1970, Day and Cu rtis 1989, Day et al. 1990). Flight activity decreases when temperatures are below 17-18C (Bidli ngmayer 1974). The time from egg hatch to adult eclosion is reduced as temp erature increases (Nayar 1982). Moon phase and wind speed have been described to affect the size of the Cx. nigripalpus collections made with various types of traps in Indian Rive r County, Florida (Bidlingmayer 1964, 1974).
84 Changes in mosquito abundance detected with traps are a consequen ce of the effects of prior environmental conditions over gravid fe male oviposition and immature development. These factors impact the timing of nulliparous emergences. The number of mosquitoes collected in traps can also be influenced by environmen tal effects on the activity of mosquitoes. If conditions are favorable, more i ndividuals can be expected to leave resting sites and become active. Trap collections cannot discriminate between these tw o possible causes of changes and therefore give us an indication of changes in both mosquito activ ity and population size. Using the parameter values of the predictive model of Cx. nigripalpus relative abundance with the highest Akaike weight (Relative abundan ce single model in Table 3-8) we can explore how environmental variables explained some of th e variation in the field data. Due to model uncertainty, we know that other variables might be supported by another data set. However, the effects of these variables on Cx. nigripalpus relative abundance agree with our knowledge on the biology of the species. The variables included in the model were the minimum temperature, modeled water table depth, and the drought index (KBDI), all averaged over the 0-6 day period be fore collections. Other variables included were moon illuminati on and collection site. A positive parameter estimate for tmin06 indicates that increases in the mini mum temperature positively impacted mosquito collections. Warmer temperatures pos sibly stimulated flight during the night of collection and accelerated immature development during the days prior to the collection. The variable mwtd06 indicates the depth of the water ta ble under the surface and it takes negative values. Here it wa s observed that as the mwtd06 decreased and became more negative, there was a reduction in the predicted number of mosquitoes. This agrees with Cx. nigripalpus biology because it suggests that reductions in ground water avai lability negatively impacted the
85 size of mosquito collections. This could be due to both fewer newly emerged mosquitoes and reductions in adult mosquito activity due to dry conditions indicated by negative values of mwtd06. A negative association between mosquito abundance and the kbdi06 was suggested by the negative sign of its parameter estimate. Increases in the valu e of the KBDI indicate drought. This result then supports that fewer mosqu itoes were collected during dry conditions. In this study, the moon effect was consider ed quantitatively as the fraction of moon illuminated (FMI = 0 for new moon, FMI ~ 0.5 for quarters, and FMI = 1 for full moon). A negative association with rela tive abundance was suggested from the negative sign of the moon illumination parameter estimate. Fewer mosquitoes were collected with lard can traps as the FMI increased. This pattern was different from previous studies which reported that moon phase had an effect on the number of Cx. nigripalpus collected with truck, suction, and animal baited traps (Bidlingmayer 1964, 1974). These studies re ported larger collections during the full moon and quarters than during the new moon (Bidlingm ayer 1964, 1974). Animal traps were less sensitive than the truck and suc tion traps to detect differences in mosquito activity due to moon phase (Bidlingmayer 1974). Light baited traps provided different re sults than suction traps and did not accurately reflect mosquito activit y under different moon conditions (Bidlingmayer 1964). The differences between previous studies and our study might due to sampling biases. Only the unfed host-seeking females of the popula tion were being targeted with the lard can traps unlike with suction and truc k traps that target al l flying mosquitoes. It is not known if unfed host-seeking mosquitoes have different behavioral responses to moon illumination than mosquitoes searching for an oviposition site or a sugar meal. However, Bidlingmayer (1985) did
86 consider moon illumination as an important fact or that can change the physiological (feeding status) composition of the flying population. Another factor that could have affected the size of the catch under different moon illumination is the trap color. Bidlingmayer ( 1985) mentions that suction traps painted black collected larger numbers of mosquitoes than gray or transparent traps. Mosquitoes are attracted to visible objects of certain size that contrast with the background. The lard can traps used here were white. During fully illuminated nights this mi ght have reduced the visual attractiveness of the trap leading to smaller collections. But careful studies would need to be conducted to test the effect of trap color on Cx. nigripalpus collections. The effects of artificial lights (street lights) on trap collections could also be investigated to determine if they introduce biases and differences between sites. The collection site was also a predictor in th e simplest model. Its parameter estimates suggest that higher collections we re commonly obtained in the Grove s Site than at the other two sites (this site had a larger in tercept). In another study of Cx. nigripalpus in Palm Beach County, Florida (Morales-Downing 1994), popul ations were sampled at four sites for one year (April 1991-March 1992). Large mosquito collections we re made year round in a site that had permanent standing water and lush vegetation. At the other three sites (scrub, mangrove, and citrus grove) mosquitoes were collected in low numbers or not at all during the dry months, but abundance increased during the wet months. Th ese observations suggest the existence of reservoir locations where mosquitoes persist ye ar round and in which mo squito production might not be as dependent on rainfall. It is importa nt to consider multiple sites when studying the dynamics of this species.
87 The variables included in the relative abundance predictiv e model agree with what would be expected based on the biology of Cx. nigripalpus. However, some of the variation (~40%) in the observed average number of mosquitoes per trap night was not explained by the model. Visual agreement between observed and predicted values was best for the year 2008. The year 2008 was characterized by an extr aordinarily wet period during th e month of August (280 mm of rain in 3 days) due to Tropical Storm Fay (Figur e 3-12 B). This was preceded by months with only isolated episodes of heavy rain (only two rainfall events 50 mm within 3 days were registered in 100 days). The relatively dry conditions followed by a wet period could have synchronized the population abundance in all thr ee sites during 2008 (Figure 3-13). The year 2007 had relatively high and frequent rain duri ng July and early August, and between late September and early October (Figure 3-11 B). Mo re frequent rainfalls could have interacted with the topography of each site to produce mo re variation in the number and permanence of oviposition sites, reducing the depe ndability on rainfall and, as a consequence, the predictability of mosquito abundance based on rainfall. Also, if rainfall events occurred when conditions were already humid and favorable for mosquito f light and reproduction, a marked change in abundance might have not been induced by rainfall. However, it was expected that groundwater accumulation (indicated by the MWTD ) could account for mosquito emergences not directly related to rainfall events. Predictability could have also been affected by sampling biases. As was mentioned before, the type of trap used in this study (a stationary CO2 baited lard can trap) attracts only unfed hostseeking females and does not targ et other flying mosquitoes or t hose that are resting. The traps were positioned at a height of ~1.8 m above th e ground, and recent studies have shown that trap height can also influence the si ze of the collections of certain Culex species. When CDC
88 miniature light traps baited with CO2 were used to collect mosqu itoes, there were no differences in the size of the catches of Culex restuans and Culex pipiens pipiens between traps located 1 m above the ground and traps placed 6-7 m above ground (Drummond et al. 2006). However with lard can traps (chicken or sparrow used as bait), there were differences in the size of the catch of Cx. restuans between ground and canopy traps although not for Cx. p. pipiens (Darbro and Harrington 2006). We do not know what the effect of trap height could be in the collections of Cx. nigripalpus, or if including data from collections made at different heights might help provide more accurate predictions of change s in mosquito abundance as a function of environmental variables. We did not account for endogenous population factors in this model, but future models could attempt to consider popula tion feedbacks to help explain the magnitude of the abundance peaks for Cx. nigripalpus The use of longer time series that include the winter and spring might be necessary to build models that include endogenous factors because the size of spring populations might partially dete rmine the abundance during the summer. A recent study used Gompertz dynamical feedback models to predict changes in the monthly relative abundance of the salt marsh mosquito Ae. vigilax from northern Australia (Ya ng et al. 2008). Gompertz models describe a negative relationship between population growth rate and mosquito density. The AIC was used to select the best predictiv e model. The selected final model included stochastic exogenous vari ables as correlate s (frequency of high tides, two month prior rainfall and relative humidity) that altered the relative rate at whic h mosquitoes responded to their own density. Our results suggest that the changes in Cx. nigripalpus relative abundance in Indian River County, Florida can be partially explained by environmental factors. A model selection
89 approach based on the AIC (Burnham and Anderson 1998) was used here to find the model (set of parameters) with the best ab ility to predict changes in mos quito relative abundance. After considering 2048 linear models as candidates, there was no support for a single best predictive model. However, further analysis supported th at the single model with the highest Akaike weight had good predictive ability explaining ~60% of the observed variation. Many statistical approaches have been us ed to study the relationships between environmental variables and mosquito relative abunda nce. Some of the approaches used in the past include simple linear regression (Shaman et al. 2002b, Wegbreit and Reisen 2000), multivariate linear regression with backward el imination of variables (DeGaetano 2005), and generalized linear models (Poisson errors) with a priori selection of explanatory variables based on cross-correlation analysis (S hone et al. 2006). When buildi ng models to explain mosquito abundance some authors average weekly mosquito collection data into a monthly estimate of abundance and they lag the explanatory variab les by 1 month (DeGaeta no 2005). Other authors use daily mosquito collections data and average the explanatory variables over a period of days before the collection date (Shaman et al. 2002b, Shone et al. 2006), similar to the approach presented here. It is common to build separate models for different coll ection sites, years, or even months. Data transformations are usually ap plied to the data, however there is almost never mention of checking for the assumptions of normality and homoscedastic ity of residuals (for example, Wegbreit and Reisen 2000, Shaman et al. 2002b, and DeGaetano 2005used linear regression but did not report on checking these a ssumptions). Other aspects that should be checked are the existence of overdispersion (Shone et al. 2006 used GLM with Poisson distributions for error terms but did not report checking for overdispersion), and independence of errors (Wegbreit and Reisen 2000, Shaman et al. 2002b, DeGaetano 2005, and Shone et al.
90 2006 did not report checking for viol ations to this assumption). Checking for such assumptions is very important when the model building proc ess relies on hypothesis te sting to select the explanatory variables in the fina l model, meaning that only thos e variables that are significant are included. It is known that th e lack of fit and violations of model assumptions can affect the variance of the parameter estimates. These can make confidence interv als too wide or too narrow and inference is not recommended under those conditions (Zuur et al. 2009). Even though the parameter estimates obtained can be used in a predictive model, if the model assumptions (linearity, normality and homoscedasticity of residuals) are not met, significance tests for the parameters cannot be trusted. The model selection approach followed here (AIC and model weights) provided an objective way to select the vari ables included in the predictive model. Our intention was to avoid over fitted and/or unstable models, which are some of the pitfalls of using hypothesis testing to build a model from a large number of possible explanatory variables (Burnhan and Anderson 1998). The approach used here is not data dredging in the sense of systematically including and removing variables from the model in order to obtain a fi nal model with all the statistically significant variables. However it is data dredging in the sense that all possible models were fitted, therefore it should be considered as an exploratory approach. The multiple regression model obtained revealed the environmental variables th at could be used to predict changes in Cx. nigripalpus abundance. Since parameter estimation and not hypothesis testing was the focus in the approach followed here, we did not check for multicollinearity effects among explanatory variables, and did not re port on normality and homoscedasticity of the residuals. However, we evaluated the adequacy of using a linear model and the goodness of fit.
91 If linearity would not have b een supported, quadratic terms or other non-lin ear expression would have been necessary to relate expl anatory and response variables. More information may be needed to build a model that better approximates the truth behind the data. New data sets could help in th e evaluation of the predictive abilities of the simplest model selected here. Th e results of this study can provide important insights to improve planning of future field studies. For example, the effects of m oon phase should always be taken into consideration when planning collections of Culex nigripalpus Taking longer series of mosquito collection data and perhaps using inform ation from different types of traps could help in the development of improved models. Another fact or that could be considered in the future to improve the explanatory ability of the model is using weather variables measured at the collection sites. Given the effects observed fo r collection site, considering fitting different models for the data by site would be important. It is possible that environmental variables have different effects depending on the site. Interac tions among environmental factors could also be explored. In addition to the prediction of changes in Cx. nigripalpus relative abundance we were interested in predicting cha nges in the physiological age st ructure of the population. Physiological age structure was approximated as th e proportion of parous females or parity. The parity of other mosquito species has been show n to be affected by weather factors such as temperature and precipitation (Rei sen et. al. 1983, Reisen et al. 1986) Here we provide evidence supporting that the changes in the estimated proportion of parous Cx. nigripalpus females can be partially explained by environmental changes that impact the availability of oviposition sites and mosquito activity, such as precipitation and temperature. There was considerable model
92 uncertainty but the single model with highest weight explained some of the variability in parity (~45%). The proportion of parous females observed in the field stayed mostly between 0.10-0.40. During the year 2007 a low of 0.02 (P ark Site) and a peak of 0.50 (Y ard Site) were observed, and during 2008 lows of 0.00 (Park Site, Yard Site) and peaks of 0.55 (Park Site) and 0.60 (Yard Site) were recorded. The model did not pred ict values above 0.37 for 2007 or 0.46 for 2008, thus the highest peaks of parity were underestimated. The model did predict the times when parity dropped to zero in 2008 (which coincided with an increase in mosqu ito abundance after the passing of Tropical Storm Fay in August). Times when parity was low (<0.20) in the Park and Yard Sites were better predicted than times wh en parity increased above 0.40. The changes in parity predicted for the Groves Sites followed a ve ry different profile than what was observed in the field (Figure 3-15). The variables in the simplest parity model were collec tion site, moon, mwtd714, prcp06, prcp714, tmin06, tmin714, and wind. Collection site was importa nt to predict parity. This is probably due to the different patterns observed fo r the Groves Site where the peaks in parity were never as high as for the other two sites. The average minimum temper ature in the 0-6 days prior to collection positively impacted parity. Th is is perhaps a result of warmer temperatures stimulating mosquito oviposition activity. Ther e was a positive association between parity and the average precipitation 0-6 days before colle ctions. Humid conditi ons probably stimulated unfed mosquitoes to bloodfeed a nd later oviposit, increasing the number of parous females in the population just prior to collections. It is interesting that modele d water table dept h averaged over the 0-6 days before collection was not included in the model selected to explain parity changes. This would have been expected considering that water availability could affect the proportion of
93 gravid females that oviposit. Precipitation and water table depth 0-6 days prior to collection are negatively correlated (r = -0.66, as precipitation increases the depth of water under the surface decreases) and they may provide simila r explanatory power to the model. The parity model seems better able to predict the times at which the proportion of parous females in the population is low (<0.20) than when it is high ( 0.50). Decreases in parity occurred with increases in prcp714 and tmin714. Wet and warm conditions in the period of 7-14 days before collections, together with rainfall, positively impacted the emergences of new mosquitoes and consequentially reduced the propor tion of parous females in the following days. The model for the number of nulliparous mosquitoes (discussed below) also included prcp714 as an important variable explaining mosquito emer gences, supporting that increases in nulliparous mosquitoes reduce the proportion of parous females. Decreases in parity also occurred when ground water availability was low in the 7-14 days prior to collections (reductions in mwtd714) and when the temperature and rainfall were low in the 0-6 days prior to collections (decreases in tmin06 and prcp06). These factors most likely decreased mosquito oviposition activity. It has been suggested in previ ous studies that wind could have an effect on the number of mosquitoes caught (Bidlingmayer 1974, 1985) but not on the parity rates. However this variable was included in the parity pred ictive model. Bidlingmayer (1974) reported effects of moon phase in the number of mosquitoes collected but not in the proporti on of parous females. In the present study, the lowest values of parity (<0.10) were only ob served during new moon, and the highest values of parity (>0.50) were only observed during full m oon nights. Higher parity rates were observed during days of higher average wi nds. Given the observa tional nature of our study, it is difficult to determine how moon and wind could affect the proportion of parous
94 females collected. However, it is possible to say that both wind and mo on phase are variables that need to be considered in Cx. nigripalpus population dynamics studies The effects of moon illumination and wind on the behavior of Cx. nigripalpus at different physiological stages require further studies. During 2008, Tropical Storm Fay passed th rough the study area between August 19th and 20th. The storm was preceded by ~16 days without any heavy rainfall events ( 50 mm within 3 days). This can be considered a long dry peri od (Day et al. 1990). The year had been dry in general and in the 100 days prior to the storm only two heavy rainfall events were registered. In the days immediately after the st orm, parity rates increased to 0.50 in the Park and Yard Sites (23rdand 22nd of August, respectively), although not in the Groves Site (the parity stayed low at 0.08). In the next collection date parous females were not coll ected and the proportion parous dropped to 0.00 by August 30th and September 1st in the Park and Yard Sites respectively. This is presumably due to a large emergence of nulliparous females. Also in 2008, in late September and early October, there was anothe r peak of parity of more than 0.50 in the Park and Yard Sites. However, by this time the temperatures we re cooler, which perhaps prevented a large synchronized mosquito emergence. These observations agree with previous studies that had demonstrated that wet conditions preceded by drier conditions could first synchronize oviposition and later the emergence of nu lliparous mosquitoes (Day et al. 1990). The parity model did not explain all of the vari ation observed in the field. It is important to remember that parity in this study was estim ated only for the unfed fraction of the mosquito population inherently biasing the estimates which c ould have an effect on the associations with explanatory variables in the model. Our estimat e of the proportion of parous females in the population (Parous/Total) was the ratio between the number of parous unfed mosquitoes at time t
95 (Put) over the total unfed mosquitoes dissected, both parous and nulliparous (Put/(Put+Nut)). Mosquitoes that were bloodfed or gravid at time t were not collected or in cluded in the estimate. Whenever Put>Nut, the estimate of the proportion parous will be higher than 0.50. In this study we observed that more often Put
96 physiological age structure of Cx. nigripalpus populations, and it encourages the development of improved models and models for other vector species. A predictive model for the average number of nulliparous mosquitoes per trap night was developed here. We considered that the a bundance of these mosqu itoes, having recently emerged from the available oviposition sites, co uld be better predicte d by recent weather conditions. Periods of large increas es in nulliparous mosquitoes coul d be expected to be more or less coincident with periods of lo w parity. This is due to the dilution effect of having a large number of nulliparous mosquitoes in the populati on. The model selection approach used here supported a model including the drought index and minimum temperature (averaged for the period of 0-6 days prior to co llection), average precipitation 714 days prior to collection, moon illumination and the collection site as explanatory variables. This model approximated times of large emergences of nulliparous females, but the magnitude and exact timing of the increases was not always well described. Similar to the model for relative abundan ce, better predictions were obtained for the year 2008 than for the year 2007. Regardless, the associations with the explanatory variables ag ree with the biology of Cx. nigripalpus. Negative effects of increased dryness on nulliparous mosquitoes relative abundance and positive effects of precipitation and minimum temperature were observed. Similar to the model for the relative abundance, increased moon illumination had a negative impact on th e abundance of nulliparous females. The variables prcp714 and tmin714 had a positive effect on the number of nulliparous mosquitoes, and this could be related to the em ergence of a new generation of mosquitoes after approximately one week of immature development. It is important to reiterate that the predicti ons made by the models can be consequence of both changes in population size and mosquito ac tivity levels. The relative abundance model
97 included the variables kbdi06 and tmin06. These variables were frequent in the confidence set (models with weights 0.01). Variables averaged 7-14 days prior were less frequent in the confidence set of relative abundance models. This result suggests that the relative abundance model is perhaps explaining changes in mosquito activity in the days prior to collections. The model for parity and nulliparous abundance cons istently includes the variables averaged 7-14 days prior in their confid ence sets (especially prcp714), together with variables averaged in the 06 prior periods. This suggests explanation of the emergence of nulliparous females 7-14 days after oviposition by the model, together with mosquito activity. The models presented here provided good predictions of the changes in Cx. nigripalpus abundance and parity for populati ons in a landscape in Indian River County, Florida. Our models support that variation in the relative abundance of mosqu itoes is influenced by factors such as rainfall, water table depth, dryness, temperature, and moon illumination. Not all the variation in the observed abunda nce was explained by the model. Improved models could be developed from new data gathered for longer time periods including winter and spring that could allow a better exploration of how endogenous factors regulat e the mosquito populations. Mosquito collections are labor intensive but perhaps making colle ctions using other types of traps and combining the information could help obtain relative abundance measures that would better represent the effect s of environmental variables on the populations. It is al so important to consider the moon phases in planning collec tions, because this affects the size of Cx. nigripalpus catches. Even though the predictions of the proportion of parous females with the model presented here did not completely explain what was obser ved in the field, models like this can still contribute to the monitoring of changes in the ag e structure. Wet and warm conditions 7-14 days
98 prior to collections can lead to increases in nulliparous mosquitoes and consequentially to a reduction of the proportion of parous females. Also, dry periods followed by heavy rains could signal important increases in th e proportion of unfed parous fe males that could be potentially infectious and looking for a bloodmeal. More investigation is needed about how water sources remaining days after rainfall, or other permanent oviposition sites, are used by Cx. nigripalpus throughout the summer and fall season. This could help explain parity fluctuations especially during long dry periods. Changes in the proportions of parous females are influenced by environmental factors. However, the chronological age distribution of th ese females is unknown. It also is difficult to predict the proportion of females that has completed the extrinsic incubation of a virus. Given that it is not possible to determ ine the chronological age of females in the field, modeling studies like the one presented in the follo wing chapter could be used to explore the possible mechanisms behind changes in chronological age structure.
99 Table 3-1. Species of mosquitoes and total number of mosquitoes collected during 2007 and 2008. 2007 2008 Species Park Site Yard Site Groves Site Park Site Yard Site Groves Site Total Frequent Species (%) Aedes aegypti 2 1 3 6 Aedes albopictus 4 9 1 4 18 Aedes triseriatus 1 1 Aedes vexans 2 18 382 50 452 Anopheles crucians 10 10 Anopheles quadrimaculatus 2 2 Coquillettidia perturbans 11 13 24 Culex erraticus 1 4 2 4 21 29 61 Culex nigripalpus 24428 22433 34554 19429 13248 23534 137626 65.51 Culex quinquefasciatus 11 1 12 Culex salinarius 189 43 232 Mansonia dyari 750 3 1645 2398 1.14 Mansonia titillans 2 13 8595 4 17 6200 14831 7.06 Ochlerotatus atlanticus/ tormentor 6 124 11 88 229 Ochlerotatus infirmatus 52 205 128 241 73 301 1000 Ochlerotatus sollicitans 2 1 1 4 Ochlerotatus taeniorhynchus 2 10 28 26 1 67 Psorophora ciliata 1 33 380 2 208 624 Psorophora columbiae 43 2001 30290 65 471 19567 52437 24.96 Psorophora ferox 14 6 1 26 3 2 52 Psorophora howardii 7 1 1 9 Total 24557 24746 75425 19814 13868 51685 210095
100 Table 3-2. Culex nigripalpus collected in the year 2007 and numb ers of mosquitoes dissected for parity determination. Site Date Total Average per trap StDev among traps Dissected Parous (C ) Proportion parous (C/A+B) Scored (A) Undetermined (B) Park Site 10-Jun 2* 0.67 1.15 24-Jun 54 13.50 8.19 2-Jul 167 41.75 25.24 8-Jul 966 241.50 286.80 30 2 7 0.22 14-Jul 4033 1008.25 403.74 34 2 4 0.11 21-Jul 459+ 229.50 33.23 34 6 7 0.18 31-Jul 1413 353.25 179.69 36 0 7 0.19 6-Aug 1961 490.25 135.29 31 9 4 0.10 12-Aug 5247 1311.75 448.43 33 15 1 0.02 22-Aug 755 188.75 106.05 36 11 6 0.13 28-Aug 1399 349.75 112.57 46 3 16 0.33 3-Sep 303 75.75 58.85 26 19 12 0.27 12-Sep 1051 262.75 101.00 38 10 8 0.17 27-Sep 573 143.25 69.34 46 2 23 0.48 3-Oct 513 128.25 101.77 27 24 9 0.18 12-Oct 1010 252.50 86.85 24 28 5 0.10 19-Oct 1092 273.00 107.72 45 11 8 0.14 25-Oct 2493 623.25 453.79 39 10 18 0.37 1-Nov 823 205.75 285.44 35 5 12 0.30 10-Nov 90 22.50 8.85 29 20 7 0.14 16-Nov 24 6.00 8.12 19 2 6 0.29 Yard Site 11-Jun 15 3.75 6.24 22-Jun 10 2.50 1.73 29-Jun 0 0.00 0.00 9-Jul 792 198.00 228.60 30 3 4 0.12 15-Jul 4151 1037.75 922.73 31 9 8 0.20 22-Jul 34 6 10 0.25 29-Jul 1303 325.75 372.43 30 10 6 0.15 7-Aug 2251 562.75 568.73 33 7 3 0.08 11-Aug 2107 526.75 256.43 35 14 4 0.08 21-Aug 974 243.50 217.58 47 1 5 0.10 27-Aug 201 50.25 31.88 45 3 26 0.54 4-Sep 536 134.00 110.20 35 14 13 0.27 11-Sep 109 27.25 25.41 31 12 8 0.19 24-Sep 419 104.75 68.36 35 11 18 0.39 5-Oct 2822 705.50 604.31 35 15 15 0.30 11-Oct 152 38.00 33.36 33 8 9 0.22 21-Oct 2941 735.25 676.42 39 16 19 0.35 24-Oct 1462 365.50 223.45 42 7 15 0.31 31-Oct 1901 475.25 716.59 43 5 11 0.23 9-Nov 198 49.50 46.06 32 28 7 0.12 17-Nov 89 22.25 19.65 32 2 9 0.26
101 Table 3-2. Continued Site Date Total Average per trap StDev among traps Dissected Parous (C ) Proportion parous (C/A+B) Scored (A) Undetermined (B) Groves Site 12-Jun 198 49.50 14.89 23-Jun 1018 254.50 182.28 30-Jun 1003 250.75 112.82 7-Jul 1759 439.75 248.64 23 7 6 0.20 13-Jul 2989 747.25 380.53 26 12 5 0.13 23-Jul 2288 572.00 240.08 37 3 8 0.20 30-Jul 943 235.75 99.14 35 3 13 0.34 8-Aug 2888 722.00 251.67 36 10 6 0.13 13-Aug 3880 970.00 424.85 35 13 3 0.06 20-Aug 2223 555.75 116.99 47 1 20 0.42 29-Aug 983 245.75 52.54 45 3 18 0.38 2-Sep 945 236.25 64.19 41 3 18 0.41 13-Sep 1842 460.50 135.31 38 7 15 0.33 26-Sep 1124 281.00 46.89 31 18 7 0.14 4-Oct 3307 826.75 437.28 30 16 6 0.13 13-Oct 1219 304.75 75.64 28 28 7 0.13 18-Oct 1956 489.00 303.27 40 12 4 0.08 26-Oct 2770 692.50 275.95 41 7 20 0.42 2-Nov 285 71.25 44.84 38 9 11 0.23 11-Nov 334 83.50 75.60 32 18 6 0.12 18-Nov 600 150.00 73.12 46 3 12 0.24 *Total, mean, and standard deviati on over three traps for this date. Missing data are represented with hyphens. + Total, mean, and standard devia tion over two traps for this date.
