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PAGE 1 ANALYSIS OF WILDLIFE ABUNDANCE ESTIMATION METHODS USING REAL AND SIMULATED DATA By SAIF Z. NOMANI A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2007 1 PAGE 2 2007 Saif Z. Nomani 2 PAGE 3 To my sister, Samia Nomani 3 PAGE 4 ACKNOWLEDGMENTS I thank my advisors M. Oli, R. Carthy, and J. Nichols for their guidance and support. I thank A. Ozgul, J. Hostetler, K. Aaltonen, A. Singh, I. Ismail, and A. Jaffery for insightful comments on this study and for assistance with statistical analysis of results. Special thanks go to L. Thomas, S. Buckland, N. Adams, H. Sultan, M. Christman, and M. Sitharam for assistance with the simulation program; and to K. Miller, E. Lang, E. Cantwell, J. Martin and M. Voight for data collection. Thanks go to S. Coates and the OrdwaySwisher Biological Station, University of Florida for use of the study area and for habitat information. I thank my parents, C. Williams, and my friends from New Jersey for their support and encouragement. The Department of Wildlife Ecology and Conservation at the University of Florida and U.S. Army Corps of EngineersConstruction Engineering Research Laboratory (ACOECERL) provided funding for this study. Funding and logistical support was also provided by the Florida Cooperative Fish & Wildlife Research Unit at the University of Florida. 4 PAGE 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ...............................................................................................................4 LIST OF TABLES ...........................................................................................................................7 LIST OF FIGURES .........................................................................................................................8 ABSTRACT .....................................................................................................................................9 CHAPTER 1 INTRODUCTION..................................................................................................................11 2 COMPARISON OF METHODS FOR ESTIMATING ABUNDANCE OF GOPHER TORTOISES...........................................................................................................................13 Introduction.............................................................................................................................13 Methods..................................................................................................................................15 Study Area.......................................................................................................................15 Line Transect Method......................................................................................................16 Pilot study.................................................................................................................16 Data collection..........................................................................................................16 Data analysis............................................................................................................17 Total Count, Sample Count, and Double Observer Methods..........................................18 Data collection..........................................................................................................18 Data analysis............................................................................................................19 Burrow Occupancy Rates................................................................................................20 Data collection..........................................................................................................20 Data analysis............................................................................................................21 Costs................................................................................................................................22 Results.....................................................................................................................................22 Line Transect...................................................................................................................22 Total Count, Sample Count, and Double Observer.........................................................23 Burrow Occupancy Rates................................................................................................24 Abundance of Gopher Tortoises......................................................................................24 Costs................................................................................................................................24 Discussion...............................................................................................................................25 Comparison of Abundance Estimation Methods.............................................................25 Burrow Occupancy..........................................................................................................27 Costs of Implementation..................................................................................................28 Conclusion..............................................................................................................................29 5 PAGE 6 3 ACCURACY OF ESTIMATES OF ABUNDANCE BASED ON THE LINE TRANSECT METHOD: INFLUENCE OF SPATIAL DISTRIBUTION OF OBJECTS, AND LENGTH, LAYOUT, AND NUMBER OF TRANSECTS.........................................36 Introduction.............................................................................................................................36 Methods..................................................................................................................................38 Simulation Inputs.............................................................................................................38 Spatial Distribution and Density of Objects....................................................................38 Layout Pattern of Line Transects....................................................................................39 Total Length of Line Transects.......................................................................................40 Number of Transects.......................................................................................................40 Data Collection and Analysis..........................................................................................41 Results.....................................................................................................................................42 Overall Results................................................................................................................42 Clumped Distribution......................................................................................................43 Effects of object density...........................................................................................43 Effects of object density and transect length............................................................44 Effects of object density and transect layout............................................................44 Effects of object density and transect number.........................................................44 Effects of object density, and transect length, layout, and number..........................45 Random Distribution.......................................................................................................45 Effects of object density...........................................................................................45 Effects of object density and transect length............................................................46 Effects of object density and transect layout............................................................46 Effects of object density and transect number.........................................................46 Effects of object density, and transect length, layout, and number..........................47 Uniform Distribution.......................................................................................................47 Effects of object density...........................................................................................47 Effects of object density and transect length............................................................48 Effects of object density and transect layout............................................................48 Effects of object density and transect number.........................................................48 Effects of object density, and transect length, layout, and number..........................49 Discussion...............................................................................................................................49 Conclusion..............................................................................................................................53 4 CONCLUSION.......................................................................................................................73 APPENDIX OVERALL RESULTS...........................................................................................................76 LIST OF REFERENCES...............................................................................................................81 BIOGRAPHICAL SKETCH.........................................................................................................87 6 PAGE 7 LIST OF TABLES Table page 11 Comparison of models fitted to line transect data.............................................................31 12 Overall summary of estimates of abundance of gopher tortoise burrows for each abundance estimation method in two strata (G5 and C3/C7), OrdwaySwisher Biological Station, Florida.................................................................................................32 13 Estimated number of gopher tortoises in stratum C3/C7, OrdwaySwisher Biological Station, Florida...................................................................................................................33 21 Density estimates by object spatial distribution and density.............................................55 A1 Simulation study results.....................................................................................................76 7 PAGE 8 LIST OF FIGURES Figure page 11 Map of OrdwaySwisher Biological Station in northcentral Florida, USA, depicting stratum G5 and stratum C3/C7, and locations of line transects and plots.........................34 12 Effects of proportion of plots sampled using sample count method on estimates of abundance in two strata (G5 and C3/C7), OrdwaySwisher Biological Station in northcentral Florida..........................................................................................................35 21 Examples of simulated spatial distributions of objects with a density of 2 objects ha 1 ....56 22 Transect layout patterns with objects simulated in a random spatial distribution with a density of 2 objects ha 1 and a transect density of 10 m ha 1 ..........................................58 23 Effect of transect length on accuracy of estimates of density for a given object spatial distribution and object densities ranging from 2 objects ha 1 to 10 objects ha 1 ................61 24 Effect of transect length on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha 1 to 10 objects ha 1 ................63 25 Effect of transect layout on accuracy of estimates of density for a given object spatial distribution and object densities ranging from 2 objects ha 1 to 10 objects ha 1 ................65 26 Effect of transect layout on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha 1 to 10 objects ha 1 ................67 27 Effect of transect number on accuracy of estimates of density for a given object spatial distribution and object densities ranging from 2 objects ha 1 to 10 objects ha 1 ....69 28 Effect of transect number on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha 1 to 10 objects ha 1 ................71 8 PAGE 9 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science ANALYSIS OF WILDLIFE ABUNDANCE ESTIMATION METHODS USING REAL AND SIMULATED DATA By Saif Z. Nomani August 2007 Chair: Madan K. Oli Cochair: Raymond R. Carthy Major: Wildlife Ecology and Conservation For most wildlife species, multiple abundance estimation methods are available and the choice of a method should depend on cost and efficacy. I fieldtested the cost and efficacy of line transect, total count, sample count, and double observer methods for estimating abundance of gopher tortoise (Gopherus polyphemus) burrows in two habitats that differed in vegetation density (sparse and dense) at the OrdwaySwisher Biological Station in northcentral Florida. In the dense vegetation stratum, the density of burrows estimated using the line transect method (8.58 0.94 burrows ha1) was lower than that obtained from total count method (11.33 burrows ha1). In the sparse vegetation stratum, the estimated burrow density using the line transect method (11.32 1.19 burrows ha1) was closer to the burrow density using the total count method (13.00 burrows ha1). The density of burrows estimated using the double observer method was identical to that obtained from the total count method in dense vegetation stratum, but slightly greater than that obtained from the total count method in sparse vegetation stratum. The density of burrows estimated using the sample count method varied widely depending on the proportion of sample plots sampled in both strata. The cost of sampling as well as estimates of burrow density varied with habitat type. The line transect method was the least costly of the 9 PAGE 10 methods. Using burrow cameras and patch occupancy modeling approach, I also estimated the probability of burrow occupancy by gopher tortoises (active: 0.50 0.09; inactive: 0.04 0.04), and used these values to estimate abundance of gopher tortoises. Using estimates of burrow abundance based on the line transect method, the density of gopher tortoises was 2.75 0.29 ha1 in the sparse vegetation stratum. I then conducted a simulation study to investigate how the spatial distribution and density of objects, and the total length, layout, and number of transects influence the accuracy of estimates of abundance obtained from the line transect method. Using MATLAB I generated objects in different spatial distributions (clumped, random, uniform) with different object densities in a simulated study area. I varied the length, layout and number of transects used. The line transect method worked best for a random distribution of objects; root mean squared error between the estimated density and the true density was 8.5% of the true density. For all spatial distributions of objects, increasing transect length increased the accuracy of estimates of abundance. For a clumped distribution, transect layout and transect number did not seem to significantly influence accuracy of estimates of abundance. For a random distribution, transect number did not seem to significantly influence accuracy of estimates of abundance. For a uniform distribution, when transect layout was random, transect number and transect length did not seem to significantly influence accuracy of estimates of abundance. For a clumped distribution I recommend using a higher transect length. For a random distribution I recommend using a systematic transect layout as this provided slightly greater accuracy. For a uniform distribution I recommend using a random transect layout as this provided substantially greater accuracy. 