UFDC Home  myUFDC Home  Help 



Full Text  
THE RELATIVE INFLUENCE OF DENSITY AND CLIMATE ON THE DEMOGRAPHY OF A SUBALPINE GROUND SQUIRREL POPULATION By EVA KNEIP 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 2010 2010 Eva Kneip To my mom, dad, and grandparents ACKNOWLEDGMENTS I thank my parents and close friends for their support and encouragement in my late career change to pursue my true passion. I am grateful to my supervisory committee for their wisdom, guidance, and time: Drs. M. K. Oli, M. E. Sunquist, and D. H. Van Vuren. My labmates and professional colleagues that contributed to my research and deserve recognition are G. Aldridge, J. A. Hostetler, G. Morris, B. Pasch, R. A. Pruner, and V. Rolland. I thank C. Floyd, K. Jenderseck, and C. Mueller for their assistance in data collection. I would also like to express special gratitude to C. McCaffery and Dr. D. L. Reed from the Mammalogy collection of the Florida Museum of Natural History for their support and faith in me. Finally, I thank the California Agricultural Experiment Station, UC Davis, the School of Natural Resources and Environment, UF, and the Department of Wildlife Ecology and Conservation, UF Gainesville for their generous financial support. TABLE OF CONTENTS page A C KNO W LEDG M ENTS ................................................ ................... ....... L IS T O F T A B L E S ............................................................................................ ............ 7 L IS T O F F IG U R E S ................................................................................ 8 A B S T R A C T ....................................................... 9 CHAPTER 1 IN T R O D U C T IO N ............................................................................................... ........ 11 2 RELATIVE INFLUENCE OF POPULATION DENSITY, CLIMATE, AND PREDATION ON THE DEMOGRAPHY OF A SUBALPINE SPECIES .................... 14 In tro d u c tio n ................................................................................................... 1 4 M atria ls a n d M eth o d s .................................. ........................................ ........ ........ 16 Study Area and Species ............................................................ ... .............16 F ie ld M e th o d s ............................................................ 17 P population S ize and Predation ......................................................................... .. 18 Abiotic Covariates .............................. ....................... ......... 18 Survival Analysis ............................... ....... ................... 19 Analysis of Reproductive Parameters ........ .............. ... ..... ........ 21 Results ....................................... ... .. ......... ......... ......... 22 Population Size and Composition ............. .. ...... ................ 22 Age, Sex, and Time Effects for Survival ..................... ....... .. .. .............. 22 Direct and Delayed DensityDependence (DD) for Survival...........................22 Effects of Abiotic Factors for Survival ................................... ...................... 23 Predation Effect for Survival .................. ................ ........ 23 DD vs. DID Models for Survival ......... .................... ..... ..........23 Breeding Probability (BP) ......... .... ..... ......................... .......... .. 24 Age, Sex, and Time Effects for BP ...... .............................. 24 Direct and Delayed Density Dependence for BP ............................25 Abiotic Impacts for BP ......................... ...... .........25 Predation Effect for BP ..................... ............. .........25 DD vs. DID Models for BP ................ .... ......... ....................... 25 L itte r S iz e ............... ................. ................................................................. 2 5 D is c u s s io n .............. .. ............... ................. .............................................. 2 6 3 STOCHASTIC POPULATION DYNAMICS OF A GOLDENMANTLED GROUND SQUIRREL POPULATION ............ ................................................. 36 Introduction .............. ....... Ss..... .......................... ...... ........... .. 36 M materials and M methods ............ ............ ........................... ................ 39 Study Area and Species ........ ..... .. .......... ................. .. .......... 39 Field Methods .............. ......................... ......... 40 Matrix Population Model ........ ................ ............ ... 40 D term inistic A analysis .................................. ....... ................................ 42 E nvironm ental S tochasticity................................................. .......... ................... 42 Density Dependence and Environmental Stochasticity................................ 44 R e s u lts ................. .. ............................................................................. 4 6 Determ inistic Analysis ................................................................. ......... .. .. .........46 Environm ental Stochasticity............................................................................. ... 47 Density Dependence and Environmental Stochasticity................................ 48 D discussion ................. ....................... ............................................ 49 4 C O N C L U S IO N ...................................................................................................... 6 3 APPENDIX A SURVIVAL MODELS TESTING FOR THE EFFECTS OF SEX, AGE, AND T IM E ................ ...................... ....... ......... ..................... .. .............. 66 B SURVIVAL MODELS TESTING FOR THE EFFECTS OF DENSITY DEPENDENT AND INDEPENDENT FACTORS ........... ...................................67 C BREEDING PROBABILITY MODELS TESTING FOR THE EFFECTS OF INTRINSIC, DENSITYDEPENDENT AND INDEPENDENT FACTORS................70 D LITTER SIZE MODELS TESTING FOR THE EFFECTS OF INTRINSINC, DENSITYDEPENDENT AND INDEPENDENT FACTORS................................ 72 LIST OF REFERENCES ....... ........................... ........ ...... .. .... ................. 74 B IO G R A P H IC A L S K E T C H .................................................................... ...................... 80 LIST OF TABLES Table page 31 Regression coefficients for logittransformed survival and logittransformed breeding probability (BP) for the goldenmantled ground squirrel population in G othic, C O ........... ....................... ............................... ..........55 32 Elasticities of stochastic population growth rate (As) to mean (Esl), variance (Eso), and both mean and variance (Es) of matrix elements.. ........................... 55 33 The number of juvenile and adult female goldenmantled ground squirrels that immigrated to our study site in Gothic, CO ............................................. 56 LIST OF FIGURES Figure page 21 Annual variation in the population size of the GMGS for the period 1990 2008. Total and age and sexspecific numbers of squirrels are presented .......32 22 Modelaveraged annual survival estimates with SE for adult (AF) and juvenile (JF) female, and adult (AM) and juvenile (JM) male GMGS during 1990 2 0 0 7 .......... .. ................... ................................................... 3 3 23 Relationship between previous year's population size and age and sex specific survival. ................................................................... .. ....... 34 24 Breeding probability and distribution of litter size of goldenmantled ground squirrels. .................................... ......................................... 35 31 Relationship between annual population density and the agespecific logit transform ed survival rate.. ........................................................................... .. 57 32 Annual variation in the deterministic population growth rate with 95% Cl for female goldenmantled ground squirrels during 19902007..............................58 33 Elasticity of projected population growth rate A to proportional changes in the lower level vital rates of the overall m atrix A..................................................... 59 34 Frequency distribution of population size in 50 years including only the effects of environm ental stochasticity................................................................. 60 35 Projected abundance of the female GMGS population for 50 years using the overall projection matrix and the average female abundance (30) under 5 scenarios for densitydependence............................................... ................ 61 36 Probability of quasi extinction under various scenarios of environmental stochasticity, densitydependence, and differing levels of quasiextinction threshold for the goldenmantled ground squirrel population..............................62 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 THE RELATIVE INFLUENCE OF DENSITY AND CLIMATE ON THE DEMOGRAPHY OF A SUBALPINE GROUND SQUIRREL POPULATION By Eva Kneip August 2010 Chair: Madan K. Oli Major: Interdisciplinary Ecology In the context of global climate change, understanding the causes and consequences of oscillations in populations is a central objective for ecologists. We utilized longterm (19902009) field data to investigate the influence of population size and extrinsic environmental factors on the demographic parameters of goldenmantled ground squirrels (Callospermophilus lateralis; formerly, Spermophilus lateralis). Moreover, we examined how these influences are translated at the population level. Survival varied by sex and age class, with highest survival for adult females (0=0.519, 95% CI: 0.462, 0.576) and lowest survival for juvenile males (0=0.120, 95% CI: 0.094, 0.152). There was evidence that population size negatively influenced survival with a time lag of 1 year. Among the extrinsic environmental factors considered, rainfall and an index of predator abundance substantially influenced survival. Breeding probability (probability that a female successfully wears1 pups) was higher for older females (0.717, 95% Cl=0.639 0.79) than for yearlings (=0.313, 95% CI: 0.228,  0.412). There was evidence that rainfall negatively influenced breeding probability of both older and yearling females with a time lag of 1 year. Litter size ranged 18 pups, with a mean of 4.81 (95% Cl: 4.532, 5.08). There was no evidence that litter size varied among age classes or over time, or was influenced by population size or extrinsic environmental factors. The yeartoyear deterministic population growth rate was highly variable, ranging from 0.445 to 1.244, and was below replacement (A<1) for 10 out of 18 years. Using 50,000 simulations and assuming a uniform independently and identically distributed environment, the stochastic population growth rate, As was 0.912 suggesting an 8.8% annual population decline. This result was less than the deterministic growth rate of the mean matrix, AM (0.944) but it was similar to the overall deterministic growth rate (A=0.905, 95% CI: 0.8120.998) which was based on pooled data. As a result of lowerlevel elasticity analysis, the deterministic population growth rate was most sensitive to proportionate changes in adult survival. All three measures of stochastic elasticity indicated that As was proportionately most sensitive to juvenile survival. The GMGS population is predicted to decline with probability of extinction approaching 90% in 50 years for the densityindependent model. When densitydependence and immigration were included in our model the risk of extinction was reduced to zero. Our results suggest that population size and extrinsic environmental factors do not affect all demographic variables in the same fashion and both factors act in concert to influence the size of our study population. As environmental variability is likely to exacerbate the fluctuations in GMGS abundance, the likelihood that the population falls below a critical threshold will increase. Therefore, the effects of an increased environmental stochasticity may amplify the risk of quasiextinction of this population. CHAPTER 1 INTRODUCTION While extinctions are a natural part of the evolutionary process, current extinction rates are estimated to be between 1,000 and 10,000 times the norm, and are solely humaninduced (Pimm et al. 1995; Rosser and Mainka 2002). The combined effects of landscape modification, resourceexploitation, invasive species introduction, and accelerated greenhousegas production greatly alter the biosphere (Krauss et al.; Lee and Jetz 2008; Rosser and Mainka 2002). Increased greenhousegas emission is changing the Earth's climate and is a major cause of concern for biodiversity as climate change affects the geographical distribution, physiology, phenology, and demography of organisms (Bernstein et al. 2007; Jenouvrier et al. 2009; Parmesan 2006). Although virtually all natural populations experience stochastic environmental variations, a growing body of evidence indicates that global climate change impacts both the mean and variance of climatic parameters, with especially pronounced effects in high altitude and latitude habitats. Organisms living in such ecosystems are particularly vulnerable; species occupying these habitats were the first to go extinct due to climate change (Bernstein et al. 2007; Jenouvrier et al. 2009; Parmesan and Yohe 2003). However, the direct impacts of anthropogenic climate change have been reported on every continent (Parmesan 2006). Therefore, climateinduced biodiversity loss is a global concern which has received much attention in a plethora of syntheses, such as the Intergovernmental Panel on Climate Change (IPCC) and the Millennium Ecosystem Assessment. The objective of my thesis was to examine the effects of environmental variability from a demographic perspective. To mitigate the potential ecological consequences of stochastic environments, it is critical to understand how the demography, dynamics, and persistence of populations are affected by the increasing environmental variability (Boyce et al. 2006). Although I did not explicitly study climate change, its effects are expressed through the increased variability of environmental variables which influence vital rates and, consequently, population growth rates (Bernstein et al. 2007). Therefore, to quantify the effect of environmental stochasticity, I examined the relative role of climatic factors, predation, and densitydependence (DD) in the dynamics of a temporally oscillating vertebrate population. The relative importance of such density independent (DID) and densitydependent mechanisms is a topic that is still hotly debated among population ecologists (Leirs et al. 1997). Hence, I studied the demographic consequences of DD and environmental variability by utilizing a demographic data set from a 19year (19902008) study on a goldenmantled ground squirrel (Callospermophilus lateralis; formerly, Spermophilus lateralis; hereafter, GMGS) (Helgen et al. 2009) population. The reliability of inference drawn from demographic studies depends largely on the availability and quality of data. The goldenmantled ground squirrel data consisted of longterm, capturemark recapture (CMR) data and it encompassed annual census counts which alleviated the need for estimating detection probability. This study was conducted at the Rocky Mountain Biological Laboratory (RMBL) near Crested Butte, Colorado (38058'N, 106059'W, elevation 2890m), a subalpine site where the climatic effects are pronounced due to climate change and several climate related research projects are underway (Inouye et al. 2000; Ozgul et al. In press). Detailed data on climatic variables were acquired from the U.S. Environmental Protection Agency Weather Station at RMBL. I obtained environmental data such as the first day that snow melt exposed bare ground from personal observations by a local resident, Billy Barr. Having access to both demographic and climatic data allowed for a full demographic analysis in which the relative roles of abiotic and other potentially important factors could be examined with respect to the population dynamics of the goldenmantled ground squirrel population. In my thesis, I attempted to answer two major questions: (1) how do density dependent and independent factors influence the demographic rates, and (2) how are these influences translated at the population level. To address these questions it was necessary to estimate agespecific vital rates (survival, breeding probability, and litter size) and evaluated the effects of various factors on these vital rates. Therefore, the second chapter is dedicated to parameter estimation. The analysis described in the second chapter revealed strong evidence of density dependent and the extrinsic environmental (current summer rainfall) effects on survival and strong impact of climatic factors (previous summer rainfall) on breeding probability. The third chapter built on these findings and investigated the standalone and combined effects of densitydependence and environmental stochasticity on the longterm population growth of the goldenmantled ground squirrel population. Therefore, the following two chapters investigate the causes and consequences of the temporal fluctuations exhibited by the ground squirrel population. The analysis focuses on the population dynamic consequences of densitydependence and environmental stochasticity. CHAPTER 2 I RELATIVE INFLUENCE OF POPULATION DENSITY, CLIMATE, AND PREDATION ON THE DEMOGRAPHY OF A SUBALPINE SPECIES Introduction Identifying and quantifying the causes and consequences of temporal fluctuations in vertebrate populations is a persistent challenge in ecology (Coulson et al. 2001; Oli and Armitage 2004; Williams et al. 2001). Factors that drive population dynamics may be densitydependent (DD) or densityindependent (DID). It is generally believed that DD feedback mechanisms play an important role in regulating populations (Hone and Sibly 2002; Royama 1992; Turchin 2003), but several studies suggest that density dependence and extrinsic environmental factors act synergistically to determine dynamics and thus regulation of populations (CluttonBrock and Coulson 2002; Coulson et al. 2001; Coulson et al. 2008; Leirs et al. 1997). However, the relative roles of DD, climatic factors, predation, and intrinsic influences on population dynamics remain poorly understood in most species (Den Boer and Reddingius 1996; Tamarin 1978). The impact of abiotic factors on population dynamics may be intensifying as a result of global climate change. A growing body of evidence demonstrates that the earth's climate is changing and that these changes will influence both the mean and variance of climatic variables (Bernstein et al. 2007). Consequently, these changes are already affecting the physiology, phenology, and demography of several species, particularly those species occupying high altitude and latitude habitats (Bernstein et al. 2007; Frederiksen et al. 2008; Hughes 2000; Inouye et al. 2000; Jenouvrier et al. 2009; Parmesan 2006; Regehr et al., 2010). Global climate change may induce changes in the length of summer or winter seasons; therefore, influence of global climate change on hibernating species is likely to be substantial (Inouye et al. 2000). Species distributions and life history traits also may be altered (McLaughlin et al. 2002). In order to mitigate the potential ecological consequences of such changes, it is critical to understand how the fluctuating environmental factors influence the demographic parameters, dynamics, and persistence of populations (Boyce et al. 2006; Jenouvrier et al. 2009). Because population growth rates are determined by demographic parameters (Caswell 2001; Oli and Armitage 2004), populationlevel impacts of anticipated global climatic change are mediated through vital demographic rates (Jenouvrier et al. 2009; Krebs 2002, 1995). Therefore, to decipher the relative roles of population density, predation, and climatic factors in determining population dynamics in stochastic environments, one must first understand their relative impacts on vital demographic rates. The goldenmantled ground squirrels (Callospermophilus lateralis; formerly, Spermophilus lateralis; hereafter, GMGS) (Helgen et al. 2009) is a hibernating species occupying montane habitats in western North America (Ferron 1985, Bartels and Thompson 1993). At a subalpine location in the Rocky Mountains, where climate change has been shown to have impacted several species (Inouye et al. 2000), a free ranging GMGS population exhibited substantial fluctuations (Figure. 21). The longterm (20 years) monitoring of this species allowed us to investigate the relative influence of population density and extrinsic factors on GMGS vital rates. Our objectives were to: (1) provide estimates of agespecific survival rates, breeding probabilities, and litter size; (2) evaluate the effects of sex, population size (with and without timelag), and extrinsic environmental factors (predation, previous and current summer rainfall, and previous and current year's first day of bare ground) on these rates; and (3) compare the relative influence of DD and DID factors on vital rates. Matrials and Methods Study Area and Species Our research was conducted at the Rocky Mountain Biological Laboratory (RMBL) near Crested Butte, Colorado (38058'N, 106059'W, elevation 2890m), USA. The 13ha study area was situated on a primarily open subalpine meadow that was interspersed with willow (Salix sp.) and aspen (Populus tremuloides) stands (Van Vuren 2001). The meadow was bordered on the west and south by the East River and Copper Creek, and on the north and east by aspen forest. The GMGS is a diurnal, asocial species whose distribution spans a broad elevational gradient from 1,220 to 3,965 m above sea level, where it occupies open habitats such as rocky mountain slopes adjoining grasslands, areas of scattered chaparral, and margins of mountain meadows (Bartels and Thompson 1993; Ferron 1985). GMGS hibernate to cope with food shortages during long winters. The entrance to and emergence from hibernation both vary depending on altitude and amount of snowfall (Bartels and Thompson 1993). At our study site, adult squirrels typically emerged from hibernation at about the time of snowmelt or before, in late May or early June. The breeding season began shortly after emergence and pups emerged from natal burrows during late June to mid July. The entire population entered hibernation by late August or early September. The GMGS is considered omnivorous (Bartels and Thompson 1993), but in our study area their diet appeared to consist mainly of herbaceous vegetation such as grasses and forbs, whose growth is stimulated by snow melt. After emergence, they gain weight rapidly, storing fat for overwinter survival and to sustain gestation the next spring until green vegetation starts growing again (Phillips 1984). Numerous mammalian and avian predators prey on GMGS (Bartels and Thompson 1993), but in our study area, we observed predation only by red foxes (Vulpes vulpes) and longtailed weasels (Mustela frenata). Field Methods For 20 consecutive years (19902009), GMGS were livetrapped augmented by almost daily observations during the active season (May to late August). Squirrels were trapped during late Mayearly June, for the annual census and marking of the resident population; late Junemid July, for trapping and marking emerging litters; and late July and again late August, for weighing squirrels and renewing marks. Observations and opportunistic trapping were conducted almost daily throughout the summer in order to capture and mark new immigrants and renew marks on residents. Squirrels were captured with singledoor Tomahawk livetraps (12.7 x 12.7 x 40.6 cm) baited with a mixture of sunflower seeds and peanut butter. Newly captured squirrels received a noncorrosive metal tag in each ear. Squirrels were distinctly dye marked with fur dye for visual recognition, and weight, sex, ear tag numbers, and reproductive condition were recorded. All juveniles were trapped at first emergence from their natal burrow, and litter size as well as the mother's identification was recorded. Animal handling followed protocols approved by the Animal Care and Use Committee at the University of California, Davis and met guidelines recommended by the American Society of Mammalogists (Gannon and Sikes 2007). Age was known for 704 squirrels that were initially captured as juveniles at their natal burrow. For an additional 127 squirrels (immigrant adults), exact age was not known; however, immigrant juveniles (<1 year) could be differentiated from adults based on body mass. Population Size and Predation We determined population size by counting individuals because we continued trapping and marking until all squirrels in the study area were trapped and identified each year; therefore the capture probability was & 1 throughout the study period. Predation (pred) was measured as an index and it was quantified as the number of predation events per year, with a predation event scored if observed or if a squirrel abruptly disappeared when red foxes or longtailed weasels were active in the study site. Abiotic Covariates Climatic factors considered in this study included summer rainfall during the current (raint) and previous year (raint_), and first day that snow melt exposed bare ground during the current (bgt) and previous year (bgt,). These variables were used as temporal covariates in our CMR analysis and they were selected based on a priori hypotheses that they influence GMGS demographic parameters (apparent survival rates, breeding probabilities, and litter size; hereafter survival, BP, LS, respectively). Data on climatic variables were obtained from the U.S. Environmental Protection Agency Weather Station at RMBL and from B. Barr (personal communication). Summer rain may prolong the growth of forbs and grasses that began when snow melted. Therefore, due to its effect on primary production, summer rainfall may be a good predictor of squirrel vital rates (Klinger 2007; Sherman and Runge 2002). Summer rainfall was calculated by summing the mean daily rainfall for the months of June and July; August precipitation was excluded because squirrels then are close to