102 Table 3-3. Culex nigripalpus collected in the year 2008 and numb ers of mosquitoes dissected for parity determination. Site Date Total Average per trap StDev among traps Dissected Parous (C ) Proportion parous (C/A+B) Scored (A) Undetermined (B) Park Site 3-Jun 56 14.00 5.60 32 9 9 0.22 10-Jun 11 2.75 2.22 9 1 3 0.30 17-Jun 6 1.50 1.73 6 0 2 0.33 25-Jun 106 26.50 2.52 36 4 4 0.10 1-Jul 11 2.75 2.75 6 2 1 0.13 11-Jul 66 16.50 10.28 36 6 4 0.10 17-Jul 425 106.25 23.10 39 1 14 0.35 23-Jul 734 183.50 24.84 39 0 4 0.10 31-Jul 510 127.50 107.48 39 1 5 0.13 8-Aug 1895 473.75 269.37 37 3 8 0.20 15-Aug 1559 389.75 329.72 38 2 6 0.15 23-Aug 1320 330.00 149.25 39 1 20 0.50 30-Aug 2147 536.75 353.13 39 1 0 0.00 6-Sep 2350 587.50 330.90 36 5 9 0.22 16-Sep 2696 674.00 416.44 36 3 9 0.23 21-Sep 1632 408.00 397.61 40 0 13 0.33 29-Sep 380 95.00 27.77 40 0 17 0.43 6-Oct 794 198.50 86.92 39 1 22 0.55 15-Oct 1061 265.25 68.83 40 0 12 0.30 22-Oct 1244 311.00 203.28 40 0 9 0.23 27-Oct 426 106.50 51.12 39 1 11 0.28 Yard Site 5-Jun 20 5.00 4.69 15 5 5 0.25 9-Jun 1 0.25 0.50 1 0 0 0.00 18-Jun 24 6.00 9.52 21 2 5 0.22 27-Jun 20 5.00 7.57 15 3 2 0.11 3-Jul 0 0.00 0.00 0 0 0 0.00 10-Jul 19 4.75 8.85 17 1 4 0.22 18-Jul 197 49.25 34.20 39 1 16 0.40 25-Jul 526 131.50 59.63 40 0 8 0.20 2-Aug 994 248.50 109.31 38 2 12 0.30 10-Aug 1048 262.00 280.05 38 2 6 0.15 16-Aug 449 112.25 72.89 37 3 8 0.20 22-Aug 1146 286.50 286.57 36 4 20 0.50 1-Sep 4693 1173.25 1568.53 33 7 0 0.00 7-Sep 1526 381.50 283.39 35 5 12 0.30 15-Sep 542 135.50 136.85 38 2 5 0.13 22-Sep 774 193.50 141.17 40 0 12 0.30 30-Sep 25 6.25 5.32 24 0 11 0.46 7-Oct 422 105.50 73.00 39 1 24 0.60 13-Oct 277 69.25 72.50 39 1 18 0.45 21-Oct 545 136.25 88.73 39 1 1 0.03
103 Table 3-3. Continued Site Date Total Average per trap StDev among traps Dissected Parous (C ) Proportion parous (C/A+B) Scored (A) Undetermined (B) Groves Site 2-Jun 252 63.00 31.49 37 3 3 0.08 11-Jun 128 32.00 21.83 40 2 14 0.33 19-Jun 330 82.50 35.49 37 3 4 0.10 26-Jun 278 69.50 57.91 38 2 8 0.20 2-Jul 64 16.00 15.21 37 1 4 0.11 7-Sep 503 125.75 109.74 40 1 6 0.15 20-Jul 734 183.50 83.84 39 1 6 0.15 24-Jul 774 193.50 121.78 39 1 5 0.13 1-Aug 681 170.25 76.39 39 1 7 0.18 7-Aug 1210 302.50 160.91 38 2 14 0.35 17-Aug 1038 259.50 189.87 37 3 5 0.13 24-Aug 3383 845.75 569.27 36 4 3 0.08 31-Aug 7429 1857.25 2429.54 38 2 1 0.03 8-Sep 612 153.00 95.09 39 1 7 0.18 17-Sep 1959 489.75 178.32 36 4 7 0.18 23-Sep 1364 341.00 235.23 38 2 10 0.25 1-Oct 789 197.25 134.24 37 3 12 0.30 8-Oct 1058 264.50 55.81 38 2 11 0.28 14-Oct 792 198.00 104.88 40 0 14 0.35 20-Oct 156 39.00 34.73 30 1 7 0.18
104 Table 3-4. Model selection results for a pr edictive model on the average number of mo squitoes collected per trap night. The 23 models (out of 2048) with weights 0.01 are shown. Model Intercept wind kbdi06 kbdi714 moonmwtd06mwtd714prcp06 prcp714 tmin06tmin714site*KDevianceAICc Weight 1 8.12 -0.04 -2.69 3.60 1.07 1 8 3731.18 786.030.00 0.05 2 7.91 -0.04 -2.72 3.50 1.09 1 8 3738.31 786.270.23 0.04 3 9.48 -0.04 3.64 0.97 1 7 3834.58 787.111.07 0.03 4 9.26 -0.04 3.52 0.99 1 7 3844.50 787.431.39 0.03 5 7.77 -0.03 -0.01 -2.58 3.33 1.09 1 9 3705.80 787.521.49 0.02 6 5.87 -0.04 -2.65 3.49 0.99 0.15 1 9 3722.62 788.082.05 0.02 7 9.07 -0.05 -0.04 -2.62 3.74 1.06 1 9 3725.26 788.172.13 0.02 8 9.01 -0.03 -0.01 3.32 0.99 1 8 3800.22 788.292.26 0.02 9 8.14 -0.04 -2.70 2.49 1.13 1.08 1 9 3729.25 788.302.27 0.02 10 7.86 -0.04 -2.86 3.49 0.03 1.08 1 9 3729.41 788.312.27 0.02 11 8.02 -0.04 -2.61 3.53 0.01 1.07 1 9 3730.11 788.332.29 0.02 12 7.58 -0.04 -3.710-3-2.66 3.25 1.10 1 9 3730.48 788.342.31 0.02 13 8.14 -0.04 -2.68 3.61 -2.910-31.07 1 9 3731.12 788.362.33 0.02 14 7.75 -0.04 -2.56 3.39 0.03 1.08 1 9 3733.86 788.452.42 0.02 15 6.29 -0.04 -2.70 3.39 1.03 0.11 1 9 3734.14 788.462.43 0.02 16 8.61 -0.04 -0.04 -2.67 3.59 1.09 1 9 3734.77 788.482.45 0.01 17 8.94 -0.04 3.39 0.05 0.95 1 8 3819.05 788.902.86 0.01 18 8.70 -0.04 3.28 0.06 0.96 1 8 3819.60 788.922.88 0.01 19 10.80 -0.07 -0.04 3.84 0.95 1 8 3821.82 788.992.95 0.01 20 6.83 -0.04 3.51 0.87 0.18 1 8 3822.87 789.022.99 0.01 21 9.60 -0.04 3.72 -0.02 0.98 1 8 3830.54 789.273.23 0.01 22 8.78 -0.04 -4.810-33.20 1.00 1 8 3830.91 789.283.24 0.01 23 9.49 -0.04 2.76 0.90 0.97 1 8 3833.36 789.363.32 0.01 *The number 1 under the variable site is not a parameter estimate but an indication that the effects of site are included in th at particular model.
105 Table 3-5. Parameter estimates and their confidence intervals for the predictive models. CI = confidence interval, LL = lower limit and UL = upper limit. The three Single models in this table correspond to Model 1 on Tables 3-4 (Relative abundance), 36 (Parity), and 3-7 (Nulliparous relative abundance), respectively. Relative abundance Averaged model Relative abundance Single model Parity Single model Nulliparous relative abundance Single model CI CI CI CI Parameter Value LL UL Value LL UL Value LL UL Value LL UL Groves Site Intercept 8.28 -3.72 20.30 8.12 -3.19 19.44 -1.27 -2.17 -0.37 1.20 -9.06 11.46 Park Site Intercept Groves Site Intercept -2.93 -5.41 -0.45 -2.92 -5.36 -0.48 0.17 -4.1010-30.35 -2.06 -4.50 0.37 Yard Site Intercept Groves Site Intercept -5.05 -7.56 -2.54 -5.05 -7.52 -2.58 0.20 0.03 0.38 -3.77 -6.23 -1.30 kbdi06 -0.04 -0.05 -0.03 -0.04 -0. 05 -0.03 -0.03 -0.04 -0.02 kbdi714 -8.9010-4 -5.0210-33.2610-3 Moon -1.75 -5.23 1.73 -2.69 -5.63 0.25 0.39 0.17 0.61 -3.61 -6.64 -0.59 mwtd06 2.09 -2.15 6.34 3.60 1.23 5.96 mwtd714 1.42 -2.48 5.32 0.34 0.16 0.51 prcp06 6.4010-4 -0.01 0.01 0.01 0.01 0.02 prcp714 4.5610-3 -0.02 0.03 -0.06 -0.08 -0.05 0.17 0.04 0.31 tmin06 1.04 0.55 1.52 1.07 0.62 1.53 0.06 0.01 0.10 0.98 0.54 1.42 tmin714 0.02 -0.08 0.11 -0.05 -0.09 -0.01 Wind 5.0010-3 -0.04 0.03 0.03 0.01 0.04
106 Table 3-6. Simple correlations among environm ental variables. The highest values of coefficients of correlation (> |0.50|) ar e shown in bold. mwtd714 mwtd06 kbdi714 kbdi06 tmin714 tmin06 prcp06 prcp714 moon mwtd714 mwtd06 -0.98 kbdi714 0.17 -0.05 kbdi06 -0.15 0.03 -0.92 tmin714 -0.18 0.12 -0.17 0.24 tmin06 0.11 -0.07 0.16 -0.15 -0.60 prcp06 0.59 -0.66 -0.44 0.47 0.07 -0.11 prcp714 0.22 -0.31 -0.43 0.53 0.12 -0.24 0.43 moon -0.16 0.14 -0.14 0.12 0.09 -0.29 -0.11 0.27 Wind -0.02 -0.02 -0.09 0.10 0.06 0.08 0.00 -0.10 -0.13
107 Table 3-7. Model selection results for a predictive model of the propor tion of parous mosquitoes. The 28 models (out of 2048) with weights 0.01 are shown. Model Intercept wind kbdi06 kbdi714 moonmwtd06mwtd714prcp06prcp714tmin06 tmin714site*K DevianceAICc Weight 1 -1.27 0.03 0.39 0.34 0.01 -0.06 0.06 -0.05 1 10248.87 663.130.000.09 2 -1.32 0.03 0.37 -0.66 0.95 0.02 -0.06 0.06 -0.05 1 11247.46 664.191.060.05 3 -1.22 0.03 0.39 0.34 0.01 -0.06 0.05 -0.04 8 254.89 664.351.220.05 4 -1.51 0.03 4.0010-4 0.39 0.31 0.02 -0.06 0.06 -0.04 1 11247.89 664.631.500.04 5 -1.31 0.03 0.40 0.33 0.01 -0.06 0.05 -0.04 1 10250.76 665.021.890.03 6 -1.28 0.03 0.37 -0.72 1.01 0.02 -0.06 0.06 -0.05 9 253.18 665.021.890.03 7 -1.40 0.03 2.0010-40.38 0.34 0.01 -0.06 0.06 -0.04 1 11248.31 665.051.920.03 8 -1.62 0.03 4.0010-4 0.37 -0.74 1.00 0.02 -0.06 0.06 -0.04 1 12246.13 665.392.260.03 9 -1.89 0.03 0.41 0.29 0.02 -0.06 0.03 1 9 254.04 665.882.740.02 10 -1.48 0.03 3.0010-40.36 -0.72 1.01 0.02 -0.06 0.06 -0.05 1 12246.65 665.922.790.02 11 -1.43 0.03 3.0010-4 0.39 0.32 0.02 -0.06 0.05 -0.04 9 254.18 666.022.880.02 12 -2.16 0.03 5.0010-4 0.41 0.27 0.02 -0.06 0.03 1 10251.88 666.143.010.02 13 -1.33 0.03 0.48 0.30 0.02 -0.06 1 8 256.73 666.193.060.02 14 -1.54 0.03 4.0010-4 0.36 -0.79 1.06 0.02 -0.06 0.06 -0.04 10252.13 666.393.260.02 15 -1.32 0.03 2.0010-40.39 0.34 0.01 -0.06 0.05 -0.04 9 254.58 666.423.290.02 16 -1.26 0.03 0.40 0.33 0.01 -0.06 0.05 -0.04 8 256.96 666.423.290.02 17 -1.80 0.03 0.41 0.30 0.02 -0.06 0.03 7 259.31 666.443.310.02 18 -1.56 0.03 4.0010-4 0.40 0.30 0.01 -0.06 0.05 -0.04 1 11249.78 666.523.380.02 19 -1.40 0.03 2.0010-40.36 -0.77 1.06 0.02 -0.06 0.06 -0.04 10252.65 666.913.780.01 20 -1.60 0.03 8.0010-4 4.0010-40.41 0.28 0.02 -0.06 0.05 -0.04 1 12247.66 666.933.790.01 21 -1.22 0.03 0.48 0.31 0.02 -0.06 6 262.19 667.033.890.01 22 -1.49 0.03 4.0010-4 0.48 0.28 0.02 -0.06 1 9 255.20 667.033.900.01 23 -1.42 0.03 2.0010-40.39 0.33 0.01 -0.06 0.05 -0.04 1 11250.34 667.083.950.01 24 -2.03 0.03 5.0010-4 0.41 0.28 0.02 -0.06 0.03 8 257.62 667.083.950.01 25 -2.03 0.03 3.0010-40.40 0.30 0.01 -0.06 0.03 1 10252.87 667.134.000.01 26 -1.89 0.03 0.42 0.29 0.01 -0.06 0.03 1 9 255.39 667.224.090.01 27 -2.28 0.03 6.0010-4 0.39 -0.65 0.87 0.02 -0.05 0.03 1 11250.50 667.244.110.01 28 -1.96 0.03 0.40 -0.52 0.77 0.02 -0.06 0.03 1 10253.15 667.414.280.01 *The number 1 under the variable site is not a parameter estimate but an indication that the effects of site are included in th at particular model.
108 Table 3-8. Model selection results for a predictive model on the average number of nulliparous mosquitoes collected per trap n ight. The 25 models (out of 2048) with weights 0.01 are shown. Model Intercept wind kbdi06 kbdi714 moon mwtd06 mwtd714 prcp06 prcp714 tmin06 tmin714 site* K Deviance AICc Weight 1 1.20 -0.03 -3.61 0.17 0.98 1 8 2870.13 678.18 0.00 0.08 2 3.25 -0.03 -3.71 1.24 0.15 0.97 1 9 2841.79 679.49 1.31 0.04 3 1.18 -0.02 -0.01 -3.29 0.19 0.98 1 9 2844.14 679.58 1.40 0.04 4 3.16 -0.03 -3.72 1.17 0.15 0.97 1 9 2846.46 679.67 1.49 0.04 5 -1.13 -0.03 -3.53 0.18 0.87 0.18 1 9 2858.65 680.13 1.95 0.03 6 1.92 -0.05 -0.03 -3.51 0.18 0.97 1 9 2864.38 680.35 2.17 0.03 7 1.22 -0.03 -3.58 -0.01 0.17 0.99 1 9 2869.35 680.54 2.35 0.02 8 4.60 -0.07 -0.03 -3.56 1.40 0.16 0.95 1 10 2829.36 681.45 3.27 0.01 9 2.78 -0.03 0.21 0.82 1 7 3025.55 681.54 3.36 0.01 10 2.62 -0.02 -0.01 -3.44 0.86 0.17 0.97 1 10 2832.69 681.58 3.40 0.01 11 2.62 -0.02 0.00 -3.47 0.87 0.17 0.97 1 10 2833.43 681.61 3.42 0.01 12 4.57 -0.07 -0.03 -3.57 1.37 0.16 0.94 1 10 2833.83 681.62 3.44 0.01 13 1.07 -0.02 -0.01 -3.31 0.05 0.19 0.97 1 10 2834.68 681.65 3.47 0.01 14 -0.75 -0.02 -0.01 -3.25 0.19 0.89 0.15 1 10 2836.39 681.72 3.54 0.01 15 1.50 -0.03 -3.64 1.11 0.16 0.90 0.12 1 10 2837.10 681.75 3.56 0.01 16 4.62 -0.03 -4.54 2.08 1.05 1 8 2966.98 681.77 3.58 0.01 17 2.54 -0.02 -0.01 0.23 0.84 1 8 2967.31 681.78 3.60 0.01 18 1.83 -0.04 -0.02 -0.01 -3.20 0.19 0.97 1 10 2839.35 681.83 3.65 0.01 19 1.20 -0.03 -3.64 1.06 0.16 0.88 0.14 1 10 2840.11 681.86 3.68 0.01 20 3.14 -0.03 -3.69 -0.78 1.96 0.16 0.97 1 10 2840.99 681.89 3.71 0.01 21 3.26 -0.03 -3.67 1.24 -0.01 0.15 0.97 1 10 2841.07 681.90 3.71 0.01 22 -0.69 -0.02 -3.02 0.13 0.23 0.96 1 9 2906.97 681.94 3.76 0.01 23 3.38 -0.03 -3.63 1.28 -0.02 0.15 0.97 1 10 2842.60 681.96 3.77 0.01 24 4.41 -0.03 -4.56 1.98 1.07 1 8 2972.94 681.98 3.80 0.01 25 -0.41 -0.05 -0.03 -3.42 0.19 0.86 0.18 1 10 2852.87 682.35 4.16 0.01 *The number 1 under the variable site is not a parameter estimate but an indication that the effects of site are included in th at particular model.
109 Figure 3-1. Collection sites in Indian River County, Florida. The star marks the loca tion of the Vero Beach Municipal Airport where a weather station is located and from which environmental data was obtained. The square marks the area west of I-95 for which MWTD and KBDI data were obtaine d and is detailed in Figure 3-10. (Florida map taken from Shaman and Day 2005)
110 Figure 3-2. Geographical overview of the Park Site. (A) The Park Site in downtown Vero Beach. (B) Trap locations in the Park Site are shown here with yellow and red circles. 500 m 50 m Park Site A B
111 Figure 3-3. Details of the Park Site. (A) Pine trees and cabbage palm in the Park Site. (B) Ditches and residences surround the Park Site. A B
112 Figure 3-4. Geographical overview of the Yard Site. (A) The Yard Site located in west ern Vero Beach. (B) Trap location in t he Yard Site are shown here with yellow and red circles. 500 m 50 m Yard Site A B
113 Figure 3-5. Details of the Yard Site. (A) The Yard Site located in a typical residential area of Vero Beach. (B) Canals and ditches that flood when it rains are common around the Yard Site. A B
114 Figure 3-6. Geographical overview of the Groves Site. (A) The Groves Site located 25 km to the west of downtown Vero Beach. (B) Trap location in the Groves Site are shown here with yellow and red circles. 500 m 50 m Groves Site A B
115 Figure 3-7. Details of the Groves Site. (A ) The Groves Site is an open field with cy press domes. (B) Water canals and citru s groves surround the site. A B
116 Figure 3-8. The lard can trap. (A) Lard can trap in the Park Site (B) and in the Groves Site. A B
117 Figure 3-9. The classifi cation of ovaries in Culex nigripalpus females based on the status of the tracheal coiling. (A) Nulliparous ovary. (B) Parous ovary. (C) Detail of nulliparous ovary show ing coiled tracheoles. (D) Detail of parous ovary showing distended tracheoles. (E) Detail of indete rminate ovary due to bad preservation. No fine tracheoles are visible. (F) Detail of indeterminate with no clear coiling status; both distended and coiled tracheoles are visible. A B C D E F100X 100X 400X 400X 400X 400X
118 Figure 3-10. Location of the reporting sites from which the KBDI and MWTD data were obtained.
119 Figure 3-11. Weather conditions 2007: (A) daily minimum temperature, (B) daily precipitation, (C) daily KBDI, and (D) daily average wind speed.
120 Figure 3-12. Weather conditions 2008: (A) daily minimum temperature, (B) daily precipitation, (C) daily KBDI, and (D) daily average wind speed.
121 Figure 3-13. Observed (solid black line) and predicted (solid red line) average numbe r of mosquitoes per trap night. Predicte d values were obtained using a linear model with the parameters show n in Table 3-5 (relative abundanc e model). Dashed lines are standard errors around the obser ved values. Note differences in the scale among panels. Average mosquitoes per trap night
122 Figure 3-14. Comparison of the average and the single models for the average number of mosquitoes per trap night. (A) Predic ted values from the average model and (B) pr edicted values from the single model.
123 Figure 3-15. Observed (solid black line) and predicted (solid red line) estimated pr oportion of parous females per site per night. Predicted values were obtained using a linear model with the parameters shown in Table 4-7 (parity model). Dashed lines are the standard error around the observed proportion. Proportion of parous females
124 Figure 3-16. Observed (solid black line) and predicted (solid red line) estimated number of nulliparous mosquitoes collected p er trap night. Predicted values were obtained using a linear model with the parame ters shown in Table 47 (nulliparous relative abundance model). Note differences in the scale among panels.
125 Figure 3-17. Graphical evaluation of residuals to evaluate the ad equacy of the linear model. The predicted values for parity in mi ddle plots have been back-transformed (BckT) to the original scale.
126 CHAPTER 4 A SPATIALLY EXPLICIT INDIVIDUAL-BAS ED MODEL TO STUDY THE EMERGENCE OF AGE STRUCTURE IN Culex nigripalpus POPULATIONS Introduction The m osquito Culex nigripalpus is a vector of various pathog ens and parasites in Florida (Nayar 1982), but most importantly it has been implicated as the main vector of St. Louis encephalitis virus (SLEV) in various epidemics in the state (Day 2001). This mosquito has also been identified as a vector of We st Nile (WNV) virus in Florida and a bridge vector of eastern equine encephalitis virus (EEEV) (Blackmore et al. 2003, Florida Department of Health 2009). The population dynamics of Cx. nigripalpus in southern Florida are driven by rainfall. During the summer and fall months rainfall creates abundan t oviposition sites in di tches and furrows that are favored by this species, contributing to ra pid population increases (Day and Curtis 1994). The increases in humidity and temperature dur ing the rainy season also create favorable conditions for enhanced Cx. nigripalpus activity and dispersal (Bidlingmayer 1974, Day et al. 1990, Dow and Gerrish 1970). Culex nigripalpus has been described as a woodland mosquito that prefers to fly and rest in wooded areas with dense understory (Bidlingmayer 1971). However, this species is known to commute to ope n areas (fields, agricultu ral sites, residential areas, etc.) during periods of high humidity when conditions are favorab le for dispersal and oviposition (Bidlingmayer and Hem 1981, Day and Carlson 1985, Day and Curtis 1994). This phenomenon is associated with a shift in host utilization by Cx. nigripalpus. During the winter and spring host selection favors birds. However, with the onset of rainfall an increasing number of mosquitoes fly into open grassy habitats where mammalian hosts such as cattle, horses, and rabbits are found, so the proportion of mosquitoes that feed on mammals increases (Edman and Taylor 1968, Edman 1974).
127 Recent studies using the modeling of past hydr ological conditions have shown that high transmission rates of SLEV and WNV in south-cent ral Florida are more like ly to take place after a spring drought followed by constant summ er rainfall (Shaman and Day 2005). During droughts Cx. nigripalpus populations may become restricted to hammock habitats where many species of birds nest (Shaman et al. 2003). This overlap of vectors and avian amplification hosts makes an ideal environment for rapid epizootic amplification of arboviruses (Shaman et al. 2002a, 2003, 2005). When the drought ends, usually in May or June, potentially infected mosquitoes disperse and initiate secondary transmission foci away from the original amplification sites (Shaman and Day 2005). Environmental changes associated with rain fall (relative humidity and oviposition site availability) interact wi th the dispersal behavior and population size of Cx. nigripalpus to create the conditions favorable for virus amplification and transmissi on. Together with population increase and spatial expansion, a change in the population age structure is also necessary to increase the risk of pathogen or parasite transmission. Specificall y, there needs to be an increase in the number of females that live long enough to complete the extrinsic incubation period to become infective (Detinova 1968, Day 2001, Eldridge 2004). The age structure of Cx. nigripalpus is probably affected by e nvironmental changes such as the onset of rainfall and increases in humidit y. Previous studies have shown that the number of gravid females of this species increases durin g dry periods in between rainfall events and is negatively correlated to daily rainfa ll 0-7 days prior to the day of collection (Day et al. 1990) and that the number of bloodfed mosquitoes is positiv ely associated with ra infall (Day and Curtis 1989). Thus changes in humidity and oviposition site availability have an impact on the composition of the population.
128 Here we explore how the heterogeneous distribu tion of resources (oviposition sites, hosts) over space, changes in humidity and ovipositi on site availability over time, and simple representations of mosquito behavior (dispersal and foraging) act together to affect the age structure, size, and spatial spread of a simulated Cx. nigripalpus population. We assume that the effectiveness of mosquitoes at locating resour ces in heterogeneous environments partially determines the time it will take them to complete a gonotrophic cycle. Dispersal and Foraging in Hetero geneous Environments The dispersal of insect vectors can be motivat ed by reproductive needs (mating), or by the need to find oviposition sites or hosts. Disper sal can also be passive when the vector is associated with a dispersing host. Dispersal of vectors will influence which hosts come in contact with the vectors and th e variation in the risk of in fection over space (Lord 2004). Here we are interested in local scale dispersal motivated by physiological needs of mosquitoes (bloodfeeding and oviposition site seeking) in a heterogeneous or patchy environment. This parallels the study of foraging behavior of pa rasitoids searching for hosts, or predators searching for prey. An important concept in foraging be havior models is the searching efficiency, which is the probability of encounter with a host or prey individual per unit time (Rogers and Hassel 1974). As the density of parasitoids increases they interact more closely and this can negatively impact each others efficiency; this known as interference (Rogers and Hassel 1974, Cronin and Strong 1993). The heterogeneous distribution of hosts in space interacts with the foraging strategy of the paras itoid to determine the fraction of hosts that are parasitized and the success of the parasito id (Vos and Hemerik 2003, Bomma rco et al. 2007, Spataro and Bernstein 2007). In some systems, host parasitis m is a positive function of host density, but in other systems it can be an inverse function or even independent of hos t density (Hassel and Wilson 1997). In spatially exp licit modeling studies of host-pa rasitoid systems, different
129 hypotheses on how parasitoids allocate the time to search for hosts have been studied. Some of those hypotheses include: 1) the parasitoid leaves the patch (spa tial unit where it searches) until it has attacked a fixed number of hosts, 2) the parasitoid search es for hosts in a patch during a fixed amount of time, or 3) the parasitoid will only leave the patch after a given period of time without finding hosts (Spataro a nd Bernstein 2007). These hypotheses will yield different results in the number of hosts attacked depending on the spatial distribution of hosts (i.e., uniform, random, aggregated) (Spataro and Bernstein 2007). Spatial considerations in models of hostparasitoid systems allow studying the impact that foraging behavior, the spatial arrangements of hosts, and the quality and connectiv ity of habitats have in host and parasitoid abundance (Cronin and Reeves 2005). A recent review on the subjec t indicates that one of the difficulties in studying these systems in spatially explicit m odels is the limited information on host and parasitoid dispersal behavi or (Cronin and Reeves 2005). In the case of mosquito foraging, the proba bility of encountering hosts and obtaining a bloodmeal is probably modified by factors such as the type of habitat where the mosquitoes search (for example, canopy versus understory), their host feeding preferences, probing behavior, and defensive behavior of the host (Edman et al. 1985). There is evid ence that increased mosquito density negatively affects the feedi ng success of a mosquito because hosts usually become more defensive (Edman et al. 1972) wh ich could be considered as interference. However, there is a lack of information on how th e density of hosts influences the probability of encountering a host. A previous modeling study assumed that the probability of mosquitoes finding a host is an increasing f unction of host density (Shaman 2007). Foraging of bloodfeeding insects has been stud ied theoretically usi ng the evolutionary perspective that these insects look to maxi mize their feeding and reproductive success by
130 choosing the least defensive hosts. A simple model (Kelly and Thompson 2000) assumed that the blood gain of the insect will increase as the feeding success on a particular host species increases. Blood gain declines with increasing vector biting density at a rate determined by a constant representing interference by the host (K elly and Thompson 2000). When more than one type of defensive host and variations in the interference parameters were introduced, biting became heterogeneous, and the host with lowest interference received a higher proportion of bites. The results suggest that interference valu es associated to suscep tible or non susceptible hosts have implications for disease transmission (Kelly and Thompson 2000). Another foraging model assumed that mosqu itoes make decisions about taking blood meals, resting, laying eggs, or taking sugar m eals in a way that maximizes lifetime reproductive success (Ma and Roitberg 2008). The model follows the energy transfers in the mosquito as it takes sugar, a bloodmeal, or develops eggs and it was based on the biology of the malaria vector Anopheles gambiae. Mosquitoes moved within a patchy environment in which they could only take bloodmeals inside and oviposit outside, in orde r to simulate movement in and out of human dwellings. Sugar was available both ins ide and outside (whe re there were no blood sources). When the probability of finding sugar inside was fixed to 1, the probabilities of finding sugar outside and blood inside inte racted to affect mosquito fitn ess. High probabilities of finding sugar outside enhanced the mosquitos longe vity, fecundity, and the number of gonotrophic cycles when the probability of finding a blood host inside was low. But when the probability of finding sugar outside was low, a high probabi lity of finding blood inside did not increase mosquito fitness. Finding sugar outside was critical to improve mosquito fitness because it was the only source of energy available after emergence or after oviposition.