10 PAGE 11 CHAPTER 1 INTRODUCTION Estimates of abundance are essential for monitoring the population status and recovery progress of threatened and endangered species (Seber 1982, Williams et al. 2002). For most wildlife species, multiple abundance estimation methods are available, including line transect, markrecapture, and double observer (Krebs 1999, Seber 1982, Williams et al. 2002) and the choice of a method should depend on cost and efficacy. Using the gopher tortoise (Gopherus polyphemus) as a test species, I compared the cost and efficacy of different abundance estimation methods. The gopher tortoise is a species of conservation concern in the southeastern US. Gopher tortoises spend much of their time in the shelter of selfconstructed underground burrows (Wilson et al. 1994), and direct observation of tortoises is difficult; consequently researchers typically estimate abundance of burrows, and frequently use it as an index of tortoise abundance (Cox et al. 1987, Smith et al. 2005, McCoy et al. 2006). However, it is not easy to estimate abundance of animals (Seber 1982). Two key issues involved in abundance estimation are detectability and spatial sampling (Royle and Nichols 2002, Williams et al. 2002). Most sampling methods do not result in the detection of all animals present in a study area so one must estimate detectability (the probability of observing an animal or object if it is present). Similarly, a sampling method often cannot be applied to the entire study area due to time and resource limitations, and typically a fraction of the area is sampled. Abundance can then be estimated considering detectability and spatial sampling simultaneously. These issues apply to the estimation of gopher tortoise abundance as well. An additional problem involved in the estimation of gopher tortoise abundance is that not every burrow is occupied by tortoises. Thus, an important issue relevant to gopher tortoise abundance estimation 11 PAGE 12 is the burrow occupancy rate (probability that a burrow is occupied by a gopher tortoise) (Diemer 1992). Estimates of abundance of gopher tortoises are then obtained by applying burrow occupancy rates to estimates of burrow abundance. Methods of estimating abundance of gopher tortoise burrows vary with respect to efficacy and cost, and given the pivotal role of gopher tortoises in ecosystems where they are found, it is essential to use rigorous methods for estimating and monitoring gopher tortoise abundance. I conducted a field study to investigate the cost and efficacy of line transect, total count, sample count, and double observer methods for estimating gopher tortoise burrow abundance, and to estimate the probability of burrow occupancy by gopher tortoises using burrow cameras and the patch occupancy modeling approach in the OrdwaySwisher Biological Station, Florida. I determined that the line transect method is an effective method for estimating abundance of gopher tortoise burrows, however, accuracy of estimates of abundance obtained from the line transect method may vary depending on the spatial distribution and density of objects, and the length, layout, and number of line transects. The spatial distribution and density of objects cannot be changed, however it is possible to design a study by varying the length, layout, and number of transects in order to maximize accuracy of estimates of abundance for a given spatial distribution and density of objects. I used a simulationbased approach in MATLAB (Mathworks 2006) to determine the influence of length, layout and number of transects on accuracy of estimates of abundance for different object spatial distributions and density levels. 12 PAGE 13 CHAPTER 2 COMPARISON OF METHODS FOR ESTIMATING ABUNDANCE OF GOPHER TORTOISES Introduction One of the most relevant questions in wildlife management is: how many are there? Indeed, estimates of abundance are a prerequisite for listing or delisting of a species, and for monitoring recovery progress (Seber 1982, Cassey and Mcardle 1999, Williams et al. 2002). Furthermore, estimates of abundance are needed for understanding densitydependent relationships, for parameterizing and evaluating population models, and for formulating or evaluating management programs (Williams et al. 2002). The gopher tortoise (Gopherus polyphemus) is a species of conservation concern in the southeastern US. It is federally listed as a threatened species in the western portion of its range (western Alabama, Mississippi, and Louisiana) (Lohoefener and Lohmeier 1984, Federal Register 1987). In Florida, gopher tortoise populations have been declining for some time (Auffenberg and Franz 1982, Schwartz and Karl 2005), and the species has recently been approved for reclassification to Threatened pending approval of a species management plan (FFWCC 2006). Several state and federal agencies in the gopher tortoise range are charged with monitoring their status and population trends which require reliable estimates of abundance. Estimating abundance of gopher tortoises is a two step process: estimation of burrow abundance and estimation of burrow occupancy rates. Gopher tortoises spend much of their time in the shelter of selfconstructed underground burrows (Wilson et al. 1994), and direct observation of tortoises is difficult. These burrows are relatively easy to see due to their halfmoon shape and large mound of sand (commonly referred to as the apron) at the burrow entrance. Because gopher tortoises are rarely seen outside their burrows, researchers typically estimate abundance of burrows, and frequently use it as an index of tortoise abundance (Cox et 13 PAGE 14 al. 1987, Smith et al. 2005, McCoy et al. 2006). The most commonly used methods for estimating the abundance of gopher tortoise burrows include line transect, total count, and sample count methods (Doonan 1986, Mann 1993, Epperson 1997, Doonan and Epperson 2001). A second issue involved in the estimation of gopher tortoise abundance is that not every burrow is occupied by tortoises; there are typically more burrows than gopher tortoises and the number of burrows does not always correspond to the number of tortoises (McRae et al. 1981, Diemer 1992, Smith et al. 1997, Eubanks et al. 2003, McCoy et al. 2006). Thus, an important issue relevant to gopher tortoise abundance estimation is the burrow occupancy rate (probability that a burrow is occupied by a gopher tortoise) (Diemer 1992). The estimates of abundance of gopher tortoises are then obtained by applying burrow occupancy rates to estimates of burrow abundance. Auffenberg and Franz (1982) reported that 61.4% of all burrows (active and inactive) were occupied in their study. Some studies have used this or other similar values (e.g., Ashton and Ashton (in press)) as a correction factor to convert the burrow abundance into an estimate of tortoise abundance (Kushlan and Mazotti 1984, Doonan 1986, Doonan and Epperson 2001, FFWCC 2006, Gregory et al. 2006). Burrow occupancy rates vary over time and space, and unreliable estimates of occupancy rates can lead to erroneous estimates of gopher tortoise abundance (Burke and Cox 1988, Breininger et al. 1991, McCoy and Mushinsky 1992, Moler and Berish 2001). The methods of estimating abundance of gopher tortoise burrows vary with respect to efficacy and cost, and rigorous field tests of these methods are needed to evaluate the efficacy relative to costs. Moreover, recent advances in the patch occupancy modeling framework (Mackenzie et al. 2002, Mackenzie et al. 2006) offer the possibility of statistically rigorous estimates of burrow occupancy rates which were not possible previously. 14 PAGE 15 My objectives were to 1) investigate the cost and efficacy of line transect, total count, sample count, and double observer methods for estimating gopher tortoise burrow abundance, and 2) estimate the probability of burrow occupancy by gopher tortoises using burrow cameras and the patch occupancy modeling approach in the OrdwaySwisher Biological Station, Florida. I then combined estimates of burrow abundance with estimates of the probability of burrow occupancy to estimate abundance of gopher tortoises. Methods Study Area This study was conducted in the OrdwaySwisher Biological Station ( http://www.ordway.ufl.edu ) located in Putnam County, Florida (29' N and 82 W) (Figure 11) in the fall of 2005. The Biological Station encompasses approximately 4000 ha, and offers over 1600 ha of potential gopher tortoise habitat with old fields, pine plantations, and sand hill habitats of several burn frequency categories. I selected a portion of the OrdwaySwisher Biological Station and stratified it into two strata (G5, and C3/C7) based on habitat maps, burn history and visual observation. Stratum G5, comprising of management unit G5, covered an area of approximately 110.3 ha, and was last burned in 2003 (two years before this study was conducted). Stratum C3/C7, comprising of management units C3 and C7, covered an area of approximately 116.5 ha, and was last burned in Feb 2005 (same year as this study). Due to the recent burn, stratum C3/C7 was more open with less dense vegetation than stratum G5 (R. R. Carthy, unpublished data). The study was conducted in two strata to investigate whether the probability of burrow detection, burrow abundance, and cost of the methods differed between the sandhill habitats with relatively high versus low vegetation density (Buckland et al. 2001). 15 PAGE 16 16 Line Transect Method TPilot study I conducted a pilot study in the OrdwaySwi sher Biological Stati on to estimate the transect length needed for r obust estimates of burrow abundance using methods described in Buckland et al. (2001). I estimated that, to achieve a coefficient of variation of 15% I needed to sample approximately 8 km of total transects in each stratum. Data collection I placed 8 km of transects in each stratum systematically at predetermined distances. I allowed sufficient spacing (30 to 60 m) between transects to ensu re that burrows would not be doublecounted, while providing an adequate sa mple size for statisti cally robust results (Buckland et al. 2001). I oriented transects so that they did not run parallel to roads or other linear topographical features (Buc kland et al. 2001, Williams et al 2002) because they can affect the distribution of gopher tortoises. I placed flags and recorded GPS coordinates at the origin and end of all transects. A team of observers, consisting of an observe r and an assistant, walked along each transect line. The observer (Observer 1) identified all burrows detected and the assistant then measured the perpendicular distance from the transect line to the burrow (Buckland et al. 2001, Williams et al. 2002). Perpendicular distance wa s measured from the transect line to either the burrow's mouth or the beginning of the burrow apron, whic hever was closest to the transect line. The assistant also recorded the GPS coordinates fo r the burrow, measured the burrow width 50 cm inside the burrow, and classified each burrow acco rding to width as juven ile (<14 cm wide), subadult (14 to 23 cm wide), and adult (>23 cm) (Alford 1980, Smith 1992). The observer classified each burrow into one of two burrow status categ ories: active and inactiv e. Active burrows had burrow aprons and entrances with little or no de bris, and had evidence of tortoise occupation. PAGE 17 Inactive burrows, on the other hand, had debris and leaf litter on the apron, at the mouth, and in the burrow tunnel. In some cases burrow mouths were degraded so that they did not have the classic, halfmoon tortoise shape. The assistant did not participate in detecting burrows but simply collected and recorded data for burrows detected by the lead observer. All detected burrows were temporarily marked with a numbered tag so as to avoid double counting of burrows. Tags were hidden from view of the second observer, but were placed in a consistent location at burrows so they were easily located by the second observer's assistant upon close examination of the burrows detected by the second observer. Once the first team completed sampling transects I used a second team to collect data in stratum G5 using the same protocol. These data were used to test for interobserver variability in detection probability and estimates of burrow abundance. One critical assumption of line transect sampling is that all objects located on the line transect are