hibernation. The duration of snow cover is suggested to influence the length of the growing season, hence squirrel food availability (Bronson 1979; Van Vuren and Armitage 1991). During years of food shortage GMGS may curtail reproduction in favor of survival (Phillips 1984; Sherman and Runge 2002). In addition, time of snowmelt affects the length of time squirrels are exposed to predation (Bronson 1979). Consequently, the first day of bare ground (i.e., no snow cover) may also be a good predictor of squirrel demographic parameters. For the investigation of lag effects, data were required from the year preceding the commencement of the study (1989), which were not available for all variables. Therefore, summer rainfall and population size data for 1989 were obtained by averaging the values from 1990 and 1991. Survival Analysis We used multistate CMR models (Williams et al. 2001) implemented in Program MARK (White and Burnham 1999) using RMark interface (Laake and Rextad 2009). We considered 2 states based on 2 ageclasses (juvenile: [<1yr olds]; adults: [>1yr olds]), and estimated and modeled the statespecific apparent annual survival (0), recapture (p), and transition (Y) rates. Preliminary analyses revealed that capture probability was close to 1.0 (>0.99); therefore we fixed p to 1.00 for all models. Conditional on survival, the transition rate yy indicates the probability of transition from state x to y the following year. Surviving juveniles automatically advanced to adult state the next year and remained adults for the rest of their life cycle. Hence, juvenile to adult and adult to adult transition rates were fixed to 1.0. The goodnessoffit (GOF) of our fully timedependent general multistate model was tested with software UCARE V2.3 (Choquet et al. 2005b), and the overdispersion parameter (6) was calculated as the X2 divided by the degrees of freedom (Burnham and Anderson 2002). There was no evidence for lack of fit or overdispersion of data (X235= 37.785, P=0.343, c=1.08). We employed Akaike's Information Criterion, corrected for small sample size (AICc) for model comparison, statistical inferences, and to select the most parsimonious model from a candidate model set (Burnham and Anderson 2002). Model comparison was based on the differences in AICc values (AAIC ). The model associated with the lowest AICc value was considered the best and models withAIC c 52 were treated as equally representative of the underlying data. The slope parameter (3) and the 95% confidence interval for 3 indicated the direction and magnitude of the relationship between each parameter and covariate (Gaillard et al. 1997; Ozgul et al. 2007). The stepwise approach was employed in the CMR analysis. First, we considered the additive and interactive effects of age class (juveniles and adults [1lyr olds]) and sex on GMGS survival. Using the most parsimonious age and sex model as the base model, we tested for the additive and interactive effects of time. Second, we tested for the additive and interactive effects of current (Nt) and previous year's population size (Nt1) to test for direct and delayed densitydependence, respectively. The size of the study site was constant for the duration of the study; therefore, we considered population size (not population density) as a timedependent covariate for these analyses. Third, we tested for the additive and interactive effects of extrinsic environmental factors (pred, raint, raint_, bgt, and bgt,). The most parsimonious model identified in step 1 was used as a base model for these analyses. Fourth, we tested for the additive and interactive effects of covariates in the best DD (Nt1) and DID (raint, raint_ and pred) models. We compared AICc values for the most parsimonious model that included the effects of population size only, extrinsic variables only, and both population size and extrinsic factors, to evaluate the influence of DD and extrinsic factors (and combination thereof) on sex and agespecific survival of GMGS. In order to determine the relative importance of our predictor variables, for each variable, we summed the Akaike weights for all models in the candidate set that contained the variable (Anderson 2008). The predictor variable with the largest sum or predictor weight was considered to be the most important. Finally, in order to address model selection uncertainty, we performed model averaging using all models from step 1 to calculate modelaveraged estimate of sex and agespecific survival (Burnham and Anderson 2002). Analysis of Reproductive Parameters We considered 2 components of reproductive rates: (1) breeding probability, BP (i.e., the probability that a female weans1 pups, conditional on survival (Doherty et al. 2004; Ozgul et al. 2007)); and (2) litter size, LS (i.e., number of weaned juveniles that emerged from natal burrows (Ozgul et al. 2007)). We utilized logistic regression to estimate and model BP. This approach was adequate because capture probability was 1.0 for every year of the study. Zerotruncated Poisson regression (generalized linear models (GLM) with Poisson distribution and log link function) was used for LS analysis. We used the same stepwise approach as described previously for the survival analysis to determine the influence of extrinsic and intrinsic factors on LS and BP. In contrast with survival analysis, however, sex effect was not relevant for reproductive parameters because only the female segment of the population was examined. We considered 2 ageclasses (yearling [=lyr olds] and older [22yr olds] females) for the reproductive analysis of adult females. GLM analyses were conducted in program R (R Development Core Team 2009). Results Population Size and Composition Total population size fluctuated markedly, ranging from 24 individuals in 1999 and 2000 to 140 squirrels in 2005. The number of individuals of each sex and age class also exhibited similar fluctuations during the study period (Figure. 21). Age, Sex, and Time Effects for Survival There was very strong evidence 6AIC c >50) that both sex and age substantially influenced apparent survival (models 3 and 4 vs. model 5, Appendix Al). The most parsimonious model showed an additive effect of age and sex (model 1, Appendix Al); annual survival rate was highest for adult females (0=0.519, 95% Cl: 0.462, 0.576) and lowest for juvenile males (0=0.120, 95% Cl: 0.094, 0.152), while survival estimates for juvenile females (0=0.310, 95% Cl: 0.265, 0.359) and adult males (0=0.247, 95% Cl: 0.197, 0.306) were intermediate with overlapping Cl. Using model 1 in Appendix Al as a base model, we tested for the additive and interactive effect of time on survival to investigate temporal variation in sex and agespecific survival. The most parsimonious model included an additive effect of age, sex, and time (model 1, Appendix A2), suggesting that survival varied substantially over time but sex and agespecific differences remained constant over time (Figure. 22). Direct and Delayed DensityDependence (DD) for Survival The analysis of the effect of current (Nt) and previous year's (Nt1) population size on survival indicated that the most parsimonious DD survival model included an additive effect of age, sex, and Nt1 (model 1, Appendix B1). Indeed, Nt1 negatively influenced survival (3=0.011, 95% CI: 0.015, 0.006) of squirrels of both sexes and age classes (Figure. 23ad). We note that models 27 in Appendix B1 also had considerable support; however, all of these models included effects of Nt1, providing strong evidence for delayed DD effects on survival. Effects of Abiotic Factors for Survival The investigation of the impact of abiotic factors (raint, rainti, bgt, and bgt,) on survival revealed that the best extrinsic survival model included an additive delayed effect of summer rainfall (raint_), and an interactive effect between age and summer rainfall of the current year (raint) (model 1, Appendix B2). There was evidence for the positive effect of raint_ on survival which was not significant (3=0.005, 95% Cl: 0.001, 0.01). Current year's summer rainfall, raint, negatively influenced the survival of juveniles (3=0.008, 95% Cl: 0.013, 0.004), but not that of adults (3=0.001, 95% Cl:  0.004, 0.007). SinceAAICc between models 1 and 2 was < 2 (Appendix B2), and raint had substantial impact on survival we included both models for subsequent analyses. Predation Effect for Survival The analysis of the effect of all extrinsic environmental factors on survival (Appendix B3) showed that the most parsimonious DID model included an additive effect of sex, age, and pred and an interactive effect of age and raint (model 1, Appendix B3). Predation negatively influenced survival of all age and sex classes (3= 0.033, 95% Cl: 0.054, 0.012). DD vs. DID Models for Survival We compared the best DD (model 1, Appendix B1) and DID (model 1, Appendix B3) models to evaluate the relative influence of DD and DID factors on squirrel survival. There was strong evidence that both DD (Nt1) and DID (raint) factors influenced survival (models 5 and 17 vs. model 20, Appendix B4). The most parsimonious model (model 1, Appendix B4) included an additive effect of Nt1 (3=0.010, 95% CI: 0.015, 0.006) and an interactive effect between age and raint (for juveniles, 3=0.008, 95% CI: 0.012,  0.003; for adults, 3=0.004, 95% CI: 0.001, 0.009). These results suggested that Nt negatively influenced survival of both sexes and age classes. In this final model, raint had no effect on adult survival; however, it impacted juvenile squirrel survival negatively. We quantified the relative importance of population density and extrinsic factors by summing the Akaike weights for all models from Appendix B4 that contained each variable. The sum of AIC weights for Nt, raint, pred, and raint_ were 0.999, 0.979, 0.351, and 0.307, respectively, indicating that pred and raint were considerably less important in explaining survival than the other 2 variables. Breeding Probability (BP) Although yearling female squirrels frequently reproduced, older (22yr old) females represented the main reproductive segment of the squirrel population. With the exception of 2003, the percentage of adult females reproducing was higher for older than yearling females (Figure. 24a). Age, Sex, and Time Effects for BP There was strong evidence for agespecific (yearling vs. older females) differences in BP (AAIC >30 and wi=1; model 1 vs. 2, Appendix C1). The estimated BP for older females was higher (0.717, 95% Cl=0.639 0.79) than for yearlings (0.313, 95% CI: 0.228, 0.412). Next, we tested for the effect of time on BP, but there was no evidence for temporal variation in this vital rate (model 2 vs. 3, Appendix C1). The effect of time may not be evident due to small sample size. Hence, we employed a model that included the age effect for all subsequent analysis. Direct and Delayed Density Dependence for BP All models investigating effects of population size on BP are provided in Appendix C2. The best DD model included an additive effect of age and Nt (model 1, Appendix C2). There was strong support 6AIC c >2) for the positive effect of Nt (model 1 vs.8, Appendix C2) on BP of both age classes (13=0.014, 95% Cl: 0.005, 0.023). Abiotic Impacts for BP The most parsimonious model (model 1, Appendix C3) showed evidence for interactive effects of age and raint_ (model 1 vs. 8, Appendix C3) where raint_ negatively influenced the breeding probability of both older (3=0.004, 95% Cl: 0.013, 0.006) and yearling (3=0.033, 95% Cl: 0.051, 0.016) females. Predation Effect for BP When we considered predation as an additional extrinsic factor in our analysis, the best resulting model was still the same as model 1 in Appendix C3. Thus, there was no evidence that predation affected BP. DD vs. DID Models for BP Although, the most parsimonious model included both DD and DID components, the additive effect of Nt, and the interactive effect of age and raint_, the model without the additive effect of Nt was only 0.22 AIC away (models 1 and 2, Appendix C4). The evidence for the relative importance of raint_, however, was strong (models 1 and 3, Appendix C4). Therefore, we chose model 2 (i.e., model with the lowest number of parameters) as our most parsimonious model for parameter estimation. Litter Size Litter size (LS) ranged from 1 to 8 pups (N=139, LS =4.806, 95% Cl: 4.532, 5.08) with mode of 5 pups per litter (Figure. 24b). Unlike BP, age of mothers did not have a major impact on LS (model 1 vs. 2, Appendix D1). There was no evidence for temporal variation (model 1 vs. 3, Appendix D1), DD (Appendix D2), or DID (Appendix D3) influences on LS. Therefore, the model with constant LS was the most parsimonious, with no evidence for the effect of age of mothers or influence of DD and DID factors on this variable. Discussion The effects of DD and DID factors on population growth rate are indirect through their influences on vital rates and hence may be unexpected. The subtle and interactive process by which these factors impact the vital rates of different segments of structured populations is a phenomenon experienced across taxa (Coulson et al. 2001; Jonzen et al. 2010; Leirs et al. 1997; Ozgul et al. 2006; Ozgul et al. 2007). Densitydependent feedback mechanisms are thought to eventually stabilize populations (Leirs et al. 1997; Royama 1992; Turchin 2003) while stochastic variations in environmental factors tend to have destabilizing effects on population dynamics (Coulson et al. 2000). Consequently, our goal was to disentangle the relative contribution of DD and DID factors on our study population in order to tease apart their singular as well as combined effects that likely underlie the extensive temporal fluctuation in GMGS abundance. Understanding these relationships is even more critical when studying a species such as GMGS that occupies habitats that may be sensitive to climate change. Our analysis revealed strong evidence for temporal and age and sexspecific variation on survival. Previous studies have also demonstrated the impact of age and sex on survival rates of highelevation sciurid species. Bronson (1979) conducted a demographic study on GMGS in California and Sherman et al. (2002) investigated the potential causes of the sudden population collapse of a Northern Idaho ground squirrel (Urocitellus brunneus brunneus) population. Both studies reported lower survival rates for juvenile versus adult squirrels and lower survival rates for males than for females. Although these studies were relatively short term, our results are consistent with the pattern they found. The survival estimates in our study site were similar to those reported for the Northern Idaho population (Sherman et al. 2002). Nevertheless, our juvenile survival rates, especially for males, likely are underestimated because of the confounding effects of emigration. Consistent with previous studies that examined reproductive parameters of high elevation sciurid species (Bronson 1979; Ozgul et al. 2007), we found that older females (22 yrs of age) were the main reproductive segment of the squirrel population (Figure. 24a). Bronson (1979) reported that many young squirrels failed to reproduce at high elevation sites. Likewise, yearlings did not reproduce in 9 out of 19 years in our study site. Indeed, there was substantial agespecific difference in breeding probability, with older females twice as likely to reproduce as yearlings. Ozgul (2007) reported temporal variation on the breeding probability of subadult and adult yellowbellied marmots (Marmota flaviventris) at the same approximate locality. However, we did not find evidence for temporal variability in breeding probability, which may be a result of our small sample size. While Ozgul et al. (2007) and Sherman et al. (2002) found support for the effect of age and time on litter size, respectively, we found no evidence that LS varied among age classes or across years. We expected that current year's population density would have a negative effect on survival because crowding during the summer reduces per capital food availability and therefore the squirrels' ability to store enough fat for overwinter survival. In addition, high population density may promote juvenile dispersal, thereby reducing their 'apparent survival'. Unexpectedly, we found that GMGS survival was negatively related with the previous year's population density while there was no support for a sameyear effect of density. Our second best DD model (model 2, Appendix B1) had considerable support (AAICc =0.84) and indicated interaction between age and last year's density. According to this model, high density had a stronger negative effect on survival of juveniles than that of adults. This is not surprising, since juveniles are more likely to disperse and settle in poor habitat within the site or leave the study area permanently. Indeed, vital rates are suggested to covary closely with population density in small mammals (Klinger 2007; Leirs et al. 1997; Ozgul et al. 2004), but a lag effect of density on survival was unanticipated. We suggest densitydependent habitat selection as a possible explanation of delayed density effects on survival. High population density in our study area results in increased occupancy of lower quality habitats (K. Ip, unpublished ms.), primarily by juveniles. Many of these juveniles originated from high quality areas where they presumably were able to accumulate sufficient fat reserves for surviving their first winter, but subsequently experience diminished resources for surviving the year after. Negative DD effects on vital rates can manifest through intraspecific competition, resource availability, and predation (Klinger 2007). The strong effect of predation on temperate small mammal populations is well established (Hanski et al. 2001) and accordingly, predation negatively influenced GMGS survival in all segments of our study population. Although there was strong support for predation in the top DID model, predation was not included in the top combined DD and DID model. Since we lacked predator abundance data, we attempted to quantify the effect of predation by recording observed or presumed predation events as they were encountered during squirrel observations. Among small mammals there is evidence for negative DD effects through density mediated reproductive suppression (Boonstra 1994; Klinger 2007), but our results showed that sameyear density had a positive effect on breeding probability. This result was perhaps caused by a matefinding Allee effect (Gascoigne et al. 2009), although interpretation was difficult. There was no evidence for the effect of population density on litter size. In our study, DID influence was expressed in both survival and reproductive rates, through the effect of current year's rainfall and previous year's rainfall, respectively. The literature suggests that increased food availability driven by rainfall improves both vital rates (Klinger 2007), but our results showed a negative correlation between rainfall and both survival and reproduction. Meadow vegetation in our study area is highly productive (Kilgore and Armitage 1978), and it is possible that squirrels experience an abundant food supply regardless of additional growth stimulated by summer rainfall. Instead, periods of prolonged rainfall may have had a negative effect on squirrels by denying them access to food (Bakker et al. 2009); squirrels in our study remained underground during rainy weather. Hence, GMGS during rainy summers may have entered hibernation with reduced fat reserves for supporting both overwinter survival and reproduction the following spring. Abiotic variables such as the amount and frequency of precipitation are projected to increasingly vary due to a globally changing climate (Bernstein et al. 2007). Stochastic perturbations to vital rates can negatively impact the persistence of populations. The GMGS population inhabits a stochastic, highaltitude environment; hence increasing perturbations to GMGS vital rates due to changing environmental factors can negatively influence the GMGS population. Future research may focus on predicting GMGS population dynamics using models that incorporate these stochastic processes. Population regulation, the process determining sizes of populations, is a controversy that is much debated among ecologists. There is general consensus, however, that some regulatory mechanisms are responsible for the persistence of most natural populations (Dobson and Oli 2001). Fluctuations in population size are due to changes in demographic rates and it is essential to understand how vital rates are impacted by DD and DID factors. Our results showed that DD and DID factors did not affect all vital rates in the same fashion. With respect to GMGS survival, both DD (previous year's population density) and DID (current summer rainfall) factors were important. Based on the sum of AIC weights, the relative importance of the 4 most critical variables on survival in decreasing order was: density the previous year, current summer rainfall, predation, and previous summer rainfall. The weights of previous year's density and current summer rainfall were equally high. Leirs et al. (1997) found a strong negative effect of direct DD for only adult multimammate rats (Mastomys natalensis), while the negative impact of delayed DD in our GMGS population was consistent in all age and sexclasses. However, Leirs et al. (1997) did not find a strong extrinsic influence of rainfall, which is surprising in an environment where water is a limiting resource. For breeding probability, the top combined model included both DD (current year's population density) and DID (rainfall the previous summer) factors, but the relative support was much higher for the model that included the effect of rainfall the previous summer. The strong contribution of DID factors to breeding probability was consistent with literature suggesting that reproduction of small mammal species is driven primarily by DID factors (Coulson et al. 2000; Klinger 2007). We conclude that both densitydependent and densityindependent factors influenced demographic variables of GMGS in our study site, but the pattern of influence differed among variables. Extrinsic environmental factors influenced both survival and reproduction of squirrels, whereas population density primarily influenced survival. Global climate change is predicted to increase variance of several climatic variables including those considered in our study. Hence, our GMGS population is likely to experience more stochastic variation in demographic variables as well as population dynamics. a) CD LO a 0 1( .N 0 O ((N Q CL 7S 1990 1993 1996 1999 2002 2005 2008 Year Figure 21. Annual variation in the population size of the GMGS for the period 1990 2008. Total and age and sexspecific numbers of squirrels are presented. 00 0 A II AF l  1990 1995 2000 2005 Year Figure 22. Modelaveraged annual survival estimates with SE for adult (AF) and juvenile (JF) female, and adult (AM) and juvenile (JM) male GMGS during 19902007. All unique models from Table 21 a and 21b were included for model averaging. I! A U tT model averaging. 0 _ r'M _ 0 CD 0 0 i I I I I I I 20 40 60 80 100 120 140 (c) 20 40 60 80 100 120 140 Previous year's population size 20 40 60 80 100 120 140 CD CD C qr 0 I I I I I I 1 20 40 60 80 100 120 140 Previous year's population size Figure 23. Relationship between previous year's population size and age and sex specific survival, a) adult female survival, b) juvenile female survival, c) adult male survival, and d) juvenile male survival. Dotted lines indicate 95% confidence intervals. Parameters were estimated based on model 1 in Appendix B1. (b) I I I I I (d) Cd t *__ *OlderFemales DYearling Females Il l .lll lll ll.l..llI OC ,M CO LO CD r M O s M O I tCD . MO OM O M O ) M 0M M) 0M 0M 0 O O O O O M O O O Year r 3 4 5 6 Litter size 8 B Figure 24. Breeding probability and distribution of litter size of goldenmantled ground squirrels. A) Percentage of yearling and older 2yrs of age) females that successfully weaned at least 1 pup during 19902008., B) Distribution of litter size during the study period (19902008). 