131 Other modeling studies have addressed the imp act that mosquito dispersal behavior in heterogeneous environments and feeding succe ss have on parasite transmission, but without incorporating fitness factors. Models suggest that when la rval habitats are aggregated and humans are homogeneously dist ributed in the environment, An. gambiae biting rates peak around larval habitats at the time when uninfected younger mosquitoes emerge. However the proportion of infectious mosquitoes peaks wherever older mos quitoes are found, usually away from larval habitats in their search for hosts and when population density is lower. When hosts are heterogeneously distributed and larval habi tats are homogenous throughout the habitat, the host searching efficiency determines the aggrega tion of mosquitoes. If host density is low and unfed mosquitoes are not efficient in encounter ing them, they will move quickly through and will tend to aggregate where host density is highest. As a consequence, the proportion of older infectious mosquitoes could be highest at intermediate and high host densities (Smith et al. 2004). In a different An. gambiae model where the adult population was further structured into fed and unfed individuals, hosts were homogene ous over the landscape but water sources were patchy and further classified as productive and non productive (Le Menach et al. 2005). It was observed that unfed infectious mosquitoes ( older) congregated around water sources because after oviposition the water source was the starting point in the search for a bloodmeal. This aggregation occurred regardless of the water source suitability for larval development. Consequently, areas of high Ento mological Inoculation Rates (the number of bites by infectious mosquitoes per person per day) appeared around water sources. This patchiness could be especially relevant during the dry season wh en oviposition sites are more aggregated around human households (Le Menach et al. 2005).
132 A recent spatially explicit individual-based model (SEIBM) explored mosquito foraging behavior in a heterogeneous envi ronment and the effects that this had on the likelihood of virus amplification in a mosquito-b ird arbovirus system (Shaman 2007). The adult mosquito population was subdivided into hostseeking, fed, and gravid classes. The probability of finding hosts and taking a bloodmeal was a function of host density, and mosquitoes always found oviposition sites when present in a patch with wate r sources. Different spatial configurations of resources in a grid were used in this model b ecause the hypothesis was that virus amplification would be more likely if avian roosts (a source of blood for female mosquitoes) and mosquito oviposition sites shared the same location. Th e results of the simula tion found support for an increased likelihood of amplification (defined as >95% of birds having been infected and recovered during the run) when there was an ovi position site in the same location as the roost where virus was introduced. Another SEIBM explored the impact of oviposition site reducti on on the population dynamics of An. gambiae (Gu and Novak 2009). The spatial c onfiguration represented a typical village in Africa with ovipositi on sites surrounding th e houses. The adult female mosquitoes were categorized as newly emerged, host-seekin g, and gravid. Mosquitoes moved between adjacent cells until they found the resources ne eded or until a maximum flight distance was reached. Mosquito abundance and malaria prevalen ce increased with mosqu ito flight distance (3 ranges tested) because resource finding was better with increasing flight distance. These modeling studies considered the interac tions among mosquito dispersal behavior in search for bloodmeals and ovipositio n sites and the heterogeneity in resource availability (hosts and oviposition sites). These interactions can aff ect individual mosquito fitness and their success
133 at finding a host and taking a bloodmeal and ca n impact characteristics such as disease transmission rates. Even though the age structure of adult mosqu ito populations has been recognized as a very important factor in the risk of parasite transmission (Detinova 1968, Day 2001), it is rarely incorporated in models. Adult populations are usually structured into infected or uninfected categories and/or subdivided according to feeding st atus (unfed or fed) because this dictates behavioral changes within the model. Add itional subdivision due to chronological age or physiological age could provide more detail in the proportion of infected mosquitoes that become infectious over time. Including information on the physiological age (parity stage) could help introduce changes in fecundity or behaviors that might arise in aging mosquitoes. The level of detail will depend on the purposes of the model. An Individual-Based Model for Culex nigripalpus In m ost of the models mentioned above ther e was some representation of dispersal, the probability of taking a bloodmeal, and also the probabi lity of laying eggs. In this study we want to focus on similar aspects of the biology of Cx. nigripalpus and develop a model to explore how dispersal and foraging behavior in heterogeneous environments, impact the age structure of the population. Individual-based models (IBMs) are simu lation models based on the fundamental assumption that the dynamics of an ecosyste m, community, or population emerge from the variability among individuals and th eir interactions with other individuals of the same species, different species, and with the environment (DeAngelis and Mooij 2005, Grimm and Railsback 2005). IBMs simulate individuals whose grow th, reproduction, and survival depend on their behavior and their interactions with their internal and external environment as modified by their age or state (Grimm and Railsback 2005).
134 A SEIBM is used here as a simulation framework to study the age structure of a mosquito population that emerges as a result of individual mosquito dispersal and foraging behavior under variable environmental conditions. The model tr acks the chronological age and parity stage of female mosquitoes and their physio logical status (unfed, fed, grav id). The model incorporates enhanced dispersal of mosquitoes after increases in relative humidity. Mosquito mortality (age dependent and age independent) is also considered because it is an important factor influencing the populations chronological and physiological age structure. Increases in mosquito density that negatively influence the prob ability of a mosquito taking a bloodmeal are included and can be seen as a representation of interference. One of the goals of the model was to understand the causes of changes in the age structure of host-seeking mosquitoes that emerges w ithin a population under variable environmental conditions. These mosquitoes were the host-seeking females that had completed their first and second gonotrophic cycles (unfed parous 1 and 2). Additionally, the impact that variations in the probability at which mosquitoes find resources (h osts or oviposition sites) have on the age of unfed parous 1 and parous 2 mosquitoes was studied. There is little information on the efficiency at which mosquitoes find resources. Therefore, it was important to explore the sensitivity of the model to changes in those probabilities. The impact of environmental changes and mosquito searching efficiency on the size and the spatial spread of the population, the physiological age structure, and the proportion of unfed parous 1 females above 12.5 days of age (older potentially infectious females) were also studied. Materials and Methods The ODD Protocol Grimm et al. (2006) proposed a standard protocol to descri be IBMs. They nam ed this protocol ODD which stands for Overview, Des ign concepts,and Details. This protocol
135 will be adopted here to describe the Cx. nigripalpus IBM. The section Details contains all the information on model initializa tion, inputs, and the submodels of the biological processes simulated. Overview Statement of model purpose The m odel simulates the individual dispersa l behavior of adult female mosquitoes searching for hosts and oviposition sites. Sugar seeking activities are not explicitly considered and it was assumed that sugar was available and not a limiting factor. These mosquitoes move within a hypothetical landscape (grid) with th ree attributes: vegetation, hosts, and oviposition sites. Humidity conditions and oviposition site availability change over time in a discrete pattern. The purpose of the model is to simula te individual mosquito behavior in a changing environment and study the age structure that emer ges in the mosquito po pulation. The spatial spread of the population over the landscape and the population size were also studied. State variables and scales The m odel has three entities represented: in dividual female adult mosquitoes, immature mosquitoes, and the simulated landscape where th e adult mosquitoes carry on their activities. Individual female mosquitoes have the following state variables: location in the grid (x, y coordinates of the cell), chronol ogical age (hours), physiological stage (nulliparous, parous 1, parous 2, etc.), feeding status (unfed, bloodfed ), and if bloodfed, hours of oocyte development since the bloodmeal. An immature mosquito is a category comprising from the egg stage until adult eclosion. Immature mosquitoes have two attributes: time of development in hours and location in the grid. The simulated landscape is a grid of cells. Each cell has an (x, y) coor dinate in the grid. Additionally each cell has the follo wing state variables: (a) vege tation quality (4-woodland with
136 dense understory, 3-woodland, 2-open with scatte red trees and some bushy vegetation, and 1open grass or urbanized). (b) Percentage of cell area covered with ovipositi on sites that could be either permanent or rainfall dependent (seasonal). (c) Total number of vertebrate hosts in the cell. The landscape is a 50 cell by 50 cell grid. Given the difficulties in determining the flight range of a mosquito such as Cx. nigripalpus the dimensions of the grid cannot be directly extrapolated to an area in a real landscape. Two different landscapes were considered and are described below in the Input section. The time step is 1 hour. It is assumed th at mosquitoes will search for resources (oviposition site or host) within one cell during one time step. If they do not find the resources they need they move to a different cell. The models simulate conditions during the summer and fall in southern Florida and each run comprise s a total of 4320 hours (6 months x 30 days x 24 hours/day). Process overview and scheduling The m odel simulates hourly ac tivities of mosquitoes for a period corresponding to the summer-fall months. After initiali zation (see below) the model starts at day one of the month of June and proceeds for 30 days at hourly time steps. It continues for another 5 months in the same manner. The model follows the life cycle of individual mosquitoes (Figure 4-1). Within each time step certain conditions are evaluated and, when necessary, actions are executed: If immature development is complete (240 hours) adults are adde d to the population. Newly emerged mosquitoes rest for 48 hours before searching for their first bloodmeal. The probability of flight initiation for hostseeking or oviposition seeking of a mosquito is a function of current environmental condi tions (temperature, re lative humidity, moon illumination). Mosquitoes that do not fly at the present time step rest in their current cell. Bloodfed mosquitoes rest until they become gravid (72 hours).
137 The probability of mortality for each mosquito depending on their age and activity status (flying or resting) is calculated. o If mosquitoes survive they complete the appropriate activities according to physiological status. Unfed mosquitoes search for hosts in thei r current cells. They find them with a probability that is a function of host density. o If the unfed mosquitoes find a host, the probability of taking a bloodmeal will be a function of the total number of empty mosquitoes that have found a host in the same cell during the same time step. o If the mosquitoes do not find a host they disperse to a different cell. Bloodfed mosquitoes that have rested for 72 hours become gravid. They will search for oviposition sites in their current cell. They find oviposition sites with a probability that is a function of the area of th e cell covered with water. o If the mosquitoes do not find oviposition sites they disperse to a different cell. Mosquitoes disperse to any of the eight neighboring cells. The probability of moving into a neighboring cell is a function of its number of hosts (or oviposition sites) and vegetation type. As humidity increases, the probabilities to disperse to cells with vegetation type 1 and 2 (open areas) increases. In nature, increased dispersal of Cx. nigripalpus to open habitat occurs when condi tions are humid after rainfall. Design Concepts Em ergence: changes in the chronological and physiological ag e structure of the population emerge from individual mos quito foraging behavior and mortality. Sensing: Individuals are assumed to know their own age, physiological status, and location during a time step. They also know the conditions of their eight neighbor cells in order to select what cell to move to. Stochasticity: stochasticity arises from the use of probability distributions to make decisions on mortality, initiation of flight host finding, oviposition site finding, taking a bloodmeal and dispersal. Interaction: mosquitoes interact indirec tly when taking a bloodmeal. The total number of mosquitoes in the cell that have encounter ed a host influences th e probability that an individual mosquito will take a bloodmeal. Observation: the response variables of interest are the average chronological age of unfed parous 1 and parous 2 females and th e changes in the proportion parous females over time. The number of occupied cells dur ing the run (spatial spread) a nd population size are also of interest.
138 Details Initialization Each run started with a 90 day run under dr y conditions (see Input section) with daily average temperatures for the m onth of May (see Input below), and the mosquitoes in the model were assumed to have gone through a spring dro ught prior to entering the month of June. The initial population for this 90 da y run was composed of 1,500 unfed (48 h old) females and 500 eggs (0 h old) that were placed in the cells with 2 permanent oviposition sites in the primary patch of the landscape (the Input section has a description of this patch). Another 504 recently bloodfed females (72 h old) and 504 gravid female s (120 h old) were placed in six cells within the primary patch (84 bloodfed and 84 gravid on each cell). This initia l distribution of the population was selected after reviewing data on the physiological st age structure from Cx. nigripalpus collected during the month of May of 1985 by J. Day, in which unfed mosquitoes constituted 60% of the population, and bloodfed and gravid mosqu itoes each constituted 20% of the population. The initialization produced different initial population sizes at the beginning of each simulation depending on the landscape and the beha vioral traits of the mosquitoes (Table 41). Input Two different landscape grids and two sim ulated weather patterns were tested in combination to study their effects on the age stru cture, size, and the sp atial spread of the mosquito population. Description of the landscapes. Landscapes were designed to observe the dispersal of mosquitoes from a central area into the rest of the landscape during the summer-fall season. The initial mosquito population that went through a 90 day initialization period under dry conditions was located in the primary patch at the center of the landscape. This patch had hosts, permanent
139 oviposition sites, and woodland ve getation (types 3 and 4). Mosqu itoes were able to disperse from this primary patch to search for resource s at any time, but their likelihood of leaving the cells of vegetation types 3 or 4 in the primary patch and moving to cells with vegetation types 1 or 2 (open vegetation) that su rrounded the primary patch, increased when humidity increased. Two landscapes named favorable (Figure 4-2) and unfavorable (Figure 4-3) were used for the simulations. Both landscapes were gr ids of 50 x 50 cells, and had three layers of information: number of hosts per cell, vegetatio n type for each cell, and percent area of the cell covered with water suitable for oviposition. The two landscapes had a primary patch in the center that had the same structure in both, but differed in the composition and arrangement of resources outside the primary patch. The primary patch (3 x 35 cells) had cells with vegetation types 3 and 4 (it was a wooded patch). Two cells in the primar y patch contained permanent ovipos ition sites and two other cells contained seasonal oviposition sites. Arranged around the oviposition sites were cells containing 2 or 3 hosts, and in between oviposition sites th ere were 2 cells with 4 hosts each. These arrangements of hosts are not based on any known distribution of hosts and were designed in a way to provide connectivity for mosquito dispersal between the elements within the primary patch. The favorable landscape was so named because it had more of the resources needed by mosquitoes than the unfavorable landscape. The mosquitoes would have to travel less to encounter these resources, although the model was stochastic and there was always a probability that they would not find them. Following is a description of the resources available in each landscape, outside the primary patch. A complete set of figures with the landscape attributes can be found in Appendix, Figures A-1 to A-8.
140 The favorable landscape (Figure 4-2): Fourteen secondary wooded patches (5 x 7 cells each) contained four oviposition sites each. Six of those patches had two permanen t and two seasonal oviposition sites. The remaining eight secondary patches had four seasonal oviposition sites. Oviposition sites: 12 permanent and 44 seasonal. Hosts were located inside and outside the secondary patches. Inside the secondary patches there were three cells with 4 hosts each. Hosts outside the secondary patches were lo cated in every other cell. There were alternating rows of cells with 2 hosts in ev ery other cell and 1 host in every other cell. This produced a total of 1681 hosts in this landscape. The unfavorable landscape (Figure 4-3): Six secondary wooded patches (5 x 7 cells each ) contained four seasonal oviposition sites each. Oviposition sites: 24 seasonal. Hosts were located inside and outside the secondary patches. Inside the secondary patches there were three cells with 4 hosts each. Hosts outside the secondary patches were locate d in alternating rows of cells with 2 hosts every other cell and 1 host every other cell, followed by two rows with no hosts. This produced a total of 984 hosts in this landscape. These landscapes were designed to provide contrasting conditions of connectivity and suitable places for reproduction by mosquitoes. The motivation came from other studies of insect dispersal (ground beet les) in fragmented landscap es (Sndgerath and Schrder 2002, Benjamin et al. 2008). The cells with hosts a nd oviposition sites are never contiguous in the landscapes. There is at least one cell without resources placed in between. Field observations suggest that Cx. nigripalpus mosquitoes do not stay in the same area where they rested the night before (Day and Curtis 1994). Thus, the intent ion of placing hosts in every other cell is to increase the chances of disp ersing to other cells.
141 The landscapes have reflective boundaries and the mosquitoes do not leave or disappear from the simulated landscape thr ough the borders. When they reach a boundary they can only choose to go back to the 5 nei ghboring cells, or move to 3 neighbor ing cells when in a corner. Reflective boundaries were also used by Smith et al. (2004). Description of the simulated weather patterns. Simulated weather patterns induced changes in (a) the pattern of hourly relative hum idity conditions and (b) the number (and area) of the oviposition sites available. Two weather patterns (W1 and W2) were created by alternating dry, average and wet conditions and are described in Table 4-2 and illustrated in Figure 4-4. The weather patterns W1 and W2 are based on a subjective interpreta tion of the possible changes in oviposition site availability that could have occurred in the simulated landscapes following the rainfall patterns in Indian River County, Florida in 2007 and 2008 (Figure 3-11, Figure 3-12). These years and th is location were chosen for re ference given that a field study was conducted here that explored the changes of physiological ag e structure as a function of weather (Chapter 3). The year 2007 (Figure 3-11) had a rainfall event above 50 mm in June. Also, multiple rainfall events of ~50 mm/day sp anned from July to mid August. From mid August through September rainfall was scarce and isolated. Hea vy rainfall was observed again in early October. To mimic this rainfall pattern, the W1 pattern was designed to have alternating wet and average conditions during June, most of July and half of August, followed by a long period of dry conditions in September and a shor t period of wet and average weather for October (Table 4-2, Figure 4-4 A). The year 2008 (Figure 3-12) had a dr y start but heavy rains were observed in mid July and then in August due to a tropical storm. A dry period in September was followed by isolated heavy rains in early October and early November. Weather pattern W2 thus
142 had a dry June but alternating we t and average conditions from mi d July to the end of August, and isolated wet events during early Octobe r and November (Table 4-2, Figure 4-4 B). For this modeling exercise, it was of interest to determine if age structure differences would emerge under different simulated weather pa tterns. Multiple weather patterns could have been designed with different sequences of the w eather types. The ones used here were only two of a large collection of possibilitie s, thus they can be considered as random effects. Rainfall occurs throughout the year in Indian River County but there ar e seasonal increases during the summer and fall. Data of the monthly average precipitation (25 year average) from the Vero Beach Airport weather station, Indian River C ounty, show how the rainy season in this region expands from June to October: Januar y, 62.73 mm of rain; February, 60.70 mm; March, 92.71 mm; April, 74.16 mm; May, 79.50 mm; June 150.11 mm; July, 148.59 mm; August, 163.57 mm; September, 197.86 mm; October, 159.76 mm ; November, 74.42 mm; and December, 49.78 mm (National Climatic Data Center 2009). There is much year-toyear variation in the monthly precipitation during the rainy season, and monthly pr ecipitation can fall to ~1 inch or be as high as 23 inches in some months. The specific changes that occur in the landsca pe (oviposition sites) and with the humidity pattern when the conditions change between dry, av erage, and wet are detailed in Table 4-3. The discrete changes from dry to average and from average to wet introduced new oviposition sites by making the seasonal sites avai lable, they also increased the area of permanent oviposition sites (Table 4-3). The discrete changes from av erage to dry weather (or from wet to dry) reduced the area of permanent oviposition sites to that of the dry weather pattern, and eliminated all seasonal oviposition sites immediately. This resulted in immature mortality since all the immature mosquitoes present in seasonal oviposi tion sites died when these sites disappeared.
143 Seasonal oviposition sites usually lasted 15 days or more, with the exception of those that appeared during early October and November in W2 when they lasted only 5 days (Figure 4-4 B). The area of the cell covered by water in th e oviposition sites takes values of 0, 5 and 10%. The simulated relative humidity conditions us ed in the model are changed hourly and are based on hourly averages of relati ve humidity for the Vero Beach ar ea (Indian River, Florida) for the months of May to November. Hourly weat her data for the Vero Beach Municipal Airport Weather Station was available for the years 2002 to 2004 from the National Climatological Data Center, National Environmental Satellite, Data and Information Service, from the National Oceanic and Atmospheric Administration ( http://www.ncdc.noaa.gov/oa/ncdc.html ). Inform ation from those three years was used to calculate hourly minimum, hourly average, and hourly maximum relative humidity for each month in the summer and fall season (Appendix, Table A-1). The hourly minimums were used as input in the model wh en the conditions were dry; the hourly averages were used when the c onditions were average, and the hourly maximums were used when the conditions were wet (Table 4-3). Other inputs: daily changes in temperature and moon illumination. Hourly changes in temperature were calculated as the hourly average temperature from hourly data for the years 2002 to 2004 from Vero Beach, Florida, also obtai ned from the from the National Climatological Data Center (Appendix, Table A-1) The daily values for the fraction of moon illuminated were introduced with the following f unction, created for this model based on a 30 day cycle of moon illumination changes (i.e., full moon every ~30 days): (4-1) where day takes values from 1-30.
144 Submodels Immatur e development. The temperature dependent development of each mosquito from egg to pupal eclosion was not modeled explicitly. A recent study estimated that Cx. nigripalpus can lay on average 273 eggs (McCann 2006). Here we assumed that each simulated female laid 200 eggs per oviposition. Ten percent of those e ggs survived to the adu lt stage, with a 50:50 sex ratio. Thus 10 females were added to the new generation per ovipos ition, after completion of immature development. This was based on fiel d data from other spec ies that suggests high mortality rates for immature mosquitoes. This mortality can reach 98-100% in the presence of parasites or in oviposition site s located in agricultural fiel ds (Campos and Sy 2002, Mwangangi et al. 2006). The mortality in temporary pools for Culex annulirostris in Australia was 65.2% in temporary pools, but rose to 95.8% and 98% in flooded grasslands and semi permanent pools where larger predators (fish) were present (Mottram and Kettle 1997). The time from egg laying to adult emergence was fixed at 240 hours. This was an approximation of the time of immature development for Cx. nigripalpus at 27C under low larval crowding: 48 h from egg laying to egg hatchi ng and 192 h from egg hatching to adult eclosion (Nayar 1982). As was mentioned before, immatu res present in seasonal aquatic habitats died without completing their development to adults when those seasonal habitats disappeared during dry conditions. Flight initiation. For simplicity, each day of the simu lation was subdivided into 12 night hours and 12 day hours and this di d not change over the season. Therefore the seasonal changes in the length of the night pe riod were not considered, alt hough we acknowledge that this potentially has an impact on the time that it w ould take a female mosquito to find resources. During the day hours, mosquitoes were not active and rested in the cell where they were last active. During the night hours, the probability that a mosquito will fly during a time step
145 occurred with a probability that was a functi on of the hourly temperat ure, hourly relative humidity, and moon phase. Bidlingmayer (1964, 1974) did not observe mosquito activity below 12C in Indian River County, Florida and observed reduced activity below 17-18C. Bidlingmayer (1985) considered th at a sigmoidal curve could repres ent mosquito flight activity as a function of temperature but he did not provide parameters. Here, a sigmoidal function that produced values from 0 to 1, and a probability of flight of 0.50 at 18C, was used to calculate the probability that a mosquito w ill initiate flight as a function of hourly temperature (pT): (4-2) The flight activity of Cx. nigripalpus increases with relative humidity (Dow and Gerrish 1970), but there is no published function to desc ribe this relationship. Thus similarly to temperature, a sigmoidal relationship between pr obability of mosquito flight and relative humidity was assumed here. The following f unction, which produced values from 0 to 1 and probabilities of flight of 0.50 at 66% relative humidity, was used to calculate the probability that a mosquito will initiate flight as a function of hourly relative humidity (pRH): (4-3) Bidlingmayer (1964, 1974) found that Cx. nigripalpus activity was influenced by moon illumination in a similar fashion as Ochlerotatus taeniorhynchus with both mosquitoes being more likely to fly during the full or quar ter moon phases, than during the new moon (Bidlingmayer 1964, 1974). The hourly probabilities of flight during different moon phases (pM) used here are shown in Table 4-4; these follow the descriptions by Bidlingmayer (1964, 1974) of mosquito flight activity using su ction traps (see Figure 1 in Bid lingmayer 1964). The probability of adult flight for a particular night hour was calculated as pflight=pT*pRH*pM. A random probability (prand1) that the mosquito would fly in that time step was generated, if prand1 pflight the
146 mosquito was active during that hour. Otherwise th e mosquito would rest in its current cell until the next time step. Resting. If the mosquito had recently emerged from the immature stage, it rested in its cell for 48 hours before becoming active (McHugh 1990). If the mosquito had recently taken a bloodmeal, it rested in its cell for 72 hours durin g oocyte development, and it became gravid afterwards (Nayar 1968b). The resting tim e was updated at each hourly time step. Adult mortality. The hourly probability of mortality was calculated as a function of mosquito age and activity status. Lord and Le Fevre (unpublished data) st udied the temperature and age dependent mortality of Cx. nigripalpus under laboratory and semi-field conditions and determined that a Gompertz function described ag e dependent mortality at all temperatures. The hourly age dependent mortality component is ex pressed with the following Gompertz function (mosquito age in hours): (4-4) The parameters of the function are higher than the ones obtained in la boratory conditions in order to account for possible differences when mosquitoes have to surv ive under variable field conditions. The age independent mortality com ponent was an hourly probability of mortality dependent on mosquito activity status. The pr obability of mortality was assumed higher for flying mosquitoes than for resting mosquitoes becau se it is believed that active mosquitoes face higher risks such as predation or of being killed by the host. Resting mosquitoes had an hourly probability of mortality of prest = 0.005. Gravid mosquitoes and unfed host-seeking mosquitoes that became active (flyer s) during a time step had an hourly probability of mortality of pfly = 0.015. The hourly probability of mortality was pmortality=page+prest or pmortality=page+pfly, depending on activity status. These parameters were select ed during preliminary assessments of the model
147 in which the cohort of mosquitoes in the initi al population was followed, and they produced a daily survival range between 76-80% This is close (although sli ghtly lower) to some estimates of survival for Culex mosquitoes during the summer m onths (Chandra et al. 1996, McHugh 1999). No effects of hourly temperature or humidity were considered in the mortality parameters to keep the focus on age and activity dependent mo rtality, and given that there is no data that describes these effects on the hourly scale. Thes e effects are probably very important in nature. Possible seasonal changes in mortality due to changes in temperature and humidity are not represented in this model. A random probability (prand2) that the mosquito will die in that time step was generated, if prand2 pmortality the mosquito died and was removed from the population. The mosquitoes that survived continued to other activities. Host searching. Unfed mosquitoes search for hosts in their current cell. The probability of finding a host was a function of the number of hosts in the cell, and it was calculated as: ). (4-5) This formula was taken from Shaman (2007) It was selected because it provides probabilities of finding hosts of exactly zero when there are no hosts present, and increases gradually as the number of hosts in the cell increa ses. The asymptote of the function is specified at 0.9 to indicate that there is al ways a small probability that the mosquito will miss a host in the cell. There is no data available on this rela tionship and, due to this uncertainty, the model outcomes were evaluated for their sensitivity to changes in this probability function. A random probability (prand3) that the mosquito will find a host in the time step was generated; if prand3 phost the mosquito found the host and could attempt to bloodfeed. If the mosquito did not find a host, it stayed in the cell until the next time step.