seen and recorded (Buckland et al. 2001, Williams et al. 2002). Gopher tortoise burrows are conspicuous, and are associated with mounds that are hard to miss from a close distance (Lohoefener 1990, Doonan and Epperson 2001). I am, therefore, confident that all tortoise burrows that were directly on the line were detected. Data analysis I used Program DISTANCE (Thomas et al. 2003) to analyze the line transect data to estimate the abundance of gopher tortoise burrows. The program provides a flexible framework for parameterization and comparison of alternative models (Buckland et al. 2001). I ran several different parametric models, each consisting of a key function and a series adjustment term (Buckland et al. 2001), using Program DISTANCE. I used Akaike's Information Criterion 17 PAGE 18 ( A IC ) values for model comparison and selected the model with the lowest A IC (Burnham and Anderson 2002). I excluded 5% of the observations (furthest from the line) from the analysis to remove possible outliers Buckland et al. (2001). Of the parametric models discussed above, I selected the most parsimonious model that allowed covariates and tested for the effect of the width of the burrow entrance (in cm) on the detection probability for Observer 1 in both strata. I then compared the A IC values for models with and without burrow width as a covariate to determine the effect of the burrow width on estimates of detection probability and density. Using the same procedure, I used observer as a covariate to test for the interobserver variability in detection probability in stratum G5. Data for the two observers were pooled together to test for interobserver variability, and the resulting A IC value was compared to the sum of the A IC values obtained from the separate analyses of data collected by the two observers without observer as a covariate (Buckland et al. 2001). Total Count, Sample Count, and Double Observer Methods Data collection I conducted a total count of burrows after line transect data had been collected. I selected six 1ha plots in each stratum. I overlaid these plots over portions of each stratum where line transect data were collected. The four corners of the plots were flagged and their coordinates were determined using a GPS unit. I further subdivided the plots into ten 20x50 m subplots. Each plot was comprehensively searched for burrows by two observers so detectability could be estimated (Nichols et al. 2000, Williams et al. 2002). Initially, I used three observers; however, the third observer consistently failed to detect any additional burrows so I continued with two observers. The observers recorded all pertinent information for detected burrows. Sample count was the total count in a sample of plots. 18 PAGE 19 I implemented the dependent double observer method following Nichols et al. (2000) and Williams et al. (2002). Each of the 20x50 m subplots was comprehensively searched for burrows by two dependent observers (primary observer and secondary observer, where the secondary observer is aware of the burrows detected by the primary observer). The primary observer surveyed the plots, and flagged and called out burrows detected to the secondary observer. The secondary observer recorded the information and proceeded to survey the plots to detect additional burrows (Nichols et al. 2000). At the completion of sampling of each subplot, the data were comprised of burrows detected by the primary observer, and burrows missed by the primary observer but detected by the secondary observer. Observers alternated roles on consecutive subplots, as recommended by Nichols et al. (2000). I conducted the total count, sample count and double observer methods on the same six 1ha plots and the field methods for the three methods were identical. I used the data collected for the total count method for the sample count calculations by selecting a subset of plots where total counts were conducted. This has been described in detail in the next section. Data analysis The estimated abundance of burrows using total count was the total number of burrows detected by both observers. Estimates of cost and abundance obtained from the sample count method can vary depending on the proportion of total area sampled, spatial distribution of burrows and the choice of the sample plots. Thus, I evaluated the effects of selecting different proportions of plots on the estimate of burrow abundance by utilizing data collected for the total count method. I selected all possible combinations of 3, 4, and 5 out of the 6 plots; each of these plots was thoroughly surveyed by two observers as described previously. The number of burrows 19 PAGE 20 20 in the sampled plots was then extrapolated to obt ain an estimate of the number of burrows to the entire 6ha area sampled. Sampling a 100% of the plots (6 out of 6) is the total count. I used Program DOBSERV (Hines 2000) to an alyze the double observe r data. The overall detectability was estimated as (Nichols et al. 2000): 12212211 1 pxxxx (11) Where p = estimate of overall detectability of both observers, 11 x = number of burrows detected by observer 1 in a primary role, 21 x = number of burrows detected by observer 2 in a primary role, 12 x = number of additional burrows detected by observer 1 in a secondary role, and 22 x = number of additional burrows detected by observer 2 in a secondary role. This estimate of overall detectability ( p ) was used to obtain the estimate for the population size for the sampling area ( N) by dividing the total number of burrows detected by all observers (.. x ) by p (Nichols et al. 2000). The standard error ( () SEN) and the 95% confidence interval for N were estimated using Program DOBSERV. I divided N obtained from each method by the area of the study site sampled to estimate the burrow density ( D ) (burrows haP1P). I multiplied D by the area of the st ratum to obtain an estimate of burrow abundance in each stratum. Burrow Occupancy Rates Data collection To estimate the probability that a burrow is occupied by a gopher tortoise (burrow occupancy rate) I conducted burrow occupancy surveys in management unit C3 of stratum C3/C7 (Figure 11). I examined a subsample of burrows from C3 that were marked during the total counts with a burrow camera on three consecutive days (begi nning either in the morning or early afternoon) to determine occupancy stat us. This subsample contained both active and inactive burrows. I used the Econo GeoVision, Jr. camera system designed by Marks Products, Inc. (Williamsville, Virginia) for use in boreh ole and water well systems. I sanitized the PAGE 21 21 equipment with diluted Nolvasan after examini ng each burrow, to minimize the risk of disease transmission. I classified the burrows as empty if the operator was cer tain that she/he had reached the end of the burrow and no gopher tortoi se was present. Burrows were considered occupied only if the operator could identify a gopher tortoise with absolute certainty. Burrow occupancy was considered "undetermined" if the operator could not maneuver the camera to the end of the burrow due to burrow ar chitecture (e.g., drama tic turns or tunnel size) or debris (e.g., leaf litter and/or sa nd). Burrows with undetermined occupanc y status were not used in analysis of occupancy rates. Data analysis Occupancy data were collected using a bur row camera and a statis tically robust occupancy modeling approach (Mackenzie et al. 2002) implemented in Program MARK (White and Burnham 1999) to estimate detection probability and burrow occupancy rate. Occupancy survey was conducted as described previously. A burrow wa s considered occupied by a tortoise (coded 1) if the observer was certain that a tortoise wa s present; it was consid ered unoccupied (coded 0) if the observer was certain the burrow was not oc cupied. Using these occupancy data collected over 3 sampling occasions, I fitted the patch oc cupancy model (Mackenzie et al. 2002). I used AIC to select the most parsimonious model. Us ing the most parsimonious model identified, I tested for the effect of the wi dth of the burrow entrance (in cm) on the detection probability and the occupancy rate by modeling the logit of each rate as a linear function of burrow width. If the 95% confidence interval for the slope parameter () did not include 0, the relationship was considered statistically signi ficant (Williams et al. 2002). PAGE 22 22 Costs I recorded the time taken for data collecti on for each method in personhours. The amount of time needed for analysis of data varied widely among individuals depending on mathematical background, computer skills, and learning curves and thus are not reported. The costs of equipment required for analysis may also va ry tremendously and thus are not reported. Results Line Transect A total of 28 line transects was placed in stratum G5 with a total length of 8025 m. Observer 1 detected 163 burrows and Observer 2 detected 150 burrows. For Observer 1, the model with the lowest A IC was Uniform Cosine (Table 11). Based on this model, the estimated burrow density ( SE) was 8.58 0.94 burrows haP1P (cv=11.0%). For Observer 2, the model with the lowest A IC was also Uniform Cosine (Table 11) Based on this model, the estimated burrow density was 8.49 0.98 burrows haP1P (cv=11.5%) (Table 12). A total of 16 line transects was placed in stra tum C3/C7 with a total length of 8003 m. The first observer (Observer 1) dete cted 262 burrows. For Observer 1, the models with the lowest A IC were Hazard Rate Cosine and Hazard Rate Si mple Polynomial (Table 11). The results for these two models were identical so I selected the Hazard Rate Cosine model. Based on this model, the estimated burrow density was 11.32 1.19 burrows haP1P (cv=10.5%) (Table 12). I did not analyze the line transect data for Observer 2 for stratum C3/C7 because Observer 2 did not collect data independently of Observer 1. In stratum G5, I evaluated the effect of burro w width on detection probability for Observer 1 using the Half Normal Cosine model. The di fference between the prob ability of detecting smaller burrows and the probability of detec ting larger burrows was not substantial ( A IC for model with burrow width as a covariate: 475.86; A IC for model without burrow width as a PAGE 23 23 covariate: 477.87). Consequently, estimates of burrow density were very similar (with burrow width as a covariate: 8.99 1.06 burrows haP1P; without burrow width as a covari ate: 8.58 0.94 burrows haP1P). In stratum C3/C7, I evaluated the effect of burrow width on detection probability for Observer 1 using the Hazard Ra te Cosine model. Although the burrow width seemed to influence detection probability ( A IC for model with burrow width as covariate: 867.97; A IC for model without burrow width as c ovariate: 957.48), the difference in the estimate of burrow density was not substant ial (with burrow width as covariate: 11.26 0.84 burrows haP1P; without burrow widt h as covariate: 11.32 1.19 burrows haP1P). Additionally, in stratum G5, I evaluated interobserver variability in detection probability using pooled data collected by the two independe nt observers and the Half Normal Cosine model. There seemed to be no difference in de tection probability between the two observers ( A IC for model with pooled observations: 1871.19; sum of A IC values for models analyzed separately for Observer 1 and Observer 2: 1871. 21), and the difference in the estimate of burrow density was not substantial (mode l with pooled observations: 8.55 0.71 burrows haP1P; model analyzed separately for Observer 1: 8.68 0.97 burrows haP1P; model analyzed separately for Observer 2: 8.41 1.01 burrows haP1P). Total Count, Sample Count, and Double Observer In stratum G5, the total number of burrows in the 6ha (six 1ha plots) sampled was 68 (Table 12). In stratum C3/C7, the total number of burrows in the 6ha (six 1ha plots) sampled was 78 (Table 12). The extrapolated abundance of burrows based on the sample count method varied widely in both strata based on the proportion of sample plots used (Figures. 