120 100 30 25 S20 o 15 10 5 0 r CHAPTER 3 STOCHASTIC POPULATION DYNAMICS OF A GOLDENMANTLED GROUND SQUIRREL POPULATION Introduction A central objective for ecologists is to understand the mechanisms that cause population fluctuations (Horvitz and Schemske 1995, Kruger 2007). In addition to investigating the causes of temporal fluctuations, there has been much interest in understanding the effects of environmental variability on vertebrate populations and making accurate longterm demographic predictions (Kalisz and McPeek 1993, Boyce et al. 2006). It is generally believed that both endogenous (densitydependent; DD) and exogenous (densityindependent; DID) processes influence population dynamics (Leirs et al. 1997, Coulson et al. 2001, Kruger 2007), but the relative roles of DD regulation and DID destabilization are still debated (Tamarin 1978, Boyce et al. 2006). With global climate change, the effects of DID processes on population dynamics are likely to become stronger; therefore, it is critical to understand how stochastic variation and densitydependent mechanisms interact to cause fluctuations in abundance and impact the future of populations (Parmesan 2006, Bernstein et al. 2007, Grotan et al. 2009). Climate change is likely to be associated with changes in magnitude and frequency of environmental events that shape the demography of a species (Jonzen et al. 2010). This is likely to exacerbate the effects of environmental variation on population demography as organisms are exposed to novel environmental conditions. Climate change would impact both the mean and variance of climatic parameters and consequently, the mean and variance of demographic rates (survival, breeding probability, litter size) (Boyce et al. 2006, Morris et al. 2008). Therefore, in the context of global climate change, understanding the demographic effects of environmental variability is critical since these perturbations are likely to influence the longterm growth rate, persistence, and resilience of populations (Caswell 2001, Haridas and Tuljapurkar 2005, Morris et al. 2008). Although most species experience temporally changing environments, population dynamics are often studied using deterministic matrix models (Caswell 2001, Haridas and Tuljapurkar 2005, Jonzen et al. 2010). These assume that environmental conditions, and therefore vital rates, remain constant over time (Kalisz and McPeek 1993). Deterministic analyses may not be informative in changing environments because large variation in a vital rate with a small deterministic elasticity may affect the population growth rate more than a small change in a less variable vital rate with high deterministic elasticity (Jonzen et al. 2010). Consequently, deterministic demography is limited in its application as it does not allow for temporal variability in vital rates (Boyce et al. 2006). The demographic consequences of variation in vital rates are better described in the context of stochastic demography (Boyce et al. 2006). Stochastic demographic models contain a relationship between the environment and the vital rates, and allow for a projection of the population using those vital rates (Caswell 2001, Hunter et al. 2007). This relationship describes temporal variation by associating a distinct projection matrix with each of several distinct environments. This stochastic modeling framework can be used to estimate the longterm growth rate of populations occupying stochastic environments (Morris et al. 2006) and to calculate the sensitivity and elasticity of stochastic population growth rate to changes in vital rates (Tuljapurkar et al. 2003, Haridas and Tuljapurkar 2005). Furthermore, stochastic sensitivity analysis permits the quantification of sensitivity and elasticity of stochastic population growth rate to the mean and variance in vital rates (Haridas and Tuljapurkar 2005, Jonzen et al. 2010). The goldenmantled ground squirrel (Callospermophilus lateralis; formerly, Spermophilus lateralis; hereafter, GMGS) (Helgen et al. 2009) is a hibernating species that occupies a subalpine habitat in the Rocky Mountains where the effect of climate change on several species has been reported (Inouye et al. 2000, Ozgul et al. In press). Over the course of a 19year study, our discrete population of GMGS exhibited substantial fluctuation in population size (Kneip et al. In review). This longterm demographic study allowed us to estimate annual vital rates (survival, breeding probability, litter size) and revealed strong DD and climatic effects on both survival and breeding probability (Kneip et al. In review). The regulatory influence of DD may have enabled our population to recover from lows of as few as 5 adult females in 1999 and 2001 to as high as 29 adult females in 2005. Using deterministic and stochastic demographic analyses of these data, we aimed to investigate how densitydependent processes interact with environmental stochasticity (ES) to cause fluctuations in the abundance of the GMGS population. Our 5step approach was to: (1) calculate overall and yearly deterministic population growth rates; (2) calculate the elasticity of deterministic population growth rate (A) to changes in vital rates; (3) calculate the stochastic population growth rate (As), and its elasticity to changes in the mean and variance of matrix elements; (4) quantify the effects of both DD and ES on the longterm population growth rate; and (5) project the probability of quasiextinction under various scenarios incorporating density dependence and ES. Materials and Methods Study Area and Species We conducted our research at the Rocky Mountain Biological Laboratory (RMBL) near Crested Butte, Colorado (38058'N, 106059'W, elevation 2890m), USA, on a 13ha open subalpine meadow. The study area was interspersed with willow (Salix sp.) and aspen (Populus tremuloides) stands and was bordered by aspen forest on the north and east, and by Copper creek and the East River on the west and south (Van Vuren 2001). The goldenmantled ground squirrel is an asocial and diurnal species that occurs at a broad range of elevations (~10004000m above sea level). It prefers open habitats such as mountain meadows and rocky mountain slopes that are adjacent to grasslands (Ferron 1985, Bartels and Thompson 1993). The GMGS survives long winters, and therefore food shortage, by hibernation. Both altitude and amount of snowfall influence squirrels when they commence and end their hibernation period (Ferron 1985, Bartels and Thompson 1993). Adult GMGS usually emerge from hibernation around the time of snowmelt (late May early June). The breeding season closely follows emergence and soon after pups emerge from natal burrows (late June midJuly). At the end of summer (late August early September) the squirrels enter hibernation. At RMBL, they mainly forage on herbaceous vegetation forbss and grasses). Snowmelt greatly influences the growth of these green, leafy plants and hence impacts squirrel food availability. Soon after emerging from hibernating burrows, the squirrels begin gaining weight, rapidly storing fat to improve their chances of survival the next winter and to sustain gestation the next spring (Phillips 1984). Field Methods GMGS were livetrapped for 19 successive years (19902008) during the active season (May to late August). In addition to trapping they were monitored daily by visual observations. The annual census (marking the entire resident population) took place from late May to early June. Pups were trapped and marked between late June and mid July as litters emerged from their natal burrows. Squirrels were trapped also in late July and late August, in order to record their weights as they were building fat reserves for hibernation. Throughout the summer, animals were observed daily and trapped opportunistically to capture and mark all new immigrants and refresh marks on residents. Singledoor Tomahawk livetraps (12.7 x 12.7 x 40.6 cm) were baited with a mixture of sunflower seeds and peanut butter to lure GMGS. Once captured, squirrels were distinctly dyemarked with fur dye, and sex, weight, and female reproductive condition were recorded. New individuals received noncorrosive metal tags for both ears. The ear tag numbers were also recorded. Emerging pups were captured, dye marked, and eartagged at first emergence from their natal burrow. Their mothers' ear tags were recorded as well as litter size. A total of 831 squirrels was captured during the study period. Age was known for 704 squirrels because they were captured as juveniles when emerging from their natal burrows. We estimated age based on mass for 127 immigrants, whose exact ages were unknown. Matrix Population Model All population projection models were femalebased models because we were not able to estimate reproductive parameters for male goldenmantled ground squirrels. There was evidence for the effect of sex on survival (Kneip et al. In review), so we used femaleonly estimates of survival. For 19 years of the study, we estimated vital rates (survival, breeding probability, litter size) for 2 ageclasses. For survival the age classes were juvenile (<1yr olds) and adult (>1yr olds); and for reproduction we considered age classes yearling (=lyr olds) and older femaleskyr olds) (Kneip et al. In review). The overall and yearspecific demographic parameter estimates are provided in Appendices A and B, respectively. We assumed that age of last reproduction was 6 years (based on current data) and constructed a 6x6 agestructured matrix population model for both deterministic and stochastic analysis. The age of last reproduction was chosen because out of 326 knownage female squirrels only 1 had a maximum life span longer than 6 years. The form of the agestructured population projection matrix including lowerlevel vital rates was: A(t)= Pj(t)* LS* BPy(t)* SRj Pa(t)* LS BPa(t)* SRj Pa(t)* LS BPa(t)* SRj Pa(t)* LS BPa(t)* SRj Pa(t)* LS BPa(t)* SRj Pa(t)* LS BPa(t)* SRj Pj(t) 0 0 0 0 0 0 Pa(t) 0 0 0 0 0 0 Pa(t) 0 0 0 0 0 0 Pa(t) 0 0 0 0 0 0 Pa(t) 0 (31) where Pj(t) denoted annual juvenile survival rate, Pa(t) represented annual adult survival rate; LS was litter size, SRj symbolized sex ratio of pups at emergence, and BPy(t) and BPa(t) stood for yearling and older female breeding probability, respectively. Yearling (Fy) and older female (Fa) fertility rates were estimated using the post breeding census method (Caswell 2001), as the product of agespecific fecundity and survival probability. Agespecific fecundity was determined as the product of breeding probability, litter size, and sex ratio. Being representative among ground squirrels, a balanced primary sex ratio (0.5) was assumed (Bronson 1979). Deterministic Analysis We constructed overall and yearspecific deterministic models. For the overall or timeinvariant model, a projection matrix A was obtained from a single estimate of the vital rates based on capturemarkrecapture data collected during the entire study period (19902008). For the yearspecific model, a separate population projection matrix At was compiled for each year t using agespecific reproductive and age and year specific survival estimates, totaling 18 projection matrices. We calculated the overall population growth rate A based on the overall projection matrix A. The yearspecific asymptotic population growth rates, At, were determined as the dominant eigenvalues of the annual projection matrices At. The mean asymptotic population growth rate, AM, was calculated as the dominant eigenvalue of the mean matrix AM. The net reproductive rate, Ro and generation time, T for the overall matrix were determined using algorithms from Caswell (2001). These values did not vary substantially over time. The elasticity of the overall and yearly population growth rates to changes in matrix elements and lowerlevel vital rates were calculated using methods described by Caswell (2001). Environmental Stochasticity Eighteen yearspecific population projection matrices At were used in the stochastic demographic analysis. There was strong evidence for temporal variation in agespecific survival rates, but not in breeding probability or litter size (Kneip et al. In review). Therefore, yearspecific matrices differed in survival rates but not in breeding probabilities or litter sizes. We assumed a uniform independent and identically distributed (iid) environment, and employed the simulationbased approach (50,000 simulations) to estimate the stochastic population growth rate as: logA, = Tl r17, where rt = log(n(t+1 )n(t)) is a onestep population growth rate (Caswell 2001, Tuljapurkar et al. 2003). Additionally, we calculated three types of elasticities of A, to matrix elements: E E and Es, which are the elasticities of As with respect to mean, variance, and both mean and variance, respectively, of the matrix element in row i and column j (Haridas and Tuljapurkar 2005) as: E = limT_ (1) ZT ,(t)cij(t)u(t) vE I(t)c y(t) (t) (32) I co Lt=l X(t) ( (t),u(t)) L A(t) (v(t),u(t)) J where u(t) and v(t) vectors refer to stochastic population structure and reproductive value at time t, respectively. The symbol A(t) represents the factor by which the population size grows from time t to t+1. The term (v(t), u(t)), stands for the scalar product of v(t) and u(t). First, we calculated the elasticity of Aregarding both the mean and the variance of matrix elements Ef as we perturbed both the mean and the variance of the matrix elements by equal proportions. Thus, we set cj(t) = Ay(t) for every t in the above equation. Second, the elasticity of A, relating to the mean of matrix elements E!' was calculated by perturbing the mean of the matrix elements without changing their variance. Therefore, we substituted ij for ciy(t), where iy is the ith entry of the matrix of mean matrix elements. Third, the elasticity of A, with respect to the variance of matrix elements Ei was calculated by perturbing the variance of the matrix elements without changing their mean. Hence, we set cj(t) = Ay(t) P. We simulated the growth of the GMGS population in an iid environment assuming that each of the 18 matrices is equally likely to occur. Each of the 50,000 independent realizations of population growth ran for 50 years and began with an initial population vector, n(0). The initial population vector was obtained by multiplying the stableage distribution from the overall matrix by the average female population size (30) observed during the study (Caswell 2001, Morris and Doak 2005). Density Dependence and Environmental Stochasticity In order to introduce density dependence into our overall matrix model A, we used the best agespecific densitydependent model from a previous study. There was strong evidence for delayed, negative DD effect on survival and direct, positive DD effect on breeding probability (Kneip et al. In review). The functional DD relationship for survival (P) and breeding probability (BP) is described by the following logistic regression equations: 1= +e(Ppo+PpN*n) (33) BP = 1 (34) l+e(PBPo+PBPN*n) (34) where p represents regression coefficients (,Sp: survival intercept, /fN: density dependent survival coefficient, ,Bpo: breeding probability intercept, fBPN: density dependent breeding probability coefficient). These slope parameters differ by ageclass and all values are reported in Table 31. These densitydependent relationships were estimated using total population size (both sexes) and our population model was femaleonly, but the observed sex ratio did not vary much by year. Therefore, the corresponding female population size was divided by the observed overall female sex ratio (0.515) to extrapolate from the number of females the approximate total population size, n. We projected the population growth for 50 years using the overall projection matrix A and an initial population vector n(0). The average observed female abundance (30) was used for initial population size. The initial population vector was calculated as described previously. We projected the future population size under 5 scenarios: (1) densityindependent model where the overall matrix was used for projection without incorporating the effects of DD; (2) densitydependent survival rate; (3) density dependent breeding probability; (4) both survival rate and breeding probability density dependent; and (5) scenario 4 extended by including immigration. Immigration was accounted for in our matrix model by adding the mean observed number of new females to the appropriate age class (1 juvenile, 0 adult) at each time step. To calculate the probability of extinction, 50,000 simulation runs of 50 years were performed under different scenarios and the proportion of the runs with adult females less than the extinction threshold after a given time period was recorded. The three main scenarios for estimating probability of extinction included: (1) ES only; (2) ES and DD where both survival and BP were affected by population density; and (3) scenario 2 extended by including immigration. ES and DD effects on survival were included by first accounting for the effects of density on survival and second by attributing the remaining variation (remainder) to ES. We estimated the remainder values as the differences between the logit survival estimates from the agespecific timedependent model and the best agespecific DD model (calculated at the population density for that year) (Figure 31). This resulted in 18 remainder values corresponding to each year of the study. Instead of selecting an entire matrix, we simulated ES by randomly selecting from the remainder values with equal probability and changing the DD survival probabilities by the corresponding remainder value at every time step: P1 1+e (Remainder+ppo+ppN*n) (35) Because the additive logistic regression coefficients for each ageclass differed between the timedependent and DD models, the remainder value for each year was different for yearlings and adults, but by a fixed amount. At every time step, immigrants were added to every age class of the current year's population vector, Nt, before projecting the population for the next year. Thus, the effects of immigration were included in the model as the observed number of immigrating individuals for each randomly selected year. The probability of quasiextinction was estimated at various levels of quasiextinction threshold (QET). We ran each of the aforementioned scenarios with QET=1, 3, and 5 adult females. True extinction was represented by QET=1, while QET=3 and 5 denoted the lowest observed adult female individuals during the study. It is useful to look at several quasiextinction thresholds set at critically low numbers to see how probability of extinction is impacted and also because low numbers are dangerous due to other stochastic processes such as demographic and genetic stochasticity. Our computations used MATLAB (2006) code that will be provided upon request. Results Deterministic Analysis The deterministic population growth rate, A, for the overall population implied a decline of 9.5% per year (A=0.905, 95% CI: 0.8120.998). The yeartoyear population growth rate was highly variable as At ranged between 0.445 and 1.244 (Figure. 32). The deterministic growth rate for the mean matrix, AM was 0.944 indicating a 5.6% per year decline. The net reproductive rate, Ro was 0.720 and the generation time, Twas estimated as 2.484. For the overall matrix, we examined the elasticity of population growth rate to matrix elements (Fy, Fa, Pj, and Pa). The A was proportionately most sensitive to Pj followed by Pa and Fa. The results of the lowerlevel elasticity analysis with respect to changes in vital rates (Pj, Pa, LS, BPy, and BPa) differed, because A was proportionately most sensitive to changes in Pa, followed by Pj, LS, BPa, and BPy (Figure. 33). The annual elasticity pattern with respect to matrix elements and vital rates was similar to that described above for the overall matrix. Environmental Stochasticity The stochastic population growth rate, As, was below replacement (As= 0.912) suggesting an 8.8% annual population decline. For our GMGS population, As responded most strongly to proportional changes in the average value of juvenile survival, followed by adult survival of the second age class, and fertility of 2 yearold and yearling females, respectively. The abovementioned matrix elements, in the same order, were also important in influencing Ej but in the opposite direction. This means that an increase in the mean of these matrix elements would increase while an increase in the variance would decrease As. The overall stochastic elasticities display the same pattern as Ej (Table 32). Including only the effects of environmental stochasticity, the distribution of total population size in 50 years for 50,000 independent realizations with initial total population size of 30 is displayed in Figure 34. In most of the realizations the total population size declined over the 50 years from the initial 30. The distribution of the final population size is skewed to the right. Corresponding to this skew, the median of the realizations is 8.48 while the mean is 10.66 female squirrels (Figure. 34). Density Dependence and Environmental Stochasticity According to our expectation, densitydependence revealed a strong impact on the viability of the GMGS population in scenarios 25 compared to the DID model (Figure. 35). Both the DID model and scenario 3 predicted that the squirrel population will go extinct within 50 years. The rate of decline was faster for scenario 3 where positive DD effects were implemented for breeding probability. After an initial decline, as A approached 1.0, the population size stabilized at 26.47, 23.65, and 18.80 for scenarios 2, 5, and 4, respectively. The logittransformed survival estimates computed by the best DD and time dependent models for adult and juvenile females are depicted in Figure 31 a and b, respectively. The differences between the estimates of the two models were attributed to environmental stochasticity. These remainder values were used in the following analysis, which combined the influence of density and environmental stochasticity in predicting probability of quasiextinction. With QET=1, probability of true extinction reached 90% after 50 years for the densityindependent model (scenario 1; Figure. 36a). This scenario included only the effects of environmental stochasticity. When we incorporated DD (scenario 2; Figure. 3 6a) and DD plus immigration (scenario 3; Figure. 36a) in addition to ES in our model, the probability of true extinction was reduced to 2% and 0%, respectively. As we raised the quasiextinction threshold, the probability of quasiextinction increased for each scenario. At QET=3, the probability of extinction for scenarios 1, 2, and 3 was 97%, 50%, and 15%, respectively (Figure. 36b). Setting QET=5, the respective extinction probabilities substantially rose to 99%, 93%, and 79% (Figure. 36c). Discussion Virtually all natural populations experience stochastic environmental variations which can influence demographic variables and population persistence (Caswell 2001, Haridas and Tuljapurkar 2005). In addition to unpredictable environmental perturbations, several other phenomena can impact the dynamics of natural populations. For instance, densitydependence, demographic stochasticity, sexratio fluctuations, and demographic heterogeneity can considerably alter the predictions of population viability analysis (Morris and Doak 2002, Kendall and Wittmann 2010). Environmental stochasticity tends to destabilize population dynamics, cause random population fluctuations, reduce longterm population growth rate, and increase extinction risk (Coulson et al. 2000, Kendall and Wittmann 2010). Densitydependent mechanisms on the other hand dampen oscillations and eventually regulate populations (Royama 1992, Leirs et al. 1997, Turchin 2003, Grotan et al. 2009). Understanding the effects of a variable environment on population dynamics is especially important for populations that occupy habitats sensitive to temporal variability and climate change (Inouye et al. 2000, Ozgul et al. In press). We hypothesized that the demography of our GMGS population inhabiting a montane ecosystem is strongly influenced by environmental stochasticity. The extensive yeartoyear fluctuations in abundance and deterministic growth rate indicated a highly variable population and formed the basis for our hypothesis. Total abundance ranged from 24 squirrels in 1999 and 2000 to 140 in 2005, almost a 6fold difference. The annual deterministic A also varied widely between 0.45 and 1.24. The overall A was 0.905 indicating a 9.5% population decline per year. This population growth rate is not as critically low as the 0.721 reported for the collapsing Northern Idaho population (Sherman and Runge 2002), but still calls for concern especially considering that for ten out of 18 years A was below replacement (A<1). The population has recovered from low numbers to viable levels during our study period which is likely caused by the regulatory densitydependence effects. In addition, despite the low number of observed immigrants, including immigration in our models substantially reduced the probability of extinction. Nonetheless, increasing environmental variation can elevate uncertainty and amplify a population's vulnerability to extinction. We found that the stochastic growth rate As was lower than the deterministic growth rate of the mean matrix AM. This result is consistent with our expectation because longterm, environmental variation is supposed to reduce the population growth rate, through environmentallyinduced variation in vital rates (Caswell 2001, Morris and Doak 2002). Indeed, the earlier study by Kneip et al. (In review) reported statistical evidence for temporal variation of survival as well as strong density independent effect of summer rainfall on this vital rate. Furthermore, our perturbation analysis showed that both deterministic and stochastic growth rates responded strongly to proportionate changes in survival matrix elements and vital rates. As expected for a population with a belowreplacement stochastic growth rate, the distribution of the population size (Figure. 34) predicted that in a stochastic environment the GMGS population would surely decline over a 50year period. Most realizations projected that the population size would be less than 10 within this time frame. The influence of environmental stochasticity is exacerbated by the effect of the predicted changes in climatic factors. The effect of climate change is anticipated to be most pronounced in polar and montane ecosystems such as the subalpine environment that the GMGS population occupies. According to a previous study by Kneip et al. (In review), both survival and reproduction were negatively affected by summer rainfall. Therefore, the potential impact of an increase in the mean and variance of precipitation is likely to influence the GMGS population's growth rate and persistence as it has been demonstrated on several species (Morris et al. 2008, Jonzen et al. 2010). In addition to the broad fluctuations, we have witnessed population lows with as few as 5 adult female squirrels in 1999 and 2001; still the population proved resilient as it rebounced and has not gone extinct. During the summer of 2001, the adult female population size dipped to 3 individuals because 2 females disappeared from the study site, most likely due to predation. We suspected that the combined effects of density dependence and immigration were responsible for the exhibited resilience. Density dependence was shown to operate in our GMGS population (Kneip et al. In review) and Grotan et al. (2009) demonstrated the strong influence of immigration on population dynamical responses. Immigration was low and variable among the years of our study period (Table 33). Interestingly, with the exception of one adult female immigrant in 1991, there was no immigration recorded until 2000, the year following the lowest total and adult female abundance. Furthermore, between 2000 and 2007, with low adult female numbers in 20002002 and 2007, immigration occurred in 6 out of 8 years. Hence, immigration has been likely an important factor in preventing extinction of our population. Indeed, when we accounted for both the effect of density on survival and breeding probability and immigration in our densitydependence analysis, after an initial decline the female population stabilized at the carrying capacity of 23.65 and did not go extinct. This is in contrast with densityindependent model and the scenario where the positive effects of density were implemented for breeding probability (Figure. 