148 Taking a bloodmeal. Unfed mosquitoes that found a host attempted to take a bloodmeal. The probability of Cx. nigripalpus taking a successful bloodmeal decreases as the number of unfed mosquitoes per host increases, and the sh ape of this decreasing function probably varies with the host species (Edman et al. 1972). The probability of taking a bloodmeal in the present model was given by: (4-6) The parameters in this function were chosen after preliminary evaluations when it was observed that this density dependent component wa s necessary to regulate population increases. This function is a representation of the negati ve effect that increases in the number of Cx. nigripalpus attempting to feed on a vertebrate host ha ve in the probability of taking a bloodmeal. The function assumes homogeneous distribution of unfed mosquito es over hosts, and provides a probability of 1 of a mosquito taking a bloodmeal when there was 1 mosquito per host, and of 0.5 when there were ~7 mosquitoes per host. A random probability (prand4) that the mosquito will take a bloodmeal in the time step was generated; if prand4 pmeal the mosquito took a bloodmeal. If the mosquito did not take a bloodmeal, it moved to a neighboring cell. Oviposition site searching. Gravid mosquitoes, those that had rested for 72 hours after a bloodmeal, searched for oviposition sites in their current cell. The proba bility of finding an oviposition site was a function of the area of the cell covered in water, and it was calculated as: ). (4-7) The shape of this relationship is the same as the one chosen for host searching, and it provides probabilities of exactly zero for finding ovi position sites when there is no water present. The probability increases as the area of the water source in the cell increases. The asymptote of
149 the function is specified at 0.9 to indicate that there is always a small probability that the mosquito will miss the oviposition site in th e cell. There are no data available on this relationship and therefore, the model outcomes were evaluated for their sensitivity to changes to this probability function. A random probability (prand5) that the mosquito will find an ov iposition site in the time step was generated, if prand5 poviposition the mosquito found the oviposition site and became empty and host-seeking again. The physiological status of the mosquito was also updated (i.e., from nulliparous to parous 1, or from parous 1 to parous 2, etc.). Dispersal. When the mosquitoes did not take a bloodmeal or did not oviposit in their current cell during a time step, th ey moved to another cell to search for resources. The mosquitoes dispersed to any of the 8 neighboring cells around their current ce ll. The selection of which cell to move to was made based on a mu ltinomial probability distribution where each cell received a probability based on attractiveness scores. The scores were a function of the vegetation type in the ce ll and the number of hosts if the mos quito was unfed, or the presence of oviposition sites if the mosquito was gravid. Research on Cx. nigripalpus in south central Florida has provided evidence that this species prefers to rest and fly in wooded ar eas (Bidlingmayer 1971). When environmental conditions of low humidity prevail, Cx. nigripalpus mostly restricts its activities to humid and vegetated areas, but increases in relative humidit y make areas with open or no vegetation more accessible for the mosquitoes (Day and Curtis 1994). A humidity dependent function was used to ca lculate an attractiveness score for the cells in the landscape depending on their vegetation type (Score1 for vegetation type 1, Score2 for
150 vegetation type 2, etc.). The scores were in a scale from 1 to 10 and were calculated with the following equations: (4-8) (4-9) (4-10) (4-11) These equations provided scores for the cells representing open gra ss or urbanized areas (1) and open areas with scattered vegetation (2) that increased as humidity increased. On the other hand, the scores for cells with woodland (3) and densely woode d with understory (4) decreased as humidity increased (F igure 4-5). This pattern signif ies that as humidity increases, cells of different type qualities become very similar in attractiveness to the mosquito. The attractiveness scores based on hosts or ov iposition sites were a simple function of the number of hosts or the cell area covered by oviposition sites. If the mosquitoes were gravid, only information from oviposition sites was consid ered to calculate the score. If mosquitoes were unfed and host-seeking, only information from hosts was considered. For example, if there were 4 hosts in a cell, the cell received a scor e of 4. Similarly, if th ere was 10% of the cell covered in water, the cell received a score of 10. If there were no hosts or oviposition sites in a cell, it received a score of zero. After the absolute scores were obtained, relative scores for vegetati on and relative scores for resources were calculated separately by di viding the individual score for the cell over the total sum of the scores for the eight neighboring cells. A probabil ity for each cell was calculated by adding the relative scores from vegetation plus the relative scores from hosts (or oviposition
151 sites, depending on the mosquito status) and dividing them by two. The final multinomial probability distribution had a total of 8 probability values (1 per neighboring cell) adding up to 1. The function rmultinom available in R 2.7.0 (R Developm ent Core Team 2008), which is a generator of multinomial distributed random number vectors, was used to se lect the cell to which the mosquito was to move. This function generate d a vector of length 8, w ith a single value of 1 assigned to the cell that was chosen based on its pr obability (the rest of cells received a value of zero). This corresponds to a typical multinomial e xperiment of placing a single object in one of eight boxes with diffe rent probabilities. The procedure used here to select cells wa s developed in preliminary studies. Other procedures were tested, specifically one where the absolute scores for cells of vegetation type 3 and 4 were kept constant (at 8 and 10, respectively). However, in this way the multinomial probabilities obtained always allo wed the cells with higher vegetation to have the highest probabilities to be chosen, overriding the presence of hosts or oviposition sites. We believed that if the mosquito has a physiological need this is not what woul d be expected, thus a methodology where absolute scores based on vegetation became similar as humidity increased provided the most logical representation of the biologi cal process that was being simulated. An example is presented next to explain the process of cell selection and to highlight the differences that arise in cell selection with ch anges in relative humid ity. If a host-seeking mosquito is located in the central cell (dark gray) of the grid presented in Figure 4-6, it can move to any of the 8 neighboring cells (light gray). Tw o of those cells have hosts. With 70% relative humidity there is a 0.47 probability (multinomia l probability column) th at the mosquito will move to the cell with vegetation type 4 and 1 host, and a 0.26 probability that it will move to the cell with vegetation type 1 and 1 host. When rela tive humidity is 90%, there is an increase in the
152 probability to move to the cell with type 1 vegetation and a decrease in the probability to move to the cell with type 4 vegetation, giving them 0.30 and 0.35 probabilities, respectively. This change in humidity makes it almost equally likely that the mosquito will move to the cell with vegetation type 1 than to the cell with vegetatio n type 4. Unfed mosquitoes do not always move to the cell with hosts, this stochastic behavio r is introduced to simulate conditions from the natural environment that could delay th e completion of a gonotrophic cycle. The rmultinom function was run 100 times with ea ch of the two multinomial probability distributions obtained. The results show that the cell with 1 host a nd vegetation 4 was chosen 53/100 times at 70% relative humidity, but only 31/100 times at 90%, and the cell with vegetation 1 was chosen 33/100 times. Simulation Experiments The m odel was implemented in R 2.7.0 (R Deve lopment Core Team 2008). For each of the two landscapes (favorable and unfavorable), 10 simulation runs were conducted with each weather pattern (W1 and W2). Each comb ination of landscape and weather pattern (favorable:W1, favorable:W2, unfavorable:W1, a nd unfavorable:W2) was called a treatment. The goal was to study how the interaction of landscape and weather pattern affected the size, spatial spread, and age structure (both chronological and physiological) that emerged in the mosquito population. The outputs of the simulations were compared qualitatively between treatments with the following summary measures: Total mosquito production ( MPtotal): to summarize the popula tion size, the total number of adult females that emerged during the 180 days on each simulation was calculated. Average spatial spread for the entire simulation run ( SStotal): the spatial spread was defined as the percentage of cells in the landscape occupied by at least one mosquito. This percentage changed daily. The aver age spatial spread throughout an entire simulation run was calculated as the av erage of the 180 daily spatial spread measurements to compare between treatments.
153 Maximum percentage of parous mosquitoes per month ( PPmonth): physiological age structure was defined as the percentage of parous mosquitoes in the population. This percentage also changed daily, and its maximu m value on each of the six months of the simulation was used as a summary to compar e between runs and treatments. This was considered better than an average because it also allowed observing if parity increased or decreased over time as the simulation progressed. Average over a month of the daily average ag e of parous 1 and parous 2 unfed females ( AAmonth): parous mosquitoes that are unfed are epidemiologically important because they have taken a bloodmeal and could have been exposed to a virus. Depending on their age and other factors (such as type of virus, temperature, and extr insic incubation of the virus), they could be ready to transmit the virus in the next bite. The average age in days of these mosquitoes was calculated daily. Th e daily average age was used as input to obtain a measure of average age for each of the six months of a simulation run. The AAmonth was used to compare age stru cture between treatments. Average over a month of the standard deviati ons around the daily average age of parous 1 and parous 2 unfed females ( SDmonth): the standard deviations around the daily average age were also averaged per month. These valu es were used as indicators of variations around the chronological age, between treatments. Average over a month of the proportion of parous 1 females over 12.5 days of age ( PP1month): older females are epidemiologically important because th ey could be ready to transmit a virus. The incubation pe riod of St. Louis en cephalitis virus in Cx. nigripalpus is between 10-14 days (Day 1997). Considering that the average age of empty nulliparous mosquitoes was around 2.5 days in the simulations, the daily proportion of parous 1 females over 12.5 days of age (2.5 days to take first bite plus a minimum of 10 days of incubation) is an indication of the fraction of the population capable of transmission. The daily values of the proportion of unfed parous 1 females over 12.5 days were calculated. These 30 daily values were averaged to obtain a monthly average. This was done for each month within a simulation run. Month-to-month patterns were used to compare between treatments. Sensitivity Analysis The sensitiv ity of the results to changes in the probability of finding a host or an oviposition site (Equation 4-5 and Equation 4-7) was evalua ted. These probabilities are important because they affect how frequently the mosquito will move to a different cell and the time it will take the mosquito to complete the gonotrophic cycle. Two other parameterizations for the probability of finding hos ts in the landscape were crea ted by varying the value of the parameter that determines the rate at which the probability of finding a ho st increases with host
154 density (denominator to the number of hosts) by one unit. These functions were called High probability and Low probability of finding hosts: High: ), (4-12) Low: ). (4-13) Equation 4-5 was considered the Medium probability function of finding hosts (function in which the denominator for host was 4). Two other parameterizations for the probability of finding oviposition sites in the la ndscape were created in a sim ilar way by varying the value of the denominator by 2 units. These functions were called High probability and Low probability of finding oviposition sites: High: ), (4-14) Low: ). (4-15) Equation 4-7 was considered the Medium probability function of finding oviposition sites (function in which the de nominator for area was 12). These probability functions were used as sets in the simulations. They will be referred to as a set of resource finding efficiency conditi ons, and they will be abbreviated H for high, M for medium, and L for low. There were 9 possibl e sets of resource finding efficiency, and each was given a short name by combining the abbrevia tions of their names pl acing the probability of finding hosts first. For example, the term HM will refer to a set where there was a high probability of finding hosts and a medium probability of finding oviposition sites. The sensitivity of MPtotal, SStotal, PPmonth, AAmonth, SDmonth and PP1month to changes in resource finding efficiency was studied.
155 Results Simulation Experiments The results of the simulations using the me dium probability of finding hosts and medium probability of finding oviposition sites (MM resour ce finding efficiency conditions, Equations 45 and 4-7) are presented with de tails on daily changes in population characteri stics (size, spatial spread, parity, chronological ag e). Also, qualitative comparisons among the four treatments (unfavorable:W1, unfavorable:W 2, favorable:W1, and favorable :W2) were made using the summary measures MPtotal, SStotal, PPmonth, AAmonth, SDmonth and PP1month. The MM resource finding efficiency conditions were considered the baseline for later comparisons with the sensitivity analysis. Population size and spatial spread with MM resource finding efficiency Description of daily changes. The results of the daily changes in the number of mosquitoes (population size, Figure 4-7) and percentage of cells occupied by mosquitoes (spatial spread, Figure 4-8) for each of the ten simula tions per treatment with MM showed a cyclical pattern over time. The peaks of population size likely correspond to periods of emergence of new mosquitoes. These cycles were consistent among simulations within the same treatment. However, the pattern broke down for the simu lations in which the number of mosquitoes declined over time. It was noted that some of the populations with in a treatment tended to increase in size and spread spatially after prolonged periods of wet or average conditions (days 31-70 for W1, and days 46-90 for W2, indicated by blue boxes in Figures 4-7 and 4-8). However other populations declined in size, and in the favorable landscape some went extinct (Table 4-5). As will be discussed later, the behavior of mosquitoes and population size dur ing periods of wet or average conditions were critical fo r population persistence.
156 The two landscapes, favorable and unfavorable produced different re sults in the spatial spread of mosquitoes. The percentage of cells occupied by one or more mosquitoes at a given day in the unfavorable landscape never exceed ed 20% and more commonly was between 5-12% under both weather patterns (Figur e 4-8 A and B). Since the pr imary patch contained 105 cells (4.2% of the landscape) cell o ccupancy above 4% indicates mo squitoes spread outside the primary patch in their search for resources. The cell occupancy in the favorable landscape reached up to 30% (Figure 4-8 C and D). This la ndscape, with its higher abundance of hosts and secondary permanent oviposition sites, allowed in some cases the broader spatial expansion of the population. However in other ca ses extinctions were observed. Comparisons among treatment s using summary measures. There were no definite differences in total mosquito production (MPtotal) (Figure 4-9 A) among treatments with the MM resource finding efficiency. There were overl aps among treatments and considerable variation within each treatment. The smallest MPtotal values (~8000 mosquitoes) emerged in the favorable:W2 treatment and the highest (~90000) in the unfavorable:W1 treatment (Figure 4-9 A). The average spatial spread for the entire run (SStotal) had a narrower range in the unfavorable landscapes than in th e favorable landscapes (Figure 4-9 B). Variation was greater in the favorable landsca pe (Figure 4-9 B). The populations in the favorable lands cape with the lowest values of MPtotal and SStotal went extinct before the end of the 180 days of the simulation (Table 4-5). The extinctions of some of the populations observed in the favorable landscape, after the relatively long periods of wet or average conditions, sugge st that medium probabilities of resource finding efficiency (MM) sometimes resulted in a very small proportion of the population finding resources. As will
157 be presented later in the sensitivity analysis re sults, no extinctions in the favorable landscape occurred when the resource finding efficienci es were HH, HM, MH, or LH and only three extinctions were observed under HL (Table 4-6). This suggests that when the probabilities of finding hosts and/or oviposition si tes increased, mosquito populat ions tended to successfully persist in the favorable landscape. Physiological age structure: percentage of pa rous females with MM resource finding efficiency Description of daily changes. The percentage of parous females in the population was calculated for each day of a simulation. The percenta ge of parous females also showed a cyclical pattern over time in each treatment (Figure 4-10), with reductions in parity likely corresponding to the times of emergence of new mosquitoes. The cyclical pattern broke dow n considerably in the favorab le:W2 treatment (Figure 4-10 D) after the prolonged period of wet or aver age conditions, with some populations reaching 100% parous females late in the season. These we re the populations that d eclined in size with populations composed mostly of older pa rous mosquitoes la te in the season. In the favorable:W1 treatment (Figure 4-10 C) there was consider able variation among runs, and parity reached 60% for some of the simulated populations. In the unfavorable:W1 and unfavorable:W2 treat ments, the percentage of parous females usually did not exceed 40% and results were very consistent among runs within a treatment. Comparisons among treatment s using summary measures. There were differences among treatments in the patterns of parity over ti me. The maximum percentage parous females for each month (PPmonth) stayed below 40% and slightly decl ined over time in the unfavorable landscape treatments (Figure 4-11). In the favorable:W1 treatment the PPmontly reached up to 60% for some of the simulations early in the season. In the favorable:W2 treatment increased
158 parity was observed for some of the simulations late in the season. The populations in the simulations that increased in percentage of paro us females later in the season were those that declined in size. There was a noticeable increase in the PPmonth from June to July in the favorable:W1 treatment. Days 31-60 in July had wet or average conditions (Table 4-2) and it is likely that more gravid females oviposited due to increased availability of oviposition sites. However, no increases in PPmonth were observed in the favorable:W2 tr eatment with the onset of wet or average conditions during July and August (days 46 to 60 in July, and days 61-90 in August had wet or average conditions for W2, Table 4-2). Chronological age structure: the age of unf ed parous 1 and parous 2 females with MM resource fin ding efficiency Daily changes The average age of unfed parous 1 and parous 2 females was calculated for each day of the simulation. These simulations allow us to provide a first theoretical description of how the chronologi cal age distribution of host-s eeking females in a mosquito population, might appear in heter ogeneous environments. Here we observed three levels of variation in age: the variati on within a day, from day-to-day, and among simulation runs within a treatment. The daily average age of unfed parous 1 females showed more varia tion among runs within a treatment in the favorable:W1 and favorable:W2 treatments than in the unfavorable:W1 and unfavorable:W2 treatments (Figure 4-12). This indicates that th e favorable landscape introduces more variation in age. Overall, the daily av erage age of unfed parous 1 females was mostly between 6 and 10 days with a marked increase in average age by November (Figure 4-12). However, there were several peaks in average ages over 10 days for some simulations in the favorable landscape (Figure 4-12 C and D).
159 The daily average age of unfed parous 2 females was very variable among runs in both landscapes (Figure 4-13). There were no clear differences in the patt erns among treatments and the daily average age of unfed parous 2 females fluctuated between 9 and 17 days and increased over time (Figure 4-13). We examined an individual simulation run from each treatment to consider variation in the age structure within a day. The runs considered are shown in Figures 4-7, 4-8, 4-10, 4-12, and 413 (black lines). The age structures of these four individual populations (1 per treatment) are detailed in Figures 4-14 and 4-15. By consider ing individual populations we can examine that each day had a different distribution of ages for the unfed parous 1 and parous 2 mosquitoes. The standard deviation around the average ag e for the unfed parous 1 females ranged between: 0.61-4.93 days for the unfavorab le:W1 treatment, 0.32-4.07 days for the unfavorable:W2 treatment, 0.61-4.41 days for th e favorable:W1 treatment, and 0.44-5.58 for the favorable:W2 treatment. The standard deviation around th e average age for the unfed parous 2 females was wider and ranged between: 0-5.54 days for the unfavorable:W1 treatment, 0-9.28 days for the unfavorable:W2 treatment, 0-5.89 days for the favorable:W1 treatment, and 0-6.84 for the favorable:W2 treatment. This daily variation in age is very important because it means that from day to day there can be shifts toward older age in the distribution and a fractio n of those parous host-seeking females could be old enough to vector a pathogen. There were times of average older ages that lasted for various days for the population in the favorable:W1 treatment (Figure 4-14 C). For ex ample, there were five consecutive days in August and seven consecutive days in September when the average age was 9 days (~2.5 day
160 standard deviation) (Figure 414 C). The whole month of Nove mber showed a very noticeable shift towards older ages. These shifts to olde r ages could be influenced by dry conditions because the months of August, September, a nd November all had prolonged periods of dry conditions. Shifts toward older ages also occu rred during wet or average weather conditions, but they werent as large in magnitude as during dr y periods nor did they la st for more than two days. Dry conditions reduced mo squito activity (less likely to initiate flight when humidity conditions were dry) which increased the time to take a bloodmeal or to find an oviposition site. Similar shifts towards older ages were observe d between June to July and from October to November for favorable:W2 (Figure 4-14 D). Thes e periods also corresponded with times of dry conditions. Shifts to older ages occurred in the unfavor able landscape populations early in the season and in November (Figure 4-14 A and B). The unfavorable:W2 treatment showed an unexpected pattern with large day to day va riations early in the season. Fewer females completed the second gonotrophi c cycle and therefore there were days without females in this group (Fi gure 4-15). There was much variab ility in all trea tments in the age of unfed parous 2 females and some age in creases during dry conditions in the favorable landscape and during November. Simulated temperatures in November were c ooler based on daily average temperatures at that time of the year in Indi an River County, FL. This, in combination with dry conditions, resulted in much reduced mosquito activity in the simulations. As a consequence, the time it took the mosquitoes to complete gonotrophic cycles was increased: how quickly they took a bloodmeal and the time it took them to find an oviposition sites.
161 Comparisons among treatment s using summary measures. After describing in detail the age structure of individual populations (day-t o-day variation and within day variation), we compared treatments considering all simulation runs using monthly summaries of the daily average age of unfed parous females (AAmonth) and the standard deviat ion around the average age (SDmonth) (Figures 4-16 and 4-17). The AAmonth for unfed parous 1 females showed different patterns among treatments (Figure 4-16 A). Landscape had an important effect. In the unfavorable landscape AAmonth were usually below 8 days from June to October and above 8 days in November (Figure 4-16 A). The value 8 days was used as a reference because th e overall average age for parous 1 females for many of the runs was ~8 days. But in the favorable landscape the AAmonth were more variable from month to month and the pattern depended on the weather (Figure 4-16 A). For the favorable:W1 treatment, average ages tended to be 8 days, except for July when average ages were 8 days, and there was a noticeable increase in average age in November. For the favorable:W2 treatment, average ages decreased from 8 days in June to <8 days in August, and went back to 8 days from September to November. Interestingly, the months when AAmonth decreased, July in W1 and August in W2, thei r entire duration was characterized by wet or average conditions, and this suggests that incr eased humidity and oviposition site availability contributed to a shift towards younger ag es in the unfed parous 1 females. The SDmonth was between 1.5 and 2 days in the unfavorable landscape (Figure 4-16 B), and this was very consistent among runs. However, in the favorable land scape the values of SDmonth decreased over time in a fe w runs. Single runs with SDmonth values close to zero in November in the favorable:W1 treatment, and October and November in the favorable:W2 treatment were observed. This was probably due to reductions in the number of unfed parous 1 females
162 (populations in decline) with all of these females being around the same age (thus the reduced variability around the average age). The AAmonth and SDmonth values for unfed parous 2 mosqu itoes (Figure 4-17) showed more variability among runs than in parous 1 mosquitoes. There was considerable overlap in the range of AAmonth from month to month in all trea tments (Figure 4-17 A). The AAmonth showed a range of values from 12-14 days for all treatments from June to October, increasing during November. The favorable:W2 landscape showed more variability among runs. There was considerable vari ability among runs in the SDmonth values for unfed parous 2 females (Figure 4-17 B). This was probably due to the large day to day cha nges in the number of parous 2 females over time in each simulation run. When the cohorts of unfed parous 2 females were small and females were of similar ages, th ere was less variability around the average age. Proportion of unfed parous 1 females over 12.5 days old (PP1month) There were no clear differences in the PP1month patterns among treatments (Figure 4-18), but it was evident that the conditions in the favorabl e landscape introduced more va riability among runs. The PP1month was usually 0.15 which suggests that in the simulated populations, less than 15% of the unfed host-seeking parous 1 females live long enough to pot entially transmit arboviruses. The highest values of PP1month occurred during the months of September to November. Simulation experiments results summary The results for the sim ulations using the MM pa ir of probability f unctions supported that: There was wide variation in total mosquito production (MPtotal) and no clear differences between treatments. Landscape type had an effect in the spatia l spread of mosquito es. The unfavorable landscape produced a narrow range of average spa tial spreads (SStotal), usually below 12%. A wider range of spatial spread (5-20%) was observed in the favorable landscape. Extinctions occurred in the favorable landscap e. Mosquitoes dispersed farther in the favorable landscapes (during wet or average periods). However due to the stochastic
163 nature of the model, the females in some of the simulations did not find resources and the populations declined. The percentage of parous females in the unfavorable landscape was always under 40%. In the favorable landscape there was more variation among runs and higher percentages of parous females (60-100%) occurred in some of the simulations, especially late in the season and in those populations with low production of new mosquitoes. Simulations provided a first description of how the chronological age structure for mosquito populations might look under heterogeneous environmental conditions. Chronological age was very variable from day to day, within a day, and among each simulation run. More variability among runs was observed under the favorable landscape. During some simulations, unfed pa rous 1 females in the favorable landscape were older than those in the unfavorable landscape in the months with mostly dry conditions. The proportion of unfed parous 1 females over the age of 12.5 days was lower than 15% through most of the season, with higher rates obs erved in some simulation runs late in the season (September to November). Overall, more variability among runs was observed in the outcomes for the favorable landscape. Sensitivity Analysis The sensitiv ity analysis results showed that changes in the simulated efficiency of mosquitoes to find resources and their interaction with landscape characteristics largely affected simulation outcomes. The outcomes with different resource finding efficiency conditions will be discussed using the summary measures MPtotal, SStotal, PPmonth, AAmonth, SDmonth and PP1month. Population size and spatial spread The total m osquito production (MPtotal) and spatial spread (SStotal) were very sensitive to changes in the probabilities of finding hosts and oviposition site s. When the resource finding efficiency was medium for host-seekers and low for oviposition seekers (ML), low for hostseekers and medium for oviposition seekers (LM) or low for both (LL), very low numbers of new mosquitoes were produced and populations went extinct (Tab le 4-6, Figure 4-19 B). After initialization these populations started the simu lation with the lowest initial population sizes
164 (<500 individuals on average, Table 4-1), and they persisted with very lo w numbers before going extinct between July and August with LL, and be tween July and September with ML and LM (a few populations went extinct in early October under ML). Only the results obtained under the other six pairs of resource finding effi ciencies will be discussed further. In contrast to the results with LL, ML, and LM conditions, the highest values of MPtotal emerged for populations in the favorable landscap es when mosquitoes had a high probability of finding hosts and oviposition sites (HH) (Figure 4-19 A). With HH conditions, more mosquitoes were produced in the favorable landscapes than in the unfavorable landscapes, regardless of the weather pattern. The mosquito production wa s also relatively high when the MH and HM resource finding efficiency conditions were used; however the differences in production between landscapes were less noticeable (F igure 4-19 A). There were sli ght differences due to weather patterns with MH but not as much with HM. When the resource finding efficiency conditions were MM, LH, or HL, mosquito production was gr eatly reduced. There was no noticeable effect of treatments on mosquito production, except in LH under the favorable landscape for some simulations (Figure 4-19 B). The average spatial spread for the entire run (SStotal) (Figure 4-20) was higher in the favorable landscape than in unfavorable landsca pe with the LH, MH, HH, and HM resource finding efficiencies, but not with MM and HL. A high probability of finding oviposition sites by individual mosquitoes interacted with the landscape to produce differences in population size and spatial sp read. Notice how the HH, MH, and to a lower degree LH show differences in mosquito production (Figure 4-19 A) and spatial spread (Figure 4-20). When the probability of finding oviposition sites was medium but accompanied by a high probability of finding hosts (H M) differences in spatial spread between
165 landscapes appeared (Figure 4-20), but there wa s overlap in mosquito production (Figure 4-19 A). The efficiency with which mosquitoes f ound oviposition sites was a critical factor for differences in population size and spread of the s imulated populations app eared in the favorable and unfavorable landscapes. However, high probab ility of finding ovipositi on sites needed to be accompanied with medium or high probability of finding hosts for populations to noticeably increase in size. Physiological age structure The changes over tim e in the maximum percentage of parous females per month (PPmonth) were also sensitive to variations in resource finding efficiency (Figures 4-21 and 4-22). Within all treatments, lower resource finding efficiency increased variation among simulation runs. With LH, MM, and HL, the monthly outcomes were more variable among r uns (these conditions also produced lower population sizes and spread ). With MH, HH, and HM, maximum parity values per month were very consistent among runs, meaning each of the ten repetitions produced very similar results. Lower resource finding efficiencies (LH, HL, and MM) introduced more stochasticity in the proportion of females in the population th at became parous, which resulted in more population size variation and sometimes populati on decline. Declining populations were composed of mostly parous female s and showed higher parity rates. The proportion of parous females in the popul ations with increased resource finding efficiency (HH, MH, and HM) mostly remained below 40% for all treatments. This was due to the constant production of new nulliparous mosquitoes which constituted the majority of individuals in the populations. A peak of increased parity and subsequent slow decline was noticea ble under all foraging probability conditions in July in the favorable:W 1 treatment (Figure 4-22 A). July was a month
166 with wet or average conditions under W1. Thus, parity increa sed when more oviposition sites became available. No clear peaks in parity were observed under favorable:W2 during the wet or average months (July and August) (Figure 4-22 B) or in the unfavorable landscapes. This result indicates that cha nges in parity could occur unde r different circumstances: increases due to the onset of wet or average conditions that allow more gravid females to oviposit, increases in the proporti on of parous females when few new mosquitoes are added to the population, and decreases in parity when th ere is a high rate of reproduction and new mosquitoes are constantly being added to the population Chronological age structure The sensitivity of the population age stru cture to the variatio n in resource finding efficiency is shown in Figures 4-23 to 4-30. Considering the average ages of parous fem ales (monthly average of the daily averages, AAmonth) and the variation in age (monthly average of the daily standard deviations, SDmonth), there were two notable results. In both unfed parous 1 and parous 2 females, there was more variation between simulations when lower probabilities of finding hosts and oviposition sites were used. The HH, HM, and MH conditions produced outcomes that were more consistent than the LH, HL, and MM conditions. The increased variability obser ved under the LH, HL, and MM pa irs, was enhanced in the favorable landscapes for both unfed parous 1 (F igures 4-25 and 4-26) and parous 2 females (Figure 4-29 and 4-30). Thus, th e combination of low resource finding efficiency combined with a more complex landscape structure, resulted in more variations in the time taken to complete gonotrophic cycles. The AAmonth was consistently higher during the mont h of November with all treatments and resource finding efficiency conditions for bot h unfed parous 1 and parous 2 females. Also, the AAmonth for the months of July for W1 and August for W2 tended to have lower values than
167 the previous and following months. These months had wet or average conditions (Table 4-2), suggesting that average chronologic al ages during wetter months tended to be lower than during drier months. The variation among runs intr oduced by the LH, HL, and MM conditions was also evident in the proportion of parous 1 females over 12.5 days of age (PP1month) (Figures 4-31 and 4-32). The variation under the low resource efficiency conditions was enhanced in the favorable landscapes where the highest proportions were obse rved late in the season (Figure 4-32). The values of PP1month ranged from 0 to 0.15 with LH, HL and MM, but were usually below 0.05 (except for November) with HH, HM, and MH. Incr eases in resource finding efficiency lead to decreases in PP1month. Sensitivity analysis results summary The results of the sensitivity analysis indicated that: When m osquitoes became more efficient a nd had an increased probability of finding resources (HH, MH, and HM), populations incr eased dramatically in size and spatial spread. Reduced probabilities of finding resources (HL, LH, and MM) combined with more complex landscape structure (favorable landscap e), introduced more va riability in the age structure of populations. This variation generated higher va lues of percentage parity, wider ranges of chronological age in the pa rous groups, and more variability in the proportion of unfed parous 1 females over 12.5 days of age. The effects of weather patterns were more ev ident in the favorable landscape, where the average chronological ages during wetter months tended to be lower than during drier or cooler months. These effects were enhanced with HL, LH, and MM conditions. Discussion An individual-based m odel was used to simula te the dispersal behavior of the mosquito Cx. nigripalpus in hypothetical heterogeneous landscapes. The model emphasized the effects of environmental inputs in adult mos quito activity and dispersal because Cx. nigripalpus is considered a highly dispersive mosquito (Day and Curtis 1994) with great flight potential (Nayar
168 and Sauerman 1973). The spread of Cx. nigripalpus to open areas during the rainy season is a well described phenomenon (Bidlingmayer 1971, Day a nd Curtis 1994). This was represented in the model as increases in the li kelihood of mosquitoes to move into open areas when relative humidity was higher. Increased dispersal raises the question of how efficient these mosquitoes are at finding resources. The model incorporated simplified represen tations of mosquito foraging and used functions to calculate the probab ility that a mosquito will find a host or find an oviposition site. The host number and distributi on was held constant, but the availability of oviposition sites changed over time in discrete ways. The main goal of the simulation model was to study the age structure of the simulated populations, with emphasis on the ch ronological age structure within parity cycles. The daily average age of unfed parous 1 and parous 2 mo squitoes was of interest because these groups include mosquitoes that could potentially tran smit disease pathogens. We observed that the chronological age structure had tw o levels of variation: within a day and between days. Age variability was affected by environmental inputs. Shifts of the average ages to older ages occurred mostly during dry conditions and during the cooler month of November, especially in the favorable landscape (Figure 414 C and D). The sensitivity analysis later highlighted that low resource finding efficiency in the favorable landscape was also an important cause of shifts to older ages in the chronologica l age of unfed parous females. A shift to older ages in the mosquito population is consider ed a risk factor for increased transmission of viruses by mosquitoes (Detinova 1968, Day 2001). Environmental factors affected the chronological age structure by introducing delays in the time to take a bloodmeal or to oviposit, because wh en dry conditions or temperatures were cooler there was a lower probability of mosquitoes becoming active. Also, there were fewer oviposition
169 sites available. Times to find resources were further delayed for less efficient mosquitoes. These mosquitoes probably moved through more cells (more time steps) even if hosts or oviposition sites were present becau se they were less likely to find them in their current cell. Some mosquitoes eventually found resources afte r a random number of time steps and this added more variability to the ages of unfed parous mosquitoes. Lower efficiency also resulted in fewer unfed mosquitoes finding hosts and taking bloodmeals or fewer gr avid mosquitoes laying eggs. Many inefficient mosquitoes probably died before completing reproductive cycles. Low efficiency negatively impacted popu lation size and spatial spread. What factors in real populations could contri bute to mosquitoes being less efficient at finding resources? We can speculate that host sp ecies, host abundance, host defensive behavior, the spatial distribution of hosts, individual mosquito variation in sensory ab ilities, or the need to find a new oviposition site to avoid predators or larval crowding, are a ll factors that could interfere with the time that it takes for mosquitoes to take meals or oviposit. The function of the probability of finding hosts and oviposition sites used here could be a representation of a wide variety of phenomena. It is known that increases in Cx. nigripalpus density irritate hosts and this reduces the probability of a mosquito taking a bloodmeal (Edm an et al. 1972). Host species differ in their defensive reactions and some of them could inf lict high mortality to mosquitoes (Edman et al. 1972, Day and Edman 1984). Kelly and Thompson (2000) defined host defensiveness as the probability of a single mosquito taking a bloodmeal from a host, and the interference as the rate at which this probability declines as the number of mosquitoes increases. Each host species probably has particular defensiveness and inte rference values (Kelly and Thompson 2000) that could be estimated in experiments of feeding success under different density conditions (such as
170 the experiment by Edman et al. 1972). We did not consider different host species in this model, and we represented interference with a function that decreased the probability of taking a bloodmeal with increased mosquito density per host. It is also possible that when populations of other mosquito species are increasing, interspeci es competition for blood sources might influence the time it takes a Cx. nigripalpus to take a bloodmeal. The feeding success of mosquitoes is the result of many inter acting factors. Host distribution over space could also im pact the success of mosquitoes taking a bloodmeal. In other biological systems such as host-parasitoid interactions, the spatial distribution of the hosts is a fact or that affects the attack effici ency and reproductive success of individual parasitoids. Parasito ids have evolved diverse foraging strategies adapted to different host distributions (e.g., aggregated versus uniform), even within the same species, in order to maximize their fitness (Vos and Hemerick 2003, Bommarco et al. 2007, Sp ataro and Bernstein 2007). In our model, hosts were placed in uni form patterns throughout the landscape and they were constant and immobile. Future models c ould consider including spatio-temporal changes in the number and distribution of hosts and study if this affects mos quito population characteristics. There is need for more information about individual Cx. nigripalpus behavior when selecting oviposition site s. A modeling study of the oviposit ion behavior of the mosquito Culiseta longiareolata predicted that mosquitoes should alwa ys avoid using water sources with predators to increase their f itness (Spencer et al. 2002). A companion laboratory study determined that when given the choice, mosquito es avoided water sources with predators 83% of the time (Spencer et al. 2002). Although avoi dance behavior was not perfect, this raises questions about the time mosquitoes spend search ing for the best oviposit ion sites to increase their fitness and how good they are at detecting predators in oviposit ion sites. Other information
171 that female mosquitoes might use to select ovipos ition sites could be larval crowding. This could be important in order to minimize competiti on and maximize resources for their offspring. We conclude that the resource finding efficiency of mosquito es was a key factor affecting the variability in the chronologi cal age structure of the simula ted mosquito populations. This factor has been considered important in other models. For example, a spatially explicit model found that the probability of host detection by An. gambiae was an important parameter that determined the aggregation of mosquitoes over space when hosts were heterogeneously distributed (Smith et al. 2004). In another model, increases in the probability of finding sugar sources in areas where blood sour ces were not available positively affected the fitness of An. gambiae (Ma and Roitberg 2008). In addition to its impact on age structure, our results also indicate that the efficiency of mosquitoes to find resources can have importa nt impacts on population size and spread. Low efficiency usually resulted in smaller populations with lower spatial spread, but as mosquitoes became more efficient a higher absolute number of females completed the gonotrophic cycles (especially the first one) and large populations emerged. When the HH, HM and MH resource finding efficiency conditions were simulated in the model, large and widespread mosquito populations emerged. Larger populations with an older age structure are usually considered to be risk ier in terms of diseases transmission (Detinova 1968, Day 2001). In the large simulated populations, there was always a small fraction (<5%) of unfed parous 1 mosquitoes above 12.5 days of ag e. This fraction was likely to increase during dry conditions and/or cool weather, because mo squito activity is reduc ed, delaying the time to take bloodmeals or oviposit.