12A and 12B, Table 12). In stratum G5, when 50%, 66%, and 83% of the plots were sampled, the extrapolated number of burrows in the samp ling area ranged from 48 to 88, 54 to 81, and 60 to 74 burrows, respectively. In stratum C3/C7, when 50%, 66%, and 83% of the plots were PAGE 24 24 sampled, the extrapolated number of burrows in the sampling area ranged from 64 to 92, 69 to 87, and 73 to 83 burrows, respectively. In stratum G5, the overall detectability ( p ) estimated using the double observer method was 1.0, and .. x and N were 68. Because p was 1.000, () SEN or 95% confidence interval could not be estimated (Table 12). In stratum C3/C7, p estimated using the double observer method was 0.997 0.003, .. x was 78, and N was 78.23 0.53 (Table 12). Burrow Occupancy Rates The most parsimonious model indicated that the detection probabil ity (probability of observing a gopher tortoise if it was in the burrow) was 0.92 0.04 and did not differ between burrows classified as active or inactive. Ho wever, the occupancy rates were significantly different between the two groups (active: 0.50 0.09; inactive: 0.04 0.04). There was no evidence that width of the burrow entrance infl uenced the occupancy ra te or the detection probability. Abundance of Gopher Tortoises Using the occupancy rates for active and inactive burrows, an d based on the proportion of active and inactive burrows I estimated the abundance of gopher tortoises in stratum C3/C7. The estimated abundance varied from 223.68 329.70 to rtoises in stratum C3/C7 (total area: 116.5 ha), depending on the method used, and in the case of sample count, depending on the proportion of plots sampled (Table 13). Costs The cost of sampling varied from 0.52 2.38 personhours haP1 Pin stratum G5, and from 0.46 2.08 personhours haP1 Pin stratum C3/C7, depending on the methods used, and in the case PAGE 25 of sample count, depending on the proportion of plots sampled (Table 12). I did not analyze cost of line transect data collected by Observer 2. Observer 2 did not lie out transects or measure and record information for burrows that had already been detected by Observer 1. Costs of implementing the double observer method were identical to the cost for the total count method. The cost of sampling burrows with a burrow camera to determine occupancy status was 0.16 personhours per burrow camera observation. A total of 168 burrow camera observations were performed (three observations for each of the 56 burrows scoped) requiring a total time of 26.88 personhours. Discussion Comparison of Abundance Estimation Methods To monitor the population status, and for appropriate recovery efforts for gopher tortoises, reliable estimates of abundance are needed. Methods that are currently used to estimate the abundance of gopher tortoises vary with respect to statistical rigor, efficacy, and cost. Given the pivotal role of gopher tortoises in ecosystems where they are found (Eisenberg 1983, Wahlquist 1991), it is essential to use rigorous yet cost effective methods for estimating and monitoring tortoise abundance. I fieldtested the efficacy and cost of line transect, total count, sample count, and double observer methods for estimating abundance of gopher tortoise burrows. In the dense vegetation stratum (G5), the estimated burrow density using the line transect method for both observers (8.58 and 8.49 burrows ha 1 respectively) was nearly 3 burrows ha 1 less than burrow density of 11.33 burrows ha 1 obtained from total count method. Estimates based on total count method did not fall within the 95% confidence intervals of those obtained from line transect method (Table 12). In the sparse vegetation stratum (C3/C7), the estimated burrow density estimated using the line transect method (11.32 burrows ha 1 ) was closer to the burrow density obtained from the 25 PAGE 26 26 total count method (13.00 burrows haP1P). The total count fell within the 95% confidence interval for estimates obtained from the line transect method (Table 12). Mann (1993) compared estimates of tort oise burrow abundance obtained from line transect and total count methods, and found th at line transect method overestimated burrow abundance by as much as 49% in 13 sites and 32 % on seven sites. Results from similar studies suggest a tendency for line tran sects to overestimate abundance when compared to total counts (Doonan 1986, Epperson 1997, Doonan and Epperson 2001). I used 2 observers to thoroughly search the sampling area, and ensured that de tection probability was 1.0. I also had a large sample size for a reasonable coefficient of vari ation. My results do not agree with findings that the line transect method tends to overestimate burrow numbers. In fact, estimates of burrow abundance obtained from the line transect met hod were lower than those obtained from total count in stratum G5; they did not differ significantly in stratum C3/C7 (Table 12). These results suggest that the estimated bu rrow abundance obtained from the line transect method are not consistently greater or smaller than those obtained from the total count method. Therefore, the line transect method likely captured a greater amount of spatial variability in distribution and abundance burrows in the study area. Consistent with previous studies (McC oy and Mushinsky 1995, Epperson 1997, Marques et al. 2001, McCoy and Mushinsky 2005), my estimat es of burrow density varied with habitat type and burn frequency. Density estimates obtai ned from all methods were higher in stratum C3/C7 which had comparatively sparse vegeta tion and a higher burn frequency. The higher density of burrows and tortoises in stratum C3/C 7 likely indicates that this stratum offered a better habitat for the tortoises. PAGE 27 27 Burrow Occupancy My estimates of burrow occupancy rates (active: 0.50 0.09; inactive: 0.04 0.04) were substantially lower than Auffe nberg and Franzs correction factor of 61.4 % for active and inactive burrows (Auffenberg and Franz 1982). Some studies have used this or a similar correction factor (e.g., Ashton and Ashton ( in press )) for converting estimates of burrow abundance to tortoise abundance (Kushlan and Mazotti 1984, Doonan 1986, Doonan and Epperson 2001, FFWCC 2006, Gregory et al. 2006). Howe ver, this approach ignores the spatial, temporal or habitatspecific va riation in occupancy rate and can cause estimates of gopher tortoise abundance to be unreliable (Burke and Cox 1988, Breininger et al. 1991, McCoy and Mushinsky 1992, Moler and Berish 2001). Moreover, my study is the first to apply the patch occupancy modeling approach (Mac kenzie et al. 2002) to estima te and model burrow occupancy rates. When appropriate data are available, th is approach also provide s framework for testing relevant biological hypotheses. Because of time and resource limitations, I conducted burrow occupancy surveys only in management unit C3 of stratum C3/C7, and I did not have empirical estimates of burrow occupancy rates for stratum G5. Assuming that th e burrow occupancy rate was the same in both strata (C3/C7 and G5), estimates of tortoise a bundance in stratum G5 (t otal area 110.3 ha) varied from 148.68 230.45 tortoises depending on the met hod used, and in the case of sample count, depending on the proportion of plots sampled. Base d on the line transect method, the estimated density of gopher tortoises was 2.06 0.23 haP1 Pin stratum G5. Occupancy rates may vary among habitats due to the ecological needs of gopher tortoises, and habitatspecific estimates of occupancy rates should be used whenever possible. Estimates of occupancy rates may also be influenced by the s eason, time of the day when data are collected, and time interval between successive samples; these factors should be considered whenever PAGE 28 possible. Additionally, there is the possibility of the same tortoise occupying more than one burrow during the burrow occupancy surveys, resulting in an overestimation of the occupancy rate. These potential problems can be minimized by appropriate sampling design. Nonetheless, I found that patch occupancy models (Mackenzie et al. 2002, Royle and Nichols 2002, Mackenzie et al. 2006) offer statistically robust approach to estimating burrow occupancy rates and should be considered in future studies. Costs of Implementation The total count and sample count methods were relatively straightforward to implement, and required no sophisticated software for data analyses. However, these methods are costly, particularly when a substantial proportion of the sites need to be sampled. Moreover, these methods do not offer rigorous estimates of precision or meaningful approaches to obtaining statistical inferences. The double observer method partially addressed some of these concerns by providing estimates of precision (when detectability is less than 1.0), but is costly to implement. Using the sample count method, the range of extrapolated estimates for burrow density became narrower as the sampling proportion increased (Figures 12A and 12B). However, there was a cost tradeoff in that more time was needed to collect the data (Table 12). The line transect method was the least costly of the methods, and I was able to sample a larger effective area with the same effort. The method is considered statistically rigorous and robust, provides statistical measures of precision, and provides a framework for statistical inferences (Buckland et al. 2001, Krzysik 2002, Williams et al. 2002). However, the low cost of sampling in the field may be somewhat offset by increased costs of study design and data analysis, as a good understanding of underlying theory, sampling protocol and working knowledge of Program DISTANCE is needed for effective implementation of this method. 28 PAGE 29 Costs of data collection differed between the two strata in the study site. The sparse vegetation stratum (C3/C7) had a lower relative cost of sampling for all the abundance estimation methods than dense vegetation stratum. In my study, sample counts and total counts were substantially more costly than line transects in both strata. Detection time may be substantially less in sparse vegetation (Lohoefener and Lohmeier 1984, Burke and Cox 1988, Diemer 1992), and prescribed burns prior to sampling may further reduce cost of sampling (Smith 1992, Mann 1993, Moler and Berish 2001). Conclusion Among other factors, the selection of an abundance estimation method should consider the habitat type of the study area, and available time and resources (Ellis and Bernard 2005). With a stratified sampling design, and an adequate sample size, the line transect method is perhaps the most efficient method for estimating gopher tortoise burrow abundance because: 1) it is less costly than total and sample count methods, 2) it is more likely to capture a wider range of spatial variation in the distribution and abundance of burrows, 3) it offers statistically robust estimates of measures of precision, and 4) provides a flexible framework for evaluating effects of covariates on estimates of abundance. If one wishes to implement the total (or sample) count method, I recommend using multiple observers in order to obtain estimates of detectability. I note, however, that the total (or sample count) method does not provide an estimate of variance, nor does it provide a framework for statistical test of hypothesis. The double observer approach is reasonable if one wishes to implement a countbased method, but is unsure that detectability is equal to 1.0. I recommend that burrow cameras (or similar technologies) should be employed, along with a patch occupancy modeling approach for data analysis, to estimate burrow occupancy rates and to test hypothesis regarding the occupancy rate or detection probability. If a study is 29 PAGE 30 conducted in >1 habitat types, I recommend obtaining habitatspecific estimates of occupancy rates. Finally, I suggest that gopher tortoise monitoring programs should simultaneously consider burrow abundance and burrow occupancy rates. This is because changes in gopher tortoise abundance may be reflected in changes in one or both of these parameters (i.e., burrow abundance and burrow occupancy rate), and changes in one may not be interpreted as an indicator of changes in tortoise abundance. 30 PAGE 31 31 Table 11. Comparison of models fitted to line transect data Observer 1 Observer 2 Stratum Model A IC Parameters A IC Parameters G5 Uniform CosinePaP 0 1 0.00 1 Half Normal Cosine 0.13 1 0.93 1 Half Normal Hermite 0.13 1 0.93 1 Uniform Simple Polynomial 1.46 2 0.98 2 Hazard Rate Cosine 2.22 2 2.31 2 Hazard Rate Simple Polynomial 2.22 2 2.31 2 C3/C7 Hazard Rate CosinePaP 0 2 Hazard Rate Simple Polynomial 0 2 Uniform Cosine 0.98 2 Half Normal Cosine 1.32 2 Half Normal Hermite 3.14 1 Uniform Simple Polynomial 3.59 3 Note: For each model the A IC values and the number of parameters are presented. A IC is the difference in the A IC (Akaikes Information Crit erion) values between each model and the model with the lowest A IC value. Pa PMost parsimonious model PAGE 32 Table 12. Overall summary of estimates of abundance of gopher tortoise burrows for each abundance estimation method in two strata (G5 and C3/C7), OrdwaySwisher Biological Station, Florida Method D ()Ntot Cost G5 Line transect a Obs 1 8.58 (6.87 10.73) 946.40 0.52 Obs 2 8.49 (6.73 10.71) 936.25 Sample count 50% b 8.00 14.66 c 882.21 1616.66 c 1.19 66% b 9.00 13.50 c 992.49 1488.74 c 1.57 83% b 10.00 12.40 c 1102.77 1367.43 c 1.98 100% b 11.33 1249.44 2.38 Double observer 11.33 1249.44 2.38 C3/C7 Line transect a,d Obs 1 11.32 (9.19 13.94) 1318.31 0.46 Sample count 50% b 10.67 15.33 c 1246.21 1781.97 c 1.04 66% b 11.50 14.50 c 1339.39 1688.79 c 1.38 83% b 12.20 13.80 c 1420.92 1607.27 c 1.73 Total count (100% b ) 13.00 1514.09 2.08 Double observer 13.04 1518.75 2.08 Note: D is the estimated burrow density (with 95% confidence interval) in burrows ha 1 and )is the estimated number of burrows in the stratum. Cost are presented in terms of time (personhours) needed to sample 1 ha. ( Ntot a Results are based on the most parsimonious model (Table 11). b Proportion of plots sampled. c Range of estimates d I did not analyze line transect data for Observer 2 for stratum C3/C7 because Observer 2 did not collect data independently of Observer 1. 32 PAGE 33 Table 13. Estimated number of gopher tortoises in stratum C3/C7, OrdwaySwisher Biological Station, Florida Burrow abundance Gopher tortoise abundance Method BN (Active) BN (Inactive) GTN (Active) GTN (Inactive) ()GTNtot C3/C7 a,b Line transect Obs1 582.62 735.69 291.31 29.43 320.74 Sample count 50% 447.36 639.68 798.85 1142.92 223.68 319.84 31.95 45.72 255.63 365.56 66% 480.81 606.23 858.58 1082.56 240.40 303.12 34.34 43.30 274.74 346.42 83% 510.07 576.97 910.84 1030.30 255.04 288.49 36.43 41.21 291.47 329.70 Total count 100% 543.52 970.57 271.76 38.82 310.58 Double observer 545.19 973.56 272.60 38.94 311.54 Note:(Active) and (Inactive) are the estimates for the total number of active and inactive burrows in the stratum, (Active) and (Inactive) are the estimated numbers of gopher tortoises in active and inactive burrows, respectively, and )t is the estimated total number of gopher tortoises in all burrows in the stratum. BN BN GTN GTN ( GTNto a Burrow occupancy surveys were conducted only in management unit C3 (estimated burrow occupancy rates were 0.50 for active burrows and 0.04 for inactive burrows), therefore I estimated gopher tortoise abundance for stratum C3/C7 only. b For stratum C3/C7, the proportion of active and inactive burrows detected using the line transect method for Observer 1 was 0.44 and 0.56, respectively. The proportion of active and inactive burrows detected using the total count methods was 0.36 and 0.64, respectively. 33 PAGE 34 Figure 11. Map of OrdwaySwisher Biological Station in northcentral Florida, USA, showing stratum G5 and stratum C3/C7, and locations of line transects and plots 34 PAGE 35 Proportion Sampled 50%66%83%100% No. of Burrows 405060708090 A) Proportion Sampled 50%66%83%100% No. of Burrows 6065707580859095 B) Figure 12. Effects of proportion of plots sampled using sample count method on estimates of abundance in two strata (G5 and C3/C7), OrdwaySwisher Biological Station in northcentral Florida. Extrapolated range of total number of burrows are plotted against the proportion of plots sampled. A) In stratum G5. B) In stratum C3/C7. 