35) because in these two cases the population headed for extinction. Similarly, when we introduced densitydependence and immigration to the stochastic model, our projections of extinction risk improved substantially even though the effect of density on breeding probability was positive. When we set quasiextinction threshold to 1 (Figure. 36a), the densityindependent, ESonly model (scenario 1) painted a pessimistic picture as extinction probability was 90% in 50 years. According to the densitydependent model (scenario 2), the population faced almost no extinction risk. The DD model, which incorporated immigration (scenario 3), further improved the population's viability by reducing probability of extinction to zero. We included the influence of immigration in our model, because the survival estimates from Kneip et al. (In review) implicitly included the confounding effects of emigration. Therefore, the results of the combined model depicted in Figures 36a describe a fluctuating but persistent population in the long term. To simulate the persistence of our GMGS population under various levels of quasi extinction threshold, we projected the probability of extinction by setting QET=3 (Figure. 36b) and 5 (Figure. 36c), representing the lowest observed adult female population sizes. It was apparent, that extinction probabilities considerably increased as QET was raised. Setting QET=5 implied a conservative approach since we anticipated quasi extinction when there are 5 adult females in the population even though we have observed the population rebound from this threshold twice during the study. However, after those years immigration took place which may have been the reason for why the population has not gone extinct. In the context of global climate change, the influence of environmental stochasticity is predicted to increase on population dynamics which suggests amplified fluctuations in abundance of our GMGS population. An increase in the frequency of population lows would mean increased uncertainty for this population because immigration events may not always come to the population's rescue. Leirs et al. (1997) also investigated the effects of both DD and DID processes in a rodent species (Mastomys natalensis) which exhibits extensive population fluctuations. They modeled DID effects on the dynamics of this species by examining only one DID factor (rainfall) but noted that this ecological variable alone did not explain all the DID variation. In our analysis, we intended to account for the effects of all environmental variation and used the remainder values (Figure. 31) to explain the effects of ES in our combined DD and ES models (Figure. 36). Our analysis predicts an uncertain future for this squirrel population. Both deterministic and stochastic growth rates as well as the simulationbased projections of the distribution of population size and time to quasiextinction predict the likelihood of nearterm extinction. However, the population persisted despite wide fluctuations in population size and bounced back from low numbers as much as 6fold. Stochastic processes such as environmental and demographic stochasticity as well as increases in the mean and variability of precipitation may increase GMGS vulnerability to extinction. This may be reduced by the regulatory effect of densitydependent mechanisms and the effect of immigration. Moreover, immigration is a likely process explaining the resilience exhibited by this population (Tamarin 1978, Boyce et al. 2006). Nevertheless, as environmental variability is likely to exacerbate the fluctuations in GMGS abundance, the population may tip over such that squirrels reach low numbers frequently enough that, without the rescue effect of immigration, persistence will become precarious. Table 31. Regression coefficients for logittransformed survival and logittransformed breeding probability (BP) for the goldenmantled ground squirrel population in Gothic, CO (Kneip et al. In review). Coefficient, 3 Parameter Intercept Density term 95% Cl Juvenile survival 0.06459 0.01068 0.015 0.006 Adult survival 0.8072 0.01068 0.015 0.006 Yearling BP 2.012253 0.01386 0.005 0.023 Older female BP 0.06594 0.01386 0.005 0.023 Table 32. Elasticities of stochastic population growth rate (As) to mean (Es'), variance (Es'), and both mean and variance (Es) of matrix elements. Notation includes fertility of yearlings (Fy) and adults (Fa(x)), juvenile recruitment (Pj), and adult survival (Pa(x)) where x denotes the age of adult female GMGS. For all 3 types of elasticities, the highest absolute values are bold. Parameters EsP Eso Es Fy 0.113 0.010 0.103 Fa(2) 0.145 0.009 0.135 Fa(3) 0.083 0.005 0.078 Fa(4) 0.048 0.003 0.045 Fa(5) 0.027 0.002 0.026 Fa(6) 0.016 0.001 0.015 Pj 0.326 0.028 0.298 Pa(2) 0.174 0.011 0.162 Pa(3) 0.091 0.006 0.085 Pa(4) 0.043 0.003 0.040 Pa(5) 0.016 0.001 0.015 Table 33. The number of juvenile and adult female goldenmantled ground squirrels that immigrated to our study site in Gothic, CO, each year of the study. Capture Year Juvenile Adult 1990 0 1991 0 1992 0 1993 0 1994 0 1995 0 1996 0 1997 0 1998 0 1999 0 2000 2 2001 0 2002 3 2003 1 2004 1 2005 0 2006 4 2007 1 C3)  (b) J I I I I I I I T 20 40 eC SC 100 120 140 20 40 60 80 100 120 140 Density Figure 31. Relationship between annual population density and the agespecific logit transformed survival rate. a) adult and b) juvenile female goldenmantled ground squirrels between 1990 and 2007. Filled circles represent the yearly logittransformed survival estimates from the full timedependent model. The solid line is a regression line connecting the densitydependent estimates from the most parsimonious densitydependent model. Open circles are the logittransformed survival estimates from the best density dependent model calculated at the population size for each year. "Remainder values" are symbolized as connector line segments between the dots and the regression line at x values denoting densities calculated for each year. 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 Year Figure 32. Annual variation in the deterministic population growth rate with 95% Cl for female goldenmantled ground squirrels during 19902007. 1.6 1.4 1.2 0.8 0.6 0.4 0.2 nL II I I / ' I ' I I ,I 1 I II I I i i 1988 I I 0.7 0.6 0. 5 o 0.4 0 2 0.3 a 0.2 0. 1 Pj Pa LS BPy BPa Vital Rates Figure 33. Elasticity of projected population growth rate A to proportional changes in the lower level vital rates of the overall matrix A. Pj represents juvenile apparent survival, Pa symbolizes adult apparent survival, LS denotes litter size, BPy stands for yearling breeding probability, and BPa is older female breeding probability. 0 Z 0 1D 20 3D 4D 50 8D 70 80 Population size at t=50 Figure 34. Frequency distribution of population size in 50 years including only the effects of environmental stochasticity. The histogram shows the results of 50,000 realizations of simulating the GMGS population in a uniform independently and identically distributed (iid) stochastic environment. All simulations start from the same initial overall age distribution and initial population size of 30 females. We discarded the first 100 transient iterations. 30 25  20 2010 20 30 40 50 the overall projection matrix and the average female abundance (30) under 5 S15 1)DID densitydependent survival rate; (3 2) DD survival S10C \,,3) DD BP Survival ra ad rd ral d d and BP scenario 5) Ful + Immir 10 20 30 40 50 Time Figure 35. Projected abundance of the female GMGS population for 50 years using the overall projection matrix and the average female abundance (30) under 5 scenarios for densitydependence. (1) densityindependent model; (2) densitydependent survival rate; (3) densitydependent breeding probability; (4) both survival rate and breeding probability densitydependent; and (5) scenario 4 was extended by including immigration. Immigration was accounted for in our matrix model by adding the mean observed number of new individuals to the appropriate age class (1 juvenile, 0 adult) at each time step. In the above scenarios, the densityindependent variables were fixed to the values estimated for the entire study period. Environmental stochasticity was not included in any of these models. S1) DI: E8 mol (GET1]  Z) E8+D( ET1) * 3) E8+D*oIiprmK mft (GET1) 1(a) ___153 .. ..... .."........................... a: I I I I I I I I I I 000 5 10 15 20 25 30 35 40 45 50 0 10 20 30 40 50 (C) / *"o DID:ESa4(GET1] / *" ^^ 1)ES ET51 2) ESDD IEIETS) .. 3) ESDDmmn lfbl (iET5) a ~ i Ii a3  C & Time Figure 36. Probability of quasi extinction under various scenarios of environmental stochasticity, densitydependence, and differing levels of quasiextinction threshold for the goldenmantled ground squirrel population. Scenarios included: 1) environmental stochasticity only; 2) environmental stochasticity and densitydependence for both survival and breeding probability; and 3) scenario 2 extended by including immigration. Immigrants were added to every age class of the current year's population vector, Nt. All simulations start from the same initial population vector (obtained as multiplying the overall stableage distribution by the average females population size of 30). Quasiextinction threshold was established as: a) 1 (true extinction), b) 3, and c) 5 adult females. CHAPTER 4 CONCLUSION To decipher the population and specieslevel consequences of anticipated climate change, it is important to quantify the influence of densitydependent and density independent factors on population fluctuations. Many studies suggest that density dependent mechanisms ultimately stabilize natural populations; others argue that random variations in climatic factors introduce destabilizing effects to population dynamics. Empirical examples demonstrating how both of these processes act in concert are rare. The goal of this research was to examine how random environmental variation and densitydependent mechanisms interact to cause fluctuations in the abundance and influence the future persistence of a goldenmantled ground squirrel population. This population was chosen because it occupies a subalpine habitat, which is sensitive to climate change. Additionally, a 19year demographic data set was available for analysis. Because the effects of environmental variability on population growth are mediated through their influence on vital rates, I examined whether climatic factors affected demographic parameters including survival rate, breeding probability, and litter size. The results from this analysis revealed that both densitydependent and extrinsic environmental factors impacted demographic variables although in different manners. While population size (previous year's) had a substantial negative effect on survival of both sexes and age classes, a climatic parameter (summer rainfall) influenced both survival and reproduction (breeding probability) of the goldenmantled ground squirrels. Current and previous summer rainfall negatively influenced juvenile survival and yearling breeding probability, respectively. Therefore, I concluded that precipitation; a densityindependent, climatic variable had a strong influence on this population. Global climate change is predicted to amplify the variance of climatic parameters. It is likely that populations inhabiting stochastic environments, such as the golden mantled ground squirrels, will experience increasing stochastic variation in vital rates and abundance. Consequently, this variability will reduce longterm population growth rate and increase extinction risk. My initial findings merited further analyses to predict the probability of extinction of this population. While there was evidence for the strong influence of one climatic factor, summer rainfall, on both survival and reproduction, I was interested in accounting for the full effects of environmental stochasticity. Therefore, in addition to the deterministic and densitydependent analysis, I also conducted stochastic demographic analyses for the goldenmantled ground squirrel population. The results from these analyses showed that environmental stochasticity increased and densitydependence decreased the goldenmantled ground squirrel population's probability of extinction. As predicted, stochastic processes increased fluctuations in population size, destabilizing the population, whereas density dependence dampened these oscillations and improved the population's likelihood of persistence. In addition to the wide fluctuations in total abundance, the population's persistence was uncertain when adult female population size dipped to as low as 5 and 3 individuals during the study period. However, the population rebounded twice from such low adult female numbers. I suspected that in addition to the regulatory effect of density dependence, another process, such as immigration most likely played a critical role in the population's resilience and included immigration in my model. According to my analysis, immigration proved an important process that rescued the population from extinction. Despite these stabilizing factors, my analysis predicted an uncertain future for this population over the long term. In the context of climate change, environmental stochasticity is likely to increase and destabilize the dynamics of the goldenmantled ground squirrel population and biological populations in general. This study highlighted the vulnerability not only of this goldenmantled ground squirrel population but also of other wildlife populations that inhabit stochastic environments. Therefore, my results may prove informative to conservation agencies attempting to protect rare or endangered species in the face of global climate change. Because endangered populations tend to be small, the effects of environmental stochasticity are likely to be exacerbated by other stochastic mechanisms such as demographic and genetic stochasticity. The combined effects of these processes are expected to make the future persistence of endangered populations precarious. APPENDIX A SURVIVAL MODELS TESTING FOR THE EFFECTS OF SEX, AGE, AND TIME Analysis of agespecific apparent survival rates for the goldenmantled ground squirrel population in Gothic, CO using multistate markrecapture models. Models testing for the effect of a) sex and age; and b) time. Constant survival and timespecific survival models also are included for comparison. In both analyses, the most parsimonious models are bold. No. Model A AICc AICc wi npar (1) 1 0(age + sex) 0.00 2071.14 0.720 3 2 0(age* sex) 1.89 2073.03 0.280 4 3 P(sex) 34.60 2105.75 0.000 2 4 0(age) 63.74 2134.89 0.000 2 5 0(.) 112.29 2183.43 0.000 1 (2) 1 0(age + sex + time) 0.00 2062.28 0.790 20 2 P(sex + age time) 2.75 2065.03 0.200 36 3 0(age + sex) 8.86 2071.14 0.009 3 4 0(age + sex time) 16.55 2078.84 0.000 37 5 0((age + sex) time) 18.22 2080.51 0.000 53 6 0(.) 121.14 2183.43 0.000 1 Differences in Akaike's information criterion corrected for small sample size (A AICc), AICc, weights (wi), and number of parameters (npar) are given for each model. The symbol 0 refers to apparent annual survival rate. Annual recapture rate and transition rate are fixed for all models, therefore they are not included in model descriptions. The symbol (.) indicates constant value of the parameter (model with intercept only). The notation ((age+sex)*time) means interaction between time and both age and sex classes. APPENDIX B SURVIVAL MODELS TESTING FOR THE EFFECTS OF DENSITYDEPENDENT AND INDEPENDENT FACTORS Models testing for the effect of a) current (Nt) and previous (Nti) year's population size; b) abiotic factors; c) environmental factors including predation; and d) the relative and synergistic effects of the best intrinsic, densitydependent, and extrinsic environmental factors on the statespecific apparent survival rates for the golden mantled ground squirrel population in Gothic, CO using multistate markrecapture models. General model (model a/12) is also included for comparison. In all analyses, the most parsimonious models are bold. Not all models are shown for parts a and b. No. Model A AICc AICc wi npar (a) 1 0(age + sex + NtI) 0.00 2047.27 0.199 4 2 0(sex + age Nt1) 0.84 2048.10 0.131 5 3 P(age + sex + Nt + Nti) 0.95 2048.22 0.123 5 4 0(age + sex Nt_) 1.14 2048.41 0.112 5 5 0((age + sex) Nt1) 1.74 2049.01 0.083 6 6 P(sex + age Nt1 + Nt) 1.77 2049.04 0.082 6 7 P(age + sex + Nt Nt1) 1.94 2049.20 0.075 6 8 P(age + sex Nt_ + Nt) 2.10 2049.37 0.070 6 9 0((age + sex) Nt1 + Nt) 2.67 2049.94 0.052 7 10 0(sex + age Nt + Nt1) 2.75 2050.02 0.050 6 11 0((age + sex) Nt + Nt1) 4.48 2051.75 0.021 7 12 0(age + sex + time) 15.02 2062.28 0.000 20 (b) 1 0(sex + age raint + rainti:A) 0.00 2060.13 0.236 6 2 P(sex + age raint) 0.92 2061.05 0.149 5 3 0(sex + age raint + rainti:A + bgt_:A) 1.02 2061.15 0.142 7 4 0(sex + age raint + rainti:A + bgt) 1.81 2061.94 0.095 7 5 P(sex + age + time) 2.15 2062.28 0.080 20 6 P(sex + age raint + bgt_:A) 2.33 2062.45 0.074 6 7 P(sex + age raint + bgt) 2.62 2062.75 0.064 6 8 P(sex + age raint + rainti:A + bgt + bgti:A) 2.91 2063.04 0.055 8 9 P(sex + age raint + bgt + bgt_:A) 10 P(sex + age + raint + rainti:A + bgt_:A) (c) 1 P(sex + age raint + pred) 2 P(sex + age raint + raint_A + pred) 3 P(sex + age pred + raint + raint_A) 4 P(sex + age pred) 5 P(age + sex + pred + raint_:A) 6 P(age + sex + pred) 7 P(age + sex + pred + raint + rainti:A) 8 P(sex + age raint + rainti:A) 9 P(sex + age pred + raint) 10 P(sex + age raint) 11 P(age + sex + pred + raint) 12 P(sex + age + time) (d) 1 P(sex + age raint + Nt1) 2 P(sex + age raint + pred + Nt1) 3 P(sex + age raint + raint_A + Nt1) 4 P(sex + age raint + raint_A + NtI + pred) 5 P(age + sex + Nt1) 6 P(age + sex + Net + pred) 7 P(age + sex + Net + raintiA) 8 P(age + sex + Net + raint_A + pred) 9 P(sex + age raint + pred) 10 P(sex + age raint + rainti:A + pred) 11 P(age + sex + rainti:A + pred) 12 P(sex + age + pred) 13 P(sex + age raint + rainti:A) 14 P(sex + age raint) 15 P(sex + age + time) 16 O(sex + age + rainti:A) 17 P(sex + age) 4.09 4.31 0.00 0.77 5.08 5.40 5.80 6.84 6.88 7.12 7.23 8.04 8.64 9.27 0.00 1.22 1.62 2.94 8.26 8.78 9.12 9.53 13.86 14.63 19.66 20.70 20.98 21.90 23.13 30.11 31.99 2064.22 0.030 7 2064.44 0.027 6 2053.01 0.489 6 2053.78 0.334 7 2058.09 0.039 7 2058.41 0.033 5 2058.81 0.027 5 2059.85 0.016 4 2059.89 0.016 6 2060.13 0.014 6 2060.24 0.013 6 2061.05 0.009 5 2061.65 0.007 5 2062.28 0.005 20 2039.15 0.441 6 2040.37 0.239 7 2040.77 0.197 7 2042.09 0.101 8 2047.41 0.007 4 2047.93 0.005 5 2048.27 0.005 5 2048.68 0.004 6 2053.01 0.000 6 2053.78 0.000 7 2058.81 0.000 5 2059.85 0.000 4 2060.13 0.000 6 2061.05 0.000 5 2062.28 0.000 20 2069.26 0.000 4 2071.14 0.000 3 For symbols and table content descriptions, refer to Table 1 footnotes. The following variable notations are used: current (Nt) and previous (Nt1) population size, current (raint) and previous (raint_) summer rain fall, current (bgt) and previous (i) first day of bare ground, and predation (pred). In addition, the effects of previous year's rain fall and previous first day of bare ground on survival were only relevant to adult animals. Hence, we analyzed the effects of these parameters only for the adult segment of the population. Notation for these parameters therefore are: raint_:A and bgt_:A, respectively. APPENDIX C BREEDING PROBABILITY MODELS TESTING FOR THE EFFECTS OF INTRINSIC, DENSITYDEPENDENT AND INDEPENDENT FACTORS Models testing for the effect of a) age and time; b) current (Nt) and previous (Nti) year's population size; c) environmental factors including predation; and d) the relative and synergistic effects of the best intrinsic, density dependent, and environmental factors on breeding probability of the goldenmantled ground squirrel population in Gothic, CO using logistic regression. In all analyses, the most parsimonious models are bold. No. Model A AICc AICc wi npar (1) 1 1(age) 0.00 295.96 1.000 2 2 W,(.) 37.11 333.07 0.000 1 3 1(time) 52.75 348.71 0.000 19 (2) 1 W(age + Nt) 0.00 287.67 0.242 3 2 W(age + Nt + Nti) 0.31 287.98 0.207 4 3 W(age *Nt) 0.93 288.60 0.152 4 4 W(age Nt + Nt) 1.32 288.99 0.125 5 5 W(age Nt + Nt1) 1.51 289.18 0.114 5 6 W(age + Nt *Nt1) 2.31 289.98 0.076 5 7 W(age + Nti *Nt) 2.31 289.98 0.076 5 8 W(age) 8.28 295.96 0.004 2 9 W(age + Nti) 8.86 296.54 0.003 3 10 W(age Nt) 9.84 297.51 0.002 4 (3) 1 W(age raint_) 0.00 279.56 0.652 4 2 W(age *rainti + pred) 1.41 280.98 0.322 5 3 W(age + rainti) 8.01 287.57 0.012 3 4 W(age + raint. + pred) 8.91 288.47 0.008 4 5 W(age *pred + rainti) 9.79 289.35 0.005 5 6 W(age *raint) 13.46 293.02 0.001 4 7 (age + raint) 14.92 294.49 0.000 3 No. Model A AICc AICc wi npar 8 W(age) 16.39 295.96 0.000 2 9 W(age *bgt) 17.38 296.94 0.000 4 10 W(age + pred) 17.92 297.49 0.000 3 11 W(age *pred) 18.00 297.56 0.000 4 12 W(age + bgt) 18.34 297.90 0.000 3 13 W(age + bgt) 18.35 297.91 0.000 3 14 W(age *bgt) 20.33 299.89 0.000 4 (4) 1 W(age raint + Nt) 0.00 279.34 0.511 5 2 W(age raint_) 0.22 279.56 0.457 4 3 W(age + Nt) 8.33 287.67 0.008 3 4 Wj(age) 16.61 295.96 0.000 2 For symbols and table content descriptions, refer to Table 2 footnotes. The symbol W refers to breeding probability. APPENDIX D LITTER SIZE MODELS TESTING FOR THE EFFECTS OF INTRINSIC, DENSITY DEPENDENT AND INDEPENDENT FACTORS Models testing for the effect of a) age and time; b) current (Nt) and previous (Nti) year's population size; c) environmental factors including predation; and d) the relative and synergistic effects of the best intrinsic, density dependent, and environmental factors on litter size for the goldenmantled ground squirrel population in Gothic, CO using Poisson regression. In all analyses, the most parsimonious models are bold. No. Model A AIC AIC wi npar (1) 1 LS (.) 0.00 532.79 0.717 1 2 LS (age) 1.87 534.66 0.282 2 3 LS (time) 13.69 546.49 0.001 19 (2) 1 LS (Nt) 0.00 531.50 0.341 2 2 LS (Nt Nt1) 1.28 532.78 0.180 4 3 LS (.) 1.29 532.79 0.179 1 4 LS (NtI) 1.37 532.87 0.172 2 5 LS (Nt + Nt1) 1.97 533.47 0.128 3 (3) 1 LS (.) 0.00 532.79 0.222 1 2 LS (bgt,) 0.70 533.50 0.156 2 3 LS (pred) 1.42 534.21 0.109 2 4 LS (age) 1.87 534.66 0.087 2 5 LS (bgt) 1.92 534.71 0.085 2 6 LS (raint_) 1.98 534.78 0.082 2 7 LS (raint) 2.00 534.79 0.082 2 8 LS (bgt1 + pred) 2.31 535.11 0.070 3 9 LS (age + bgt1) 2.64 535.44 0.059 3 10 LS (bgt1 *pred) 4.31 537.10 0.026 4 11 LS (age bgt.) 4.58 537.37 0.022 4 (4) 1 LS (Nt) 0.00 531.50 0.221 2 2 LS (bgt1 + Nt) 0.52 532.02 0.171 3 3 LS (.) 1.29 532.79 0.116 1 4 LS (bgt1 *Nt) 1.50 533.00 0.105 4 5 LS (bgt1) 2.00 533.50 0.082 2 6 LS (bgt1 + Nt + pred) 2.09 533.59 0.078 4 7 LS (pred) 2.71 534.21 0.057 2 8 LS (bgt1 Nt + pred) 3.14 534.65 0.046 5 9 LS (age) 3.16 534.66 0.046 2 10 LS (bgt1 + pred) 3.60 535.11 0.037 3 11 LS (bgt1 pred + Nt) 4.04 535.54 0.029 5 12 LS (bgt1 *pred) 5.60 537.10 0.013 4 13 LS (time) 14.99 546.49 0.000 19 For symbols and table content descriptions, refer to Table 2 footnotes. The symbol LS refers to litter size. LIST OF REFERENCES ANDERSON, D. R. 2008. Model Based Inference in the Life Sciences, 1st ed. Springer Science+Business Media, LLC, New York, NY. BAKKER, V. J., ET AL. 2009. Incorporating ecological drivers and uncertainty into a demographic population viability analysis for the island fox. Ecological Monographs 79:77108. BARTELS, M. A., AND D. P. THOMPSON. 1993. Spermophilus lateralis. Mammalian Species 440:18. BERNSTEIN, L., ET AL. 2007. Climate change 2007: Synthesis Report. BOONSTRA, R. 1994. Populationcycles in microtines The senescence hypothesis. Evolutionary Ecology 8:196219. BOYCE, M. S., C. V. HARIDAS, C. T. LEE, AND N. S. DEMOGRAPHY. 2006. Demography in an increasingly variable world. Trends in Ecology & Evolution 21:141148. BRONSON, M. T. 1979. Altitudinal variation in the lifehistory of the goldenmantled ground squirrel (Spermophilus lateralis). Ecology 60:272279. BURNHAM, K. P., AND D. R. ANDERSON. 2002. Model selection and multimodal inference: A practical information theoretic approach. SpringerVerlag, New York. CASWELL, H. 2001. Matrix population models: Construction, analysis, and interpretation, 2nd ed. Sinauer Associates, Sunderland, Massachusetts. CHOQUET, R., M. REBOULET, J. D. LEBRETON, O. GIMENEZ, AND R. PRADEL. 2005b. U CARE 2.2 user's manual, Montpellier, France. CLUTTONBROCK, T. H., AND T. COULSON. 2002. Comparative ungulate dynamics: the devil is in the detail. Philosophical Transactions of the Royal Society of London Series B 357:12851298. COULSON, T., ET AL. 2001. Age, sex, density, winter weather, and population crashes in Soay sheep. Science 292:15281531. COULSON, T., ET AL. 2008. Estimating the functional form for the density dependence from lifehistory data. Ecology 89:16611674. COULSON, T., E. J. MILNERGULLAND, AND T. CLUTTONBROCK. 2000. The relative roles of density and climatic variation on population dynamics and fecundity rates in three contrasting ungulate species. Proceedings of the Royal Society of London Series B Biological Sciences 267:17711779. DEN BOER, P. J., AND J. REDDINGIUS. 1996. Regulation and stabilization paradigms in population ecology. Chapman & Hall, London, U.K. DOBSON, F. S., AND M. K. OLI. 2001. The demographic basis of population regulation in Columbian ground squirrels. American Naturalist 158:236247. DOHERTY, P. F., ET AL. 2004. Testing lifehistory predictions in a longlived seabird: A population matrix approach with improved parameter estimation. Oikos 105:606618. FERRON, J. 1985. Social behavior of the goldenmantled groundsquirrel (Spermophilus lateralis). Journal of Zoology 63:25292533. FREDERIKSEN, M., F. DAUNT, M. P. HARRIS, AND S. WANLESS. 2008. The demographic impact of extreme events: Stochastic weather drives survival and population dynamics in a longlived seabird. Journal of Animal Ecology 77:10201029. GAILLARD, J. M., J. M. BOUTIN, D. DELORME, G. VANLAERE, P. DUNCAN, AND J. D. LEBRETON. 1997. Early survival in roe deer: causes and consequences of cohort variation in two contrasted populations. Oecologia 112:502513. GANNON, W. L., AND R. S. SIKES. 2007. Guidelines of the American Society of Mammalogists for the use of wild mammals in research. Journal of Mammalogy 88:809823. GASCOIGNE, J., L. BEREC, S. GREGORY, AND F. COURCHAMP. 2009. Dangerously few liaisons: a review of matefinding Allee effects. Population Ecology 51:355372. GROTAN, V., B. E. SAETHER, S. ENGEN, J. H. VAN BALEN, A. C. PERDECK, and M. E. VISSER. 2009. Spatial and temporal variation in the relative contribution of density dependence, climate variation and migration to fluctuations in the size of great tit populations. Journal of Animal Ecology 78:447459. HANSKI, I., H. HENTTONEN, E. KORPIMAKI, L. OKSANEN, AND P. TURCHIN. 