172 When the mosquitoes were assumed to have higher efficiencies in finding resources (HH, HM, and MH), clear differences in population si ze and spread were observed between favorable and unfavorable landscapes. It was expected th at larger and more widespread populations would arise in favorable landscapes because they have more permanent and seasonal oviposition sites. However the results showed that this depended on the resource finding efficiency of mosquitoes especially on a higher probability of finding ovipos ition sites. In contrast, the discrete weather patterns used did not appear to have a strong effect on the total mosqu ito production and average spatial spread of the populations within the same type of landscape. Th e weather patterns did influence the times at which rapid population growth and dispersal occurred. There were prolonged wet or average periods between days 31 and 70 in W1 and days 46-90 in W2, and it was during those periods that populations experienced rapid expans ions in size and over space. When lower efficiency of finding hosts and/or oviposition sites was simulated, the populations were smaller, there was more vari ability among the outcomes of each simulation run, and there were also many runs where the popul ation went extinct. In the simulations using the MM resource finding efficiency, some of the populations with smaller sizes after initialization were the ones that did not pers ist until the end of the 180 days of a simulation (Table 4-5). The small populations that produced fewer mosquitoes before the onset of the prolonged dry periods were the ones th at declined or did not persist. Both environmental variability and mosquito behavior were important factors influencing chronological age structure, but in this particular model th e physiological age structure (percentage of parous females) appeared less re sponsive to changes in the environment and more a function of population size. P hysiological age structure tended to vary cyclically at the beginning of simulations, with peaks every 16-20 da ys (the approximate times that females took
173 to complete the first gonotrophic cycle, 6-10 days, plus the 10 days of immature development). This cyclic pattern changed in some populations after they ei ther declined or increased considerably in size. When populations decline d, the percentage of parous females tended to increase over time because fewer new mosquitoes were being produced and the majority of females were parous. However when populations were increasing, several cohorts of mosquitoes were reproducing at asynchr onous times producing large numbers of new mosquitoes, and the percentage of parous females tende d to decrease over time. Therefore changes in the percentage of parous females are not directly associated with changes in weather in this model. The field study in Chapter 3 supported that the proportion of parous females in the population increased noticeably during rainy periods preceded by long dry periods. This could be large numbers of gravid females that accumu late during dry conditions and oviposit in aquatic habitats that appear af ter heavy rainfall (Day et al. 1990). Laboratory experiments have shown that fewer Cx. nigripalpus females oviposit in low humidity: an average of 3.1 females (in groups of 100) oviposited when relative humid ity was between 50-70%, versus 57.4 females at >90% relative humidity (Day et al. 1990). Culex nigripalpus gravid females can hold their eggs for long periods until oviposition sites become available (Day and Edman 1988). This information supports that weather changes can influence the number a nd proportion of parous mosquitoes in the population. The individual-based model simulations produced an increase in the absolute number of gravid mosquitoes during dry periods, especially in the favorable landscapes (see Figure 4-33 for examples). The number of gravid females did not stay elevated throughout dry periods. It declined due to both mosquito mortality and be cause the simulated gravid females oviposited in the permanent oviposition sites. Perhap s more information is needed about Cx. nigripalpus
174 preferences between permanent and flooded ovipos ition sites during the summer and fall months. Both types of oviposition sites were represented in the model. In the field, an example of a permanent oviposition site used by Cx. nigripalpus could be a pond with emergent vegetation, while seasonally flooded oviposition sites can incl ude storm water drainage and retention swales (OMeara et al. 2003). Results of the field study in Chapter 3 suggested that changes in Cx. nigripalpus parity over time could not be fully e xplained by weather ch anges, and it was suggested that perhaps oviposition sites that are not completely de pendent on rainfall play a role in population changes. These aspe cts of behavioral responses of Cx. nigripalpus to different qualities of oviposition sites need to be studied further to im prove the representations of mosquito oviposition behavior in models and might help better explain cha nges in parity in the populations. This individual-based model had other parame ters that could have also affected the outcomes observed. The time for a female to become gravid was fixed at 3 days and this had an impact on the duration of a gonotrophic cycle. In reality this parameter is temperature dependent (Clements 2000). Shorter egg development times in warmer temperature could have allowed females to complete the cycles faster. Temper ature dependencies were also not considered in immature development or mortality, primarily to avoid too much complexity in the model and to focus on the effects of environmental inputs on adult mosquito dispersal. Considering temperature dependent rates of development and mortality in immatures could have impacted the rate at which new mosquitoes were added to the population. The mortality rates used here were selected because they produced ~80% daily survival when a cohort was followed. Mosquito survival in the field during the summer months for another Culex species ( Culex quinquefasciatus ) was estimated at 81% (Chandra et al. 1996). If
175 reductions in daily mortality were introduced in the model, females could potentially live longer and complete more gonotrophic cycles affecting th e age distribution of unfed parous groups and also population size. In spite of its many simplifications, this model provided interes ting insights into the factors (other than temperature) that could affect th e chronological age distri bution of unfed parous females. It illustrated how variable the age st ructure of a mosquito population can be due to the interactions between mosquito behavior and en vironmental heterogeneity. The results suggest that changes in the environment (like long dry periods between rainfall s) could introduce more variability in the age structure, especially in very heterogene ous landscapes (like the favorable landscape) that could result in a shift of the daily average ag e towards older ages. If the mosquitoes are efficient in findi ng resources populations will incr ease in size and spread even under variable environments. There is a hypothesis about Cx. nigripalpus which indicates that when dry periods last between 10-20 days the viral incubation could be completed by females during a single gonotrophic cycle (Day et al. 199 0, Day and Curtis 1994). Our observations with this simple model give support to this hypothesis because we did find shifts to older ages during dry and/or cool periods that lasted more than 10 days. It would be difficult to test pr edictions like this in the field, especially because we do not have practical ways to determine the chronological age of a field collected mosquito. Extensive studies of the environmental factors that drive St. Louis encephalitis epidemics in Florida using hydrological modeling have id entified weather patterns in epidemic years. Culex nigripalpus is the main vector of this virus in the state. Epid emic years have a particul ar profile of changes in the water table depth which includes alterna ting drought and wet periods (Day and Shaman 2008): drought in late spring, wet event in earl y summer, drought in late summer, wet event in
176 the fall. Based on observations from our indi vidual-based model we can propose that these environmental changes can indeed shift the age of mosquito populations towards older ages during dry conditions and this co uld favor epidemics. The mechanisms behind the shift could involve reduced mosquito activity which increas es the time it takes some females to take a bloodmeal or find oviposition sites (e.g., when temp erature or humidity, or both, are low). Or the shift could be due to factors that reduce th e efficiency of mosquitoes to find and utilize resources (e.g. aggregation of hosts, reduced numb er of oviposition sites, etc.). We have data available supporting the effects low humid ity, moon illumination, wind, and temperature on Cx. nigripalpus activity. More research is needed on behavioral factors. Laboratory studies on Cx. nigripalpus feeding behavior using differe nt compositions and density of hosts could be carried out to determine how this affects the time to take a bloodmeal. Studies on Cx. nigripalpus preferences for oviposition between fresh and old oviposition sites could also be performed to determine if changes in the composition of available water sources could affect the time to oviposition. The age distri bution of unfed parous Cx. nigripalpus females is a very important population characteristic that depends not only on environmental factor s but possibly also on behavioral aspects of mosquitoes. Discussion Summary Previous studies had shown that a large proportion of older Cx. nigripalpus parous fem ales could be expected in the populati on after long dry periods followed by rainfall. This is due to accumulation of gravid females that retain eggs and finally oviposit when aquatic habitats become available. However, we did not have a description of the chrono logical age structure of Cx. nigripalpus females under such changing environmental conditions. The results of this model provide a theoretical repr esentation of the chr onological age structure of unfed parous females and present possible causes for its va riability. The results suggest that certain
177 environmental conditions in heterogeneous landscap es can cause shifts to older chronological ages that can last for various consecutive days. These environmental conditions are low humidity, fewer oviposition sites, and cooler temperatures. Even though this result might seem intuitive, we previously did not have a descript ion of the distribution of chronological ages of unfed parous females under changing environments The effects on age structure of individual variations in the mosquitoes ability to detect resources were also expl ored. We observed that these individual variations had an important im pact on model outcomes. Mosquito behavior interacted with resource abundance and distribu tion (hosts and aquatic habitats) to impact chronological age structure. Th is suggests that changes in ho st composition and abundance in a landscape, for example, could also influence th e age structure of a mosquito population in a similar way as changes in weather could. If the mosquitoes are less efficient acquiring bloodmeals, it will take them longer to comple te gonotrophic cycles and the average age of parous females could increase. The model pres ented here assumed that females did not have preferences for different types of oviposition sites (permanent versus flooded). More information on Cx. nigripalpus oviposition behavior would be necessary to improve the model. The results from this model illustrate how e nvironmental factors othe r than temperature can induce changes in the chronological age structure of females wh ich is associated with the occurrence of infectious mos quitoes in the population.
178 Table 4-1. Mosquito population sizes after initialization under diffe rent resource finding efficiency conditions for the two landscapes The resource finding efficiency conditions correspond to the probability (h igh, medium, or low) of findi ng hosts or oviposition sites, depending on the mosquito physiolo gical status, during a time step. (See sensitivity analysis section). Favorable Landscape Unfavorable Landscape Resource finding efficiency conditions (Host: Oviposition sites) Initial population size Standard deviation Initial population size Standard deviation High:High (HH) 1595.30 174.65 1627.20 316.36 High:Low (HL) 751.60 148.67 748.15 150.25 High:Medium (HM) 1032.15 244.36 1097.65 213.40 Low:High (LH) 678.15 115.74 617.90 116.50 Low:Low (LL) 243.95 85.61 234.80 55.59 Low:Medium (LM) 452.20 110.42 458.15 138.73 Medium:High (MH) 1180.70 182.08 1062.50 206.68 Medium:Low (ML) 410.65 108.32 476.05 92.66 Medium:Medium (MM) 657.90 157.94 715.75 127.21
179 Table 4-2. Weather conditions by mont h for weather patterns W1 and W2. Weather pattern W1 W2 Month Dates Days Continuous scale Conditions Dates Days Continuous scale Conditions June 1-5 1-5 Wet 1-30 1-30 Dry 6-10 6-10 Average 11-30 11-30 Dry July 1-5 31-35 Wet 1-15 31-45 Dry 6-10 36-40 Average 16-20 46-50 Wet 11-15 41-45 Wet 21-30 51-60 Average 16-20 46-50 Average 21-25 51-55 Dry 26-30 56-60 Wet August 1-10 61-70 Average 1-5 61-65 Wet 11-30 71-90 Dry 6-15 66-75 Average 16-25 76-85 Wet 26-30 86-90 Average September 1-30 91-120 Dry 1-30 91-120 Dry October 1-5 121-125 Wet 1-5 121-125 Wet 6-10 126-130 Average 6-30 126-130 Dry 11-30 131-150 Dry November 1-30 151-180 Dry 1-5 131-135 Wet 6-30 136-130 Dry
180 Table 4-3. Description of the relative humidity an d oviposition site availab ility in the landscapes for each simulated weather condition. Weather conditions Favorable Landscape Unfavorable Landscape Dry Oviposition sites 14 oviposition sites 2 oviposition sites Primary patch 2 permanent: 10% of their area with water. 2 permanent: 10% of their area with water. Secondary patches 12 permanent: 5% of their area with water. None with water. Relative Humidity Hourly minimum relative humidity Average Oviposition sites 60 oviposition sites 28 oviposition sites Primary patch 2 permanent: 10% of their area with water. 2 seasonal: 5% of their area with water. 2 permanent: 10% of their area with water. 2 seasonal: 5% of their area with water. Secondary patches 12 permanent: 5% of their area with water. 44 seasonal: 5% of their area with water. 24 seasonal: 5% of their area with water. Relative Humidity Hourly average relative humidity Wet Oviposition sites 60 oviposition sites 28 oviposition sites Primary patch 2 permanent: 10% of their area with water. 2 seasonal: 10% of their area with water. 2 permanent: 10% of their area with water. 2 seasonal: 10% of their area with water. Secondary patches 12 permanent: 10% of their area with water. 44 seasonal: 10% of their area with water. 24 seasonal: 10% of their area with water. Relative Humidity Hourly maximum relative humidity
181 Table 4-4. Probabilities of flight initiation during the night h ours as a function of the fraction of the moon illuminated. Fraction of moon illuminated 0.9-1 0-0.1 0.1-0.9 (day > 15) 0.1-0.9 (day < 15) Night hours Full moon New moon First quarter Last quarter 18 0.98 0.98 0.84 0.98 19 0.98 0.83 0.84 0.71 20 0.98 0.56 0.84 0.42 21 0.98 0.49 0.91 0.35 22 0.98 0.42 0.98 0.28 23 0.98 0.42 0.84 0.28 24 0.98 0.42 0.70 0.28 1 0.98 0.35 0.58 0.35 2 0.98 0.28 0.42 0.42 3 0.98 0.14 0.28 0.70 4 0.98 0.14 0.28 0.56 5 0.42 0.70 0.70 0.84 Table 4-5. Total mosquito production and average spatial spread for each of the 10 runs with the MM foraging probability functions. Runs that went extinct are in bold numbers. Total Mosquito Production Average Spatial Spread Favorable Unfavorable Favorable Unfavorable Run W1 W2 W1 W2 W1 W2 W1 W2 1 60416 9919 29631 20850 18.59 5.51 6.58 5.33 2 21624 21283 34775 66432 8.40 8.53 7.49 10.22 3 64402 68280 69931 24433 19.29 20.06 10.16 5.63 4 31611 33851 66482 29817 11.75 12.32 10.25 6.64 5 11002 11111 73773 33080 5.03 5.66 11.29 6.70 6 23561 8484 90949 58522 9.20 4.71 12.09 9.32 7 37543 13691 64954 65951 13.71 6.18 9.81 9.95 8 55279 59072 66257 52410 17.92 18.64 9.62 8.95 9 42930 15860 51357 49840 14.84 7.17 8.79 9.08 10 14487 10240 32759 45285 6.54 5.23 6.97 8.58
182 Table 4-6. Numbers of extinctions (out of 10 runs) observed u nder different resource finding efficiency conditions. Favorable Landscape Unfavorable Landscape Resource finding efficiency (Hosts: Oviposition sites) W1 W2 W1 W2 High:High (HH) 0 0 0 0 High:Medium (HM) 0 0 0 0 High:Low (HL) 1 2 0 0 Medium:High (MH) 0 0 0 0 Medium:Medium (MM) 2 6 0 0 Medium:Low (ML) 10 10 10 10 Low:High (LH) 0 0 1 3 Low:Medium (LM) 10 10 10 10 Low:Low (LL) 10 10 10 10
183 Figure 4-1. Simplified life cy cle of an individual Culex nigripalpus used in the modeling study. A mos quito can die at any stage of its life (not shown for simplicity). The dash ed line illustrates that the mosquito can potentially complete multiple gonotrophic cycles in its lifetime (parous 1, parous 2, parous 3, etc.).
184 Figure 4-2. The favorable landscape. The pr imary patch is in the center with 2 perm anent oviposition sites (dark gray) and 2 s easonal oviposition sites (light gray). Six of the fourteen secondary patches have 2 permanent oviposition sites each, the rest are seasonal. The bold numbers mark the cells where vegetation is type 3 or 4. The numbers indicate the number of hosts in the cell.
185 Figure 4-3. The unfavorable landscape. The primary patch is in the center with 2 permanent ovi position sites (dark gray) and 2 seasonal oviposition sites (light gray). The six secondary patches have seasonal oviposition sites. The bold numbers mark the cells where vegetation is type 3 or 4. The numbers indicate th e number of hosts in the cell.
186 Figure 4-4. Discrete changes in the area available for ovipositi on for each treatment. These plots show the schedule of chan ges between wet, average and dry weather type s on pattern W1 (A) and W2 (B), and how these changes affect the percentage of area in a landscape that can be used for oviposition. 0 0.05 0.1 0.15 0.2 0.25 0.3 161116212616111621261611162126161116212616111621261611162126 JuneJulyAugustSeptemberOctoberNovemberPercentage area in landscape with water Favorable:W2 Unfavorable:W2B 0 0.05 0.1 0.15 0.2 0.25 0.3 161116212616111621261611162126161116212616111621261611162126 JuneJulyAugustSeptemberOctoberNovemberPercentage area in landscape with water Favorable:W1 Unfavorable:W1A Wet Average Dry
187 Figure 4-5. Changes in the attractiveness sc ores of cells on the basis of their vege tation type as a function of relative hu midity. As conditions become more humid, the attrac tiveness score for cells without vegeta tion or open with scattered vegetation (types 1 and 2) becomes more similar to that of cells with wooded areas or wooded areas w ith understory (types 3 and 4). 0 1 2 3 4 5 6 7 8 9 10 0102030405060708090100ScoreRelative Humidity (%) Open Open+scattered vegetation Woodland Woodland+understory
188 Figure 4-6. Example of the process to sele ct a cell during mosquito dispersal on the ba sis of vegetation type and number of hosts. As the humidity conditions in the landscape change, the probabilities of selecting cells wi th different qualitie s also change. A host-seeking mosquito is in the dark gray cell and has to choose one of the light gray cells to move to. When humidity is 70% it will have a higher probabi lity of moving to the cell wi th one host and vegetation 4 (p = 0.47). When humidity is 90% it will have almost equal probability of moving to either of the cells with one host but with different vegetation (p = 0.35 for cell with vegetation 4, p = 0.30 for cell with vegetation 1). Vegetation typeHosts Score vegetation Vegetation (A) Hosts (B) Multinomial Probability (A+B)/2 Results rmultinom (100 reps) Score vegetation Vegetation (A) Hosts (B) Multinomial Probability (A+B)/2 Results rmultinom (100 reps) 41 9.520.430.500.4753 6.600.200.500.3531 30 7.710.350.000.1816 5.960.180.000.0910 11 0.480.020.500.2619 3.400.100.500.3033 10 0.480.020.000.010 3.400.100.000.055 10 0.480.020.000.012 3.400.100.000.055 10 0.480.020.000.014 3.400.100.000.056 10 0.480.020.000.011 3.400.100.000.055 20 2.290.100.000.055 4.040.120.000.065 21.911.001.001.0010033.581.001.001.00100 Relative ScoreRelative Score 70% Relative Humidity90% Relative Humidity 4431100000 4431101010 22 1 1100 0 00 1111100000 3321100000 Vegetation typeHosts
189 Figure 4-7. Daily changes in the size of the mosquito population (number of females) for each treatment. Each line represents one simulation using the MM resource finding efficiency for the (A) unfavorable:W1, (B) unfavorable:W2, (C) favorable:W1, and (D) favorable:W2 treatments The blue boxe s indicate the times when the conditions in the landscape were wet or average. Th e age structure of the highlighted (black line) populations is presented in more detail in Figures 4-13 and 4-14.
190 Figure 4-8. Daily changes in th e spatial spread of the mosquito population (percent of cells occupied) for each treatment. Each lin e represents one simulation using the MM resource finding efficiency for the (A ) unfavorable:W1, (B) unfavorable:W2, (C) favorable:W1, and (D) favorable:W2 treatmen ts. The blue boxes indicate the times when the conditions in the landscape were wet or average. Black line is as in Figure 4-7.
191 Figure 4-9. Differences in mosquito produc tion and spatial spread among the treatment s with the MM resource finding efficiency (A) Total mosquito production (MPtotal) and (B) average spatial spread (SStotal) for 10 simulations in each treatment. The letter F denotes favorable landscapes and th e letter U denotes unfavorable landscapes.
192 Figure 4-10. Daily changes in th e percentage of parous females of the mosquito population for each treatment. Each line represents one simulation using the MM resource finding efficiency for the (A) unfavorable:W1, (B) unfavorable:W2, (C) favorable:W1, and (D) favorable:W2 treatments. The blue boxe s indicate the times when the conditions in the landscape were wet or average. Black line is as in Figure 4-7.
193 Figure 4-11. Maximum percentage of parous females per month (PPmonth) in each treatment. Each triangle represents one of ten simulations with the MM resource finding efficiency.
194 Figure 4-12. Daily changes in the average age in days of unfed parous 1 females (days) for each treatment. Each line represents one simulation using the MM resource finding efficiency for the (A) unfavorable:W1, (B) unfavorable:W2, (C) favorable:W1, and (D) favorable:W2 treatments. The blue boxe s indicate the times when the conditions in the landscape were wet or average. Black line is as in Figure 4-7.
195 Figure 4-13. Daily changes in the average age in days of unfed parous 2 females (days) for each treatment. Each line represents one simulation using the MM resource finding efficiency for the (A) unfavorable:W1, (B) unfavorable:W2, (C) favorable:W1, and (D) favorable:W2 treatments. The blue boxe s indicate the times when the conditions in the landscape were wet or average. Black line is as in Figure 4-7.
196 Figure 4-14. Daily changes in average age of unfed parous 1 females for one population per treatment with the MM resource find ing efficiency. The gray bars represen t one standard deviation around the av erage age. (A) unfavorable:W1, (B) unfavorable:W2, (C) favorable:W1, and (D) favorable:W2 treatments. 5 6 7 8 9 10 11 12 13 14 15 16 17 18 171319251713192517131925171319251713192517131925 JuneJulyAugustSeptemberOctoberNovemberAverage age in days 5 6 7 8 9 10 11 12 13 14 15 16 17 18 171319251713192517131925171319251713192517131925 JuneJulyAugustSeptemberOctoberNovemberDulce 5 6 7 8 9 10 11 12 13 14 15 16 17 18 171319251713192517131925171319251713192517131925 JuneJulyAugustSeptemberOctoberNovemberDulce 5 6 7 8 9 10 11 12 13 14 15 16 17 18 171319251713192517131925171319251713192517131925 JuneJulyAugustSeptemberOctoberNovemberAverage age in days A -Unfavorable:W1 B -Unfavorable:W2 C -Favorable:W1 D -Favorable:W2
197 Figure 4-15. Daily changes in average age of unfed parous 2 females for one population per treatment with the MM resource find ing efficiency. The gray bars represen t one standard deviation around the av erage age. (A) unfavorable:W1, (B) unfavorable:W2, (C) favorable:W1, a nd (D) favorable:W2 treatments. 5 7 9 11 13 15 17 19 21 23 25 27 29 171319251713192517131925171319251713192517131925 JuneJulyAugustSeptemberOctoberNovemberDulce 5 7 9 11 13 15 17 19 21 23 25 27 29 171319251713192517131925171319251713192517131925 JuneJulyAugustSeptemberOctoberNovemberAverage age in days 5 7 9 11 13 15 17 19 21 23 25 27 29 171319251713192517131925171319251713192517131925 JuneJulyAugustSeptemberOctoberNovemberDulce 5 7 9 11 13 15 17 19 21 23 25 27 29 171319251713192517131925171319251713192517131925 JuneJulyAugustSeptemberOctoberNovemberAverage age in days A -Unfavorable:W1 B -Unfavorable:W2 C -Favorable:W1 D -Favorable:W2
198 Figure 4-16. Differences in age structure of unfed parous 1 females among treatments with the MM resource finding efficiency. (A) Averages per month of th e daily average age (AAmonth) and (B) averages per month of th e daily standard deviation around the mean age (SDmonth). Each dot represents one of 10 simulations for e ach treatment. The line in plot (A) is provided for reference to compare among panels. Runs in which populations went extinct befo re month 10 or month 11 did not have values of AAmonth or SDmonth; therefore there are less than 10 points for those months.