35 PAGE 36 CHAPTER 3 ACCURACY OF ESTIMATES OF ABUNDANCE BASED ON THE LINE TRANSECT METHOD: INFLUENCE OF SPATIAL DISTRIBUTION OF OBJECTS, AND LENGTH, LAYOUT, AND NUMBER OF TRANSECTS Introduction Estimates of abundance are necessary for monitoring population status and for assessing the impacts of management actions. Obtaining these estimates is notoriously difficult (Seber 1982). Several methods have been developed to estimate abundance, including line transect, markrecapture, and double observer (Krebs 1999, Seber 1982, Williams et al. 2002). Line transect is a distancebased method and is statistically robust for estimating abundance (Buckland et al. 2001, Krzysik 2002, Williams et al. 2002). Implementation of the line transect method involves laying out transects either randomly or systematically at predetermined distances, walking along the line transects detecting objects, and recording sighting angles and sighting distances, or perpendicular distances of objects to the line. If assumptions are met, the line transect method is efficient, costeffective and provides rigorous estimates of abundance. Consequently, this method has been used to estimate abundance for many species of birds (Jarvinen and Vaisanen 1975, Hanowski et al. 1990), terrestrial and marine mammals (Jefferson 1996, Plumptre 2000, Ruette et al. 2003, Calambokidis and Barlow 2004), reptiles (Lewis et al. 1985, Krzysik 2002), amphibians (Lewis et al. 1985, Donnelly and Guyer 1994), and plants (Abrahamson 1984, Gentry and Emmons 1987). Additionally, line transect method has been used to estimate abundance of many inanimate objects including nests (Hashimoto 1995), dung (Marques et al. 2001, Ellis and Bernard 2005), and burrows (Lohoefener 1990, Swann et al. 2002) as an index of animal abundance (Borchers et al. 1998, Buckland et al. 2001). 36 PAGE 37 The accuracy of estimates of abundance obtained from the line transect method may vary depending upon the spatial distribution and density of objects, and the length, layout, and number of line transects. Researchers cannot change the spatial distribution and density of objects, but it is possible to design a study by varying the length, layout, and number of transects in order to maximize accuracy and precision of estimates of abundance for a given spatial distribution and density of objects. My objectives were to address the following questions: 1) Which spatial distribution pattern of objects is the line transect method most appropriate for? 2) For a given spatial distribution, does the line transect method depend on object density? 3) For a given spatial distribution and density of objects, how can one optimize the study design by varying total transect length, transect layout pattern, and number of transects in order to maximize accuracy of estimates of abundance? Given the large number of factors involved and due to limitations of time and resources, questions such as these can only be addressed effectively using simulations. Thus I used a simulationbased approach to achieve my objectives. The methodology and results in this study could be applied to a number of objects or organisms, including invertebrates, plants, and nests (Buckland et al. 2000), provided some of the basic assumptions of line transect abundance estimation (Burnham et al. 1980, Buckland et al. 2001) are not violated. I hypothesized that: 1) Estimates of abundance obtained from the line transect method would be more accurate when objects were randomly or uniformly distributed in space; 2) For a given spatial distribution pattern, precision of estimates of abundance would increase with increasing object density; 3) increasing transect length would increase the accuracy of estimates 37 PAGE 38 of abundance for all spatial distribution patterns and density levels; 3) for a clumped distribution of objects, a random transect layout and several short transects would provide more accurate estimates of abundance because such a study design would provide greater spatial coverage; 4) for a uniform distribution of objects, a random transect layout would provide more accurate estimates of abundance; and 5) for a random distribution of objects, transect layout and transect number would not have a substantial effect on the accuracy of estimates of abundance. Methods Simulation Inputs I considered three spatial distributions of objects: clumped, random and uniform. Within each spatial distribution I used three levels of object densities: low (2 objects ha 1 ), medium (6 objects ha 1 ), and high (10 objects ha 1 ). For each combination of spatial distribution and density level, I used a) three transect lengths: 10 m ha 1 20 m ha 1 and 30 m ha 1 d) two types of transect layout patters: random transect layout and systematic transect layout, e) and two levels of total number of transects: few long and several short transects. There were a total of 216 unique combinations of input variables. Spatial Distribution and Density of Objects Using MATLAB I designed an 800 ha study area and simulated locations of objects within the study area using the following spatial distributions: uniform grid (hereafter, uniform), uniform random (hereafter, random), and clumped (Krebs 1999). For a uniform distribution, I evenly spaced the objects throughout the study area (Zollner and Lima 1999) (Figure 21C). For a random distribution, each object was distributed independently of all other objects (Figure 21B). I implemented this by generating the x and coordinates for the object using a uniform random distribution throughout the study area (Zollner and Lima 1999). For a clumped distribution, objects were aggregated in groups or patches (Figure 21A). To implement this I y 38 PAGE 39 39 randomly distributed parent obj ects throughout the study area, and using a random Gaussian distribution with the parent obj ect as the mean, and variance v (ranging from 2 to 5) depending upon the density of objects, I generated offsprin g around each parents object (Zollner and Lima 1999, Conradt et al. 2003). The number of pa rent objects was selected randomly from a range of 25 to 50. I divided the total population size by the number of parent objects to determine the number of offspring around each parent. Offs pring that fell outside the borders of the study area were deleted and the overall object density was readjusted. To evaluate the effect of object density on estimates of abundance obtained from the line transect method I varied the obj ect densities from 2 objects haP1P to 10 objects haP1P in increments of 4 objects haP1 Pfor each spatial distribution. Layout Pattern of Line Transects I laid out line transects in two different pa tterns: systematic and random. For a systematic transect layout (Figur es 22C and 22D), x and y coordinates and the angle for the first transect were predetermined. The coordinates were chosen to ensure that all line transects would fall inside the study area. I us ed 0, 45 and 90 degrees for in order to provide an adequate representation of system atic transect layouts. Subsequent transects were then placed at 90 m intervals so as to prevent doublecounting of obj ects from two adjacent transects. For a random transect layout (Figures 22A and 22B) several different sets of transects were laid out throughout the study area. The x and y coordinates and the angle for the first transect of each transect set was chosen at random. Subseque nt transects were then placed at 90 m intervals parallel to the first transect. I ensured that all tr ansect sets were located inside the study area and did not overlap each other. PAGE 40 Total Length of Line Transects The total transect length was determined using transect density in m ha 1 For instance, a transect density of 10 m ha 1 would result in a total transect length of 8000 m in an 800 ha study area. I used transect densities ranging from 10m ha 1 to 30m ha 1 in increments of 10m ha 1 The lengths of all transects were equal within each simulation run. Based on the transect density used I chose the total number of transect sets in the study area as well as the number of transects in each set. Number of Transects The number of transect sets and the number of transects in each set varied with transect density and were chosen to meet either of two conditions: a few long transects, or several short transects in each transect set (Figures 22A, 22B, 22C, and 22D). For a random transect layout with few long transects (Figure 22A) the number of transect sets for a transect density of 10 m ha 1 was 2, and for transect densities of 20 m ha 1 and 30 m ha 1 the number of transect sets was a randomly chosen number between 3 or 4. The number of transects in each transect set was a randomly chosen number between 4 and 6. For a systematic transect layout with few long transects (Figure 22C) the number of transect sets was 1 for all transect densities. The number of transects for a transect density of 10 m ha 1 was 7, and for transect densities of 20 m ha 1 and 30 m ha 1 the number of transects was a randomly chosen number between 8 and 14. For a random transect layout with several short transects (Figure 22B) the number of transect sets for a transect density of 10 m ha 1 was 3, and for transect densities of 20 m ha 1 and 30 m ha 1 the number of transect sets was a randomly chosen number between 4 or 5. The number of transects in each transect set was a randomly chosen number between 7 and 10. For a systematic transect layout with several short transects (Figure 22D) the number of transect sets 40 PAGE 41 41 was 1 for all transect densities. The number of transects for a transect density of 10 m haP1P was 10, and for transect densities of 20 m haP1P and 30 m haP1P the number of transect was a randomly chosen number between 11 and 19. Data Collection and Analysis I set the transect strip width (w) at 30 m. This was the width of the area searched on each side of the line transect; obj ects beyond 30 m were not consid ered. I used the half normal detection function to determine whether objects within 30 m were detected. The half normal detection function is often a good choice as a key functi on in line transect sa mpling (Buckland et al. 2001). This took the form 22()exp(/2) gxx (21) Where () gx= probability of detecting an ob ject at perpendicular distance x from the line, and = scale parameter, which I estimated following Brown and Cowling (1998) 122(2) w (22) For each object within the strip width I gene rated a uniform random number between 0 and 1. If the random number was greater than or equa l to the detection probab ility obtained from the half normal detection function, the object was ma rked as detected. If the random number was less than the detection probabi lity, the object was considered undetected. I measured the perpendicular distance of every object detected w ithin the transect strip width of 30 m. I called Program DISTANCE (Thomas et al. 2003) from within MATLAB to analyze the data using a half normal cosine detecti on function to estimate th e density of objects as: (0) 2 nf D L (23) Where D = estimate of density, n= number of objects detected, L= total transect length, (0) f = estimated probability distribution functi on at the line and was determined as 01 (0) ()wf gxdx (24) PAGE 42 42 I also calculated the number of objects det ected as a percentage of the total number of objects in the study area. I ran 100 simulations fo r each combination of spatial distribution of objects and density of objects, and the layout, dens ity and number of transects. The total number of simulation runs was 21,600 for 216 different comb inations of input variab les. I then compared the estimated density obtained fr om the line transect method ( D ) with the actual true density (TD) for each combination of spatial distribution, transect layout pattern, transect density, and number of transects. To measure accuracy of estim ates of abundance I calculated the root mean squared error between D and TD (RMSE) following Williams et al. (2002). 