2001. Small rodent dynamics and predation. Ecology 82:15051520. HARIDAS, C. V., and S. TULJAPURKAR. 2005. Elasticities in variable environments: Properties and implications. American Naturalist 166:481495. HELGEN, K. M., F. R. COLE, L. E. HELGEN, AND D. E. WILSON. 2009. Generic revision in the holarctic ground squirrel genus Spermophilus. Journal of Mammalogy 90:270 305. HONE, J., AND R. M. SIBLY. 2002. Demographic, mechanistic and densitydependent determinants of population growth rate: a case study in an avian predator. Philosophical Transactions of the Royal Society of London Series B 357:11711177. HORVITZ, C. C., and D. W. SCHEMSKE. 1995. Spatiotemporal variation in demographic transitions of a tropical understory herb projection matrix analysis. Ecological Monographs 65:155192. HUGHES, L. 2000. Biological consequences of global warming: is the signal already apparent? Trends in Ecology & Evolution 15:5661. HUNTER, C. M., H. CASWELL, M. C. RUNGE, E. V. REGEHR, S. C. AMSTRUP, and I. STRIRLING. 2007. Polar bears in the Southern Beaufort Sea II: demography and population growth in relation to Sea Ice Conditions. INOUYE, D. W., B. BARR, K. B. ARMITAGE, AND B. D. INOUYE. 2000. Climate change is affecting altitudinal migrants and hibernating species. Proceedings of the National Academy of Sciences USA 97:16301633. JENOUVRIER, S., H. CASWELL, C. BARBRAUD, M. HOLLAND, J. STROEVE, AND H. WEIMERSKIRCH. 2009. Demographic models and IPCC climate projections predict the decline of an emperor penguin population. Proceedings of the National Academy USA 106:18441847. JONZEN, N., T. POPLE, J. KNAPE, AND M. SKOLD. 2010. Stochastic demography and population dynamics in the red kangaroo Macropus rufus. Journal of Animal Ecology 79:109116. KALISZ, S., and M. A. MCPEEK. 1993. Extinction dynamics, populationgrowth and seed banks an example using an agestructured annual. Oecologia 95:314320. KENDALL, B. E., and M. E. WITTMANN. 2010. A stochastic model for annual reproductive success. American Naturalist 175:461468. KILGORE, D. L., AND K. B. ARMITAGE. 1978. Energetics of yellowbellied marmot populations. Ecology 59:7888. KLINGER, R. 2007. Catastrophes, disturbances and densitydependence: population dynamics of the spiny pocket mouse (Heteromys desmarestianus) in a neotropical lowland forest. Journal of Tropical Ecology 23:507518. KNEIP, E., D. H. VAN VUREN, J. A. HOSTETLER, and M. K. OLI. In review. Relative influence of population density, climate, and predation on the demography of a subalpine species. Journal of Mammalogy. KRAUSS, J., et al. Habitat fragmentation causes immediate and timedelayed biodiversity loss at different trophic levels. Ecology Letters 13:597605. KREBS, C. J. 1995. Two paradigms of population regulation. Wildlife Research 22:110. KREBS, C. J. 2002. Two complementary paradigms for analysing population dynamics. Philosophical Transactions of the Royal Society of London Series B 357:12111219. KRUGER, O. 2007. Longterm demographic analysis in goshawk Accipiter gentilis: the role of density dependence and stochasticity. Oecologia 152:459471. LAAKE, J., AND E. REXTAD. 2009. RMark an alternative approach to building linear models in MARK in Program MARK: a gentle introduction (E. Cooch and G. White, eds.). http://www.phidot.org/software/mark/docs/book/. LEE, T. M., and W. JETZ. 2008. Future battlegrounds for conservation under global change. Proceedings Of The Royal Society BBiological Sciences 275:12611270. LEIRS, H., N. C. STENSETH, J. D. NICHOLS, J. E. HINES, R. VERHAGEN, AND W. VERHEYEN. 1997. Stochastic seasonality and nonlinear densitydependent factors regulate population size in an African rodent. Nature 389:176180. MATLAB. 2006. Mathworks, Natick, Mass. MCLAUGHLIN, J. F., J. J. HELLMANN, C. L. BOGGS, AND P. R. EHRLICH. 2002. Climate change hastens population extinctions. Proceedings of the National Academy USA 99:60706074. MORRIS, W. F., and D. F. DOAK. 2002. Quantitative Conservation Biology. Sinauer Associates Inc, Sunderland, MA. MORRIS, W. F., and D. F. DOAK. 2005. How general are the determinants of the stochastic population growth rate across nearby sites? Ecological Monographs 75:119137. MORRIS, W. F., et al. 2008. Longevity can buffer plant and animal populations against changing climatic variability. Ecology 89:1925. MORRIS, W. F., S. TULJAPURKAR, C. V. HARIDAS, E. S. MENGES, C. C. HORVITZ, and C. A. PFISTER. 2006. Sensitivity of the population growth rate to demographic variability within and between phases of the disturbance cycle. Ecology Letters 9:13311341. OLI, M. K., AND K. B. ARMITAGE. 2004. Yellowbellied marmot population dynamics: Demographic mechanisms of growth and decline. Ecology 85:24462455. OZGUL, A., K. B. ARMITAGE, D. T. BLUMSTEIN, AND M. K. OLI. 2006. Spatiotemporal variation in survival rates: Implications for population dynamics of yellowbellied marmots. Ecology 87:10271037. OZGUL, A., L. L. GETZ, AND M. K. OLI. 2004. Demography of fluctuating populations: Temporal and phaserelated changes in vital rates of Microtus ochrogaster. Journal of Animal Ecology 73:201215. OZGUL, A., M. K. OLI, L. E. OLSON, D. T. BLUMSTEIN, AND K. B. ARMITAGE. 2007. Spatiotemporal variation in reproductive parameters of yellowbellied marmots. Oecologia 154:95106. OZGUL, A., et al. In press. Coupled dynamics of body mass and population growth in response to environmental change. Nature. PARMESAN, C. 2006. Ecological and evolutionary responses to recent climate change. Annual Review of Ecology Evolution and Systematics 37:637669. PARMESAN, C., and G. YOHE. 2003. A globally coherent fingerprint of climate change impacts across natural systems. Nature 421:3742. PHILLIPS, J. A. 1984. Environmental influences on reproduction in the goldenmantled ground squirrel in The biology of grounddwelling squirrels: annual cycles, behavioral ecology, and sociality (J. O. Murie and G. R. Michener, eds.). University of Nebraska Pr, Lincoln. PIMM, S. L., G. J. RUSSELL, J. L. GITTLEMAN, and T. M. BROOKS. 1995. The Future of Biodiversity. Science 269:347350. R DEVELOPMENT CORE TEAM. 2009. R: a language and environment for statistical computingin R Foundation for Statistical Computing. http://www.rproject.org/, Vienna, Austria. REGEHR, E. V., C. M. HUNTER, H. CASWELL, S. C. AMSTRUP, AND I. STIRLING. 2010. Survival and breeding of polar bears in the southern Beaufort Sea in relation to sea ice. Journal of Animal Ecology 79:117127. ROSSER, A. M., and S. A. MAINKA. 2002. Overexploitation and species extinctions. Conservation Biology 16:584586. ROYAMA, T. 1992. Analytical population dynamics. Chapman & Hall, London, U.K. SHERMAN, P. W., AND M. C. RUNGE. 2002. Demography of a population collapse: The Northern Idaho ground squirrel (Spermophilus brunneus brunneus). Ecology 83:28162831. TAMARIN, R. H. 1978. Population regulation. Dowden, Hutchinson & Ross, Inc., Stroudsburg, Pennsylvania. TULJAPURKAR, S., C. C. HORVITZ, and J. B. PASCARELLA. 2003. The many growth rates and elasticities of populations in random environments. American Naturalist 162:489 502. TURCHIN, P. 2003. Complex population dynamics. Princeton University Press. VAN VUREN, D. H. 2001. Predation on yellowbellied marmots (Marmota flaviventris). American Midland Naturalist 145:94100. VAN VUREN, D. H., AND K. B. ARMITAGE. 1991. Duration of snow cover and its influence on lifehistory variation in yellowbellied marmots. Canadian Journal of Zoology 69:17551758. VAN VUREN, D. H. 2001. Predation on yellowbellied marmots (Marmota flaviventris). American Midland Naturalist 145:94100. WHITE, G. C., AND K. P. BURNHAM. 1999. Program MARK: Survival estimation from populations of marked animals. Bird Study 46:120139. WILLIAMS, B. K., J. D. NICHOLS, AND M. J. CONROY. 2001. Analysis and management of animal populations. Academic Press, San Diego, California, USA. BIOGRAPHICAL SKETCH Eva Kneip received a Bachelor of Business Administration degree in management information systems with concentration in computer science from the University of Wisconsin in 1996. She obtained a Certificate in Conservation Biology from Columbia University's Center for Environmental Research and Conservation in 2004. Between 1996 and 2007, she worked in information technology consulting and financial services. Her first employer was Technology Solutions Company, a Chicagobased information technology consulting firm and in 1998 she joined Goldman Sachs Co. in New York City, as a software engineer. Ms. Kneip volunteered as a research assistant at various ecologyrelated field study sites, including a population genetics project of the small Indian mongoose in Jamaica and a guenon behavior study in Kenya. She has been involved with WildMetro, a New Yorkbased, nonprofit, conservation organization since 2004 focusing on mammalrelated studies in the New York metropolitan area. In order to pursue her passion of conservation biology, Ms. Kneip began her graduate education in University of Florida, Gainesville in Dr. Madan Oli's population ecology lab in 2008. Her thesis focuses on the demography of a goldenmantled ground squirrel population occupying a dynamic subalpine habitat. Furthermore, her research interest includes the population dynamics and conservation of mammalian predator species. PAGE 1 1 THE RELATIVE INFLUENCE OF DENSITY AND CLIMATE ON THE DEMOGRAPHY OF A SUBALPINE GROUND SQUIRREL POPULATION By VA KNEIP 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 2010 PAGE 2 2 2010 va Kneip PAGE 3 3 To my mom, dad, and grandparents PAGE 4 4 ACKNOWLEDGMENTS I thank my parents and close friends for their support and encouragement in my late career change to pursue my true passion. I am grateful to my supervisory committee for their wisdom, guidance, and time: Drs. M. K. Oli, M. E. Sunquist, and D. H. Van Vuren. My lab mates and professional colleagues that contributed to my research and deserve recognition are G. Aldridge, J. A. Hostetler, G. Morris, B. Pasch, R. A. Pruner, and V. Rolland. I thank C. Floyd, K. Jenderseck, and C. Mueller for their assistance in data collection. I would also like to express special gratitude to C. McCaffery and Dr. D. L. Reed from the Mammalogy collection of the Florida Museum of Natural History for their support and faith in me. Finally, I thank the California Agricultural Experi ment Station, UC Davis, the School of Natural Resources and Environment, UF, and the Department of Wildlife Ecology and Conservation, UF Gainesville for their generous financial support. PAGE 5 5 TABLE OF CONTENTS ACKNOWLEDGMEN TS ...................................................................................................... 4 page LIST OF TABLES ................................................................................................................ 7 LIST OF FIGURES .............................................................................................................. 8 ABSTRACT .......................................................................................................................... 9 CHAPTER 1 INTRODUCTION ........................................................................................................ 11 2 RELATIVE INFLUENCE OF POPULATION DENSITY, CLIMATE, AND PREDATION ON THE DEMOGRAPHY OF A SUBALPINE SPECIES .................... 14 Introduction ................................................................................................................. 14 Matrials and Methods ................................................................................................. 16 Study Area and Species ...................................................................................... 16 Field Methods ....................................................................................................... 17 Population Size and Predation ............................................................................ 18 Abiotic Covariates ................................................................................................ 18 Survival Analysis .................................................................................................. 19 Analysis of Reproductive Parameters ................................................................. 21 Results ........................................................................................................................ 22 Population Size and Composition ....................................................................... 22 Age, Sex, and Time Effects for Survival .............................................................. 22 Direct and Delayed Density Dependence (DD) for Survival ............................... 22 Effects of Abiotic Factors for Survival ................................................................. 23 Predation Effect for Survival ................................................................................ 23 DD vs. DID Models for Survival ........................................................................... 23 Breeding Probability (BP) .................................................................................... 24 Age, S ex, and Time Effects for BP ...................................................................... 24 Direct and Delayed Density Dependence for BP ................................................ 25 Abiotic Impacts for BP .......................................................................................... 25 Predation Effect for BP ........................................................................................ 25 DD vs. D ID Models for BP ................................................................................... 25 Litter Size.............................................................................................................. 25 Discussion ................................................................................................................... 26 3 STOCHASTIC POPULATION DYNAMICS OF A GOLDEN MANTLED GROUND SQUIRREL POPULATION ....................................................................... 36 Introduction ................................................................................................................. 36 Materials and Methods ............................................................................................... 39 PAGE 6 6 Study Area and Species ...................................................................................... 39 Field Methods ....................................................................................................... 40 Matrix Population Model ...................................................................................... 40 Deterministic Analysis .......................................................................................... 42 Environmental Stochasticity ................................................................................. 42 Density Dependence and Environmental Stochasticity ...................................... 44 Results ........................................................................................................................ 46 Deterministic Analysis .......................................................................................... 46 Environmental Stochasticity ................................................................................. 47 Density Dependence and Environmental Stochasticity ...................................... 48 Discussion ................................................................................................................... 49 4 CONCLUSION ............................................................................................................ 63 APPENDIX A SURVIVAL MODELS TESTING FOR THE EFFECTS OF SEX, AGE, AND TIME ............................................................................................................................ 66 B SURVIVAL MODELS TESTING FOR THE EFFECTS OF DENSITYDEPENDENT AND INDEPENDENT FACTORS ..................................................... 67 C BREEDING PROBABILITY MODELS T ESTING FOR THE EFFECTS OF INTRINSIC, DENSITY DEPENDENT AND INDEPENDENT FACTORS ................ 70 D LITTER SIZE MODELS TESTING FOR THE EFFECTS OF INTRINSINC, DENSITYDEPENDENT AND INDEPENDENT FACTORS .................................... 72 LIST OF REFERENCES ................................................................................................... 74 BIOGRAPHICAL SKETCH ................................................................................................ 80 PAGE 7 7 LIST OF TABLES Table page 3 1 Regression coefficients for logit transformed survival and logit transformed breeding probability (BP) for the goldenmantled ground squirrel population in Got hic, CO .............................................................................................................. 55 3 2 Elasticities of stochastic population growth rate ( s) to mean ( E), variance (E), and both mean and variance ( ES) of matrix elements.. .............................. 55 3 3 The number of juvenile and adult female goldenmantled ground squirrels that immigrated to our study site in Gothic, CO. ................................................... 56 PAGE 8 8 LIST OF FIGURES Figure page 2 1 Annual variation in the population size of the GMGS for the period 19902008. Total and ageand sex specific numbers of squirrels are presented. ....... 32 2 2 Model averaged annual survival est imates with SE for adult (AF) and juvenile (JF) female, and adult (AM) and juvenile (JM) male GMGS during 19902007.. ...................................................................................................................... 33 2 3 Relationship between previous years population size and age and sex specific survival.. .................................................................................................... 34 2 4 Breeding probability and distribution of litter size of golden mantled ground squirrels. ................................................................................................................. 35 3 1 Relationship between annual population density and the age specific logi t transformed survival rate.. ..................................................................................... 57 3 2 Annual variation in the deterministic population growth rate with 95% CI for female goldenman tled ground squirrels during 19902007. ................................ 58 3 3 lower level vital rates of the overall matrix A .. ....................................................... 59 3 4 Frequency distribution of population size in 50 years including only the effects of environmental stochasticity.. .................................................................. 60 3 5 Proj ected abundance of the female GMGS population for 50 years using the overall projection matrix and the average female abundance (30) under 5 scenarios for density dependence. ........................................................................ 61 3 6 Probability of quasi extinction under various scenarios of environmental stochasticity, density dependence, and differing levels of quasi extinction threshold for the goldenmantled ground squirrel population. .............................. 62 PAGE 9 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 THE RELATIVE INFLUENCE OF DENSITY AND CLIMATE ON THE DEMOGRAPHY OF A SUBALPINE GROUND SQUIRREL POPULATION By va Kneip August 2010 Chair: Madan K. Oli Major: Interdisciplinary Ecology In the context of global climate change, understanding the causes and consequences of oscillations in populations is a central objective for ecologists. We utilized longterm (19902009) field data to investigate the influence of population size and extrinsic environmental factors on the demographic parameters of g oldenmantled ground squirrels ( Callospermophilus lateralis ; formerly, Spermophilus lateralis ). Moreover, we examined how these influences are translated at the population level. Survival varied by sex and age class, with highest survival for adult females ( =0.519, 95% CI: 0.462, 0.576) and lowest survival for juvenile males ( =0.120, 95% CI: 0.094, 0.152 ). There was evidence that population size negatively influenced survival with a time lag of 1 year. Among the extrinsic environmental factors considered, rainfall and an index of predator abundance substantially influenced survival. Breeding probability (probability that a female successfully weans for older females (=0.717, 95% CI=0.639 0.79) than for yearlings (=0.313, 95% CI: 0.228, 0.412). There was evidence that rainfall negatively influenced breeding probability of both older and yearling females with a time lag of 1 year Litter size ranged 1 8 pups PAGE 10 10 with a mean of 4.8 1 ( 95% CI: 4.532 5.08 ). There was no evidence that litter size varied among age classes or over time, or was influenced by population size or extrinsic environmental factors. The year to year deterministic population growth rate was highly variable, r Using 50,000 simulati ons and assuming a uniform independently and identically s was 0.912 suggesting an 8.8% annual population decline. This result was less than the deterministic growth M (0.944) but it was similar to the overall deterministic growth =0. 905 95% CI: 0.8120.99 8) which was based on pooled data. As a result of lo wer level elasticity analysis, the deterministic population growth rate was most sensitive to proportionate changes in adult survival. All three measures of stochastic s was proportionately most sensitive to juvenile survival. Th e GMGS population is predicted to decline with probability of extinction approaching 90% in 50 years for the density independent model. When density dependence and immigration were included in our model the risk of extinction was reduced to zero. Our resu lts suggest that population size and extrinsic environmental factors do not affect all demographi c variables in the same fashion and both factors act in concert to influence the size of our study population. As environmental variability is likely to exacer bate the fluctuations in GMGS abundance, the likelihood that the population falls below a critical threshold will increase. Therefore, the effects of an increased environmental stochasticity may amplify the risk of quasi extinction of this population. PAGE 11 11 CHAPTER 1 INTRODUCTION While extinctions are a natural part of the evolutionary process, current extinction rates are estimated to be between 1,000 and 10,000 times the norm, and are solely humaninduced (Pimm et al. 1995; Rosser and Mainka 2002) The combined effects of landscape modification, resource exploitation, invasive species introduction, and accelerated greenhousegas production greatly alter t he biosphere (Krauss et al.; Lee and Jetz 2008; Rosser and Mainka 2002). Increased greenhousegas emission is changing the Earths climate and is a major cause of concern for biodiversity as climate change affects the geographical distribution, physiology, phenology, and demography of organisms (Bernstein et al. 2007; Jenouvrier et al. 2009; Parmesan 2006). Although v irtually all natural populations experience stochastic environmental variations, a growing body of evidence indicates that global climate change impacts both the mean and variance of climatic parameters, with especially pronounced effects in high altitude and latitude habitats. Organisms living in such ecosystems are particularly vulnerable; species occupying these habitats were the first to go extinct due to climate change (Bernstein et al. 2007; Jenouvrier et al. 2009; Parmesan and Yohe 2003) However, the direct impacts of anthropogenic climate change have been reported on every continent (Parmesan 2006). Therefore, climateinduced biodiversity loss is a global concern which has received much attention in a plethora of syntheses, such as the Intergovernmental Panel on Climate Change (IPCC) and the Millennium Ecosystem Assessment. The objective of my thesis was to examine the effects of environ mental variability from a demographic perspective. To mitigate the potential ecological consequences of PAGE 12 12 stochastic environments it is critical to understand how the demography, dynamics, and persistence of populations are affected by the increasing environmental variability (Boyce et al. 2006). Although I did not explicitly study climate change, its effects are expressed through the increased variability of environmental variables which influence vital rates and, consequently, population growth rates (Bernstein et al. 2007). Therefore, to quantify the effect of environmental stochasticity, I examined the relative role of climatic factors, predation, and density dependence (DD) in the dynamics of a temporally oscillating vertebrate population. The relative i mportance of such density independent (DID) and density dependent mechanisms is a topic that is still hotly debated among population ecologists (Leirs et al. 1997). Hence, I stud ied the demographic consequences of DD a nd en vironment al variability by utilizing a demographic data set from a 19year (19902008) study on a golden mantled ground squirrel ( Callospermophilus lateralis ; formerly, Spermophilus lateralis ; hereafter, GMGS) (Helgen et al. 2009) population The reliability of inference drawn f rom demographic studies depends largely on the availability and quality of data. T he goldenmantled ground squirrel data consisted of long term capture mark recapture (CMR) data and it encompassed annual census counts which alleviated the ne ed for estimat ing detection probability. Th is study was conducted at the Rocky Mountain Biological Laboratory (RMBL) near Crested Butte, Colorado (38o58N, 106o59W, elevation 2890m), a subalpine site where the climatic effects are pronounced due to climate change and several climaterelated research projects are underway (Inouye et al. 2000; Ozgul et al. In press) D etailed d ata on climatic variables were acquired from the U.S. Environmental PAGE 13 13 Protection Agency Weather Station at RMBL. I obtained environmental data such as the first day that snow melt exposed bare ground from personal observations by a local resident, Billy Barr Having access to both demographic and climatic data allowed for a full demographic analysis in which the relative roles of abiotic and other pot entially