199 Figure 4-17. Differences in age structure of unfed parous 2 females among treatments with the MM resource finding efficiency. (A) Averages per month of th e daily average age (AAmonth) and (B) averages per month of th e daily standard deviation around the mean age (SDmonth). Each dot represents one of 10 simulations for e ach treatment. The line in plot (A) is provided for reference to compare among panels. Runs in which populations went extinct befo re month 10 or month 11 did not have values of AAmonth or SDmonth; therefore there are less than 10 points for those months.
200 Figure 4-18. Averages per month of the proportion of parous 1 fema les over the age of 12.5 days (PP1month) for each treatment with the MM resource finding efficiency. Each tr iangle represents one of ten simulations.
201 Figure 4-19. Sensitivity of th e total mosquito production (MPtotal) to changes in the resource finding efficiency. (A) The six resource finding efficiency conditions (LH, MH, MM, HH, HL, and HM ) where populations persisted for one or more runs per treatment. (B) Three resource finding e fficiency conditions where popul ations went extinct for all treatments. Notice the differences in scales. The first letter in the resource finding efficiency label de notes the probability of finding hosts and the second the probability of finding oviposition si tes (i.e., LH is low probability of fi nding hosts and high probability finding oviposition sites). The abbrevia tions in the x axis denote the treatments, th e letter F corresponds to favorable landscapes and the letter U to unfavorable landscapes.
202 Figure 4-20. Sensitivity of the average spatial spread (SStotal) to changes in the resource finding efficiency. The letter F denotes favorable landscapes and the lette r U denotes unfavorable landscapes in the x axis label. The first letter in the resource finding efficiency label denotes the probabi lity of finding hosts and the second the probability of findi ng oviposition sites.
203 Figure 4-21. Sensitivity of the maximum percentage of parous females per month (PPmonth) to changes in the resource finding efficiency. (A) Unfavorable:W1 and (B) unfavorable:W2 treatments.
204 Figure 4-22. Sensitivity of the maximum percentage of parous females per month (PPmonth) to changes in the resource finding efficiency. (A) Favorable:W1 and (B) favorable:W2 treatments.
205 Figure 4-23. Sensitivity of the age structures of parous 1 fema les to changes in resource finding efficiency in the unfavorabl e:W1 treatment. (A) Averages per month of the daily average age (AAmonth) and (B) averages per month of the daily standard deviation around the mean age (SDmonth).
206 Figure 4-24. Sensitivity of the age structures of parous 1 fema les to changes in resource finding efficiency in the unfavorabl e:W2 treatment. (A) Averages per month of the daily average age (AAmonth) and (B) averages per month of the daily standard deviation around the mean age (SDmonth).
207 Figure 4-25. Sensitivity of the age structures of parous 1 fema les to changes in resource finding efficiency in the favorable: W1 treatment. (A) Averages per month of the daily average age (AAmonth) and (B) averages per month of the daily standard deviation around the mean age (SDmonth).
208 Figure 4-26. Sensitivity of the age structures of parous 1 fema les to changes in resource finding efficiency in the favorable: W2 treatment. (A) Averages per month of the daily average age (AAmonth) and (B) averages per month of the daily standard deviation around the mean age (SDmonth).
209 Figure 4-27. Sensitivity of the age structures of parous 2 fema les to changes in resource finding efficiency in the unfavorabl e:W1 treatment. (A) Averages per month of the daily average age (AAmonth) and (B) averages per month of the daily standard deviation around the mean age (SDmonth).
210 Figure 4-28. Sensitivity of the age structures of parous 2 fema les to changes in resource finding efficiency in the unfavorabl e:W2 treatment. (A) Averages per month of the daily average age (AAmonth) and (B) averages per month of the daily standard deviation around the mean age (SDmonth).
211 Figure 4-29. Sensitivity of the age structures of parous 2 fema les to changes in resource finding efficiency in the favorable: W1 treatment. (A) Averages per month of the daily average age (AAmonth) and (B) averages per month of the daily standard deviation around the mean age (SDmonth).
212 Figure 4-30. Sensitivity of the age structures of parous 2 fema les to changes in resource finding efficiency in the favorable: W2 treatment. (A) Averages per month of the daily average age (AAmonth) and (B) averages per month of the daily standard deviation around the mean age (SDmonth).
213 Figure 4-31. Sensitivity of the monthly average of the proportion of parous 1 females over 12.5 days of age (PP1month) to changes in resource finding efficiency in the unfavorable landscape.
214 Figure 4-32. Sensitivity of the monthly average of the proportion of parous 1 females over 12.5 days of age (PP1month) to changes in resource finding efficiency in the favorable landscape.
215 Figure 4-33. Changes over time in the abso lute number of gravid females in four simulated populations in the favorable landsca pe. (A) Population in the favorable landscap e, W1 weather pattern, medium:medium (MM) resource finding efficiency. (B) Favorable landscape, W1 weather pattern, high:high (HH) resource finding efficiency. (C) Favorable landscape, W2 weather pattern, MM resource finding efficiency. (D) Favorable landscape, W2 weather pattern, HH resource finding efficiency. 0 100 200 300 400 500 600 161116212616111621261611162126161116212616111621261611162126 JuneJulyAugustSeptemberOctoberNovember 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 161116212616111621261611162126161116212616111621261611162126 JuneJulyAugustSeptemberOctoberNovember 0 100 200 300 400 500 600 161116212616111621261611162126161116212616111621261611162126 JuneJulyAugustSeptemberOctoberNovember 0 1000 2000 3000 4000 5000 6000 7000 161116212616111621261611162126161116212616111621261611162126 JuneJulyAugustSeptemberOctoberNovemberNumber of gravid femalesA -Favorable:W1 MM C-Favorable:W2 MM B -Favorable:W1 HH D -Favorable:W2 HH
216 CHAPTER 5 SOURCES OF ERROR IN THE ESTIMATION OF ARBOVI RUS INFECTION RATES IN MOSQUITOES Introduction There are about 100 arboviruses that can infect hum ans causing considerable morbidity and mortality and another 40 that can infect livestock with important economic impacts (Eldridge et al. 2004). The prevalence of viral infection in field collected mosquitoes is a common surveillance indicator that is used to asse ss the risk of transmissi on of viruses such as West Nile virus (WNV) or western equine encephalomyelitis virus (WEEV) to humans and domestic animals. Other surveillance indicators of risk include sentinel animal seroconversions and animal or human infection data (Moore et al. 1993) When uninfected mosquitoes acquire virus from a vertebrate host they go through a latent phase known as the extrinsic incuba tion period (EIP), which is the tim e that it takes the virus to disseminate into mosquito organs including th e salivary glands from which transmission to subsequent vertebrate hosts o ccurs (Kyle and Harris 2008). Th e duration of the EIP varies among mosquito species, individual mosquitoes, a nd virus species, and is modulated by external factors such as temperature. In this study we refer to those mosquitoes that have the ability to transmit virus as infectious. Uninfected, latent, and infectious mosquitoes can all potentially be found in a sample of mosquitoes collected for arb oviral surveillance. Idea lly we would use that sample to estimate the proportion of mosquitoes in the population that are infectious since this measure would be more directly related to ri sk of arbovirus transmission. This would involve individual mosquito testing for virus disseminatio n to the salivary glands or actual transmission (e.g., salivation into a capillary tube). However, there is no practical way to do this with large numbers of field-collected mosquitoes and, s o, the proportion of inf ected mosquitoes, or infection rate (Chiang and R eeves 1962) is estimated as a substitute (Figure 5-1).
217 It is assumed that when the mosquito inf ection rate increases, the risk of arbovirus transmission also increases (C hiang and Reeves 1962). This assumption relies on the proportion of infected mosquitoes being a good approximation of the proportion of infectious mosquitoes. It also requires reliable estimates of the pr oportion of infected mosquitoes in the population. However, there are many factors that could inva lidate this assumption. Climate variation could introduce unpredictability into how many latent mo squitoes survive to become infectious and the reliability of estimated infection rates can be compromised by biases (discussed below) introduced during mosquito co llecting and virus testing. Temperature is one of the best studied fact ors affecting the EIP and the rate of virus dissemination in a mosquito, thus directly influencing the proportion of latent mosquitoes that become infectious. Laboratory studies have shown that approximately 40% of Culex pipiens mosquitoes infected with WNV will develop a disseminated infection after fifteen days of incubation at 20C, but this fraction increases to almost 90% at 30C (Dohm et al. 2002). In the case of Culex pipiens quinquefasciatus and WNV, 33% of infected mosquitoes will develop disseminated infections after thirteen days of incubation at 25C, and 81% will have disseminated infections af ter thirteen days at 30C (Richa rds et al. 2007). Dissemination is necessary for viral transmission, and some studies report that 90% of Cx. pipiens mosquitoes with disseminated WNV infections transmit the vi rus by bite (Turell et al. 2000, Turell et al. 2001). Another example of temperature modulating transmission is WEEV vectored by Culex tarsalis. In a laboratory experiment 30% of mosquitoes were capable of transmitting virus to chickens after six days of inc ubation at 32C, but the proportion decreased to 20% after twelve days. At 25C, only 4% of mosquitoes were capable of transmission after six days, but the
218 fraction increased to 35% after twelve days (Kramer et al. 1983). A different experiment found that approximately 70% of the infected Cx. tarsalis transmitted virus orally to capillary tubes seven days post-infection at 30C, and after twel ve days this fraction had dropped to ~12%. At 20C about 25% of mosquitoes were transmitting virus after seven days, but the percentage increased to ~60% after twelve days (Reisen et al. 1993). Possible expl anations for a reduction in transmission over time at 30-32 C include the ability of some Cx. tarsalis females to modulate viral dissemination from the mese nteron to the salivary glands or a decrease in the secretory function of the salivary glands due to cell pathology (Kramer et al. 1983, Reisen et al. 1993). Dissemination responses to changes in temperature are non-linear for WEEV in Cx. tarsalis Clearly, temperature is a critical factor that modifies the response of mosquitoes to the virus, and this induced variation reduces our capacity to predict the relati onship between the proportion of infected and infectious mosquitoes. In the field, mosquitoes endure daily changes in temperature and variations of the microclimatic conditions in their resting sites during non-active periods (M eyer et al. 1990). This temperature variability will cause a population of mosquitoes to contai n infected individuals of different ages to be at various stages in the development of a disseminated infection. Consequently, mosquito samples taken on cons ecutive days could yield similar estimated infection rates, but th e infectiousness rate could be di fferent from one day to the next. Ideally, to estimate the proportion of infected mosquitoes in a population we would take a large sample of mosquitoes using an unbiased trapping method such that all individuals are equally likely to be collected. The mosquitoes w ould be tested individually for the presence of the virus with an assay that can detect the sp ecific virus every time a nd at any concentration.
219 Those ideal conditions are usually not met and su rveillance methods introdu ce biases that affect the reliability of the estimated infection rates. Trapping methods often introduce biases since th ey target a particular physiological stage of the adult mosquito population (host-seeking females, gravid fe males, resting adults) or they attract some mosquito species more than othe rs (Moore et al. 1993). Sampling techniques will also affect the sample size obtained, both in absolute numbers of mo squitoes and in the proportion of the population. Because not all mos quitoes are equally likely to be captured, sampling introduces a bias that affects the rela tionship between the actual population infection prevalence and the estimated infec tion rate. Is important to remember that in some cases a collecting bias towards a particular mosquito stage in the population, like gravid females is desirable in order to increase th e chances of detecting virus pres ence in the mosquito population. Other biases are introduced by th e virus detection process. Individual testing of mosquitoes in most cases is not feasible for logistic and fina ncial reasons; thus, a cost-effective alternative to individual testing is to aggreg ate mosquitoes in groups or pools and test those for virus (Chiang and Reeves 1962, Cowling et al. 1999). There are many assays that can be used to detect virus in mosquito pools including plaque assays in Vero cell culture, TaqMan assays (RT-PCR), VecTest, ELISAs, or immunoassays. These assays differ in their power to discriminate among viruses and in their ability to de tect the virus particle s or plaque forming units (PFU) at different concentrations (Ryan et al. 2003, Chiles et al. 2004). The quantity of virus in a mosquito pool a ffects the outcome of the different assays because each assay has a threshold concentration below which virus usually cannot be detected. The quantity of virus in the mosquitoes themselves is affected by time since infection (related to their age) and temperature. The mean body titer of Cx. tarsalis females infected with WNV held
220 at temperatures between 22-30C wa s significantly higher than the t iter in those females held at temperatures between 14-18C (Reisen et al. 2006). In another study with Cx. tarsalis and WEEV, body titers after incuba tion at 15C ranged between 102.8 and 108.7 PFU/body (mean 106.0) for mosquitoes that did not transmit virus into a capillary tube (latent), and between 105 and 108.1 PFU/body (mean 106.9) for those mosquitoes that did transmit the virus (infectious). At 30C the titers ranged between 102.7 and 107.5 PFU/body (mean 105.6) for latent mosquitoes, and between 104.1 and 107.7 PFU/body (mean 106.4) for infectious mosquito es (Reisen et al. 1993). Statistical tests comparing those means were not re ported by the authors. Virus titer distributions for other mosquito-virus systems in the field or in the laboratory are largely unknown. Failure to detect virus can occur when the infected mosqu itoes (or mosquito) present in a pool have low virus titers, and the assay used needs a high conc entration of virus partic les to produce a positive result. After mosquito pool assaying, the information on the number of mosquitoes collected in the sample, the number of pools that tested positiv e for virus, and the number of mosquitoes in each individual pool are used to ca lculate the estimated in fection rate. There are various ways to conduct this calculation but the two most commonly reported are the Minimum Infection Rate (MIR) and the Maximum Likelihood Estimator (MLE) of the proportion of infected mosquitoes. The MIR is the ratio of the number of positive po ols to the total number of mosquitoes in the sample. It is by definition the minimum in fection proportion and it assumes that only one infected individual is present in a positive pool (G u et al. 2003). The MLE is the value of the proportion of infected mosquitoes P that maximi zes the likelihood of n poo ls of size m to be virus positive, where P is the parameter for a binomial distribution (Chiang and Reeves 1962, Walter et al. 1980, Gu et al. 2004). The MIR is considered appropriate to use when infections in
221 the mosquito population are at low levels, but du ring periods of high transmission it will largely underestimate mosquito infections, and so the us e of the MLE coupled w ith variable size pooling is recommended (Gu et al. 2004, Gu et al. 2008). A field study comparing the MIR and MLE estimated infection rates (pool size = 5) with the infection rates calcu lated from individual mosquitoes, did not find major differences am ong the values generated (Condotta et al. 2004), however this pool size is rather small for ar bovirus surveillance and th e lack of a difference might not have much relevance for field studie s. The MLE has the advantage that there are algorithms available that consider varia tions in pool size (Gu et al. 2004). The MIR is perhaps the most often reported measure of virus activity among the mosquito population in the United Sates. Using MIR repor ts, the seasonal activity among mosquitoes has been well characterized for many viruses, more recently for WNV. In the states of Florida (Butler 2004), California (Kramer 2005) and Vi rginia (Gaines 2007), WNV isolates from mosquitoes increase during the months of July th rough September and start declining in October. Virus infections in humans, domestic animals a nd sentinel animals mostly occur during the well characterized transmission season, but it is not unusual to observe virus activity among mosquitoes but no human infections. For exampl e, Anderson et al. (2006) reported a peak of WNV MIR of 7.1 among Culex pipiens mosquitoes from Faifield County, Connecticut during 2004 but no human cases. The ne xt year the peak MIR for Cx. pipiens was 83.9 and there were six human cases. On the other hand the lack of detection of virus among mosquitoes is not necessarily an indication of abse nce of viral activity (Georgia Department of Community Health 2009). Also, the magnitude of the MIR might not always been an indication of the expected number of human cases in different areas. In East Baton Rouge Parish, Louisiana the peak MIR detected in Culex quinquefasciatus mosquitoes during 2002 was 8 a nd there were a total of 49
222 WNV human infection cases (Gleiser et al. 2007) In the City of Davis, California WNV mosquito surveillance during 2006 revealed a peak MIR of 45 for Cx. tarsalis that year, but only 15 human infection cases were reported (Nielsen et al. 2008). Due to the non linear relationship between the MIR and the risk of virus transmi ssion, surveillance program s in different states have adopted thresholds of virus activity above which reactions from authorities and mosquito control are necessary. For example, in Arizona an MIR of 4 or above for WNV from weekly Culex mosquito pools is considered a high level of viral activity and human cases are expected to occur (Frank 2004). In California a MIR of 5 or above for WNV, also from weekly Culex mosquito pools, is an indicator of increased ri sk of transmission and could lead to emergency planning or to the declaration of an epidemic if other risk factor s have also increased concurrently (California Depart ment of Public Health 2009). Mosquito arbovirus assaying has some drawbacks that can hinder its use in regu lar surveillance, such as the low proportion of infected mosquitoes in the population especia lly during interepidemi c periods, the possible detection of virus in mosquitoes when the virus is not alive (using PCR methods), and our inability to easily separate infected and infectious mosquitoes (Day et al. 2003). In this study we asses some of the factors th at affect the assumption that changes in the magnitude of the estimated infection rate among mosquitoes (i.e., MIR or MLE) are associated with changes in the risk of tr ansmission of arboviruses to humans and animals. We examined two basic questions that arise from this a ssumption: does the pr oportion of infectious mosquitoes change with the proportion of inf ected mosquitoes, and can we obtain reliable estimates of infection that re flect changes in the proportion of infected mosquitoes in the population? We used a model to examine how incubation temperature, mosquito survival, mosquito species and virus species, influence th e relationship between th e proportion of infected
223 and infectious mosquitoes (Model I, Figure 5-1). Additionally, we used nu merical simulations to examine how the process of mosquito sampling, poo ling, and virus testing, affect the relationship between the proportion of infected mosquitoes in the population and the proportions estimated from field samples (Model II, Figure 5-1). The va riability in titer distributions that could arise from having mosquitoes of different chronological ages in the population at various stages of virus dissemination was considered. The results of our study are a reminder of why changes in infection rates are not always associated with changes in risk of transmission and that this can be due to both biological and methodological factors. They also indicate that our estimated infection rates usually underestimate the population prevalen ce of infection, that they might not be direct indicators of increases in transmission risk, and that they should always be used in conjunction with other indicators and variables when making an evaluation of virus tr ansmission risk. Integrated approaches toward mosquito surveillance usi ng infection rate in conjunction with other indicators of risk are necessary to assess cha nges in the risk of arbovirus transmission and to determine the actual need for public health alerts. Methods and Results Model I: Relationship between Mosquito Infection and Infectiousness This m odel follows a cohort of mosquitoes that became infected with a virus during the first bloodmeal, and calculates the proportion of those infected mosquitoes that become infectious at different times t as a result of virus dissemination. Data on arbovirus dissemination in mosquitoes from two different and well doc umented mosquito-virus systems were obtained from the literature and were used as parameters in this model: Cx. tarsalis-WEEV and Cx. p. quinquefasciatus-WNV. Two constant incubation temp eratures of 20C and 30C were considered.
224 Following previous similar models (R eisen et al. 1983, Gordon-Smith 1987), the proportion of surviving mosquitoes in a c ohort that are infecti ous at time t (INSt), was calculated as: (5-1) where p is the daily survival rate of the mosquitoes and pt is the proportion of mosquitoes surviving after t days, INFt is the proportion of mosquitoes at time t that carry the virus, and Dt-t1 is the percentage of infected mosqu itoes that show dissemination after t-t1 days of incubation under a particular temperature. Here, t1 is the time (in days) of the first and only infectious bloodmeal. Dissemination was used here as an approximation for infectiousness for the Cx. p. quinquefasciatus-WNV system (Dohm et al. 2002, Rich ards et al. 2007). Data on WEEV transmission by Cx. tarsalis in the laboratory were available (Kramer et al. 1983, Reisen et al. 1993). A single value for the proportion of infected mosquitoes (INFt) was considered for the present model. It was assumed that 1% of the surviving mosquitoes in the cohort became infected with the virus during the first bloodmeal at time t1. This is a combination of the proportion of blood meals taken on in fectious hosts and the probabi lity of infection after an infectious meal. Infection ra tes in cohorts of mosquitoes in the laboratory do not tend to decrease with time at fixed temperatures (Dohm et al. 2002, Reisen et al. 1993). Thus, the proportion of infected mosquitoes was kept constant at 1% of the su rviving mosquitoes at subsequent times. The term INFt included latent and infectious mosquitoes as dissemination progressed over time. The time of mosquito emergence was t0. The model followed the proportion of infected and infectious mosquitoes in a cohort during four gonotrophic cycles. A gonotrophic cycle was
225 considered as the time required for a mosquito to take a bloodmeal, go through oogenesis and lay eggs. We assumed that the mosquitoes can ta ke a bloodmeal immediatel y after oviposition and that they all took the bloodmeal at the same time. We calculated INSt at the end of each of 5 gonotrophic cycles because they marked the time s of a potential bloodmeal, thus the times of potential transmission of the virus from the mosqu ito to a vertebrate host. The times t at which INSt was calculated were: t1 = time of the first bloodmeal and the only bloodmeal when mosquitoes became infected, t2-5 = times of the second, third, fourth and fifth blood meals. Estimates of the minimum duration of the gonotrophic cycle for Cx. tarsalis and Cx. p. quinquefasciatus are shown in Table 1. It has been obs erved for other mosquito species that increases in temperature reduce the duration of the gonotrophic cycle. In a laboratory study conducted on Anopheles albimanus the duration of the gonotrophi c cycle was significantly reduced from 88.4 h (81.8-94.9) at 24C, to 69.1 h (64.6-73.6) at 30C (Rua et al. 2005). This indicates that an increase of 6C would reduce the gonotrophic cycle of this mosquito by an average of 19.3 h. The field calculations of longer lived Cx. p. quinquefasciatus during the winter in Calcutta (Table 51) and the information from An. albimanus support our assumption that the gonotrophic cycle length should decrease about 1 d from 20C to 30C. In this study we consider a gonotrophic cycle of 5 d at 20C and 4 days at 30C, for both species. Time from emergence to the first bloodmeal is about 2 d for Cx. tarsalis and Cx. p. quinquefasciatus (McHugh 1999, Elizondo-Quiroga et al. 2006). A previous modeling study with Cx. tarsalis used a value of 2.5 d from emergence to the firs t blood meal to represen t variations in their calculations (2-3 d) (Reisen et al 1983). Here we consider that at 30C blood meals were taken at 2.5 (first), 6.5, 10.5, 14.5, and 18.5 days of age. Adjusting for a longe r lifespan at lower
226 temperatures we consider that at 20C the first bloodmeal was taken at 3.5 days of age and the subsequent meals were ta ken at 8.5, 13.5, 18.5, and 23.5 days. Two daily survival rates were used in the mode l. A survival rate of p = 0.85 was used for the 30C temperature for both mosquito species, a nd p = 0.90 was used for the 20C temperature. The possible effects of age and infection status on mosquito survival were not considered here. Estimates of survival rates for Cx. tarsalis and Cx. p. quinquefasciatus are shown in Table 5-1. In Calcutta, India, higher surv ival rates were observed for Cx. p. quinquefasciatus during the winter months than for the summer months (Chandr a et al. 1996). Higher surv ival rates at cooler temperatures have also been observed for Cx. tarsalis in the laboratory (R eisen 1995). These observations support the selection of p = 0.90 for the 20C temperature. Rates of dissemination previously repo rted in the literature for WNV in Cx. pipiens complex mosquitoes and for WEEV in Cx. tarsalis studied under constant temperature conditions, are presented in Figur e 5-2. Those dissemination rates were the bases for estimating Dt-t1 at different times in the model. Given that for all mosquitoes the infectious bloodmeal was the first one, t1 was equal to 3.5 d at 20C, and 2.5 d at 30C. The Dt-t1 values for the all time steps are shown in Figure 5-2. The model was implemented using Microsoft Excel (Microsoft Corporation 2007). The mosquito-virus systems selected to illustrate different patterns of dissemination over time are only two among many types in these systems, and simplifications such as constant survival rates, fixed temperatures, and equating dissemination to infectiousness are ac knowledged. However, this model illustrates the variation of patterns th at can arise in the rela tionship between infection and infectiousness and, therefore has broader implications.
227 Results for Model I The results of this m odel illustrate differe nces in viral dissemination in a cohort of mosquitoes at two different temperatur es (Figure 5-3). At 20C, WEEV in Cx. tarsalis starts disseminating faster than WNV in Cx. p. quinquefasciatus. In the cohort, the highest proportion of surviving Cx. tarsalis mosquitoes that became infectious occurred 10 d afte r the infectious bloodmeal (t = 13.5 d). After that, the proportion of infectious mosquitoes decreased due to both mosquito mortality and a declin e in WEEV dissemination. The highest proportion of surviving Cx. p. quinquefasciatus that became infectious at 20C occurr ed 20 d after initial exposure with the virus (t = 23.5 d). Under these cond itions, the peak of infectiousness of Cx. tarsalis with WEEV would be by the third bloodmeal, while for WVN in Cx. p. quinquefasciatus it would be by the fifth bloodmeal, a point not likely to be reached by mosquitoes in nature. At 30C dissemination progressed fa ster for both viruses, and Cx. tarsalis infectiousness with WEEV peaked by the second blood meal (t = 6.5 d). Infectiousness for Cx. p. quinquefasciatus with WNV increased steadily until all surviving mosquitoes became capable of virus transmission by the fourth bloodmeal. Considering both temperature regimens, th e peak of the proportion of surviving mosquitoes that were infected occurred dur ing the first bloodmeal, but the peaks in the proportion of surviving mosquitoes that were infectious occurred da ys after, thus the peaks of infection and infectiousness do not coincide. Thus, variability in dissemination over time causes the proportion of infectious mosquitoes to not be a constant fraction of the number of infected mosquitoes, even under th ese simplified conditions.
228 Model II: Relationship between Population Infection Prevalence a nd Estimated Infection Rate The process of estimating infection rates us ing samples taken from a mosquito population was modeled using numerical simulations. The simulations consisted of sampling a hypothetical population of mosquitoes with a known inf ection rate, and randomly grouping the sampled individuals into pools and, finally, simulating viral assays with different abilities to detect virus (Figure 5-4). Variations were introduced on sample size ( 200, 2000), pool size (20, 50) and in the ability of the assay to detect the virus (low, high). All the si mulations were conducted using R software 2.7.0 (R Development Core Team 2008). Hypothetical mosquito populations consisted of 100,000 individuals. Each population had two attributes: proportion of in fected mosquitoes and a dist ribution of virus titers among infected mosquitoes. Four diffe rent proportions of infected mo squitoes in the population were considered: 1/1000, 5/1000, 10/1000, or 15/1000. Tw o virus titer distributions were used. Distribution 1 had titers between 101.5 and 104 PFU/body, and Distribution 2 included titers between 102 and 106 PFU/body. These patterns a pproximate those observed in Cx. pipiens 4-30 days post-infection with WNV at 18-20C (Distribution 1) an d at 26-30C (Distribution 2) (Dohm et al. 2002). Titers were assigned randoml y to each infected mosquito in the population using a uniform distribution. By randomly assigni ng titers we were assuming that mosquitoes of different ages and at any point in the virus extrinsic incubation period could be collected at any particular time. The two distributions overl ap, but this has also been observed in Cx. tarsalis infected with WEEV and WNV (Reisen et al. 1993, Reisen et al. 2006). Our goal was to determine how these titer distributions interact w ith the virus detection ability of the assays to influence the resulting value of the estimated infection rate.