2 11 () 1n iT iRMSEDD n (25) Where n= number of samples I also calculated RMSE as a percentage of TD (RMSE%). To measure bias of the estimates I calcul ated the mean of the difference between D and TD as a percentage of TD (Bias%). Precision of estimates wa s quantified as the coefficient of variation of D (CV( D )). I also calculated the percentage of times the 95% CI of estimates of density computed by Prog ram DISTANCE contained TD. I performed all statistical analyses using SAS software (SAS Institute, 2004). Results Overall Results Detailed results are provided in the Appendi x (Table A1). The estimated scale parameter ( ) for all simulation runs was 0.24. Ignoring all factors (spatial distri bution and density of objects, and length, layout, a nd number of transects) RMSE% was 26.8%, Bias% was 3.9%, CV( D ) was 60.4%, and the 95% CI of D contained TD 83.2% of the time, 11.3% of the time it was underestimated (below the lower limit of C I), and 5.5% of the time it was overestimated PAGE 43 (above upper limit of CI) (Table 21). Accuracy, as well as bias and precision, of estimates of density varied among spatial distribution patterns and densities of objects depending upon the length, layout, and number of transects (Table 21). The Bias% across all three spatial distributions (clumped, random and uniform) was less than 10%. RMSE% ranged from 8.5% to 36.4%, and CV( D ) ranged from 55.0% to 63.4% depending upon the spatial distribution of objects (Table 21). The probability of detecting an object in the strip of area ( 2wL p ) was 79.5%, 79.4%, and 83.8% for clumped, random, and uniform distributions respectively and did not vary substantially within spatial distributions. Clumped Distribution Ignoring all other factors, RMSE% was 36.4%, Bias% was 6.1%, CV () D was 63.4%, and 95% CI of D contained 67.9% of the time, 20.0% of the time it was underestimated, and 12.1% of the time it was overestimated (Table 21). The number of objects detected as a percentage of the total number of objects simulated was 4.9%, 9.9% and 14.8% when using a transect density of 10 m ha TD 1 20 m ha 1 and 30 m ha 1 respectively. Effects of object density Estimates of density were less biased when object density was the highest. Bias% ranged from 9.6% when object density was 2 objects ha 1 to 5.6% when object density was 10 objects ha 1 RMSE% ranged from 37.3% when object density was 2 objects ha 1 to 31.9% when object density was 10 objects ha 1 with no clear trend. CV () D ranged from 33.0% when object density was 2 objects ha 1 to 30.1% when object density was 10 objects ha 1 with no clear trend (Table 21). Surprisingly, the percentage of times 95% CI of D contained was only 64.3% to 72.6% depending upon object density, with no clear trend (Table 21). The percentage of times it was TD 43 PAGE 44 underestimated ranged from 18.5% to 21.5%, and the percentage of times it was overestimated ranged from 8.8% to 13.3% (Table 21). Effects of object density and transect length Accuracy of estimates of density increased with increasing transect density for all object densities with RMSE% ranging from 22.7% to 49.7% depending upon object density and transect density (Figure 23A). When object density was low, Bias% decreased from 13.7% to 6.4% with increasing transect density, however, when object density was medium or high, Bias% ranged from 5.3% to 6.8%, with no clear trend (Table A1). Precision ranged from 21.2% to 42.1% depending upon object density and transect density (Table A1). For all object densities, the percentage of times 95% CI of D contained increased with increasing transect density. The range of values was 59.4% to 76.5% (Figure 24A) depending upon object density and transect density. TD Effects of object density and transect layout RMSE% ranged from 28.1% to 40.4% depending upon object density and transect layout, with no clear trend (Figure 25A). For all object densities the bias of estimates of density was less for a systematic transect layout, however precision was lower. Bias% ranged from 5.0% to 17.6%, and CV () D ranged from 25.7% to 33.4% (Table A1) depending upon object density and transect layout. The percentage of times 95% CI of D contained ranged from 61.3% to 73.7% with no clear trend (Figure 26A). TD Effects of object density and transect number RMSE% ranged from 31.5% to 37.5% depending upon object density and transect layout, with no clear trend (Figure 27A). For all object densities the bias of estimates of density when using few long transects was less than when using several short transects, however, the precision 44 PAGE 45 was lower. Bias% ranged from 4.9% to 11.0%, and CV () D ranged from 29.4% to 33.6% (Table A1) depending upon object density and transect number. The percentage of times 95% CI of D contained ranged from 63.0% to 73.1% and there was no clear trend (Figure 28A). TD Effects of object density, and transect length, layout, and number Taking into account all factors for a clumped object distribution, the lowest RMSE% was 17.8% for an object density of 6 objects ha 1 a transect density of 30 m ha 1 a random transect layout, and few long transects. Bias% was 2.8%, CV () D was 17.5%, and 95% CI of D contained 78.0% of the time. TD Random Distribution Ignoring all other factors, RMSE% was 8.5%, Bias% was 0.7%, CV () D was 55%, and the 95% CI of D contained 94.0% of the time, 3.6% of the time it was underestimated, and 2.4% of the time it was overestimated (Table 21). The number of objects detected as a percentage of the total number of objects simulated was 4.7%, 9.5% and 14.2% when using a transect density of 10 m ha TD 1 20 m ha 1 and 30 m ha 1 respectively. Effects of object density Accuracy of estimates of density increased with increasing object density. RMSE% decreased from 14.3% when object density was 2 objects ha 1 to 6.6% when object density was 10 objects ha 1 (Table 21). Precision of estimates of density increased with increasing object density. CV () D decreased from 14.1% when object density was 2 objects ha 1 to 6.5% when object density was 10 objects ha 1 (Table 21). Bias% ranged from 0.5% to 1.7% depending upon object density with no clear trend (Table 21). The percentage of times 95% CI of D contained ranged from 93.5% to 94.4% with no clear trend (Table 21). The percentage of times it was TD 45 PAGE 46 underestimated ranged from 3.0% to 4.1%, and the percentage of times it was overestimated ranged from 2.1% to 2.7% (Table 21). Effects of object density and transect length Accuracy of estimates of density increased with increasing transect density for all object densities. RMSE% ranged from 5.0% to 17.7% depending upon object density and transect density (Figure 23B). Bias% ranged from 0.2% to 1.9% depending upon object density and transect density with no clear trend (Table A1). Precision of estimates of density increased with increasing transect density with CV () D ranging from 4.9% to 17.5% depending upon object density and transect density (Table A1). The percentage of times 95% CI of D contained ranged from 93.1% to 95.1% with no clear trend (Figure 24B). TD Effects of object density and transect layout Accuracy of estimates of density was slightly higher when using a systematic transect layout for all object densities. RMSE% ranged from 6.5% to 14.5% depending upon object density and transect layout (Figure 25B). Bias% ranged from 0.3% to 1.6% depending upon object density and transect layout with no clear trend (Table A1). Precision of estimates of density was slightly higher when using a systematic transect layout for all object densities. CV () D ranged from 6.5% to 14.2% depending upon object density and transect layout (Table A1). The percentage of times 95% CI of D contained ranged from 93.2% to 94.8% with no clear trend (Figure 26B). TD Effects of object density and transect number For all object densities there was no clear trend in the effect of transect number on accuracy of estimates of density. RMSE% ranged from 6.5% to 14.6% (Figure 27B), Bias% ranged from 0.3% to 2.0%, and CV () D ranged from 6.4% to 14.2% depending upon object 46 PAGE 47 density and transect number (Table A1). The percentage of times 95% CI of D contained Dranged from 93.1% to 94.8% with no clear trend (Figure 28B). Effects of object density, and transect length, layout, and num T ber lowesSE% was 4.8% for Taking into account all factors for a random object distribution, the t RM an object density of 10 objects ha 1 a transect density of 30 m ha 1 a systematic transect layout, and several short transects. Bias% was 0.4%, CV() D was 4.8%, and 95% CI of D contained TD 94.7% of the time. Uniform Distribution For a uniform dist ribution, ignoring all other factors, RMSE% was 28.1%, Bias% was 5.0%, CV() D was 62.1%, and 95% CI of D contained TD 87.5% of the time, 10.4% of the tit was underestimated, and 2.1% of the timit was overestimated (Table 21). For a uniform distribution the number of objects detected as a percentage of the total number of objects simulated was 4.7%, 9.5%, and 14.1% when using a transect density of 10 m ha ime e 1, and 1y end in the effect of object density on accuracy of estimates of density. RMS 1 20 m ha30 m ha respectively. Effects of object densit There was no clear tr E% ranged from 8.8% to 28.4%, Bias% ranged from 3.7% to 10.1%, and CV() D ranged from 8.3% to 24.6% depending upon object density (Table 21). The percentage ofes 95% Cof tim I D contained TD ranged from 88.0% to 92.8% with no clear trend (Table 21). The perntage of tim it was underestimated ranged from 4.0% to 15.3%, and the percentatimes if was overestimated ranged from 0.3% to 3.3% (Table 21). ceesge of 47 PAGE 48 Effects of object density and transect length estimates of density increased with increasing transe% n f When object density was low, accuracy of ct density, however for medium or high object densities, there was no clear trend in the effect of object density on accuracy of estimates of density. RMSE% ranged from 7.2% to 47.8depending upon object density and transect density (Figure 23C). Bias% ranged from 1.0% to 24.7% depending upon object density and transect density with no clear trend (Table A1). Wheobject density was low, precision of estimates of density increased with increasing transect density, however for medium or high object densities, there was no clear trend in the effect oobject density on the precision of estimates of density. CV() D ranged from 5.4% to 32.7% depending upon object density and transect density (Table A1). The percentage of times 95%of CI D contained TD ranged from 62.0% to 98.6% with no clear trend (Figure 24C). Effects of object density and transect layout For all object densities the accuracy of est imates of density was significantly higher when using a random transect layout. RMSE% ranged from 4.9% to 32.6% (Figure 25C), Bias% ranged from 0.1% to 13.5%, CV() D ranged from 4.9% to 27.0% (Table A1), and the percentage of times 95% CI of D co ntained TD ranged from 77.2% to 99.3% dependinobject density and transect layout (Figure 26C). Effects of object density and transect number g upon ates of density was higher when using several short cision For all object densities the accuracy of estim transects with RMSE% ranging from 8.5% to 28.8% depending upon object density and transect number (Figure 27C). Bias% ranged from 3.3% to 12.2% depending upon object density and transect number with no clear trend (Table A1). For all object densities the preof estimates of density was higher when using several short transects with CV(D) ranging from 48 PAGE 49 8.1% to 25.4% depending upon object density and transect number (Table A1). The percentage of times 95% CI of D contained TD ranged from 79.8% to 93.3% and was slightly higher when using several short transects (Figure 28C). Effects of object density, and transect leng th, layout, and number lowest RMSE% was 2.6 Taking into account all factors for a uniform object distribution, the % for an object density of 6 objects ha 1 a transect density of 30 m ha 1 a random transectlayout, and several short transects. Bias% was 0.2%, CV() D was 2.6%, and 95% CI of D contained TD 100.0% of the time. Discussion Accuracy of estimates of abundance this method may vary with respect to spatiaer of ary and number of transel ) For a influence accuracy of density estimates? obtained from l distribution and density of objects, but it is typically not possible to alter the spatial distribution or density study objects. However, it might be possible to improve accuracy of estimates of density through study design, for example, by altering layout, length, and numbtransects. This, however, requires an understanding of how layout, length, and number of transects influence accuracy of estimates of densities, and of how these influences might vdepending upon the spatial distribution pattern and density of study objects. I conducted a simulation study to determine the effect of length, layout cts on estimates of density and the precision of these estimates for different object spatiadistributions and densities. Specifically, I asked the following questions: (1) How does accuracyand of estimates of abundance obtained from the line transect method vary across spatial distribution patterns? (2) How might these patterns be influenced by density of objects? (3given spatial distribution and density level, how does the layout, length, and number of transects 49 PAGE 50 Overall, density estimated using the line transect method was within 3.9% of the true density, but it varied substantially dependi ng upon spatial distribution pattern of objects (Table 21). this y ightly ensity n of objects was clumped. Bias of estimates of density increased with iere ias, The line transect method was most accurate when objects were distributed randomly; incase root mean squared error (RMSE) between estimated density and true density was 8.5% of the true density (Table 21). Consequently, this method may be most appropriate for objects or organisms that exhibit a random distribution pattern. In contrast, the line transect method was least accurate when object were distributed in a clumped pattern; in this case the root mean squared error (RMSE) between estimated density and true density was 36.4% of the true densit(Table 21). The spatial distribution of objects did not seem to substantially influence the precision of estimates of density (Table 21). The percentage of times 95% CI of estimated density contained true density was highest for a random distribution of objects (94.0%), slless for a uniform distribution of objects (87.5%), and lowest for a clumped distribution of objects (67.9%) (Table 21). There was no clear trend for the effect of object density on accuracy of estimates of dwhen the pattern of distributio ncreasing object density, but there was no clear trend for precision of estimates of density. When objects were distributed randomly, accuracy of estimates of density increased with increasing object density. Precision of estimates of density increased with increasing object density; however, there was no clear trend in bias of estimates of density. When objects wdistributed uniformly, there was no clear trend for the effect of object density on accuracy, bor precision of estimates of density. The percentage of times 95% CI of estimated density contained the true density did not seem to be affected by object density for any object distribution. 