important factors could be examined with respect to the population dynamics of the golden mantled ground squirrel population. In my thesis, I attempted to answer two major questions: (1) how do density dependent and independent factors influenc e the demographic rates, and (2) how are these influences translated at the population level. To address these questions it was necessary to estimate agespecific vital rates (survival, breeding probability, and litter size) and evaluated the effects of various factors on these vital rates. Therefore, the second chapter is dedicated to parameter estimation. The analysis described in the second chapter revealed strong evidence of density dependen t and the extrinsic environment al (current summer rainfall) effects on survival and strong impact of climatic factors ( previous summer rainfall ) on breeding probability. T he third chapter built on these findings and investigated the standalone and combined effects of density dependence and environmental stochastici ty on the long term population growth of the golden mantled ground squirrel population. Therefore, the following two chapters investigate the causes and consequences of the temporal fluctuations exhibited by the ground squirrel population. The analysis fo cuses on the population dynamic consequences of density dependence and environmental stochasticity. PAGE 14 14 CHAPTER 2 I RELATIVE INFLUENCE O F POPULATION DENSITY CLIMATE, AND PREDA TION ON THE DEMOGRAPHY OF A SUBALPINE SPECIES Introduction Identifying and quantifying the causes and consequences of temporal fluctuations in vertebrate populations is a persistent challenge in ecology (Coulson et al. 2001; Oli and Armitage 2004; Williams et al. 2001) Factors that drive population dynamics may be density dependent (DD) or density independent (DID) It is generally believed that DD feedback mechanisms play an important role in regulating populations (Hone and Sibly 2002; Royama 1992; Turchin 2003) but several studies suggest that density dependence and extrinsic environmental factors act synergistically to determine dynamics and thus regulation of populations (CluttonBrock and Coulson 2002; Coulson et al. 2001; Coulson et al. 2008; Leirs et al. 1997) However, the relative roles of DD climatic factors, predatio n, and intrinsic influences on population dynamics remain poorly understood in most species (Den Boer and Reddingius 1996; Tamarin 1978) The impact of abiotic factors on population dynamics may be intensifying as a result of global climate change. A growi ng body of evidence demonstrates that the earths climate is changing and that these changes will influence both the mean and variance of climatic variables (Bernstein et al. 2007). Consequently, th ese changes are already affecting the physiology, phenolo gy and demography of several species, particularly those species occupying high altitude and latitude habitats (Bernstein et al. 2007; Frederiksen et al. 2008; Hughes 2000; Inouye et al. 2000; Jenouvrier et al. 2009; Parmesan 2006; Regehr et al., 2010) G lobal climate change may induce changes in the length of summer or winter seasons ; therefore influence of global climate change on hibernating species is likely to be substantial (Inouye et al. 2000) Species PAGE 15 15 distributions and life history traits also may be altered (McLaughlin et al. 2002) In order to mitigate the potential ecological consequences of such changes, it is critical to understand how the fluctuating environmental factors influence the demographic parameters, dynamics and persistence of p opulations (Boyce et al. 2006; Jenouvrier et al. 2009) Because population growth rates are determined by demographic parameters (Caswell 2001; Oli and Armitage 2004) populationlevel impacts of anticipated global climatic change are mediated through vital demographic rates (Jenouvrier et al. 2009; Krebs 2002, 1995). Therefore, to decipher the relative roles of population density, predation, and climatic factors in determining population dynamics in stochastic environments, one must first understand their relative impacts on vital demographic rates. The g oldenmantled ground squirrels ( Callospermophilus lateralis ; formerly, Spermophilus lateralis ; hereafter, GMGS) (Helgen et al. 2009) is a hibernating species occupying montane habitats in western North Amer ica (Ferron 1985, Bartels and Thompson 1993) At a subalpine location in the Rocky M ountains where climate change has been shown to have impacted several species (Inouye et al. 2000), a free ranging GMGS population exhibited substantial fluctuations ( Figu re 2 1). The long term (20 years) monitoring of this species allowed us to investigate the relative influence of population dens ity and extrinsic factors on GMGS vital rates. Our objectives were to: (1) provide estimates of age specific survival rates, br eeding probabilities, and litter size ; (2) evaluate the effects of sex, population size (with and without time lag), and extrinsic environmental factors (predation, previous and current summer rainfall, and previous PAGE 16 16 and current years first day of bare ground) on these rates; and (3) compare the relative influence of DD and DID factors on vital rates. Matrials and Methods Study A rea and Species Our research was conducted at the Rocky Mountain Biological Laboratory (RMBL) near Crested Butte, Colorado (38o58N, 106o59W, elevation 2890m), USA. The 13ha study area was situated on a primarily open subalpine meadow that was interspersed with willow ( Salix sp. ) and aspen ( Populus tremuloides ) stands (Van Vuren 2001). The meadow was bordered on the west and south by the East River and Copper Creek, and on the north and east by aspen forest. The GMGS is a diurnal, asocial species whose distribution spans a broad elevational gradient from 1,220 to 3,965 m above sea level where it occupies open habitats such as r ocky mountain slopes adjoining grasslands, areas of scattered chaparral, and margins of mountain meadows (Bartels and Thompson 1993; Ferron 1985) GMGS hibernate to cope with food shortages during long winters. The entrance to and emergence from hibernation both vary depending on altitude and amount of snowfall (Bartels and Thompson 1993). At our study site, adult squirrels typically emerged from hibernation at about the time of snow melt or before, in late May or early June. The breeding season began shor tly after emergence and pups emerged from natal burrows during late June to midJuly. T he entire population entered hibernation by late August or early September The GMGS is considered omnivorous (Bartels and Thompson 1993) but in our study area their di et appeared to consist mainly of herbaceous vegetation such as grasses and forbs, whose growth is stimulated by snow melt After emergence, they gain weight PAGE 17 17 rapidly, storing fat for overwinter survival and to sustain gestation the next spring until green v egetation starts growing again (Phillips 1984). Numerous mammalian and avian p redators prey on GMGS (Bartels and Thompson 1993) but in our study area, we observed predation only by red foxes ( Vulpes vulpes ) and longtailed weasels ( Mustela frenata). Field M ethods For 20 consecutive years (19902009), GMGS were live trapped augmented by almost daily observations during the active season (May to late August). Squirrels were trapp ed during late May early June, for the annual census and marking of the residen t population; late Junemid July, for trapping and marking emerging litters; and late July and again late August, for weighing squirrels and renewing marks. O bservations and opportunistic trapping were conducted almost daily throughout the summer in order to capture and mark new immigrants and renew marks on residents. Squirrels were captured with singledoor Tomahawk livetraps (12.7 x 12.7 x 40.6 cm) baited with a mixture of sunflower seeds and peanut butter. Newly captured squirrels received a noncorrosi ve metal tag in each ear. Squirrels were distinctly dyemarked with fur dye for visual recognition, and weight, sex, ear tag numbers, and reproductive condition were recorded. All juveniles were trapped at first emergence from their natal burrow, and litter size as well as the mothers identification was recorded. Animal handling followed protocols approved by the Animal Care and Use Committee at the University of California, Davis and met guidelines recommended by the American Society of Mammalogists (Gann on and Sikes 2007). Age was known for 704 squirrels that were initially captured as juveniles at their natal burrow. For an additional 127 squirrels (immigrant adults) exact age was not PAGE 18 18 known; however, immigrant juveniles ( < 1 year) could be differentiated from adults based on body mass. Population Size and P redation We determined population size by counting individuals because we continued trapping and marking until all squirrels in the study area were trapped and identified each year ; therefore the captur e probability was 1 throughout the study period. Predation ( pred) was measured as an index and it was quantified as the number of predation events per year with a predation event scored if observed or if a squirrel abruptly disappeared when red foxes o r long tailed weasels were active in the study site. Abiotic C ovariates C limatic factors considered in this study included summer rainfall during the current ( raint) and previous year ( raint 1), and first day that snow melt exposed bare ground during the c urrent ( bgt) and previous year ( bgt 1). These variables were used as temporal covariates in our CMR analysis and they were selected based on a priori hypotheses that they influence GMGS demographic parameters (apparent survival rates, breeding probabilitie s, and litter size; hereafter survival, BP, LS, respectively). Data on climatic variables were obtained from the U.S. Environmental Protection Agency Weather Station at RMB L and from B. Barr (personal communication). Summer rain may prolong the growth of forbs and grasses that began when snow melted. Therefore, due to its effect on primary production, summer rainfall may be a good predictor of squirrel vital rates (Klinger 2007; Sherman and Runge 2002) Summer rainfall was calculated by summi ng the mean daily rainfall for the months of June and July ; August precipitation was excluded because squirrels then are close to hibernation. PAGE 19 19 The duration of snow cover is suggested to influence the length of the growing season hence squirrel food availability (Bronson 1979; Van Vuren and Armitage 1991) During years of food shortage GMGS may curtail reproduction in favor of survival (Phillips 1984; Sherman and Runge 2002) In addition, time of snowmelt affects the length of time squirrels are exposed to predation (Bronson 1979) Consequently, the first day of bare ground (i.e., no snow cover) may also be a good predictor of squirrel demographic parameters. For the investigation of lag effects, data were required from the year preceding the commencement o f the study (1989), which were not available for all variables. Therefore, summer rainfall and population size data for 1989 were obtained by averaging the values from 1990 and 1991. Survival A nalysis We used multistate CMR models (Williams et al. 2001) i mplemented in Program MARK (White and Burnham 1999) using RMark interface (Laake and Rextad 2009). We considered 2 states based on 2 ageclasses (juvenile: [<1yr olds] ; adult s: [ 1yr olds] ), and estimated and modeled the statespecific apparent annual surv ival ( ), recapture (p ), and transition ( ) rates. Preliminary analyses revealed that capture probability was close to 1.0 ( p to 1.00 for all models. Conditional on survival, the transition rate xy indicates the probability of transition from state x to y the following year. Surviving juveniles automatically advanced to adult state the next year and remained adults for the rest of their life cycle. Hence, juvenile to adult and adult to adult transition rates were fixed to 1.0. The goodness of fit (GOF) of our fully time dependent general multistate model was tested with software UCARE V2.3 (Choquet et al. 2005b), and the over dispersion PAGE 20 20 parameter ( ) was calculated as the 2 divided by the degrees of freedom (Burnham and Anderson 2002). There was no evidence for lack of fit or over dispersion of data 2 35= 37.785, P =0.343, =1.08). We employed Akaikes Information Criterion, corrected for small sample size (AICc) for model comparison, statistical inferences, and to select the most p arsimonious model from a candidate model set (Burnham and Anderson 2002). Model comparison was based on the differences in AICc values ( c). The model associated with the lowest AICc value was considered the best and models with c between each parameter and covariate (Gaillard et al. 1997; Ozgul et al. 2007) The s tep wise approach was employed in the CMR analysis. First, we considered the additive and interactive effects of age class (juveniles and adults [ yr olds]) and sex on GMGS survival. Using the most parsimonious age and sex model as the base model, we tested f or the additive and interactive effects of time. Second, we tested for the additive and interactive effects of current ( Nt) and previous years population size (Nt 1) to test for direct and delayed density dependence, respectively. The size of the study site was constant for the duration of the study; therefore, we considered population size (not population density) as a timedependent covariate for these analyses. Third, we tested for the additive and interactive effects of extrinsic environmental factors ( pred, raint, raint 1, bgt, and bgt 1). The most parsimonious model identified in step 1 was used as a base model for these analyses. Fourth, we tested for the additive and interactive effects of covariates in the best DD ( Nt 1) and DID ( raint, PAGE 21 21 raint 1 and pred) models. We compared AICc values for the most parsimonious model that included the effects of population size only, extrinsic variables only, and both population size and extrinsic factors, to evaluate the influence of DD and extrinsic factors (and combination thereof) on sex and age specific survival of GMGS. In order to determine the relative importance of our predictor variables, for each variable, we summ ed the Akaike weights for all models in the candidate set that contained the variable (Anderson 2008). The predictor variable with the largest sum or predictor weight was considered to be the most important. Finally, in order to address model selection uncertainty, we performed model averagi ng using all models from step 1 to calculate model averaged estimate of sex and agespecific survival (Burnham and Anderson 2002). Analysis of R eproductive Parameters We considered 2 components of reproductive rates: (1) breeding probability, BP (i.e., th e probability that a female weans (Doherty et al. 2004; Ozgul et al. 2007) ); and (2) litter size, LS (i.e., number of weaned juveniles that emerged from natal burrows (Ozgul et al. 2007)). We utilized logistic regression to estimate and model BP. This approach was adequate because capture probability was 1.0 for every year of the study. Zerotruncated P oisson regression (generalized linear models (GLM) with Poisson distribution and log link function) was used for LS analysis We used the same stepwise approach as described previously for the survival analysis to determine the influence of extrinsic and intrinsic factors on LS and BP. In contrast with survival analysis, however, sex effect was not relevant for reproductive par ameters because only the female segment of the population was examined. We considered 2 ageclasses ( yearling [=1yr olds] and older [ yr olds] females ) for the reproductive PAGE 22 22 analysis of adult females. GLM analyses were conducted in program R (R Development Core Team 2009). Results Population Size and C omposition Total population size fluctuated markedly, ranging from 24 individuals in 1999 and 2000 to 140 squirrels in 2005. The number of individuals of each sex and age class also exhibited similar fluctuati ons during the study period ( Figure. 2 1). Age, Sex, and Time Effects for S urvival There was very strong evidence ( c >50 ) that both sex and age substantially influenced apparent survival (models 3 and 4 vs. model 5, Appendix A1 ). T he most parsimonious model showed an additive effect of age and sex (model 1, Appendix A1 ) ; annual survival rate was highest for adult females ( =0.519, 95% CI: 0.462, 0.576) and lowest for juvenile males ( =0.120, 95% CI: 0.094, 0.152), while survival est imates for juvenile females ( =0.310, 95% CI: 0.265, 0.359) and adult males ( =0.247, 95% CI: 0.197, 0.306) were intermediate with overlapping CI. Using model 1 in Appendix A1 as a base model, we tested for the additive and interactive effect of time on su rvival to investigate temporal variation in sex and agespecific survival. The most parsimonious model included an additive effect of age, sex, and time (model 1, Appendix A2 ), suggesting that survival varied substantially over time but sex and age speci fic differences remained constant over time ( Figure. 2 2). Direct and D elayed D ensity D ependence (DD) for Survival The analysis of the effect of current ( Nt) and previous years ( Nt 1) population size on survival indicated that the most parsimonious DD survival model included an additive effect of age, sex, and Nt 1 (model 1, Appendix B1 ). Indeed, Nt 1 negatively influenced PAGE 23 23 0.011, 95% CI: 0.015, 0.006) of squirrels of both sexes and age classes (Figure. 2 3a d). We note that models 27 in Appendix B1 also had considerable support; however, all of these models included effects of Nt 1, providing strong evidence for delayed DD effects on survival. Effects of A biotic F actors for Survival The investigation of the impact of abiotic factors ( raint, raint 1, bgt, and bgt 1) on survival revealed that the best extrinsic survival model included an additive delayed effect of summer rainfall ( raint 1), and an interactive effect between age and summer rainfall of the current year ( raint) (model 1, Append ix B2 ). There was evidence for the positive effect of raint 1 on survival which was not significant 0.001, 0.01) Current years summer rainfall, raint, negatively influenced the survival of 0.008, 95% CI: 0.013, 0.004), 0.004, 0.007). Since c between models 1 and 2 was < 2 ( Appendix B2 ), and raint had substantial impact on survival we included both models for subsequent analyses. Predation Effect for Survival The analysis of the effect of all extrinsic environmental factors on survival (Appendix B3) showed that the most parsimonious DID model inc luded an additive effect of sex age, and pred and an interactive effect of age and raint (model 1, Appendix B3). Pre dation negatively influenced survival of 0.033, 95% CI: 0.054, 0.012). DD vs. DID M odels for Survival We compared the best DD (model 1, Appendix B1) and DID (model 1, Appendix B3 ) models to evaluate the relative influence of DD and DID factors on squirrel survival There was strong evidence that both DD ( Nt 1) and DID ( raint) factors influenced survival PAGE 24 24 (models 5 and 17 vs. model 20, Appendix B4 ) T he most parsimonious model (model 1, Appendix B4) included an additive effect o f Nt 1 0.010, 95% CI: 0.015, 0.006) and an interactive effect between age and raint 0.008, 95% CI: 0.012, 0.001, 0.009). These results suggested that Nt 1 negatively influenced survival of bot h sexes and age classes. In this final model, raint had no effect on adult survival; however, it impacted juvenile squirrel survival negatively. We quantified the relative importance of population density and extrinsic factors by summing the Akaike weights for all models from Appendix B4 that contained each variable. The sum of AIC weights for Nt 1, raint, pred, and raint 1 w ere 0.999, 0.9 79 0.351, and 0. 307, respectively indicating that pred and raint 1 w ere considerably less important in explaining survival than the other 2 variables. Breeding P robability (BP) Although yearling female squirrels frequently reproduced, older ( yr old) females represented the main reproductive segment of the squirrel population With the exception of 2003, the percentage of adult females reproducing was higher for older than yearling females ( Figure. 2 4a). Age, S ex, and T ime Effects for BP There was strong evidence for age specific (yearling vs. older females) differences in B P (c >30 and wi=1; model 1 vs. 2, Appendix C1). The estimated BP for older females was higher (=0.717, 95% CI=0.639 0.79) than for yearlings (=0.313, 95% CI: 0.228, 0.412). Next, we tested for the effect of time on BP but there was no evidence for temporal variation in this vital rate (model 2 vs. 3, Appendix C1). The effect of time may not be evident due to small sample size. Hence, we employed a model that included the age effect for all subsequent analysis. PAGE 25 25 Direct and D elayed D ensity D ependence for BP All models investigating effects of population size on BP are provided in Appendix C2 The best DD model included an additive effect of age and Nt (model 1, Appendix C2 ). There was strong support ( c >2) for the pos itive effect of Nt (model 1 vs.8, Appendix C2 Abiotic I mpacts for BP The most parsimonious model (model 1, Appendix C3) showed evidence for interactive effects of age and raint 1 (model 1 vs. 8, A ppendix C3) where raint 1 0.004, 95% CI: 0.013, 0.033, 95% CI: 0.051, 0.016) females. Predation Effect for BP When we considered predation as an additional extrinsi c factor in our analysis, the best resulting model was still the same as model 1 in Appendix C3 Thus, there was no evidence that predat ion affected BP. DD vs. DID M odels for BP Although, the most parsimonious model included both DD and DID components, the additive effect of Nt, and the interactive effect of age and raint 1, the model without the additive effect of Nt was only 0.22 AIC away (models 1 and 2, Appendix C4 ). The evide nce for the relative importance of raint 1, however, was strong (models 1 and 3, Appendix C4). Therefore, we chose model 2 (i.e., model with the lowest number of parameters) as our most parsimonious model for parameter estimation. Litter Size Litter size ( LS ) ranged from 1 to 8 pups ( N =139, LS =4.806, 95% CI: 4.532, 5.08 ) with mode of 5 pups per litter ( Figure. 2 4b). Unlike BP, age of mothers did not have a PAGE 26 26 major impact on LS (model 1 vs. 2, Appendix D1 ). There was no evidence for temporal variation (model 1 vs. 3, Appendix D1), DD ( Appendix D2), or DID ( Appendix D3) influences on LS Therefore, the model with constant LS was the most parsimonious, with no evidence for the effect of age of mothers or i nfluence of DD and DID factors on this variable. Discussion The effects of DD and DID factors on population growth rate are indirect through their influences on vital rates and hence may be unexpected. The subtle and interactive process by which these factors impact the vital rates of dif ferent segments of structured populations is a phenomenon experienced across taxa (Coulson et al. 2001; Jonzn et al. 2010; Leirs et al. 1997; Ozgul et al. 2006; Ozgul et al. 2007) Density dependent feedback mechanisms are thought to eventually stabilize populations (Leirs et al. 1997; Royama 1992; Turchin 2003) while stochastic variations in environmental factors tend to have destabilizing effects on population dynamics (Coulson et al. 2000) Consequently, our goal was to disentangle the relative contribution of DD and DID factors on our study population in order to tease apart their singular as well as combined effect s that likely underlie the extensive temporal fluctuation in GMGS abundance. Understanding these relationships is even more critical when st udying a species such as GMGS that occupies habitats that may be sensitive to climate change. Our analysis revealed strong evidence for temporal and ageand sex specific variation on survival Previous studies have also demonstrated the impact of age and sex on survival rates of highelevation sciurid species. Bronson (1979) conducted a demographic study on GMGS in California and Sherman et al. (2002) investigated the potential causes of the su dden population collapse of a Northern Idaho ground squirrel PAGE 27 27 (U rocitellus brunneus brunneus ) population Both studies reported lower survival rates for juvenile versus adult squirrels and lower survival rates for males than for females Although these stud ies were relatively short term, our results are consistent with the pattern they found. The survival estimates in our study site were similar to those reported for the Northern Idaho population (Sherman et al. 2002) Nevertheless, our juvenile survival rat es, especially for males, likely are underestimated because of the confounding effects of emigration. Consistent with previous studies that examin ed reproductive parameters of highelevation sciurid species (Bronson 1979; Ozgul et al. 2007) we found that older females ( were the main reproductive segment of the squirrel population ( Figure. 