229 Simple random sample sizes of 200 and 2000 were drawn with replacement so each repeated sample was taken from the original pop ulation. A total of 1000 samples of each size were taken from each hypothetical population. It was assumed that only females were sampled and that they were all equally lik ely to be collected regardless of their age, gonotrophic status or feeding status (empty, bloodfed). These sample si zes were selected to represent small and large values that could be common dur ing surveillance. The probabili ty of the sample containing infected mosquitoes increases asymptotically fo r small and large samples as the proportion of infected mosquitoes in the population increases. Each sample was divided into groups or pools, as is usually done in surveillance studies to screen large numbers of mosquitoes, and each pool was tested for the presence of virus. Two pool sizes were considered, 20 and 50 mosquitoes. Each sample of 200 mosquitoes was divided into 4 pools of 50, or 10 pools of 20. Each sample of 2000 mosquitoes was divided into 40 pools of 50, or 100 pools of 20. The mosquitoes were randomly assigned to each pool. Each simulated pool was individually evaluated for the presence of virus. Plaque forming units of virus were assumed to be individual di screte units, and if more than one infected mosquito was present in the pool their titers were summed. The total PFUs in the pool was then divided by 2.5 to generate a PFU/mL concen tration for each pool, to simulate typical homogenization and extraction met hods (using 2.5 mL of diluent as for VecTest) (Ryan et al. 2003). Two viral assays with differen t virus detection ability were simulated. The first one was an assay that could only dete ct virus at concentrations equal to or greater than 103.8 PFU/mL. This was called the low detec tion ability assay. Th e second one was an assay that detected virus at concentrations e qual to or greater than 102.5 PFU/mL. This was called the high
230 detection ability assay. The concentration thres hold for the low detection ability assay is based on reports that WNV in a pool can be dete cted up to a minimum concentration of 103.8 PFU/mL with VecTest (Ryan et al. 2003), or 103.7 PFU/mL with RT-PCR (Hadfield et al. 2001). The threshold for the high detection ability assay was selected based on reports that both VecTest and RT-PCR can detect virus in pools of 50 Cx. tarsalis containing only one infected female which had been inoculated with 100 PFU of virus and held at 28C for 3 d.14 Culex tarsalis females that were infected with WNV by feeding on infe cted birds developed vi rus titers close to 102.5 PFU/mL, 2 to 3 d post infection (Reisen et al. 2006). This suggests that WNV could be detected at lower levels than other studi es have reported, and we used 102.5 PFU/mL as a conservative threshold. The low detection ability assay will of ten require two infected mosquitoes in a pool using Distribution 2 (only one if titer is 104.2 PFU/mL or higher) to det ect virus, and will always require three or more mosqu itoes using Distribution 1. Once the results for all the pools from a gi ven sample were obtained, the estimated infection rate was calculated for that sample using the Maximum Likelihood Estimator (MLE) (Chiang and Reeves 1962). The MLE was calculated using PoolInfRate 3.0 from the Division of Vector-Borne Infectious Diseases of the Center s for Disease Control and Prevention available at www.cdc.gov/ncidod/dvbid/westnile /software.htm. The MLE expresses the number of infected mosquitoes per 1000 in the population. When all pools are positive, PoolInfRate will not calculate the MLE. Theoretically in that cas e, the estimate of the proportion of infected mosquitoes in the population would be 1 (100% infected). For each of the 8 populations studied (4 infecti on prevalence values x 2 titer distributions), a total of 8 estimated infection rate (MLE) freque ncy distributions was obtained with each of the sampling and testing procedures (2 sample sizes 2 pool sizes 2 virus testing schemes). Each
231 frequency distribution has a particular number of possible MLE outcomes determined by sample size. For example, a sample of 200 can be di vided into 4 pools of 50 while a sample of 2000 mosquitoes can be divided into 40 pools of 50. When one has 4 pools, and 0, 1, 2, or 3 of the pools are virus positive, the only possible MLE outc omes (as calculated with PoolInfRate 3.0) in those cases are 0, 4.93, 11.35, and 20.20 infected mosquitoes per 1000, respectively. To explore which sample sizes, pool sizes, or virus detection assays were more likely to produce estimated infection rates close to the true population inf ection rate, their MLE frequency distributions were compared using descriptive statistics (within population comparisons). The median, the minimum and maximum values, and the percentage of samples that produced estimates under the population infec tion rate (percentage of underest imation), were calculated for each frequency distribution. Even MLE values of 0.01 infected mosquitoes per thousand below the population infection rate were considered underestimates. To determine if the MLE distributions we re different between populations, pairwise comparisons of the distributions were conduc ted using a Kolmogorov-Smirnov test (between population comparisons). The pairwise comparis ons tested differences between MLE frequency distributions for populations with 1/1000 in fected mosquitoes versus MLE frequency distributions for population with 5/1000 infected mosquitoes. It follows that the other comparisons were between 1/1000 versus 10/1000, 1/1000 versus 15/1000, 5/1000 versus 10/1000, 5/1000 versus 15/1000, a nd 10/1000 versus 15/1000. A Bonferroni correction for multiple comparis ons was applied and the overall probability to test the null hypothesis of equal distribut ions was 0.05/6=0.0083. Comparisons were made between distributions that were generated with the same sample size, pool size, and virus detection method. This was necessary because those factors determine the number of outcomes
232 in the distribution, and for the Kolmogorov-Smirnov test one needs the same number of outcomes in both groups being compared. Results for Model II Frequency distributions with a total of 1000 MLE values we re obtained after sim ulated sampling, pooling, and testing of mosquitoes from hypothetical populations. A total of 8 frequency distributions were obtaine d for each population (Figure 5-5). The descriptive statistics for the within population comp arisons of the frequency distributions are shown in Tables 5-2 and 5-3. When hypothetical populations followed viral titer Distribution 1 (101.5-104 PFU/mosquito body), the median MLE values fell well below the population infection rate that th ey were attempting to estimate (Figure 5-6 A and 5-6 B) and underestimation was always above 80% (Table 52). When simulated tests with low virus detection ability were used with samples fr om a population with tite r Distribution 1, virus detection failed in a large number of positive samples and most MLE had values of zero (Table 5-2). For example, we knew that 17.4% of the 1000 samples of size 200 taken for the population with infection rate 1/1000 and Di stribution 1 contained at least one infected mosquito. However, none of those samples produced positive pools after the simulation with the low detection ability assay and the MLE values were all zero. When hypothetical populations had a viral titer Distribution 2 (102-106 PFU/mosquito body) median estimated infection rates (MLE) were relatively closer to the population infection rate, especially when a test with high viral de tection ability was simulated (Table 5-3 and Figure 5-6 C,56 D). However, underestimation remained the rule. The freque ncy distributions with median MLE closer to the true value were obt ained when population infection rates were 5/1000, and the high viral detection ability test was simulated. Sample sizes of 2000 tended to produce
233 frequency distributions with median MLEs that increased with the popula tion values, especially when combined with high viral det ection ability tests (Figure 5-6 D). These results suggest that viral titer interacts with the ability of the test to detect virus, affecting the distribution of MLE outcomes: lower titers are la rgely undetected by assays with low ability to detect virus. Also, simulated la rge sample sizes and assa ys with high detection ability produced median MLE values that best approximated the population infection rate in the hypothetical populations (Figure 56 D). The two pool sizes pr oduced almost identical MLE frequency distributions, thus the impact of pool size in these simulations was minimal. Kolmorogov-Smirnov pairwise comparisons test ed if the MLE frequency distributions were significantly different as the population infection rate s increased (between population comparisons). Significant differences in the MLE frequency distributions were detected only between populations with infection preval ence of 1/1000 and 10/1000, and between 1/1000 and 15/1000, but only when the frequency distributio ns came from samples size 2000 and when the populations had titer Distribution 2 (Table 5-4). Thus estimated infection rates only reflected changes in the actual population infection when the difference in prevalence was 10 times larger or more, and when titers in mosquitoes were high and large samples were taken. Discussion The results of this study sugge st that estim ated infection ra tes are more likely to reflect changes in infection prevalence in the mosqu ito population only when the sampling and virus testing are conducted in the best available conditions (i.e. large sa mples paired with assays that can detect virus at low concentrations). Bu t even under those conditions, infection estimates from samples are highly likely to underestimate the infection rate in th e mosquito population. More importantly, these estimated infection rates ar e not straightforward indicators of changes in the risk of arbovirus transmission. This is due to the variation among mosquitoes to complete
234 the EIP and disseminate virus as a consequence of temperature, the time elapsed after initial infection, and the particular mosquito and virus species. For example, consider the cohort in Model I. If mosquitoes in the cohort were samp led shortly after the ini tial bloodmeal and tested under the best available conditions, the estimate of infection prevalence would be around 1%, the hypothetical population value. However, the risk of transmission at this poi nt is null since there has not been any virus dissemination. On the other hand, if the surviv ing mosquitoes were sampled around the time of the second or th ird bloodmeal, the proportion of infectious mosquitoes would be greater, but there would not be an associated significant increase in the estimated infection rate (still at 1%). Thus wh en similar estimated infection rates are obtained from mosquito samples taken at different times or places, these estimates may not carry the same information about risk of virus transmission. In a la rger context, if similar values of estimates of infection are obtained for the same mosquito-virus system at different time periods, these might not be equivalent due to va riation introduced by differences in mosquito survival and environmental temperature over time. Similar infection rates estimated for two different mosquito-virus systems would also be not comparab le because of the variations in the rate of virus dissemination associated with the biology of the system. Model I is restricted to a si ngle cohort of mosquitoes, but a population would be composed of numerous cohorts of mosquito es at different ages. New mos quitoes are added to populations either constantly or in sporadic recruitments The frequency at which these new mosquitoes acquire new infections or if they remain uni nfected, would impact th e relationship between infection and infectiousness and future stud ies should address thes e additional issues. In order to have a more direct measure of in fectiousness, field collected mosquitoes could be tested individually in the laboratory for viru s dissemination to the salivary glands. Also, traps
235 baited with susceptible hosts could be placed in the field in order to capture biting mosquitoes, test them for virus, and later test the host for infection. In that way, one would have an estimate of mosquito infection paired w ith a measure of transmission (R utledge et al. 2003, Vitek et al. 2008). However, these methods are seldom feasib le, practical, or affordable for long term surveillance programs. Thus, estimated infection rates are necessary, and there is a large body of research dealing with ways to increase the reliability of our estimates of infecti on (Chiang and Reeves 1962, Walter et al. 1980, Abel et al. 1999, Cowling et al. 1999, Gu et al. 2003, Gu and Novak 2004, Gu et al. 2004, Katholi and Unnasch 2006, Gu et al. 2008). One common recommendation is to take large samples of mosquitoes (Gu and Novak 2004, Katholi and Unnasch 2006), because infection is a rare event and a large sample increases the probability of collecting an infected mosquito, improving the accuracy of the estimated infection rate. In the laboratory, grouping mosquitoes in small pools is recommended to minimize the random error of the estimated infection rate, because small pools approach in dividual mosquito testing (Chiang and Reeves 1962, Abel et al. 1999, Katholi and Unnasch 2006). However, smaller pools would make the testing less cost-effective (Cowling et al. 1999), and may be beyond the reasonable limits of public health infrastructures in many areas. The limits of pool size would not only be determined by budget and facilities but also by the maximum pool size recommended for a particular assay on the basis of its chemistry (Chiang and Reeves 1962, Katholi and Unnasch 2006). Results from our numerical simulations point to the ability of an assay to detect virus, together with the sample size, as very important factors affecting the reliability of the estimates of infection. When viral titer s in the population were low (Dis tribution 1) or the population infection rate was low (1/1000), the viral assay with low viru s detection ability (meaning it
236 needed relatively high concentrations of virus to produce a positive result) frequently underestimated (or failed to detect ) the population infection prevalen ce. Therefore, using assays with the highest known detecti on ability is recommended. As ideal conditions to estimate infection rates (large samples, small pools, and assa ys high ability to detect virus) are difficult to achieve, it is of utmost importance to unde rstand how biases accumulate throughout the estimation process and to be aware of them when making assessments or decisions about transmission risk based on infection rates. One of the most important goals when monitori ng infection rates is to detect changes that could be related to increased risk of arbovirus tr ansmission to animals and humans. In order to determine if changes are unusual, it is necessary to calculate a baseline infection rate (Shroyer 1991). Increases in infection ra tes could occur prior to or during outbreaks due to virus amplification events when biolog ical and environmental factors are ideal for large numbers of mosquitoes to transmit virus to a large population of susceptible amplifi cation hosts (Day 2001). Infection rates could also change after viremic hos ts are introduced into an area (Broom et al. 1995). The reliability of the methods that we use to estimate infection rates, and the range of the baseline information that we have, will determ ine our capacity to identify unusual changes in virus activity. However, in addition to baseline estimate d infection rate data, information on other mosquito population parameters and climate vari ables is necessary to determine if unusual arboviral transmission is occurring. Monitoring changes in the abundance of parous females, changes in the relative abundan ce of the total mosquito popula tion, temperature, and rainfall patterns are necessary indicators th at should be used in conjuncti on with estimated infection rates in assessing risk (Moore et al. 1993). These should also be inve stigated for extended periods to
237 determine baseline patterns during transmission s eason and then compare these values to periods of epizootic and epidemic transmission. The use of multiple criteria for the assessment of the risk of arbovirus transmission is in use in states like California and Florida, for ex ample. Surveillance progr ams have a series of criteria to determine the level of risk of mos quito-borne arbovirus transmission and have defined the appropriate responses according to the assesse d level of risk (California Department of Public Health 2009, Florida Department of Health 2009). Data on factors such as weather conditions, vector abundance, mo squito infection rates, sentin el chicken seroconversion, dead bird detection and human cases is contrasted to hi storical data to determine the level of risk (e.g., normal season versus emergency) and the actions that need to be taken (public announcements, mosquito control, etc.) (Calif ornia Department of Public H ealth 2009, Florida Department of Health 2009). We acknowledge that the risk of transmissi on is not only a function of the proportion of infectious mosquitoes in a population, but also a function of th eir abundance and biting preferences. Recently, new measures of risk as sessment have been proposed and could be more useful when comparing the risk in different areas or seasons, or the risk arising from different mosquito species. These are (a) the density of in fected mosquitoes, resulting from the product of mosquito abundance and the estimated infection prevalence (Ezenwa et al. 2006, Gu et al. 2008), (b) the probability that a mosquito species wi ll infect a mammal (Kilpatrick et al. 2005), calculated as the product of a bundance, proportion of blood meal s taken from mammals, the estimated infection rate, and the fraction of inf ected mosquitoes that will subsequently transmit virus by bite, and (c) the vector index, which cons iders multiple species and is calculated as the summation of the product of the average number of mosquitoes of each species per trap, times
238 the proportion of infected mosquito es on each species (Gujral et al. 2007) Even though some of these indicators of risk need more parameters and consequently need to meet more assumptions, they might be better than infec tion rates alone given that they c onsider more complexities of the systems under surveillance. The calculation of the parameters for these risk estimates for different species and for different geographical areas is necessary. If used for surveillance, indicators of risk should not be aggregated ove r broad areas or long periods of time in order to account for the spatio-temporal heterogeneity in virus transmi ssion (Gu et al. 2008). In addition to the factors examined here, there are many others that may influence the relationships between infection rates and risk of transmission. For example, the risk of transmission of a particular virus can change when multiple mosquito vector species are considered together. Virus strains could also vary in their dissemination rates under different temperatures (Kilpatrick et al. 2008), adding another level of complexity to the relationship. In this study, we did not examine other environmental factors such as larval rearing conditions that can affect the susceptibility of mosquitoes to become infected and/or infectious (Alto et al. 2005). In our second model we simulated two viral tit er distributions and we found that they were very important to determine the bias of th e MLE (low viral titers resulted in large underestimation). However, empirical data on the distribution of viral titers in field collected mosquitoes is limited. One study documented coarse variations in titers among different virus and mosquito species over space and time, and s uggested that monitoring hi gh titers of virus in mosquitoes in the field could help to identify species with higher vector competence, and to observe the effects of temperature in the progres sion of the virus amplification cycle (Nasci and Mitchell 1996). In our study we assumed that vi ral titers can be summed when more than one
239 infected mosquito is present in a pool, but it is necessary to investigate how having multiple positive mosquitoes in a pool determines virus con centration. We did not consider other factors that could introduce biases and error in estimati on, such as trapping biases and the false positive detection of virus. In Florida, field experiment s using sentinel chickens to estimate the rate of virus transmission by Culex nigripalpus showed that transmission is low in relation to estimated infection rates (Rutledge et al 2003, Vitek et al. 2008), and many f actors that we studied here were considered to explain this occurrence. These field studies support that the in corporation of information on the mosquito population (age struct ure, abundance and estimated infection rate), virus (strain, species-specific dissemination rates) and the environment (temperature) are necessary to make assessments of the risk of virus transmission. The results from our simplified models remind us that estimates of mosquito infection prevalence may not be directly re lated to the risk of transmissi on of arboviruses to animals and humans. The general assumption that increases in infection rates indicates increases in the risk of arbovirus transmission might not be reliable as supported by fi eld data. It is important to remember that (a) there are biases that sampling and virus testing methods introduce in our estimates which will cause them to generally underestimate the populati on infection rate; (b) similar estimated infection rates across locations time, and for different mosquito and virus species, might not indicate similar risk of arbovirus transmission due to variations in dissemination rates; (c) arbovirus baseline data are necessary to define unusual changes in transmission activity; and (d) the use of othe r surveillance indicator s in conjunction with estimated infection rates is necessary to fu lly assess the risk of arboviral transmission.
240 Table 5-1. Duration of the gonotrophic cycle and daily surviv al rates obtained fr om the literature for Cx. tarsalis and Cx. p. quinquefasciatus. Species Minimum duration of gonotrophic cycle Daily survival rate ( p ) Location of collection Reference Cx. tarsalis 4 d 0.87 Bakersfield, Kern County, CA: May and August. Average temperatures for Bakersfield are 22C(May), 29C (August) (Country Studies US 2003) Reisen et al. (1983) 5 d 0.84 Sheridan, Placer County, CA: July. Average temperatures for Yuba City (30 km NW of Sheridan) is 25C (July) (Country Studies US 2003) McHugh (1999) Cx. p. quinquefasciatus 6 d 0.91 Calcutta, India: winter months. Winter temperatures in Calcutta range between 12 and 27C. (Kolkata UK 2008) Chandra et al. (1996) 4 d 0.81 Calcutta, India: summer months. Summer temperatures in Calcutta range between 24 and 38C. (Kolkata UK 2008) Chandra et al. (1996) 2-3 d 0.87-0.88 Monterrey, Mexico: June. Mean annual temperature in Monterrey is 28C. Elizondo-Quiroga et al. (2006)
241 Table 5-2. Results of Model I for mosquito po pulations with viral t iter distribution 1 (101.5-104 PFU/mosquito). Median MLE, minimum and maximum values (Min-Max), and percentage of underestimates (MLE values under the population infection rate) for 32 frequency distributions. Low virus detection ability ( 103.8 PFU/mL) High virus detection ability ( 102.5 PFU/mL) Population Infection rate Sample size Pool size Median MLE Min-Max %Underestimate Median MLE Min-Max %Underestimate 1/1000 200 20 0 0 100 0.00 0-10.51 99.80 50 0 0 100 0.00 0-11.35 99.90 2000 20 0 0 100 0.50 0-2.03 82.60 50 0 0 100 0.50 0-2.08 82.30 5/1000 200 20 0 0 100 0.00 0-16.68 91.90 50 0 0 100 0.00 0-20.20 92.80 2000 20 0 0-0.50 100 2.03 0-6.90 98.50 50 0 0-0.50 100 2.08 0-7.71 97.80 10/1000 200 20 0 0-4.99 100 4.99 0-23.67 81.50 50 0 0-4.93 100 4.93 0-20.20 83.20 2000 20 0 0-0.50 100 4.14 0-10.43 99.80 50 0 0-0.50 100 4.39 0-10 99.90 15/1000 200 20 0 0 100 4.99 0-31.77 97.30 50 0 0-4.93 100 4.93 0-20.20* 98.00 2000 20 0 0-0.50 100 4.14 0.5-9.23 100.00 50 0 0-0.50 100 4.39 0.5-10.83 100.00 *2 of the samples produced all positive pools and were excluded because MLE cannot be calculated with all positive pools.
242 Table 5-3. Results of Model I for mosquito po pulations with viral t iter distribution 2 (102-106 PFU/mosquito). Median MLE, minimum and maximum values (Min-Max), and percentage of underestimates (MLE values under the population infection rate) for 32 frequency distributions. Low virus detection ability ( 103.8 PFU/mL) High virus detection ability ( 102.5 PFU/mL) Population Infection rate Sample size Pool size Median MLE Range Min-Max %Underestimate Median MLE Range Min-Max %Underestimate 1/1000 200 20 0.00 0-4.99 92.30 0.00 0-10.51 85.30 50 0.00 0-4.93 92.30 0.00 0-11.35 85.30 2000 20 0.50 0-2.03 80.00 0.50 0-3.60 52.50 50 0.50 0-2.08 80.10 0.50 0-3.79 53.20 5/1000 200 20 0.00 0-23.67 92.60 4.99 0-31.77 80.70 50 0.00 0-20.20* 93.30 4.93 0-20.20* 85.50 2000 20 2.03 0-6.34 98.80 4.14 1-11.04 75.30 50 2.08 0-7 97.30 3.79 1.01-10.83 70.90 10/1000 200 20 4.99 0-23.67 80.80 4.99 0-31.77 58.80 50 4.93 0-20.20 82.60 4.93 0-20.20* 62.30 2000 20 4.14 0.50-9.23 100.00 7.47 2.03-16.20 86.10 50 4.39 0.50-9.21 100.00 7.71 2.08-14.51 78.40 15/1000 200 20 4.99 0-41.38 86.10 10.51 0-53.20 63.70 50 4.93 0-20.20* 91.90 11.35 0-20.20* 75.20 2000 20 6.90 2.03-14.20 100.00 10.50 4.68-21.94 88.90 50 7.00 1.54-14.51 100.00 11.69 4.39-24.86 83.20 *Some samples (<5%) produced all positive pools and were exclude d because MLE cannot be calculated with all positive pools.
243 Table 5-4. Results of the Kolmogorov-Smirnov te st comparing MLE fre quency distributions from Model II. Significant differences ex isted among the distributions obtained for populations with infection ra te 1/1000, and populations with infection rate 10/1000 or 15/1000. Bonferroni correction was applied (alpha = 0.05/6). 1/1000 vs. 10/10001/1000 vs. 15/1000 Ability to detect virusPool sizeD p D p Sample size 2000 viral titer distribution 2 Low 20 0.46 8.10x10-4 0.51 1.20x10-4 50 0.33 0.07 (NS) 0.47 3.00x10-3 High 20 0.32 0.04 (NS) 0.46 8.10x10-4 50 0.40 0.02 (NS) 0.43 7.00x10-3 NS = no significant difference.