50 PAGE 51 The results of my study were consistent with most of my hypotheses. The line tramethod worked well for a random nsect distribution of objects (RMSE% was 8.5% of the true densi density; effect y was ed rovide a basis for adequate variance estimal ty). However, accuracy of estimates of density was less than desired for a uniform distribution of objects (RMSE% was 28.1% of the true density) (Table 21). For a randomdistribution of objects, precision of estimates of density increased with increasing object however, when object distribution was clumped or uniform, there was no clear trend in the of object density on precision of estimates of density. Consistent with my hypothesis, accuracy of estimates of density increased with an increasing transect length for random and clumped distributions. However, for a uniform distribution of objects with medium and high object density, there was no clear trend in the effect of transect length on accuracy of estimates of density (Figures 23A, 23B, and 23C). Consistent with my hypothesis, for a clumped distribution of objects, a random transect layout worked better than when using a systematictransect layout when object density was medium and high, however, when object densitlow, a systematic transect layout provided slightly greater accuracy (Figure 25A). Transect number did not seem to have a substantial effect on accuracy of estimates of density for all object densities (Figure 27A). Consistent with my hypothesis, a random transect layout workvery well when objects were distributed uniformly (Figure 25C), and when objects were distributed randomly, transect layout and transect number did not have a substantial effect on the accuracy of estimates of density (Figures 25B and 27B). Buckland et al. (2001) note the importance of replication of transects and stress that a minimum of 10 to 20 replicate lines should be surveyed to p ation. In my study, the average number of transects simulated for each of the three spatidistributions (clumped, random, and uniform) was approximately 11 and 18 when using few long 51 PAGE 52 transects and several short transects respectively. Additionally, Buckland et al. (2001) note that asystematic placement of lines provides better spatial coverage and has superior precision to lines that are randomly and independently distributed. In my study, transect layout did not seem to affect the spatial coverage of transects, and the number of objects detected as a percentage of the total number of objects simulated ranged from 9 to 10% for both random and systematic transelayouts for all spatial distributions. However, transect layout did have an influence on the precision of estimates of abundance. For a clumped distribution, a random transect layout provided greater precision than using a systematic transect layout for all object densities. Frandom distribution, using a systematic transect layout provided slightly greater precision fobject densities. For a uniform distribution, using a random transect layout provided substantiallgreater precision for all object densities (Table A1). Williams et al. (2002) note that systematic positioning of transects is acceptable if the animal or object locations are random, else random tra ct or a or all y nsect placement is necessary to ensure accurties e found that transect lengths did not ate statistical inferences. My results were consistent with this observation. I found that when objects followed a random distribution, results from the line transect method using a systematic transect layout and a random transect layout were very similar for all object densi(Figures 25B and 26B, and Table A1). However, for uniformly distributed objects, the lintransect method worked better when using a random transect layout than a systematic transect layout (Figures 25C and 26C, and Table A1). When objects followed a clumped distributionresults from the line transect method using a systematic transect layout and a random transect layout were similar (Figures 25A and 26A, and Table A1). Fowler (1986) conducted a study to assess the effect of transect length on estimates of density and precision for species of coral reef fish. The study 52 PAGE 53 signify d f icantly affect estimates of density; however, precision was variable with the smallest transect length providing the least precise estimates of density. In my study, for a clumped distribution, accuracy of estimates of density (Figure 23A), precision of estimates of densit(Table A1), and 95% CI coverage of TD (Figure 24A) increased with increasing transect density for all object densities. For a random distribution, accuracy of estimates of density (Figures 23B), and precision of estima of density (Table A1) increased with increasing transect density for all object densities. However increasing transect density did not seem tosignificantly influence the 95% CI coverage of TD for any object density (Figure 24B). For a uniform distribution with low and object density, increasing the transect density increased the accuracy and precision of estimates of density (Fure 23C and Table A1). However, there seemed to be a contradictory effect on estimates of density when object density was medium anhigh (Figures 23C and 24C). One reason for this could be the relatively poor performance othe line transect method for a uniform distribution with an object density of 10 objects ha1, a transect density of 20 m ha1, and a systematic transect layout (RMSE% = 55.1%, Bias% = 32.7%, CV() tes ig D = 33.3%, and 95% CI coverage of TD = 50.7%). Conclusion For objects that are distributed in a clumped distribution, there was no clear trend in th e effect of object density on accuracy of estidance. Bias of estimates of density decref mates of abun ased as object density was increased; however, there was no clear trend in the effect of object density on precision of estimates of abundance. The percentage of times the 95% CI oestimated density contained true density was very low for a clumped distribution of objects which is troubling because most organisms occur in clumped distributions. There was no significant effect of transect layout on estimates of abundance. I recommend using a higher 53 PAGE 54 transect length as this increased the accuracy of estimates of density, and the 95% CI covetrue density. The number of transects did not have a significant effect on accuracy of estimatabundance. For objects that are distributed in a random distribution, accuracy of estimates of abundance in rage of es of creased with increasing object density. I recommend using a systematic transect layoudom ial. of or all object densities, I recommend using a random transect layout as this pt cts. t as accuracy of estimates of abundance was slightly greater than when using a rantransect layout. I also recommend using a higher transect length as accuracy of estimates of abundance increased with increasing transect density; however, this increase was not substantThe number of transects (few long, or several short) did not significantly affect the accuracy estimates of abundance. For objects distributed in uniform distribution, the line transect method worked best for a medium object density. F rovided significantly greater accuracy than when using a systematic transect layout. When using a random transect layout, total transect length increased the accuracy of estimates of abundance and I recommend using a higher transect length. I also recommend using several shortransects as accuracy of estimates of abundance was higher than when using few long transe 54 PAGE 55 Table 21. Density estimates by object spatial distribution and density Input TD D 95% CI( D ) RMSE% CV( D ) Bias% 95% D CI Under Over Overall 5.94 6.17 6.12 6.22 26.8% 60.4% 3.9% 83.2% 11.3% 5.5% Clumped 5.79 6.14 5.72 5.86 36.4% 63.4% 6.1% 67.9% 20.0% 12.1% 2 objects ha 1 1.97 2.13 2.13 2.19 37.3% 33.0% 9.6% 72.6% 18.5% 8.8% 6 objects ha 1 5.75 6.08 6.01 6.16 31.6% 29.7% 5.8% 64.3% 21.5% 14.2% 10 objects ha 1 9.65 10.19 10.07 10.32 31.9% 30.1% 5.6% 66.9% 19.8% 13.3% Random 6.00 6.04 5.92 6.08 8.5% 55.0% 0.7% 94.0% 3.6% 2.4% 2 objects ha 1 2.00 2.03 2.02 2.04 14.3% 14.1% 1.5% 93.5% 4.1% 2.4% 6 objects ha 1 6.00 6.03 6.01 6.05 8.4% 8.4% 0.5% 94.3% 3.0% 2.7% 10 objects ha 1 10.00 10.07 10.05 10.10 6.6% 6.5% 0.7% 94.4% 3.5% 2.1% Uniform 6.02 6.32 5.94 6.09 28.1% 62.1% 5.0% 87.5% 10.4% 2.1% 2 objects ha 1 2.00 2.20 2.19 2.22 21.5% 17.2% 10.1% 88.0% 11.8% 0.3% 6 objects ha 1 6.04 5.81 5.80 5.83 8.8% 8.3% 3.7% 92.8% 4.0% 3.3% 10 objects ha 1 10.01 10.94 10.83 11.05 28.4% 24.6% 9.2% 81.9% 15.3% 2.8% Note: is the true object density, TD D is the estimated object density, 95% CI( D ) is the 95% confidence interval of D RMSE% is the root mean squared error between D and as a percentage of CV( TD TD D ) is the coefficient of variation of D Bias% is the mean difference between D and TD as a p ercentage of TD, 95% D CI is the p ercentage of times that the 95% CI computed by Program DISTANCE for D contained Under is the percentage of times that was below the lower limit of TD TD 95% D CI and Over is the percentage of times that D was above the upper limit of 95% T D CI. 55 PAGE 56 0 5 10 15 20 25 0 5 10 15 20 25 A) 0 5 10 15 20 25 0 5 10 15 20 25 B) Figure 21. Examples of simulated spatial distributions of objects with a density of 2 objects ha 1 A) For a clumped distribution. B) For a random distribution. C) For a uniform distribution. 56 PAGE 57 0 5 10 15 20 25 0 5 10 15 20 25 C) Figure 21. Continued 57 PAGE 58 0 5 10 15 20 25 0 5 10 15 20 25 A) Figure 22. Transect layout patterns with objects simulated in a random spatial distribution with a density of 2 objects ha, and a transect density of 10 m ha 1 1 For the systematic layouts the starting x and y coordinates for the first transect line were chosen as 10 and 10 respectively to ensure that all transects fell inside the study area. A) Random transect layout with few long transects. B) Random transect layout with several short transects. C) Systematic transect layout with few long transects. D) Systematic transect layout with several short transects. 58 PAGE 59 0 5 10 15 20 25 0 5 10 15 20 25 B) 0 5 10 15 20 25 0 5 10 15 20 25 C) Figure 22. Continued 59 PAGE 60 0 5 10 15 20 25 0 5 10 15 20 25 D) Figure 22. Continued 60 PAGE 61 A) 0102030405060 10 m ha1 20 m ha1 30 m ha1 Object density (Objects ha1)2610Transect DensityRMSE% Figure 23. Effect of transect length on accuracy of estimates of density for a given object spatial distribution and object densities ranging from 2 objects ha to 10 objects ha 1 1 The root mean squared error between estimated object density ( D ) and true object density () as a percentage of (RMSE%) is plotted against transect density (m ha TD TD 1 ) for different object densities. A) In a clumped distribution. B) In a random distribution. C) In a uniform distribution. 61 PAGE 62 02468101214161820 10 m ha1 20 m ha1 30 m ha1 Object density (Objects ha1)2610Transect DensityRMSE%B) 0102030405060 10 m ha1 20 m ha1 30 m ha1 Object density (Objects ha1)2610Transect DensityRMSE%C) Figure 23. Continued 62 PAGE 63 95% CI of density estimate 020406080100 10 m ha1 20 m ha1 30 m ha1 Object density (Objects ha1)2610Transect densityA) Figure 24. Effect of transect length on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha to 10 objects ha 1 1 The percentage of times that the 95% CI computed by Program DISTANCE for each density estimate ( D ) contained true object density () is plotted against transect density (m ha TD 1 ) for different object densities. A) In a clumped distribution. B) In a random distribution. C) In a uniform distribution. 63 PAGE 64 95% CI of density estimate 020406080100 10 m ha1 20 m ha1 30 m ha1 Object density (Objects ha1)2610Transect densityB) 95% CI of density estimate 020406080100120 10 m ha1 20 m ha1 30 m ha1 Object density (Objects ha1)2610Transect densityC) Figure 24. Continued 64 PAGE 65 01020304050 Random Systematic Object density (Objects ha1)2610Transect layoutRMSE%A) Figure 25. Effect of transect layout on accuracy of estimates of density for a given object spatial distribution and object densities ranging from 2 objects ha to 10 objects ha 1 1 The root mean squared error between estimated object density ( D ) and true object density () as a percentage of (RMSE%) is plotted against transect layout (random, and systematic) for different object densities. A) In a clumped distribution. B) In a random distribution. C) In a uniform distribution. TD TD 65 PAGE 66 0246810121416 Random Systematic Object density (Objects ha1)2610Transect layoutRMSE%B) 05101520253035 Random Systematic Object density (Objects ha1)2610Transect layoutRMSE%C) Figure 25. Continued 66 PAGE 67 95% CI of density estimate 020406080 Random Systematic Object density (Objects ha1)2610Transect layoutA) Figure 26. Effect of transect layout on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha to 10 objects ha 1 1 The percentage of times that the 95% CI computed by Program DISTANCE for each density estimate ( D ) contained true object density () is plotted against transect density (m ha TD 1 ) for different object densities. A) In a clumped distribution. B) In a random distribution. C) In a uniform distribution. 67 PAGE 68 95% CI of density estimate 020406080100 Random Systematic Object density (Objects ha1)2610Transect layoutB) 95% CI of density estimate 020406080100120 Random Systematic Object density (Objects ha1)2610Transect layoutC) Figure 26. Continued 68 PAGE 69 010203040 Few long Several short Object density (Objects ha1)2610Transect numberRMSE%A) Figure 27. Effect of transect number on accuracy of estimates of density for a given object spatial distribution and object densities ranging from 2 objects ha to 10 objects ha 1 1 The root mean squared error between estimated object density ( D ) and true object density () as a percentage of (RMSE%) is plotted against transect layout (random, and systematic) for different object densities. A) In a clumped distribution. B) In a random distribution. C) In a uniform distribution. TD TD 69 PAGE 70 0246810121416 Few long Several short Object density (Objects ha1)2610Transect numberRMSE%B) 05101520253035 Few long Several short Object density (Objects ha1)2610Transect numberRMSE%C) Figure 27. Continued 70 PAGE 71 Distance 95% CI 020406080 Fewlong Severalshort Object density (Objects ha1)2610Transect numberA) Figure 28. Effect of transect number on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha to 10 objects ha 1 1 The percentage of times that the 95% CI computed by Program DISTANCE for each density estimate ( D ) contained true object density () is plotted against transect density (m ha TD 1 ) for different object densities. A) In a clumped distribution. B) In a random distribution. C) In a uniform distribution. 