2 4a). Bronson (1979) reported that many young squirrels failed to reproduce at high elevati on sites. Likewise, yearlings did not reproduce in 9 out of 19 years in our study site. Indeed, there was substantial agespecific difference in breeding probability with older females twice as likely to reproduce as yearlings Ozgul (2007) reported temporal variation on the breeding probability of sub adult and adul t yellow bellied marmots (Marmota flaviventris ) at the same approximate locality. However we did not find evidence for temporal variability in breeding probability, which may be a result of our small sample size. While Ozgul et al. (2007) and Sherman et al. (2002) found support for the effect of age and time on litter size respectively, we found no evidence that LS varied among age classes or across years We expected that current years population density would have a negative effect on survival because crowding during the summer reduces per capita food availability PAGE 28 28 and therefore the squirrels ability to store enough fat for overwinter survival. In addition, high population density may promote juvenile dispersal, thereby reducing their apparent survival Unexpectedly, we found that GMGS survival was negatively related with the previous years population density while there was no support for a sameyear effect of density. Our second best DD model (model 2, Appendix B 1 ) had considerable support (c =0 .84) and indicated interaction between age and last years density. According to this model, high density had a stronger negative effect on survival of juveniles than that of adults. This is not surprising, since juveniles are more likely to disperse and s ettle in poor habitat within the site or leave the study area permanently. Indeed, vital rates are suggested to covary closely with population density in small mammals (Klinger 2007; Leirs et al. 1997; Ozgul et al. 2004), but a lag effect of density on sur vival was unanticipated We suggest density dependent habitat selection as a possible explanation of delayed density effects on survival. High population density in our study area results in increased occupancy of lower quality habitats (K. Ip, unpublished ms.), primarily by juveniles Many of these juveniles originated from high quality areas where they presumably were able to accumulate sufficient fat reserves for surviving their first winter, but subsequently experience diminished resources for surviving the year after Negative DD effects on vital rates can manifest through intraspecific competition, resource availability and predation (Klinger 2007). The strong effect of predation on temperate small mammal populations is well established (Hanski et al. 2001) and accordingly, predation negatively influenced GMGS survival in all segments of our study population. Although there was strong support for predation in the top DID model predation was not included in the top com bined DD and DID model. Since we lacked PAGE 29 29 predator abundance data, we attempted to quantif y the effect of predation by recording observed or presumed predation events as they were encountered during squirrel observations Among small mammals there is evidence for negative DD effec ts through density mediated reproductive suppression (Boonstra 1994; Klinger 2007) but our results showed that sameyear density had a positive effect on breeding probability. This result was perhaps caused by a mate finding Allee effect (Gascoigne et al. 2009) although interpretation was difficult. There was no evidence for the effect of population density on litter size In our study, DID influence was expressed in both survival and reproductive rates through the effect of current years rainfall and previous years rainfall, respectively The l iterature suggests that increased food availability driven by rainfall improves both vital rates (Klinger 2007) but o ur results showed a negative correlation between rainfall and both survival and reproduction Meadow vegetation in our study area is highly productive (Kilgore and Armitage 1978), and it is possible that squirrels experience an abundant food supply regardless of additional growth stimulated by summer rainfall Instead, periods of prolonged rainfall may have had a negative effect on squirrels by denying them access to food (Bakker et al. 2009); squirrels in our study remained underground during rainy weather Hence, GMGS during rainy summers may have entered hibernation with reduced fat reserves for supporting both overwinter survival and reproduction the following spring. Abiotic variables such as the amount and frequency of precipitation are projected to increasingly vary due to a globally changing climate (Bernstein et al. 2007). PAGE 30 30 Stochastic pertur bations to vital rates can negatively impact the persistence of populations The GMGS population inhabits a stochastic, highaltitude environment; hence increasing perturbations to GMGS vital rates due to changing environmental factors can negatively influ ence the GMGS population. Future research may focus on predicting GMGS population dynamics using models that incorporate these stochastic processes. Population regulation, the process determining sizes of populations is a controversy that is much debated among ecologists. There is general consensus, however, that some regulatory mechanisms are responsible for the persistence of most natural populations (Dobson and Oli 2001) Fluctuations in population size are due to changes in demographic rates and it is essential to understand how vital rates are impacted by DD and DID factors. Our results showed that DD and DID factors did not affect all vital rates in the same fashion. With respect to GMGS survival, both DD ( previous years population density ) and DID (current summer rainfall ) factors were important Based on the sum of AIC weights, the relative importance of the 4 most critical variables on survival in decreasing order was: density the previous year current summer rainfall predation, and previous sum mer rainfall. The weight s of previous years density and current summer rainfall were equally high. Leirs et al. (1997) found a strong negative effect of direct DD for only adult multi mammate rats ( Mastomys natalensis ), while the negative impact of delayed DD in our GMGS population was consistent in all ageand sex classes. However, Leirs et al. (1997) did not find a strong extrinsic influence of rainfall, which is surprising in an environment where water is a limiting resource. PAGE 31 31 For breeding probability the top combined model included both DD ( current years population density ) and DID ( rainfall the previous summer ) factors, but the relative support was much higher for the model that included the effect of rainfall the previous summer. The strong c ontribution of DID factors to breeding probability was consistent with literature suggesting that reproduction of small mammal species is driven primarily by DID factors (Coulson et al. 2000; Klinger 2007) We conclude that both density dependent and densi ty independent factors influenced demographic variables of GMGS in our study site, but the pattern of influence differed among variables. Extrinsic environmental factors influenced both survival and reproduction of squirrels, whereas population density pri marily influenced survival. Global climate change is predicted to increase variance of several climatic variables including those considered in our study. Hence, our GMGS population is likely to experience more stochastic variation in demographic variables as well as population dynamics. PAGE 32 32 Figure 21. Annual variation in the population size of the GMGS for the period 1990 2008. Total and ageand sex specific numbers of squirrels are presented. PAGE 33 33 Figure 22. Model averaged annual survival estimates with SE for adult ( AF ) and juvenile ( JF) female, and adult (AM ) and juvenile (JM) male GMGS during 19902007. All unique models from Table 21a and 2 1 b were included for model averaging PAGE 34 34 Figure 23. Relationship between previous years population size an d age and sex specific survival. a) adult female survival, b) juvenile female survival, c) adult male survival, and d) juvenile male survival. Dotted lines indicate 95% confidence intervals. Parameters were estimated based on model 1 in Appendix B1. PAGE 35 35 A B Figure 24. Breeding probability and distribution of litter size of goldenmantled ground squirrels. A) P ercentage of yearling and older ( female s that successfully weaned at least 1 pup during 19902008., B) Distribution of litter size during the study period (1990 2008) PAGE 36 36 CHAPTER 3 STOCHASTIC POPULATION DYNAMICS OF A GOLDEN MANTLED GROUND SQUIRREL POPULATION Introduction A central objective for ecologists is to understand the mechanisms that cause population fluctuations (Horvitz and Schemske 1995, Kruger 2007). In addition to investigating the causes of temporal fluctuations, there has been much interest in understanding the effects of environmental variability on vertebrate populations and making accurate longterm demographic predictions (Kalisz and McPeek 1993, Boyce et al. 2006). It is generally believed that both endogenous (density dependent; DD) and exogenous (densi ty independent; DID) processes influence population dynamics (Leirs et al. 1997, Coulson et al. 2001, Kruger 2007), but the relative roles of DD regulation and DID destabilization are still debated (Tamarin 1978, Boyce et al. 2006). With global climate change, the effects of DID processes on population dynamics are likely to become stronger; therefore, it is critical to understand how stochastic variation and density dependent mechanisms interact to cause fluctuations in abundance and impact the future of p opulations (Parmesan 2006, Bernstein et al. 2007, Grotan et al. 2009). Climate change is likely to be associated with changes in magnitude and frequency of environmental events that shape the demography of a species (Jonzn et al. 2010). This is likely t o exacerbate the effects of environmental variation on population demography as organisms are exposed to novel environmental conditions. Climate change would impact both the mean and variance of climatic parameters and consequently, the mean and variance o f demographic rates (survival, breeding probability, litter size) (Boyce et al. 2006, Morris et al. 2008). Therefore, in the context of global climate change, understanding the demographic effects of environmental PAGE 37 37 variability is critical since these pertur bations are likely to influence the longterm growth rate, persistence, and resilience of populations (Caswell 2001, Haridas and Tuljapurkar 2005, Morris et al. 2008). Although most species experience temporally changing environments, population dynamics a re often studied using deterministic matrix models (Caswell 2001, Haridas and Tuljapurkar 2005, Jonzn et al. 2010). These assume that environmental conditions, and therefore vital rates, remain constant over time (Kalisz and McPeek 1993). Deterministic an alyses may not be informative in changing environments because large variation in a vital rate with a small deterministic elasticity may affect the population growth rate more than a small change in a less variable vital rate with high deterministic elasti city (Jonzn et al. 2010). Consequently, deterministic demography is limited in its application as it does not allow for temporal variability in vital rates (Boyce et al. 2006). The demographic consequences of variation in vital rates are better described in the context of stochastic demography (Boyce et al. 2006). Stochastic demographic models contain a relationship between the environment and the vital rates, and allow for a projection of the population using those vital rates (Caswell 2001, Hunter et al 2007). Th is relationship describes temporal variation by associating a distinct projection matrix with each of several distinct environments. This stochastic modeling framework can be used to estimate the long term growth rate of populations occupying st ochastic environments (Morris et al. 2006) and to calculate the sensitivity and elasticity of stochastic population growth rate to changes in vital rates (Tuljapurkar et al. 2003, Haridas and Tuljapurkar 2005). Furthermore, stochastic sensitivity analysis permits the PAGE 38 38 quantification of sensitivity and elasticity of stochastic population growth rate to the mean and variance in vital rates (Haridas and Tuljapurkar 2005, Jonzn et al. 2010). The goldenmantled ground squirrel ( Callospermophilus lateralis ; form erly, Spermophilus lateralis ; hereafter, GMGS) (Helgen et al. 2009) is a hibernating species that occupies a subalpine habitat in the Rocky Mountains where the effect of climate change on several species has been reported (Inouye et al. 2000, Ozgul et al. In press). Over the course of a 19year study, our discrete population of GMGS exhibited substantial fluctuation in population size (Kneip et al. In review). This longterm demographic study allowed us to estimate annual vital rates (survival, breeding probability, litter size) and revealed strong DD and climatic effects on both survival and breeding probability (Kneip et al. In review). The regulatory influence of DD may have enabled our population to recover from lows of as few as 5 adult females in 1999 and 2001 to as high as 29 adult females in 2005. Using deterministic and stochastic demographic analyses of these data, we aimed to investigate how density dependent processes interact with environmental stochasticity (ES) to cause fluctuations in the abun dance of the GMGS population. Our 5step approach was to: (1) calculate overall and yearly deterministic population growth rates; (2) calculate the elasticity of stochast variance of matrix elements; (4) quantify the effects of both DD and ES on the long term population growth rate; and (5) project the probability of quasi extinction under various scenarios incorporating density dependence and ES. PAGE 39 39 Materials and Methods Study A rea and Species We conducted our research at the Rocky Mountain Biological Laboratory (RMBL) near Crested Butte, Colorado (38o58N, 106o59W, elevation 2890m), USA on a 13 ha open subalpine meadow. The study area was interspersed with willow ( Salix sp. ) and aspen ( Populus tremuloides ) stands and was bordered by aspen forest on the north and east, and by Copper creek and the East River on the west and south (Van Vuren 2001). T he goldenmantled ground squirrel is an asocial and diurnal species that occurs at a broad range of elevations (~10004000m above sea level). It prefers open habitats such as mountain meadows and rocky mountain slopes that are adjacent to grasslands (Ferro n 1985, Bartels and Thompson 1993) The GMGS survives long winters, and therefore food shortage, by hibernation. Both altitude and amount of snowfall influence squirrels when they commence and end their hibernation period (Ferron 1985, Bartels and Thompson 1993) Adult GMGS usually emerge from hibernation around the time of snow melt (late May early June). The breeding season closely follows emergence and soon after pups emerge from natal burrows (late June mid July). At the end of summer (late August early September) the squirrels enter hibernation. At RMBL, they mainly forage on herbaceous vegetation (forbs and grasses) Snow melt greatly influences the growth of these green, leafy plants and hence impacts squirrel food availability. Soon after emer ging from hibernating burrows, the squirrels begin gaining weight, rapidly storing fat to improve their chances of survival the next winter and to sustain gestation the next spring (Phillips 1984). PAGE 40 40 Field Methods GMGS were livetrapped for 19 successive years (1990 2008) during the active season (May to late August). In addition to trapping they were monitored daily by visual observations. The annual census (marking the entire resident population) took place from late May to early June. Pups were trapped and marked between late June and mid July as litters emerged from their natal burrows. Squirrels were trapped also in late July and late August, in order to record their weights as they were building fat reserves for hibernation. Throughout the summer, animal s were observed daily and trapped opportunistically to capture and mark all new immigrants and refresh marks on residents. Si ngle door Tomahawk livetraps (12.7 x 12.7 x 40.6 cm ) were baited with a mixture of sunflower seeds and peanut butter to lure GM GS. Once captured, squirrels were distinctly dyemarked with fur dye, and sex, weight, and female reproductive condition were recorded. New individuals received noncorrosive metal tags for both ears. The ear tag numbers were also recorded. Emerging pups we re captured, dyemarked, and ear tagged at first emergence from their natal burrow Their mothers ear tags were recorded as well as litter size A total of 831 squirrels was captured during the study period. Age was known for 704 squirrels because they were captured as juveniles when emerging from their natal burrows. We estimated age based on mass for 127 immigrants, whose exact ages were unknown. Matrix Population Model All population projection models were female based models because we were not able to estimate reproductive parameters for male goldenmantled ground squirrels. PAGE 41 41 There was evidence for the effect of sex on survival (Kneip et al. In review), so we used female o nly estimates of survival For 19 years of the study, we estimated vital rates (survival, breeding probability, litter size) for 2 age classes. For survival the age classes were juvenile (<1yr olds) and adult ( 1yr olds); and for reproduction we considered age classes yearling (=1yr olds) and older females ( overall and year specific demographic parameter estimates are provided in Appendices A and B, respectively. We assumed that age of last reproduction was 6 years ( based on current data) and constructed a 6x6 agestructured matrix population model for both deterministic and stochastic analysis The age of last reproduction was chosen because out of 326 knownage female squirrels only 1 had a maximum life span longer than 6 years. The form of the agestructured population projection matrix including lower level vital rates was: A(t)= Pj(t)* LS* BPy(t)* SRjPa(t)* LS BPa(t)* SRjPa(t)* LS BPa(t)* SRjPa(t)* LS BPa(t)* SRjPa(t)* LS BPa(t)* SRjPa(t)* LS BPa(t)* SRj P j ( t )00000 0P a ( t )0000 00P a ( t )000 000P a ( t )00 0000P a ( t )0 (3 1) where Pj (t ) denoted annual juvenile survival rate, Pa (t) represented annual adult survival rate; LS was litter size, SRj symbolized sex ratio of pups at emergence, and BPy(t) and BP a(t) stood for yearling and older female breeding probability, respectively. Yearling ( Fy ) and older female ( Fa ) fertility rates were estimated using the post breeding census method (Caswell 2001), as the product of age specific fecundity and PAGE 42 42 survival probability. Agespecific fecundity was determined as the product of breeding probability, litter size, and sex ratio. Being representative among ground squirrels, a balan ced primary sex ratio (0.5) was assumed (Bronson 1979). Deterministic Analysis We constructed overall and year specific deterministic models. For the overall or time invariant model, a projection matrix A was obtained from a single estimate of the vital ra tes based on capturemark recapture data collected during the entire study period (19902008). For the year specific model, a separate population projection matrix At was compiled for each year t using agespecific reproductive and ageand year specific survival estimates, totaling 18 projection matrices. We calculated the overall population growth rate based on the overall projection matrix A The year specific asymptotic population growth rates, t, were determined as the dominant eigenvalues of the annual projection matrices At. The mean asymptotic population growth rate, M, was calculated as the dominant eigenvalue of the mean matrix AM. The net reproductive rate, R0 and generation time, T for the overall matrix were determined using algorithms from Caswell (2001). These values did not vary substantially over time. The elasticity of the overall and yearly population growth rates to changes in matrix elements and lower level vital rates were calculated using methods described by Caswell (2001). Environmental Stochasticity Eighteen year specific population projection matrices At were used in the stochastic demographic analysis. There was strong evidence for temporal variation in agespecific survival rates, but not in breeding probability or litter size (Kneip et al. In PAGE 43 43 review). Therefore, year specific matrices differed in survival rates but not in breeding probabilities or litter sizes. We assumed a uniform independent and identically distributed ( iid ) environment, and employed the simulationbased app roach (50,000 simulations) to estimate the stochastic population growth rate as: log = where rt = log( n (t +1)/ n ( t )) is a onestep population growth rate (Caswell 2001, Tuljapurkar et al. 2003). Additionally, we calculated three types of elasticities of to matrix elements: and which are the elasticities of s with respect to mean, variance, and both mean and variance, respectively, of the matrix element in row i and column j (Haridas and Tuljapurkar 2005) as: = lim ( ) ( ) ( ) ( ) ( ) ( ) = ( ) ( ) ( ) ( ) ( ) ( ) (3 2) where u (t) and v (t) vectors refer to stochastic population structure and reproductive value at time t respectively. The symbol represents the factor by which the population size grows from time t to t +1 The term ( ) ( ) stands for the scalar product of v (t) and u (t) First, we calculated the elasticity of regarding both the mean and the variance of matrix elements as we perturbed both the mean and the variance of the matrix elements by equal proportions. Thus, we set ( ) = ( ) for every t in the above equation. Second, the elasticity of relating to the mean of matrix elements was calculated by perturbing the mean of the matrix elements without changing their variance. Therefore, we substituted for ( ), where is the ij th entry of the matrix of mean matrix elements. Third, the elasticity of with respect to the PAGE 44 44 variance of matrix elements was calculated by perturbing the variance of the matrix elements without changing their mean. Hence, we set ( ) = ( ) We simulated the grow th of the GMGS population in an iid environment assuming that each of the 18 matrices is equally likely to occur. Each of the 50,000 independent realizations of population growth ran for 50 years and began with an initial population vector, n (0). The initi al population vector was obtained by multiplying the stableage distribution from the overall matrix by the average female population size (30) observed during the study (Caswell 2001, Morris and Doak 2005). Density Dependence and Environmental Stochasticity In order to introduce density dependence into our overall matrix model A we used the best age specific density dependent model from a previous study. There was strong evidence for delayed, negative DD effect on survival and direct, positive DD effect on breeding probability (Kneip et al. In review). The functional DD relationship for survival (P) and breeding probability (BP) is described by the following logistic regression equations: = ( ) (3 3) = ( ) (3 4) where represent s regression coefficients ( : survival intercept, : density dependent survival coefficient, : breeding probability intercept, : density dependent breeding probability coefficient ). These slope param eters differ by ageclass and all values are reported in Table 31. These density dependent relationships were estimated using total population size (both sexes) and our population model was female only, but the observed sex ratio did not vary much by year Therefore, the PAGE 45 45 corresponding female population size was divided by the observed overall female sex ratio (0.515) to extrapolate from the number of females the approximate total population size n We projected the population growth for 50 years using the overall projection matrix A and an initial population vector n (0) The average observed female abundance (30) was used for initial population size. The initial population vector was calculated as described previously We projected the future population size under 5 scenarios: (1) density independent model where the overall matrix was used for projection without incorporating the effects of DD ; (2) density dependent survival rate; (3) density dependent breeding probability ; (4) both survival rate and breeding probability density dependent; and (5) scenario 4 extended by including immigration. Immigration was accounted for in our matrix model by adding the mean observed number of new females to the appropriate age class (1 j uvenile, 0 adult) at each time step. To calculate the probability of extinction, 50,000 simulation runs of 50 years were performed under different scenarios and the proportion of the runs with adult females less than the extinction threshold after a given time period was recorded. The three main scenarios for estimating probability of extinction included: (1) ES only; (2) ES and DD where both survival and BP were affected by population density; and (3) scenario 2 extended by including immigration ES and DD effects on survival were included by first accounting for the effects of density on survival and second by attributing the remaining variation (remainder) to ES. We estimated the remainder values as the differences between the logit survival estimates fro m the agespecific time dependent model and the best age specific DD model (calculated at the population density for that year) PAGE 46 46 (Figure 3 1). This resulted in 18 remainder values corresponding to each year of the study. Instead of selecting an entire matri x, we simulated ES by randomly selecting from the remainder values with equal probability and changing the DD survival probabilities by the corresponding remainder value at every time step: = ( ) (3 5) Because the additive logistic regression coefficients for each ageclass differed between the time dependent and DD models, the remainder value for each year was different for yearlings and adults, but by a fixed amount. At every time step, immigrants were added to eve ry age class of the current years population vector, Nt, before projecting the population for the next year. Thus, the effects of immigration were included in the model as the observed number of immigrating individuals for each randomly selected year. The probability of quasi extinction was estimated at various levels of quasi extinction threshold (QET). We ran each of the af orementioned scenarios with QET= 1, 3, and 5 adult females. True ex tinction was represented by QET=1, while QET= 3 and 5 denoted the lo west observed adult female individuals during the study. It is useful to look at several quasi extinction thresholds set at critically low numbers to see how probability of extinction is impacted and also because low numbers are dangerous due to other stoc hastic processes such as demographic and genetic stochasticity. Our computations used MATLAB (2006) code that will be provided upon request. Results Deterministic A nalysis The deterministic de =0. 905 95% CI: 0.8120.99 8). The year to year population PAGE 47 47 t ranged between 0.445 and 1.24 4 ( Figure. 3 2). M was 0.944 indicating a 5.6% per year decline. The net reproductive rate, R0 was 0.720 and the generation time, T was estimated as 2.484. For the overall matrix, we examined the elasticity of population growth rate to matrix elements ( F y F a Pj and Pa ). The was proportionately most sensitive to P j followed by Pa and Fa The results of the lower level elasticity analysis with respect to changes in vital rates ( Pj Pa LS B Py and BP a ) differed, because was proportionately most sensitive to changes in Pa followed by Pj LS BPa and BPy (Figure. 