244 Figure 5-1. Relationships studied with Model I and Model II. The direct estimation of the proportion of infected mosquitoes th at are infectious is not practical; in stead the proportion of infected mosquitoes is estimated and us ed to assess risk. For this estimation to be useful in the assessment of risk it is important to understand the relationships between infected and infectious mosquitoes, and between the population infection rate and its estimate. Model II: Relationship between proportion of infected and estimated infected Proportion of INFECTED mosquitoes in a population at time t ESTIMATED proportion of infected mosquitoes in a population at time t Proportion of infected mosquitoes that are also INFECTIOUS in a population at time t ESTIMATED proportion of infected mosquitoes that are also infectious in a population at time t Direct estimation is not practical. The proportion of infected mosquitoes is estimated instead and used to assess risk. Surveillance estimate Mosquito populationModel I Relationship between proportion infected and infectious
245 Figure 5-2. Dissemination of virus in mosquito es at different temperatures. Each panel shows two dissemination curves with val ues taken from the literature (references cited in parenthesis in legends), and a third curve of values that were estimated and used as parameters ( D ) for Model I. (A and B) West Nile virus dissemination in Culex pipiens and Culex pipiens quinquefasciatus. (C and D) Western equine encephalomyelitis virus dissemination in Culex tarsalis For the Cx. tarsalisWEEV system, percentages correspond to oral transmission and not dissemination, and the values were approximated from figures in the original publications. 80 60 90 100100 81 20 70 1001000 20 40 60 80 100 120 0 5 10152025 30C (Dohm et al. 2002) 30C (Richards et al. 2007) 30C (D) 0000 40 25 40 33 00 40 500 20 40 60 80 100 120 0510152025 20C (Dohm et al. 2002) 25C (Richards et al. 2007) 20C (D) 30 20 50 70 40 12 000 40 60 40 100 20 40 60 80 100 120 0510152025 32C (Kramer et al. 1983) 30C (Reisen et al. 1993) 30C (D) 25 60 65 50 45 20 45 4 35 36 10 70 50 300 20 40 60 80 100 120 051015202530 20C (Kramer et al. 1983) 25C (Reisen et al. 1993) 20C (D)Days of incubation (t-t1)B(c) (a)Percentage of mosquitoes with disseminate infection (infectious)D A Cx. p. quinquefasciatus -WNV C Cx. tarsalis WEEV
246 Figure 5-3. Relationship between infection a nd infectiousness, modified by incubation time and temperature on two mosquito-viru s systems studied with Model I. The number of mosquitoes in the cohort declin es over time (daily survival rate p = 0.90 at 20C, p = 0.85 at 30C), and 1% of the surviving mosquitoes ac quire virus during the first blood meal. The proportion of infectious mosquitoes in the cohort changes as disse mination occurs. Simulated dissemination for WEEV in Culex tarsalis shows a different pattern than simulated dissemination for WNV in Culex pipiens quinquefasciatus at both temperatures. 30C 05101520 Infected Infectious Cx. p. quinquefasciatus WNV Infectious Cx. tarsalis WEEV Time (days) 20C 0510152025Proportion of surviving mosquitoes in the cohort 0.000 0.002 0.004 0.006 0.008 Time of first bloodmeal
247 Figure 5-4. Design for the simulations of Model II to study the re lationship between proportion of infected mosquitoes in a pop ulation and the infection rate. POPULATION INFECTIONProportion of infected mosquitoes in a population at time t 1/1000 5/1000 10/1000 15/1000 Population size 100,000 SAMPLINGSimple random sample size 200 2000 POOLINGSample divided into pools (groups) of mosquitoes 20 50 Titers summed if more than one infected mosquito present in the pool VIRUS TESTINGAbility of the assay for virus detection: concentration above which virus is detected in the pool Low=10 3.8PFU/mL High=102.5PFU/mL ESTIMATED INFECTIONEstimated proportion of infected mosquitoes in a population at time t Estimated infection rate MLE Each infected mosquito had a virus titer at the moment when it was sampled Distribution 1= titers from 101.5to 104 PFU/body Distribution 2= titers from 102to 106 PFU/body
248 Figure 5-5. Results of Model II for the population with 15 infected mosquitoes per 1000 and virus titer distribution 2. Each of the eight frequency distributions has 1000 MLE values. Notice how the majority of outcomes fell below the population infection rate (dashed vertical line) that they attempt to estimate. Descriptiv e statistics for these di stributions can be foun d in Table 4. Sample size 2000 051015202530 High detection ability, pool = 50 Low detection ability, pool = 50 High detection ability, pool = 20 Low detection ability, pool = 20 MLE Sample size 200 0102030405060Frequency in 1000 samples 0 100 200 300 400 500 15/1000 infected mosquitoes in the population
249 Figure 5-6. Median outcomes of the estimated infection rates (MLE) resulting from Model II. The median outcomes (MLE) of the frequenc y distributions (see Ta bles 5-2 and 5-3) were obtained after simulated sampling a nd testing of mosquitoes coming from hypothetical populations with increasing infection prevalence (1, 5, 10, and 15 infected mosquitoes per 1000). Plots A and B correspond to median MLE outcomes for populations with viral titer Distribution 1. Note that the estimation usually did not differ between using different pool sizes, so the lines are sometimes superimposed. Plots C and D correspond to median MLE outcomes for populations with viral titer Distribution 2. A gray solid line indicati ng the perfect agreement between population prevalence and estimated infection rate is included for comparison purposes. Titer Distribution 2 0246810121416 0 2 4 6 8 10 12 14 16 Sample size 200 Titer Distribution 1 0 2 4 6 8 10 12 14 16 0246810121416 Number of infected mosquitoes in the population (per 1000 mosquitoes) Sample size 2000 Perfect agreement High detection ability, pool = 50 Low detection ability, pool = 50 High detection ability, pool = 20 Low detection ability, pool = 20 Estimated number of infected mosquitoes per 1000 (MLE)C A D B
250 CHAPTER 6 GENERAL DISCUSSION The monitoring of mosquito populations is an important component of some arbovirus surveillance programs in Florida. Mosquito populations are primarily monitored for increases in abundance. Besides abundance, changes in the proportion of parous fema les in the population can be tracked by examining the parity status of field collected mosquito es (Moore et al. 1993). The proportion of parous females is important becau se it is an approximation of the fraction of older females in the populati on that have completed at leas t one gonotrophic cycle. These females could be potentially infectious if they were previously exposed to a virus during a bloodmeal. Mosquitoes can also be tested for virus presence to obtain an estimate of the proportion of mosquitoes that have come into co ntact with viruses in th e past (Rutledge 2004). Surveillance activities can benefit from new information about the causes of changes in mosquito population size and in the proportion of pa rous females. If estimates of the proportion of infected mosquitoes are obtai ned from mosquito samples, it is also important to know how reliable these estimates are when using them for surveillance. The result s from the present work can contribute to an understanding of the external causes of varia tion in mosquito population size and age structure. The results can also he lp to identify some of the biological and methodological factors that can infl uence the reliability of estimate s of infection obtained from samples of field colle cted mosquitoes. Culex nigripalpus is one of the most important vectors of arboviruses in Florida. The population dynamics of this mosquito are clos ely linked to environm ental conditions. For example, Cx. nigripalpus population size increases with ra infall (Provost 1969, Nayar 1982, Day and Curtis 1994), and temperature, rela tive humidity, moon phase and wind affect Cx. nigripalpus activity (Bidlingmayer 1974, 1985). In Chap ter 3, data from a field study conducted
251 in Indian River County, Florida, were used to de velop the first multivariate regression model for the prediction of changes in Cx. nigripalpus relative abundance. Variables not previously evaluated for their associations with Cx. nigripalpus abundance such as the Keetch Byram Drought Index (KBDI) and daily modeled water ta ble depth (MWTD) were included in model development. A multivariate regression model was also developed to predict changes in the proportion of parous Cx. nigripalpus females. There were no previous models exploring the relationships between Cx. nigripalpus parity and environmental vari ables, but univariate models for other species had shown that temperature and ra infall can be associated with parity changes in Culex mosquitoes (Reisen et al. 1983, 1986). A m odel to predict the abundance of nulliparous females was also developed. The model for mosquito relative abundance e xplained 60% of the variability observed in the field and supported associations between mosquito relative abundance and the minimum temperature, MWTD, and KDBI, all averaged acr oss the 0-6 days prior to collection. Moon illumination and collection site were also explanatory variables in the model. Models to forecast the times of highest mosquito abundance such as the one presented in Chapter 3, can complement empirical knowledge of mosquito ac tivity and can help improve planning of control activities such as a dulticiding. The Florida Departme nt of Health (2009) guidebook for arbovirus surveillance states that the number of mosquitoes collected is not as important as the day-to-day changes in the number collected. M odels such as the one presented here for the prediction of changes in the number of nulliparous females, could help make predictions of approximate dates when the population size could dramatically change in the near future. The associations found in the model between Cx. nigripalpus abundance, MWTD and KBDI support other arbovirus surveillance activities in Florida. These indicators (MWTD and
252 KBDI) are already in use for the monitoring of the weather events that can favor arbovirus epidemics in the state (Day and Shaman 2008). It was observed here that decreases in the MWTD and increases in the KBDI have a negative impact on mosquito abundance. Both of these variables are indicators of oviposition site availabil ity and humidity conditions. Hydrological models have been used to model the water table depth profiles of years during which St. Louis encephalitis epidemics have occu rred in Florida (Day and Shaman 2008). These years were characterized by a part icular pattern of changes in th e water table depth: drought in late spring, wet event in early summer, drought in late summer, and wet event in the fall (Day and Shaman 2008). Based on our m odel results, we can expect Cx. nigripalpus populations to increase in size during the early summer and in th e fall of epidemic years, and to decrease during the spring and late summer. The proportion of parous females in the popul ation was estimated from dissected fieldcollected Cx. nigripalpus females using the Detinova tracheol ar distension method (Detinova 1962). The effects of environmental variables on the proportion of parous females were assessed with a generalized multiple lin ear regression model. The mode l explained about 45% of the variation observed in the field. The model pr ovided good predictions of the times when parity decreased, most likely as a consequence of la rge emergences of young mosquitoes 7-14 days after increases in precipitation a nd temperature. Other causes of decreases in parity suggested by the parameters in the model were reductions in te mperature and rainfall in the 0-6 days prior to collections and low ground water av ailability 7-14 days prior. The results of the parity mode l also supported previous stud ies indicating that prolonged dry periods (no heavy rainfall of 50 mm within 3 days lasting fo r 10-20 days, Day et al. 1990) followed by rainfalls can cause a dramatic increase in the proportion of parous females. This is
253 followed by declines in parity when large num bers of new mosquitoes emerge. Dramatic increases in parity indicate times when a larg e number of mosquitoes simultaneously become host-seeking. Some of these mosquitoes might be old enough to transmit pathogens if they were previously infected. Here we observed for the year 2008 that after more than 10 days without heavy rainfall, the proportion of parous females (gravid females that oviposited) increased to more than 50% with the arrival of heavy rain. This increase in parity was predicted by the model. Monitoring changes in the number of gravid females provides valuable information to study changes in the structure of the population, but requires sp ecialized collection techniques (aspirator collections). Mon itoring changes in parity coupled with weather information can provide similar predictions and can be done with unfed mosquitoes captured in traps regularly used to monitor changes in mosquito abundance. The scoring of mosquitoes parity status with the Detinova method is also easily imp lemented and provides good results for Culex mosquitoes. The models did not fully explain the ch anges in population size and parity in Cx. nigripalpus Many factors could have contributed to this includi ng biases in population size estimates due to the type of trap used for collec tions, or not considering other biological factors, such as population feedbacks, in the model. Mosquito production and oviposition in aquatic habitats that are less dependent on rainfall was considered as a po ssible cause of variation that was not explained by the model. The preferences of mosquitoes for different types of oviposition sites (containers, ditches, lakes, grassy pools, etc.) or for permanent versus temporary sites (based on their dependence on ra infall) should be studied furthe r. If mosquitoes are capable of discriminating among types of oviposition site s, maybe this has an effect on population changes. Preferences for temporary sites after rainfall evidently contributes to synchronized
254 emergence of mosquitoes. But the abundance an d location of sites where mosquitoes oviposit during drier periods could help explain spatia l variability in mosquito production, population size, and the changes in parity pr oportions that are not directly related to increases in rainfall. Culex nigripalpus is a highly dispersive mosquito that will leave secluded wooded areas to search for resources in open areas when relativ e humidity is high (Day and Curtis 1994). The flight activity of this mosquito is affected not only by relative humidity, but also by temperature, moon illumination and wind (Bidlingmayer 1985, Day and Curtis 1989, Day and Edman 1988, Day et al. 1990, this work). As shown in the field study in Chapter 3, the proportion of parous females (an approximation of age structure) can be influenced by external factors such as rainfall, ground water availabi lity and temperature. We speculated that those environmental factors that could modify flight activity could also affect the times required by a mosquito to fi nd a bloodmeal or an oviposition site, therefore affecting parity rates and age structure. Additio nally, the individual efficiency of a mosquito to find resources (probability of fi nding a host, taking a bloodmeal, or finding an oviposition site) could affect the time a mosquito spends searching. We hypothesized that these external factors can partially determine the age distribution of mosquitoes that have completed gonotrophic cycles. Other factors that affect age structure include mosquito daily su rvival and environmental temperature. Temperature affects survival rate s, the time required for immature development, and the time that it takes for eggs to develop in the mosquito after a bl oodmeal (Clements 2000). The effects of changes in survival rates or temperature on the age structure of females were not explored in this study in detail in order to focus on the eff ects that mosquito behavior and resource availability have on the amount of time re quired to take a bloodmeal or to lay eggs, and subsequently on mosquito age.
255 In Chapter 4, an individual-based model was designed to simulate the dispersal and searching behavior of adult Cx. nigripalpus females. Heterogeneous environments that changed in space and time were also simulated. We examin ed the effects of mosquito searching behavior, landscape structure, and weather changes on the age distribution of unfed parous females. The chronological age of unfed parous females wa s expressed as the time in days since adult eclosion. The chronological age distribution of parous females is important because these females have taken at least one bloodmeal and c ould have become infected with virus. The proportion of older parous females is an index of the potentially infectio us mosquitoes in the population that are searching for a bloodmeal and could infect a susceptible host. There are no measures of the chronological age distributions of mosquitoes in the field. The results of this modeling study provided a th eoretical description of the chronological age distribution of parous mosquitoes and its variability within a day and from day-to-day. The study also provided information on some of the possible causes of age structure variation. It was observed that the averag e age of unfed parous mosquito es in the population can shift towards younger or older ages depending on si mulated environmental events and mosquito behaviors. The two factors in this model that in troduced more variability in the age structure of the unfed parous mosquitoes were: (1) reductions in the efficiency of individual mosquitoes in finding resources (reduced probabil ities of finding hosts and ovipos ition sites) and (2) simulated weather changes when mosquitoes were in the more complex landscape. Mosquito resource finding efficiency was defi ned by the probability of finding hosts (high, medium or low) and the probability of findi ng oviposition sites (high, medium or low). Inefficient mosquitoes were those with low :low, low:medium, medium:low, medium:medium, low:high, or high:low probabilities of finding hosts and oviposition sites, respectively.
256 Efficient mosquitoes were those with hi gh:high, high:medium or medium:high resource finding probabilities. Inefficient mosquitoes moving within variable environments resulted in a wider range of ages for unfed parous females, indicating more variability in the time required to take a bloodmeal and/or find oviposition sites. Ine fficient mosquitoes completed fewer gonotrophic cycles than efficient mosquitoes. This negativ ely affected the size and spatial spread of the population and frequently led to pop ulation declines and extinctions. In contrast, more efficient mosquitoes resulte d in more mosquitoes completing at least the first gonotrophic cycle leading to population growth, spatial spr ead of the population, and less variability in the age ranges of unfed parous mosquitoes. When the favorable landscape was used for simulations the age di stribution of unfed parous mosquitoes showed changes in response to simulated weather. Months that had wet or average conditions caused a reduction in the average age of females, regardless of the searching efficiency of mosquitoes. This suggested th at during a wet or average month, mosquitoes required less time to find hosts or oviposition si tes because mosquitoes were more active and more oviposition sites were available. The mode l also showed that during periods of dry conditions or lower temperatures (when mosquito activity was reduced), shifts of the age structure to older ages occurre d. Reduced mosquito activity proba bly increased the time to take a bloodmeal or oviposit. The model results suggest that mosquito res ource searching behavior and environmental changes (reductions in humidity and temperature, variation in the number and distribution of oviposition sites) are two important sources of variability in population age structure, population size and spatial spread. Other possible sources of variability include mosquito survival,
257 fecundity, and temperature effects on development. Those were not explored in the model and were held constant. The regularity of older ages of Cx. nigripalpus females during dry conditions observed in the model supports previous observations that dry periods (no heavy rainfall 50 mm in 3 days) lasting between 10-20 days could induce gravid fe males to hold their eggs until new oviposition sites become available (Day et al. 1990). Gravid females that do not ovipo sit in 10 or more days could complete the viral incubation of a vi rus (10-14 days) during a single gonotrophic cycle (Day et al. 1990, Day and Curtis 1994). In th e model, gravid females accumulated for a few consecutive days during dry conditions because they became less active and did not oviposit. However gravid female numbers declined due to mortality and the presence of permanent oviposition sites. This highlights the need for more research on the role of permanent and temporary (rainfall depende nt) oviposition sites, on Cx. nigripalpus population dynamics and to examine the preferences of gravid Cx. nigripalpus females for different types of oviposition sites. Field studies could be conducted to determine if Cx. nigripalpus females have differential preferences for fresh oviposition sites that appear after rainfall versus old oviposition sites. Oviposition sites in the field could be followed ove r time and their colonization status could be monitored and the physical and biological properties of the oviposition site examined. More research is necessary on mosquito resour ce searching behavior. Little is presently known regarding how host or oviposition site ab undance and distributi on over space affect mosquito searching efficiency. The effects of different host species and their relative abundance on the probability of mosquitoes taking a bloodm eal are also not known. This could be very important because f eeding patterns of Cx. nigripalpus change from mostly a host preference for birds during the spring season, to increased feeding on mammals during the summer and fall
258 months (Edman and Taylor 1968). More laborato ry experiments could be conducted to study the effect of host species and relativ e abundance on the time required to take a bloodmeal. Hosts of different species could be placed together in the same cage to be offered to mosquitoes and the time to take a bloodmeal could be observed. Thes e experiments could be carried out at various mosquito densities. Given that the fitness of fiel d mosquitoes is difficult to determine, models that explore strategies to increase fitness in heterogeneous environments could be a first step towards better understanding mosqu ito resource searching behavior. In order to improve simulations of the mos quito environments in models, studies on the abundance and spatial distribution of hosts and ovi position sites in the fi eld could be conducted. Simplified representations of the distribution an d abundance of hosts and oviposition sites have been used in previous models that consider the effects of mosquito dispersal on parasite transmission (Smith et al. 2004, Le Menach et al. 2005, Gu and Novak 2009). Host and oviposition site distribution, and mosquito sear ching behavior, have been found to be very important factors that determine the distribution of infectious mo squitoes (Smith et al. 2004, Le Menach et al. 2005) and the prevalence of inf ection among hosts (Smith et al. 2004, Le Menach et al. 2005, Gu and Novak 2009). Another model ev aluated the effects of host and oviposition site spatial distributions on the likelihood of arbovirus amplificat ion, and found that when hosts and water sources were in close proximity the pr obability of infection in amplification hosts (such as birds) increased considerably (Shaman 2007). The use of heterogeneous environments in the present model was also motivated by models on the dispersal and reproductive behavi or of ground beetles in agricultural landscapes (Sndgerath and Shrder 2002, Benjamin et al. 2008) These models addr essed the importance of spatial connectivity a nd the fecundity of beetles in different habitats on the viability of ground
259 beetle populations and their spatial spread. Th ese models predicted th at the existence of stepping stone habitats where beetles can successfully reproduce, highly favors population spread, especially for those species with limited dispersal capability. The Cx. nigripalpus model presented here suggested that the spatial distri bution of oviposition sites can affect the expansion of mosquito populations. However, the impact of oviposition site availa bility on the expansion of mosquito populations appeared to be depende nt on mosquito resource finding efficiency. Culex nigripalpus preferences for oviposition sites, the spatial distribution of oviposition sites, and immature mosquito survival on different qua lities of oviposition sites, probably have an influence on the spatial expansion of the mosquito population. The field and modeling study conducted here on Cx. nigripalpus age structure supported that age variability can arise from environmen tal changes that affect mosquito activity, the landscape structure and mosquito resource finding efficiency. Variability in mosquito age can also impact our capabilities of monitoring virus infection in the field. The study in Chapter 5 dealt with some of the biologi cal and methodological sources of error in the estimation of arbovirus infection using samples of field caught mosquitoes. Mosquito populations at a part icular time may have a propor tion of individuals infected with virus. These include mosquitoes that have come in contact with the virus but are not ready to transmit, and those older mosquitoes that have undergone the extr insic incubation period and can transmit virus. The true proportion of infected mosquitoes proba bly varies from day-today as a consequence of changes in the mosqu ito population due to mortality, aging, and changes in the environmental conditions. The true proportion of infected mosquitoes in the population can be estimated by sampling mosquitoes in the field and testing them for virus. Examples of such estimates commonly
260 reported in the literature include the Maxi mum Likelihood Estimate (MLE) and the Minimum Infection Rate (MIR). Surveillance for virus in field mosquitoes has several drawbacks, such as low virus detection during inter-epidemic periods, the possi ble detection of virus in mosquitoes when the virus is not alive (using PCR methods), and our inability to easily separate infected and infectious mosquitoes (Day et al. 2003, Rutledge 2004). If virus testing of field collected mosquitoes is used regardless of these drawbacks, it is important to understand the sources of error th at can impact the value of virus infection estimates. Here we explored some of those s ources of error that can undermine the assumption that increases in the value of estimated infection rates in mo squitoes are associated with increases in arbovirus transm ission to humans and animals (Chiang and Reeves 1962). A simple model was developed which illust rated how infected mosquitoes become infectious over time, at a rate determined by mo squito survival, temperat ure, and the type of virus and mosquito (Chapter 5, Model I). The model showed that the number of infectious mosquitoes is not simply a constant proportion of the infected mosquitoes, but this proportion changes over time as dissemination progresses. The pattern of changes depends on the mosquito and virus species involved. The model results imply that infection rates in different mosquito species and with different viru ses are not directly comparable because dissemination occurs differently among species. Similar infection rate s estimated from different locations and at different dates may not be an indication of sim ilar proportions of infecti ous mosquitoes in the population. As viruses disseminate in the mosquitoes, fact ors such as time since the exposure to the virus and temperature, introduce variability in the virus titers among individual mosquitoes (see
261 Reisen et al. 1993 for an example of titer variatio n in infected and infectious mosquitoes as a function of temperature). We used a numeri cal simulation model (Chapter 5, Model II) to evaluate how the true proportion of infected mos quitoes in the population and the distribution of their virus titers in mosquitoes interacts with methodological aspects of mosquito assaying to introduce biases in estimates of infection (M LE). Assuming random sampling of the hostseeking population, the model results suggested that the sample size of mosquitoes and the ability of the biochemical assay to detect virus at low concentrations, wi ll strongly affect the relationship between the true pr oportion of infected mosquito es in the population and the estimated infection rate (MLE). Even when large mosquito samples and tests that can detect virus at low concentrations are used, estimates of infections are highl y likely to underestimate the true proportion of infected mosquitoes in th e population. Low levels of viral titers in the mosquitoes introduce even larger biases to the estimated infection rates. Estimated infection rates in mosquitoes ha ve been observed to increase during the arbovirus transmission season. For in stance, the MIR of mosquitoes with West Nile virus in the states of Florida (Bu tler 2004), California (Kramer 2005) and Virginia (Gaines 2007), increases during the months of July through September and declines in October. However, the model results show that the magnitude of the estimated in fection rates cannot be di rectly correlated with the proportion of infectious mosqu itoes in the field nor with th e true infection rate in the population, because underestimation is common. Theref ore, estimates of infection rate appear as indicators of virus presence in mosquitoes. However, when estimates are used for surveillance, they need to be used in conj unction with other indicators of ri sk (such as weather, sentinel chicken seroconversions), and long term data need to be examined in order to determine periods of atypical virus activity.
262 This work has produced new information towa rds understanding the causes of variability in the age structure of mos quito populations resulting from environmental heterogeneity, mosquito searching efficiency. It also pr ovided more information on the biological and methodological sources of biases of estimates of infection rates including vi ral titer distributions in the field, sample size, and assay thresholds fo r virus detection. It provides information that can be used for the interpretation of surveilla nce activities and highlights the importance of understanding changes in population age structure. This work also generates questions for further research, especially regarding the possi ble impact of mosquito foraging behavior in heterogeneous environments on population size, spatial spread, and age structure.
263 APPENDIX INPUTS FOR THE Culex nigripalpus SPATIALLY EXPLICIT INDIVIDUAL BASED MODEL
264 Table A-1. Relative humidity and temperature inputs for the Culex nigripalpus SEIBM. Values are based on weather data from Vero Beach Airport weather station for the years 2000-2002. Hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Hourly minimum relative humidity (%) May 74.22 76.13 76.90 77.5678.0478.20 73.71 64.34 59.94 54.82 51.94 51.37 50.14 51.20 52.79 54.81 57.05 62.73 68.37 71.93 73.53 71. 84 72.27 73.93 Jun 86.31 87.28 87.64 88.6788.9088.77 81.94 72.44 65.40 60.78 56.78 56.03 56.92 58.13 60.30 62.34 64.31 68.01 72.78 76.42 78.57 81. 47 83.20 84.85 Jul 87.54 89.48 90.67 91.9492.9292.35 86.76 76.13 69.05 61.91 57.59 56.68 57.93 58.18 61.00 62.50 65.93 68.95 74.29 78.37 80.19 80. 98 83.57 84.96 Aug 85.50 86.52 87.84 88.0588.9689.38 86.54 75.91 68.94 63.51 59.03 58.87 59.64 60.81 61.16 64.26 65.76 70.31 75.08 78.57 79.82 82. 38 83.50 84.62 Sep 81.52 82.86 83.72 84.3484.5884.68 83.49 75.52 70.79 66.08 62.16 61.15 61.27 61.94 63.06 64.69 67.59 72.23 77.28 77.34 78.15 78. 95 80.52 81.08 Oct 77.93 78.41 79.47 79.7879.9878.85 78.05 71.76 63.49 58.04 55.08 54.02 53.74 52.75 54.05 56.50 60.57 66.21 68.47 69.54 70.89 72. 59 73.22 74.93 Nov 70.08 71.13 72.55 71.7572.1873.98 73.80 69.71 60.98 53.48 50.13 48.63 48.69 49.31 49.53 51.92 55.83 62.80 64.95 65.66 67.21 68. 43 69.07 70.45 Hourly average relative humidity (%) May 86.17 87.82 88.91 89.7190.1390.53 86.23 76.25 69.67 65.21 62.73 61.83 61.43 62.78 64.76 66.68 68.38 73.25 77.61 80.79 82.28 83. 07 83.59 85.44 Jun 91.87 92.86 93.31 94.2794.6194.03 89.37 81.17 74.49 69.61 66.76 67.49 67.81 69.15 72.23 74.07 75.57 78.39 82.07 84.81 86.69 88. 24 89.57 90.72 Jul 92.88 93.88 94.81 95.3796.0295.67 92.00 83.45 76.26 70.16 66.60 66.80 68.50 68.73 70.80 72.87 74.30 77.29 81.48 85.03 86.75 88. 12 89.67 90.73 Aug 90.91 91.48 92.27 92.6392.9893.30 91.26 82.36 75.30 70.08 67.01 67.52 69.82 71.73 72.36 74.29 75.65 78.63 82.91 85.37 86.42 88. 38 89.47 89.92 Sep 89.25 89.93 90.90 91.3891.7191.96 90.77 83.69 77.55 72.77 70.24 68.75 69.33 69.82 71.63 73.79 76.13 79.97 83.79 84.53 85.63 86. 33 87.64 88.12 Oct 87.18 87.89 88.65 89.2689.4689.14 88.54 82.53 72.69 66.61 63.74 62.19 62.54 63.09 63.96 65.75 69.06 73.94 76.82 77.96 79.73 81. 51 82.87 84.89 Nov 82.92 83.79 84.49 84.7384.9086.01 86.06 82.17 72.91 65.58 62.13 60.27 60.51 60.84 62.11 62.55 66.55 72.54 75.67 76.93 78.47 80. 03 80.89 82.48 Hourly maximum relative humidity (%) May 98.13 99.50 100.00 100.00100.00100.00 98.76 88.17 79.40 75.59 73.52 72.28 72.72 74.37 76.73 78.55 79.70 83.77 86.86 89.66 91.04 94.29 94.92 96.95 Jun 97.43 98.43 98.98 99.86100.0099.29 96.79 89.89 83.58 78.43 76.75 78.96 78.70 80.16 84.17 85.79 86.83 88.77 91.35 93.20 94.81 95.02 95.93 96.60 Jul 98.23 98.29 98.94 98.8099.1399.00 97.24 90.77 83.48 78.41 75.62 76.93 79.07 79.28 80.59 83.24 82.67 85.64 88.67 91.70 93.31 95. 26 95.76 96.50 Aug 96.32 96.44 96.70 97.2197.0097.23 95.98 88.80 81.67 76.64 74.99 76.16 79.99 82.65 83.56 84.33 85.53 86.96 90.75 92.17 93.02 94. 39 95.43 95.23 Sep 96.98 97.00 98.09 98.4298.8599.25 98.06 91.85 84.32 79.45 78.33 76.34 77.38 77.70 80.20 82.89 84.66 87.70 90.30 91.72 93.11 93. 71 94.77 95.16 Oct 96.43 97.38 97.82 98.7498.9599.43 99.03 93.29 81.89 75.18 72.41 70.37 71.34 73.42 73.86 75.00 77.56 81.67 85.16 86.38 88.57 90. 42 92.52 94.86 Nov 95.76 96.45 96.43 97.7097.6198.04 98.31 94.63 84.84 77.67 74.12 71.91 72.33 72.37 74.70 73.18 77.27 82.28 86.39 88.20 89.74 91. 64 92.71 94.52 Average temperature (C) May 23.11 22.64 22.23 21.9421.7121.56 23.52 25.66 26.91 27.84 28.55 28.93 29.06 28.82 28.41 27.98 27.45 26.47 25.43 24.82 24.53 24. 12 23.82 23.32 Jun 24.20 23.85 23.64 23.3423.2423.42 25.32 27.15 28.43 29.37 29.91 29.97 30.04 29.79 28.89 28.42 27.80 27.15 26.43 25.81 25.34 25. 04 24.69 24.42 Jul 24.47 24.15 23.79 23.5223.3823.39 25.27 27.20 28.69 29.79 30.44 30.65 30.46 30.14 29.75 29.24 28.75 28.06 27.22 26.44 25.98 25. 60 25.28 24.95 Aug 24.51 24.30 24.15 24.0223.9123.75 24.96 27.24 28.68 29.71 30.37 30.34 29.81 29.38 29.15 28.65 28.10 27.45 26.64 26.07 25.76 25. 36 25.11 24.83 Sep 25.31 25.01 24.74 24.6324.4624.41 25.08 26.87 28.07 28.97 29.49 29.93 29.79 29.55 29.14 28.65 28.07 27.22 26.53 26.38 26.16 26. 02 25.77 25.60 Oct 22.43 22.25 22.01 21.8721.7021.61 21.88 24.25 26.42 27.52 28.11 28.45 28.47 28.32 28.00 27.46 26.71 25.53 24.77 24.44 24.13 23. 67 23.30 22.82 Nov 19.05 18.73 18.52 18.2618.1517.82 17.78 19.46 22.10 23.90 24.76 25.35 25.46 25.33 24.93 24.58 23.55 22.08 21.24 20.82 20.48 19. 97 19.58 19.20
265 Figure A-1. Vegetation types per cell for the favorable landscape.
266 Figure A-2. Vegetation types per cell for the unfavorable landscape.
267 Figure A-3. Percentage of th e cells area with water for oviposition under dry conditions for the favorable landscape.
268 Figure A-4. Percentage of th e cells area with water for oviposition under dry conditions for the unfavorable landscape.
269 Figure A-5. Percentage of th e cells area with water for oviposition under av erage conditions for the favorable landscape.
270 Figure A-6. Percentage of the cells area with water for oviposition under aver age conditions for the unfavorable landscape.
271 Figure A-7. Percentage of th e cells area with water for oviposition under wet conditions for the favorable landscape.
272 Figure A-8. Percentage of th e cells area with water for oviposition under wet conditions for the unfavorable landscape.
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288 BIOGRAPHICAL SKETCH Dulce Mara Bustamante Zamora was born in Villa Canales, Guatemala in 1979. Her mother is Clelia Leticia Zamora Solrzano, a La wyer, and her brother is Jose Mara Bustamante Zamora, a Systems Engineer. In 1996 she enro lled in the Biology program at San Carlos University, Guatemala. Under the supervision of Dr. Carlota Monroy, she started her career in Medical Entomology at the Laboratorio de En tomologia Aplicada y Parasitologia (LENAP, Laboratory of Applied Entomology and Parasitology). At LENAP she participated in various projects relating to the ecology a nd control of Triatominae bugs, the vectors of Chagas disease. In 2003 she was awarded a scholarship from the J. William Fulbright Foreign Scholarship Board from the United States to conduct her Masters studi es in Applied Statistics at Louisiana State University and Mechanical College. Her a dvisor was Dr. Luis Escobar. In 2005 she was accepted to the University of Florida to work w ith Dr. Cynthia Lord to conduct her doctoral studies and research re lating to the ecology of Culex nigripalpus a mosquito vector of arboviruses in Florida. After completing her degree, she will return to Guatemala to be an instructor at the Department of Biology at San Carlos University.