71 PAGE 72 95% CI of density estimate 020406080100 Fewlong Severalshort Object density (Objects ha1)2610Transect numberB) 95% CI of density estimate 020406080100 Fewlong Severalshort Object density (Objects ha1)2610Transect numberC) Figure 28. Continued 72 PAGE 73 CHAPTER 4 CONCLUSION The overall goal of my research was to analyze abundance estimation methods using real and simulated data. I fieldtested the efficacy and costeffectiveness of line transect, total count, sample count, and double observer methods for estimating gopher tortoise burrow abundance. I applied these methods to estimate burrow abundance in two strata in the Ordway Swisher Biological Station, Florida. Additionally, I also addressed the issue of gopher tortoise burrow occupancy, and used estimates of burrow abundance and occupancy rates to estimate abundance of gopher tortoises. I then further analyzed the line transect method using a simulationbased approach in MATLAB. The results of my field study indicated that habitat type of the study area, and available time and resources should be taken into consideration when selecting an abundance estimation method. The line transect method is perhaps the most efficient method for estimating gopher tortoise burrow abundance because it is less costly than total and sample count methods, and it is more likely to capture a wider range of spatial variation in the distribution and abundance of burrows, while providing statistically robust estimates of precision. However, a good understanding of the method as well as some understanding of underlying theory and working knowledge of Program DISTANCE is needed for effective implementation of this method. If one wishes to implement the total count or sample count method, I recommend using multiple observers in order to obtain estimates of detectability. The total count and sample count methods are relatively straightforward to implement, and require no sophisticated software for data analyses. However, these methods are costly, particularly when a substantial proportion of the sites needed to be sampled. Moreover, these methods do not offer rigorous estimates of 73 PAGE 74 74 precision. The double observer method partially a ddressed some of these concerns by providing estimates of precision (when detectability is less than one), but is costly to implement. My estimates of burrow occupancy rates (active: 0.50 0.09; inactive: 0.04 0.04) were substantially lower than Auffenberg and Franz s correction factor of 61.4% (Auffenberg and Franz 1982). Some studies have us ed this or a similar correcti on factor (e.g., Ashton and Ashton ( in press )) for converting estimates of burrow abundan ce to tortoise abundance (Kushlan and Mazotti 1984, Doonan 1986, Doonan and Eppe rson 2001, FFWCC 2006, Gr egory et al. 2006). However, this approach ignores the spatial, tem poral or habitatspecific variation in occupancy rate and can cause estimates of gopher tortoise abundance to be unreliabl e (Burke and Cox 1988, Breininger et al. 1991, McCoy a nd Mushinsky 1992, Moler and Be rish 2001). I recommend that burrow cameras (or similar technologies) shou ld be used, along with a patch occupancy modeling approach for data analysis, to estima te habitatspecific burrow occupancy rates. The results of the simulation study provided valuable informa tion about the influence of length, layout and number of transects on the acc uracy of estimates of abundance for different spatial distribution patterns and density levels of objects. The accuracy of estimates of abundance obtained from the line transect method varied substantially depending up on spatial distribution pattern of objects. The line tr ansect method was most accurate when objects were distributed randomly. Consequently, this method may be most appropriate for object s or organisms that exhibit a random distribution pa ttern. In contrast, the line tran sect method was least accurate when object were distributed in a clumped pattern, which is tr oubling because most organisms occur in clumped distributions. Increasing transect length had a positive e ffect on the accuracy of estimates of abundance for random and clumpe d spatial distributions of objects, and I recommend that researchers use, at a minimum, a transect length that will provide 60 to 80 PAGE 75 observations as recommended by Buckland et al. (2001). For a clumped distribution of objects, the positive effect of an increasing transect length on accuracy of estimates of abundance was greater, as this likely captured the greater spatial variation in distribution of objects, and I recommend that researchers try to maximize the total transect length when determining study design. Transect layout pattern had a significant effect for a uniform distributions of objects; in this case, accuracy and precision of estimates of abundance were substantially higher, and bias was lower when using a random transect layout. Furthermore, when using a random transect layout, increasing transect length increased the accuracy of estimates of abundance. For a random distribution of objects, using a systematic transect layout provided slightly greater accuracy than when using a random transect layout. For a clumped distribution, there was no significant effect of transect layout on estimates of abundance. The number of transect used did not significantly affect the accuracy of estimates of abundance when the object distribution pattern was random or clumped. However, for a uniform distribution of objects, accuracy of estimates of abundance was higher when using several short transects than when using few long transects. 75 PAGE 76 APPENDIX OVERALL RESULTS 76 Table A1. Simulation study results Dist ODens TDens TL TNum T D D 95% CI( D ) RMSE RMSE% CV( D ) Bias% 95% D CI Sim Runs 5.94 6.17 6.12 6.22 1.59 26.8% 60.4% 3.9% 83.2% 21600 clumped 5.79 6.14 5.72 5.86 2.11 36.4% 63.4% 6.1% 67.9% 7200 random 6.00 6.04 5.92 6.08 0.51 8.5% 55.0% 0.7% 94.0% 7200 uniform 6.02 6.32 5.94 6.09 1.69 28.1% 62.1% 5.0% 87.5% 7200 clumped 2 1.97 2.16 2.13 2.19 0.73 37.3% 33.0% 9.6% 72.6% 2400 clumped 6 5.75 6.08 6.01 6.16 1.82 31.6% 29.7% 5.8% 64.3% 2400 clumped 10 9.65 10.19 10.07 10.32 3.08 31.9% 30.1% 5.6% 66.9% 2400 random 2 2.00 2.03 2.02 2.04 0.29 14.3% 14.1% 1.5% 93.5% 2400 random 6 6.00 6.03 6.01 6.05 0.51 8.4% 8.4% 0.5% 94.3% 2400 random 10 10.00 10.07 10.05 10.10 0.66 6.6% 6.5% 0.7% 94.4% 2400 uniform 2 2.00 2.20 2.19 2.22 0.43 21.5% 17.2% 10.1% 88.0% 2400 uniform 6 6.04 5.81 5.80 5.83 0.53 8.8% 8.3% 3.7% 92.8% 2400 Note: Dist is the spatial distribution of objects, ODens is the density of objects in objects ha1, TDens is the transect density in m ha1, TL is the transect layout (r is random, and s is systematic), TNum is the transect number (f is few long, and s is several short), T D is the true object density in objects ha 1 D is the estimated object density in objects ha 1 95% CI( D ) is the 95% confidence interval of D RMSE is the root mean squared error between D and T D RMSE% is RMSE as a percentage of T D CV( D ) is the coefficient of variation of D Bias% is the mean of the difference between D and T D as a percentage of T D 95% D CI is the percentage of times that the 95% CI computed by Program DISTANCE for D covered T D and Sim runs indicates the total number of simulation runs upon which the associated results are based. PAGE 77 77 Table A1. Continued Dist ODens TDens TL TNum T D D 95% CI( D ) RMSE RMSE% CV( D ) Bias% 95% D CI Sim Runs uniform 10 10.01 10.94 10.83 11.05 2.85 28.4% 24.6% 9.2% 81.9% 2400 clumped 10 5.79 6.17 6.00 6.34 2.70 46.6% 68.1% 8.4% 64.0% 2400 clumped 20 5.79 6.17 6.01 6.32 1.92 33.2% 62.2% 6.9% 68.4% 2400 clumped 30 5.79 6.09 5.95 6.24 1.55 26.7% 59.4% 5.5% 71.4% 2400 random 10 6.00 6.05 5.92 6.19 0.65 10.8% 55.5% 0.9% 93.9% 2400 random 20 6.00 6.03 5.90 6.17 0.46 7.7% 54.9% 0.8% 93.8% 2400 random 30 6.00 6.04 5.91 6.17 0.37 6.2% 54.6% 1.0% 94.4% 2400 uniform 10 6.02 5.97 5.84 6.10 0.61 10.1% 53.5% 2.0% 95.5% 2400 uniform 20 6.02 6.87 6.68 7.07 2.79 46.4% 71.2% 10.7% 77.8% 2400 uniform 30 6.02 6.11 5.98 6.25 0.64 10.6% 55.7% 3.0% 89.3% 2400 clumped r 5.79 6.27 6.09 6.44 1.90 32.8% 60.3% 10.4% 72.8% 1800 clumped s 5.76 6.10 6.00 6.21 2.18 37.6% 64.4% 5.8% 66.3% 5400 random r 6.00 6.04 5.88 6.19 0.53 8.8% 55.0% 0.9% 93.8% 1800 random s 6.00 6.05 5.96 6.11 0.50 8.4% 55.0% 0.9% 94.1% 5400 uniform r 6.01 6.02 5.88 6.19 0.48 8.0% 55.3% 0.1% 97.9% 1800 uniform s 6.02 6.41 6.30 6.52 1.93 32.1% 63.9% 6.9% 84.1% 5400 clumped f 5.79 6.11 5.98 6.21 2.11 36.4% 63.5% 6.1% 68.2% 3600 PAGE 78 78 Table A1. Continued Dist ODens TDens TL TNum T D D 95% CI( D ) RMSE RMSE% CV( D ) Bias% 95% D CI Sim Runs clumped s 5.79 6.18 6.06 6.31 2.11 36.5% 63.2% 7.7% 67.7% 3600 random f 6.00 6.05 5.94 6.16 0.52 8.6% 55.1% 0.8% 94.1% 3600 random s 6.00 6.04 5.93 6.15 0.50 8.3% 54.8% 1.0% 94.0% 3600 uniform f 6.02 6.30 6.17 6.42 1.72 28.5% 61.8% 5.5% 86.1% 3600 uniform s 6.02 6.34 6.21 6.47 1.67 27.7% 62.4% 4.9% 88.9% 3600 clumped 2 10 1.97 2.24 2.17 2.30 0.98 49.7% 42.1% 13.7% 68.4% 800 clumped 2 20 1.97 2.14 2.09 2.18 0.65 33.1% 29.5% 8.8% 73.0% 800 clumped 2 30 1.97 2.09 2.06 2.13 0.49 24.7% 22.8% 6.3% 76.5% 800 clumped 6 10 5.75 6.12 5.96 6.28 2.35 40.9% 38.2% 6.3% 59.4% 800 clumped 6 20 5.75 6.05 5.94 6.17 1.65 28.7% 27.1% 5.2% 64.8% 800 clumped 6 30 5.75 6.08 5.99 6.17 1.30 22.7% 21.2% 5.6% 68.8% 800 clumped 10 10 9.64 10.16 9.89 10.43 3.92 40.6% 38.5% 5.3% 64.4% 800 clumped 10 20 9.66 10.31 10.12 10.51 2.82 29.2% 26.9% 6.7% 67.5% 800 clumped 10 30 9.66 10.11 9.95 10.27 2.29 23.8% 22.6% 4.6% 68.9% 800 random 2 10 2.00 2.02 2.00 2.05 0.35 17.7% 17.5% 1.2% 93.4% 800 random 2 20 2.00 2.03 2.01 2.05 0.27 13.4% 13.1% 1.5% 93.1% 800 random 2 30 2.00 2.04 2.02 2.05 0.22 11.2% 10.8% 1.9% 93.9% 800 random 6 10 6.00 6.04 6.00 6.09 0.65 10.8% 10.7% 0.7% 94.6% 800 random 6 20 6.00 6.01 5.98 6.05 0.47 7.8% 7.8% 0.2% 93.3% 800 random 6 30 6.00 6.03 6.00 6.05 0.35 5.9% 5.9% 0.4% 95.0% 800 random 10 10 10.00 10.09 10.04 10.15 0.84 8.4% 8.3% 0.9% 93.8% 800 random 10 20 10.00 10.06 10.02 10.10 0.60 6.0% 5.9% 0.6% 95.1% 800 random 10 30 10.00 10.06 10.03 10.10 0.50 5.0% 4.9% 0.6% 94.3% 800 PAGE 79 79 Table A1. Continued Dist ODens TDens TL TNum T D D 95% CI( D ) RMSE RMSE% CV( D ) Bias% 95% D CI Sim Runs uniform 2 10 2.00 2.23 2.20 2.26 0.46 23.0% 17.9% 11.5% 91.5% 800 uniform 2 20 2.00 2.18 2.15 2.20 0.42 21.1% 17.7% 8.7% 86.1% 800 uniform 2 30 2.00 2.20 2.18 2.23 0.40 20.1% 15.8% 10.2% 86.3% 800 uniform 6 10 6.04 5.76 5.73 5.79 0.54 8.9% 8.0% 4.6% 98.6% 800 uniform 6 20 6.04 5.95 5.91 5.99 0.61 10.0% 10.1% 1.5% 85.3% 800 uniform 6 30 6.04 5.73 5.71 5.76 0.44 7.2% 5.4% 5.0% 94.4% 800 uniform 10 10 10.01 9.92 9.86 9.97 0.78 7.8% 7.8% 1.0% 96.4% 800 uniform 10 20 10.01 12.49 12.77 12.21 4.78 47.8% 32.7% 24.7% 62.0% 800 uniform 10 30 10.01 10.41 10.35 10.47 0.93 9.3% 8.1% 3.9% 87.4% 800 clumped 2 r 1.97 2.31 2.26 2.37 0.79 40.4% 31.0% 17.6% 71.3% 600 clumped 2 s 1.97 2.10 2.07 2.14 0.71 36.3% 33.4% 6.9% 73.1% 1800 clumped 6 r 5.75 6.10 5.97 6.23 1.62 28.1% 26.0% 6.0% 73.3% 600 clumped 6 s 5.75 6.08 5.99 6.16 1.88 32.8% 30.9% 5.6% 61.3% 1800 clumped 10 r 9.66 10.39 10.17 10.60 2.75 28.5% 25.7% 7.6% 73.7% 600 clumped 10 s 9.65 10.13 9.98 10.28 3.19 33.0% 31.4% 4.9% 64.7% 1800 random 2 r 2.00 2.03 2.01 2.06 0.29 14.5% 14.2% 1.7% 93.7% 600 random 2 s 2.00 2.03 2.02 2.04 0.29 14.3% 14.0% 1.5% 93.4% 1800 random 6 r 6.00 6.02 5.97 6.06 0.54 9.0% 8.9% 0.3% 94.5% 600 random 6 s 6.00 6.03 6.01 6.05 0.49 8.2% 8.2% 0.5% 94.2% 1800 random 10 r 10.00 10.07 10.01 10.12 0.68 6.8% 6.7% 0.7% 93.2% 600 random 10 s 10.00 10.08 10.05 10.11 0.65 6.5% 6.5% 0.8% 94.8% 1800 uniform 2 r 2.00 2.00 1.99 2.01 0.16 8.1% 8.1% 0.1% 99.3% 600 uniform 2 s 2.00 2.27 2.25 2.29 0.49 24.3% 17.9% 13.5% 84.2% 1800 uniform 6 r 6.04 6.01 5.99 6.03 0.30 4.9% 4.9% 0.5% 98.5% 600 PAGE 80 80 Table A1. Continued Dist ODens TDens TL TNum T D D 95% CI( D ) RMSE RMSE% CV( D ) Bias% 95% D CI Sim Runs uniform 6 s 6.04 5.75 5.73 5.77 0.59 9.8% 8.9% 4.8% 90.8% 1800 uniform 10 r 10.01 10.08 10.02 10.14 0.76 7.6% 7.5% 0.7% 96.0% 600 uniform 10 s 10.01 11.22 11.08 11.36 3.26 32.6% 27.0% 12.1% 77.2% 1800 clumped 2 f 1.97 2.13 2.09 2.17 0.73 37.1% 33.6% 8.3% 72.2% 1200 clumped 2 s 1.96 2.18 2.14 2.22 0.74 37.5% 32.5% 10.9% 73.1% 1200 clumped 6 f 5.75 6.06 5.96 6.17 1.83 31.8% 30.1% 5.4% 65.6% 1200 clumped 6 s 5.75 6.10 6.00 6.20 1.81 31.5% 29.4% 6.0% 63.0% 1200 clumped 10 f 9.65 10.12 9.95 10.29 3.07 31.8% 30.3% 4.8% 66.8% 1200 clumped 10 s 9.65 10.26 10.09 10.44 3.10 32.1% 29.9% 6.3% 67.0% 1200 random 2 f 2.00 2.02 2.00 2.04 0.28 14.1% 13.9% 1.0% 93.8% 1200 random 2 s 2.00 2.04 2.02 2.06 0.29 14.6% 14.2% 2.0% 93.1% 1200 random 6 f 6.00 6.03 6.00 6.06 0.52 8.6% 8.6% 0.6% 94.5% 1200 random 6 s 6.00 6.02 5.99 6.05 0.49 8.2% 8.2% 0.3% 94.1% 1200 random 10 f 10.00 10.09 10.05 10.13 0.67 6.7% 6.6% 0.9% 93.9% 1200 random 10 s 10.00 10.06 10.02 10.09 0.65 6.5% 6.4% 0.6% 94.8% 1200 uniform 2 f 2.00 2.24 2.22 2.27 0.49 24.3% 18.7% 12.2% 86.3% 1200 uniform 2 s 2.00 2.16 2.14 2.18 0.36 18.2% 15.1% 8.1% 89.6% 1200 uniform 6 f 6.04 5.79 5.76 5.82 0.55 9.1% 8.5% 4.1% 92.3% 1200 uniform 6 s 6.04 5.84 5.81 5.86 0.51 8.5% 8.1% 3.3% 93.3% 1200 uniform 10 f 10.01 10.85 10.70 11.01 2.88 28.8% 25.4% 8.4% 79.8% 1200 uniform 10 s 10.01 11.02 10.88 11.17 2.82 28.1% 23.9% 10.1% 84.0% 1200 PAGE 81 LIST OF REFERENCES Abrahamson, W. 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Relationship between gopher tortoise body size and burrow width. Herpetological Review 22:122124. Zollner, P. A., and S. L. Lima. 1999. Search strategies for landscapelevel interpatch movements. Ecology 80:10191030. 86 PAGE 87 BIOGRAPHICAL SKETCH Saif Z. Nomani was born in 1978 in Karachi, Pakistan. He graduated from Karachi Grammar School in 1996 and attended college at the Lahore University of Management Science, Lahore, Pakistan. He transferred to Rutgers University, New Brunswick, NJ, in January 1998. Upon graduating in January 2002 with his B.S. in computer science he worked as a physical security consultant at Constantin WalshLowe LLC. After 4 years of working as a consultant he was admitted to the Master of Science program at the Department of Wildlife Ecology and Conservation at University of Florida, Gainesville, FL, in 2005. 87 