3 3). The annual elasticity pattern with respect to matrix elements and vital rates was similar to that described above for the overall matrix. Environmental Stochasticity The stochastic population growth rate, s, was below replacement ( s= 0.912) suggesting an 8.8% annual population decline. For our GMGS population, s responded most strongly to proportional changes in the average value of juvenile survival, followed by adult survival of the second age class, and fertility of 2 year old and yearling females, respectively. The abovementioned matrix elements, in the same order, were also important in influencing but in the opposite direction. This means that an i ncrease in the mean of these matrix elements would increase while an increase in the variance would decrease s. The overall stochastic elasticities display the same pattern as (Table 32). Including only the effects of environmental stochastici ty, the distribution of total population size in 50 years for 50,000 independent realizations with initial total PAGE 48 48 population size of 30 is displayed in Figure 3 4. In most of the realizations the total population size declined over the 50 years from the ini tial 30. The distribution of the final population size is skewed to the right. Corresponding to this skew, the median of the realizations is 8.48 while the mean is 10.66 female squirrels ( Figure. 3 4). Density Dependence and Environmental Stochasticity Acc ording to our expectation, density dependence revealed a strong impact on the viability of the GMGS population in scenarios 2 5 compared to the DID model ( Figure. 3 5). Both the DID model and scenario 3 predicted that the squirrel population will go extinc t within 50 years. The rate of decline was faster for scenario 3 where positive DD effects were implemented for breeding probability. After an initial decline, as approached 1.0, the population size stabilized at 26.47, 23.65, and 18.80 for scenarios 2, 5, and 4, respectively. The logit transformed survival estimates computed by the best DD and timedependent models for adult and juvenile females are depicted in Figure 3 1a and b, respectively. The differences between the estimates of the two models were attributed to environmental stochasticity. These remainder values were used in the following analysis, which combined the influence of density and environmental stochasticity in predicting probability of quasi extinction. With QET = 1, probability of true extinction reached 90% after 50 years for the density independent model (scenario 1; Figure. 3 6a). This scenario included only the effects of environmental stochasticity. When we incorporated DD (scenario 2; Figure. 3 6a) and DD plus immigration (scenario 3; Figure. 3 6a) in addition to ES in our model, the probability of true extinction was reduced to 2% and 0%, respectively. As we raised the quasi extinction threshold, the probability of quasi extinction increased for each PAGE 49 49 scenario. At QET= 3, the probability of extinction for scenarios 1, 2, and 3 was 97%, 50%, and 15%, respectively ( Figure 3 6b). Setting QET= 5, the respective extinction probabilities substantially rose to 99%, 93%, and 79% ( Figure. 3 6c). Discussion Virtually all natural populations experience stochastic environmental variations which can influence demographic variables and population persistence (Caswell 2001, Haridas and Tuljapurkar 2005). In addition to unpredictable environmental perturbations, s everal other phenomena can impact the dynamics of natural populations. For instance, density dependence, demographic stochasticity, sex ratio fluctuations, and demographic heterogeneity can considerably alter the predictions of population viability analysi s (Morris and Doak 2002, Kendall and Wittmann 2010). Environmental stochasticity tends to destabilize population dynamics, cause random population fluctuations, reduce longterm population growth rate, and increase extinction risk (Coulson et al. 2000, Ken dall and Wittmann 2010). Density dependent mechanisms on the other hand dampen oscillations and eventually regulate populations (Royama 1992, Leirs et al. 1997, Turchin 2003, Grotan et al. 2009). Understanding the effects of a variable environment on popul ation dynamics is especially important for populations that occupy habitats sensitive to temporal variability and climate change (Inouye et al. 2000, Ozgul et al. In press). We hypothesized that the demography of our GMGS population inhabiting a montane e cosystem is strongly influenced by environmental stochasticity. The extensive year to year fluctuations in abundance and deterministic growth rate indicated a highly variable population and formed the basis for our hypothesis. Total abundance ranged from 2 4 squirrels in 1999 and 2000 to 140 in 2005, almost a 6fold difference The PAGE 50 50 annual deterministic also varied widely between 0.45 and 1.24. The overall was 0.905 indicating a 9.5% population decline per year. This population growth rate is not as criti cally low as the 0.721 reported for the collapsing Northern Idaho population (Sherman and Runge 2002) but still calls for concern especially considering that for ten out of 18 years was below replacement ( <1). The population has recovered from low numb ers to viable levels during our study period which is likely caused by the regulatory density dependence effects. In addition, despite the low number of observed immigrants, including immigration in our models substantially reduced the probability of extin ction. Nonetheless, increasing environmental variation can elevate uncertainty and amplify a populations vulnerability to extinction. We found that the stochastic growth rate s was lower than the deterministic growth rate of the mean matrix M. This result is consistent with our expectation because longterm, environmental variation is supposed to reduce the population growth rate, through environmentally induced variation in vital rates (Caswell 2001, Morris and Doak 2002). Indeed, the earlier study by Kneip et al. (In review) reported statistical evidence for temporal variation of survival as well as strong density independent effect of summer rainfall on this vital rate. Furthermore, our perturbation analysis showed that both deterministic and stoch astic growth rates responded strongly to proportionate changes in survival matrix elements and vital rates. As expected for a population with a below replacement stochastic growth rate, the distribution of the population size ( Figure. 3 4) predicted that in a stochastic environment the GMGS population would surely decline over a 50year period. Most PAGE 51 51 realizations projected that the population size would be less than 10 within this time frame. The influence of environmental stochasticity is exacerbated by the effect of the predicted changes in climatic factors. The effect of climate change is anticipated to be most pronounced in polar and montane ecosystems such as the subalpine environment that the GMGS population occupies. According to a previous study by Kneip et al. (In review), both survival and reproduction were negatively affected by summer rainfall. Therefore, the potential impact of an increase in the mean and variance of precipitation is likely to influence the GMGS populations growth rate and per sistence as it has been demonstrated on several species (Morris et al. 2008, Jonzn et al. 2010). In addition to the broad fluctuations, we have witnessed population lows with as few as 5 adult female squirrels in 1999 and 2001; still the population proved resilient as it re bo unced and has not gone extinct. During the summer of 2001, the adult female population size dipped to 3 individuals because 2 females disappeared from the study site, most likely due to predation. We suspected that the combined effect s of density dependence and immigration were responsible for the exhibited resilience. Density dependence was shown to operate in our GMGS population (Kneip et al. In review) and Grotan et al. (2009) demonstrated the strong influence of immigration on population dynamical responses. Immigration was low and variable among the years of our study period ( Table 3 3). Interestingly, with the exception of one adult female immigrant in 1991, there was no immigration recorded until 2000, the year following the lowest total and adult female abundance. Furthermore, between 2000 and 2007, with low adult female numbers in 20002002 and 2007, immigration occurred in 6 out of 8 years. PAGE 52 52 Hence, immigration has been likely an important factor in preventing extinction of our p opulation. Indeed, when we accounted for both the effect of density on survival and breeding probability and immigration in our density dependence analysis, after an initial decline the female population stabilized at the carrying capacity of 23.65 and did not go extinct. This is in contrast with density independent model and the scenario where the positive effects of density were implemented for breeding probability ( Figure. 3 5) because in these two cases the population headed for extinction. Similarly, w hen we introduced density dependence and immigration to the stochastic model, our projections of extinction risk improved substantially even though the effect of density on breeding probability was positive. When we set quasi extinction threshold to 1 ( Fig ure. 3 6a), the density independent, ES only model (scenario 1) painted a pessimistic picture as extinction probability was 90% in 50 years. According to the density dependent model (scenario 2), the population faced almost no extinction risk. The DD model which incorporated immigration (scenario 3), further improved the populations viability by reducing probability of extinction to zero. We included the influence of immigration in our model, because the survival estimates from Kneip et al. (In review) im plicitly included the confounding effects of emigration. Therefore, the results of the combined model depicted in Figures 3 6a describe a fluctuating but persistent population in the long term. To simulate the persistence of our GMGS population under various levels of quasi extinction threshold, we projected the probability of extinction by setting QET= 3 ( Figure. 3 6b) and 5 ( Figure. 3 6c), representing the lowest observed adult female population sizes. It was apparent, that extinction probabilities considerably increased as QET was PAGE 53 53 raised. Setting QET= 5 implied a conservative approach since we anticipated quasi extinction when there are 5 adult females in the population even though we have observed the population re bound from this threshold twice during the study. However, after those years immigration took place which may have been the reason for why the population has not gone extinct. In the context of global climate change, the influence of environ mental stochasticity is predicted to increase on population dynamics which suggests amplified fluctuations in abundance of our GMGS population. An increase in the frequency of population lows would mean increased uncertainty for this population because imm igration events may not always come to the populations rescue. Leirs et al. (1997) also investigated the effects of both DD and DID processes in a rodent species ( Mastomys natalensis ) which exhibits extensive population fluctuations. They modeled DID eff ects on the dynamics of this species by examining only one DID factor (rainfall) but noted that this ecological variable alone did not explain all the DID variation. In our analysis, we intended to account for the effects of all environmental variation and used the remainder values ( Figure. 3 1) to explain the effects of ES in our combined DD and ES models ( Figure. 3 6). O ur analysis predicts an uncertain future for this squirrel population. Both deterministic and stochastic growth rates as well as the simulation based projections of the distribution of population size and time to quasi extinction predict the likelihood of near term extinction. However, the population persisted despite wide fluctuations in population size and bounced back from low numbers as much as 6 fold. Stochastic processes such as environmental and demographic stochasticity as well as increases in the mean and variability of precipitation may increase GMGS vulnerability to extinction. PAGE 54 54 This may be reduced by the regulatory effect of densi ty dependent mechanisms and the effect of immigration Moreover, immigration is a likely process explaining the resilience exhibited by this population (Tamarin 1978, Boyce et al. 2006) Nevertheless, as environmental variability is likely to exacerbate th e fluctuations in GMGS abundance, the population may tip over such that squirrels reach low numbers frequently enough that without the rescue effect of immigration, persistence will become precarious. PAGE 55 55 Table 3 1. Regression coefficients for logit transf ormed survival and logit transformed breeding probability (BP) for the goldenmantled ground squirrel population in Gothic, CO (Kneip et al. In review) Coefficient, Parameter Intercept Density term 95% CI Juvenile surviv al 0.06459 0.01068 0.015 0.006 Adult surviv al 0.8072 0.01068 0.015 0.006 Yearling BP 2.012253 0.01386 0.005 0.023 Older female BP 0.06594 0.01386 0.005 0.023 Table 3 2. Elasticities of stochastic population growth rate ( s) to mean ( E), variance (E), and both mean and variance ( ES) of matrix elements. Notation includes f ertility of yearlings ( Fy ) and adults ( F a( x )), juvenile recruitment ( Pj ), and adult survival ( Pa( x )) where x denotes the age of adult female GMGS. For all 3 types of elasticities, the highest a bsolute values are bold. Parameters E E E S Fy 0.113 0.010 0.103 Fa (2) 0.145 0.009 0.135 Fa (3) 0.083 0.005 0.078 Fa (4) 0.048 0.003 0.045 Fa (5) 0.027 0.002 0.026 Fa (6) 0.016 0.001 0.015 Pj 0.326 0.028 0.298 Pa (2) 0.174 0.011 0.162 Pa( 3 ) 0.091 0.006 0.085 Pa( 4 ) 0.043 0.003 0.040 Pa( 5 ) 0.016 0.001 0.015 PAGE 56 56 Table 3 3. The number of juvenile and adult female goldenmantled ground squirrel s that immigrated to our study site in Gothic, CO each year of the stud y. Capture Year Juvenile Adult 1990 0 0 1991 0 1 1992 0 0 1993 0 0 1994 0 0 1995 0 0 1996 0 0 1997 0 0 1998 0 0 1999 0 0 2000 2 0 2001 0 0 2002 3 0 2003 1 0 2004 1 0 2005 0 0 2006 4 0 2007 1 0 PAGE 57 57 Figure 31. Relationship between annual population density and the agespecific logit transformed survival rate. a) adult and b) juvenile female goldenmantled ground squirrels between 1990 and 2007. Filled circles represent the yearly logit transformed survival estimates from the full timedependent model. The solid line is a regression line connecting the density dependent estimates from the most parsimonious density dependent model. Open circles are the logit transformed survival estimates from the best density dependent model calculated at the population size for each year. Remainder values are symbolized as connector line segments between the dots and the regression line at x values denoting densities calculated for each year. PAGE 58 58 Figure 32. Annual variation in the deterministic population growth rate with 95% CI for female goldenmantled ground squirrels during 1990 2007 PAGE 59 59 Figure 3the lower level vital rates of the overall matrix A Pj represents juvenile apparent survival, Pa s ymbolizes adult apparent survival, LS denotes litter size, BPy stands for yearling breeding probability, and BPa is older female breeding probability. PAGE 60 60 Figure 34. Frequency distribution of population size in 50 years including only the effects of envir onmental stochasticity. The histogram shows the results of 50,000 realizations of simulating the GMGS population in a uniform independently and identically distributed (iid) stochastic environment. All simulations start from the same initial overall age di stribution and initial population size of 30 females. We discarded the first 100 transient iterations. PAGE 61 61 Figure 35. Projected abundance of the female GMGS population for 50 y ears using the overall projection matrix and the average female abundance (30) under 5 scenarios for density dependence (1) density independent model; (2) density dependent survival rate; (3) density dependent breeding probability; (4) both survival rate and breeding probability density dependent; and (5) scenario 4 was extended by including immigration. Immigration was ac counted for in our matrix model by adding the mean observed number of new individuals to the appropriate age class (1 juvenile, 0 adult) at each time step. In the above scenarios, the density independent variables were fixed to the values estimated for the entire study period. Environmental stochasticity was not included in any of these models. PAGE 62 62 Figure 36. Probability of quasi extinction under various scenarios of environmental stochasticity, density dependence, and differing levels of quasi extinction threshold for the goldenmantled ground squirrel population. Scenarios included: 1) environmental stochasticity only; 2) environmental stochasticity and density dependence for both survival and breeding probability; and 3) scenario 2 extended by including immigration. Immigrants were added to every age class of the current years population vector, Nt. All simulations start from the same initial population vector (obtained as multiplying the overall stable age distribution by the average females population size of 30 ). Quasi extinction threshold was established as: a) 1 (true extinction), b) 3, and c) 5 adult females. PAGE 63 63 CHAPTER 4 CONCLUSION To decipher the population and species level consequences of anticipated climate ch ange, it is important to quantify the influence of density dependent and density independent factors on population fluctuations Many studies suggest that density dependent mechanisms ultimately stabilize natural populations; others argue that random varia tions in climatic factors introduce destabilizing effects to population dynamics Empirical examples demonstrating how both of these processes act in concert are rare. The goal of this research was to examine how random environmental variation and density dependent mechanisms interact to cause fluctuations in the abundance and influence the future persistence of a golden mantled ground squirrel population This population was chosen because it occupies a subalpine habitat, which is sensitive to climate chan ge. Additionally, a 19 year demographic data set was available for analysis Because the effects of environmental variability on population growth are mediated through their influence on vital rates, I examined whether climatic factors affected demographic parameters including survival rate, breeding probability, and litter size. The results from this analysis revealed that both density dependent and extrinsic environmental factors impacted demographic variables although in different manners. While populati on size (previous years) had a substantial negative effect on survival of both sexes and age classes, a climatic parameter (summer rainfall) influenced both survival and reproduction (breeding probability) of the goldenmantled ground squirrels. Current and previous summer rainfall negatively influenced juvenile survival and PAGE 64 64 yearling breeding probability, respectively. Therefore, I concluded that precipitation; a density independent, climatic variable had a strong influence on this population. Global clima te change is predicted to amplify the variance of climatic parameters. It is likely that populations inhabiting stochastic environments, such as the golden mantled ground squirrels will experience increasing stochast ic variation in vital rates and abundance Consequently, this variability will reduce longterm population growth rate and increase extinction risk My initial findings merited further analyses to predict the probability of extinction of this population. While there was evidence for the strong influence of one climatic factor, summer rainfall on both survival and reproduction, I was interested in accounting for the full effects of environmental stochasticity Therefore, in addition to the deterministic and density dependent analysis I also conducted stochastic demographic analyses for the golden mantled ground squirrel population. The results from these analyses showed that environmental stochasticity increased and density dependence decreased the goldenmantled ground squirrel populations probability of extinction. As predicted, stochastic processes increased fluctuations in population size, destabilizing the population, whereas density dependence dampened these oscillations and improved the populations likelihood of persistence. In addition to the wide fluctuations in total abundance, the populations persistence was uncertain when adult female population size dipped to as low as 5 and 3 individuals during the study period. However, the population rebounded twice from such low adult female numbers. I suspected that in addition to the regulatory effect of density  PAGE 65 65 dependence, another process, such as immigration m ost likely played a critical role in the populations resilience and included immigration in my model. According to my a nalysis, immigration proved an important process that rescued the population from extinction. Despite these stabilizing factors, my analysis predicted an uncertain future for this population over the long term. In the context of climate change, environment al stochasticity is likely to increase and destabilize the dynamics of the golden mantled ground squirrel population and biological populations in general. This study highlighted the vulnerability not only of this golden mantled ground squirrel population but also of o ther wildlife populations that inhabit stochastic environments. Therefore, my results may prove informative to conservation agencies attempting to protect rare or endangered species in the face of global climate change. Because endangered populations tend to be small, the effects of environmental stochasticity are likely to be exacerbated by other stochastic mechanisms such as demographic and genetic stochasticity. The combined effects of these processes are expected to make the future persist ence of endangered populations precarious. PAGE 66 66 APPENDIX A SURVIVAL MODELS TEST ING FOR THE EFFECTS OF SEX, AGE, AND TIM E Analysis of agespecific apparent survival rates for the goldenmantled ground squirrel population in Gothic, CO using multistate mark recapture models Models testing for the effect of a) sex and age ; and b) time Constant survival and time specific survival models also are incl uded for comparison. In both analyses, the most parsimonious models are bold. No. Model AICc w i npar (1 ) 1 ( age + sex ) 0.00 2071.14 0.720 3 2 (age sex ) 1.89 2073.03 0.280 4 3 ( sex ) 34.60 2105.75 0.000 2 4 ( age ) 63.74 2134.89 0.000 2 5 (.) 112.29 2183.43 0.000 1 (2 ) 1 ( age + sex + time ) 0.00 2062.28 0.790 20 2 ( sex + age time ) 2.75 2065.03 0.200 36 3 (age + sex ) 8.86 2071.14 0.009 3 4 ( age + sex time ) 16.55 2078.84 0.000 37 5 (( age + sex ) time ) 18.22 2080.51 0.000 53 6 (.) 121.14 2183.43 0.000 1 AICc, weights (wi), and number of parameters (npar) are given for each model. The symbol refers to apparent annual survival rate. Annual recapture rate and transition rate are fixed for all models, therefore they are not included in model descriptions. The symbol (.) indicates constant value of the parameter (model with intercept only). The notation (( age+ sex )* time ) means interaction between time and both age and sex c lasses. PAGE 67 67 APPENDIX B SURVIVAL MODELS TEST ING FOR THE EFFECTS OF DENSITYDEPENDENT AND INDEPENDENT FACTORS Models testing for the effect of a) current ( Nt) and previous ( Nt 1) year's population size; b) abiotic factors; c) environmental factors including predation; and d) the relative and synergistic effects of the best intrinsic, density dependent, and extrinsic environmental factors on the state specific apparent survival rates for the goldenmantled ground squirrel population in Gothic, CO using multistate mark recapture models. General model (model a/12) is also included for comparison. In all analyses, the most parsimonious models are bold. Not all mod els are shown for parts a and b. No. Model AICc w i npar (a) 1 ( age + sex + N t 1 ) 0.00 2047.27 0.199 4 2 ( sex + age N t 1 ) 0.84 2048.10 0.131 5 3 ( age + sex + N t + N t 1 ) 0.95 2048.22 0.123 5 4 ( age + sex N t 1 ) 1.14 2048.41 0.112 5 5 (( age + sex ) N t 1 ) 1.74 2049.01 0.083 6 6 ( sex + age N t 1 + N t ) 1.77 2049.04 0.082 6 7 ( age + sex + N t N t 1 ) 1.94 2049.20 0.075 6 8 ( age + sex N t 1 + N t ) 2.10 2049.37 0.070 6 9 (( age + sex ) N t 1 + N t ) 2.67 2049.94 0.052 7 10 ( sex + age N t + N t 1 ) 2.75 2050.02 0.050 6 11 (( age + sex ) N t + N t 1 ) 4.48 2051.75 0.021 7 12 ( age + sex + time ) 15.02 2062.28 0.000 20 (b) 1 ( sex + age rain t + rain t 1 :A ) 0.00 2060.13 0.236 6 2 ( sex + age rain t ) 0.92 2061.05 0.149 5 3 ( sex + age rain t + rain t 1 :A + bg t 1 :A ) 1.02 2061.15 0.142 7 4 ( sex + age rain t + rain t 1 :A + bg t ) 1.81 2061.94 0.095 7 5 ( sex + age + time ) 2.15 2062.28 0.080 20 6 ( sex + age raint + bg t 1 :A ) 2.33 2062.45 0.074 6 7 ( sex + age rain t + bg t ) 2.62 2062.75 0.064 6 8 ( sex + age rain t + rain t 1 :A + bg t + bg t 1 :A ) 2.91 2063.04 0.055 8 PAGE 68 68 9 ( sex + age rain t + bg t + bg t 1 :A ) 4.09 2064.22 0.030 7 10 ( sex + age + rain t + rain t 1 :A + bg t 1 :A ) 4.31 2064.44 0.027 6 (c) 1 ( sex + age rain t + pred ) 0.00 2053.01 0.489 6 2 ( sex + age rain t + rain t 1 :A + pred ) 0.77 2053.78 0.334 7 3 ( sex + age pred + rain t + rain t 1 :A ) 5.08 2058.09 0.039 7 4 ( sex + age pred ) 5.40 2058.41 0.033 5 5 ( age + sex + pred + rain t 1 :A ) 5.80 2058.81 0.027 5 6 ( age + sex + pred ) 6.84 2059.85 0.016 4 7 ( age + sex + pred + rain t + rain t 1 :A ) 6.88 2059.89 0.016 6 8 ( sex + age rain t + rain t 1 :A ) 7.12 2060.13 0.014 6 9 ( sex + age pred + rain t ) 7.23 2060.24 0.013 6 10 ( sex + age rain t ) 8.04 2061.05 0.009 5 11 ( age + sex + pred + rain t ) 8.64 2061.65 0.007 5 12 ( sex + age + time ) 9.27 2062.28 0.005 20 (d) 1 ( sex + age rain t + N t 1 ) 0.00 2039.15 0 .441 6 2 ( sex + age rain t + pred + N t 1 ) 1.22 2040.37 0.23 9 7 3 ( sex + age rain t + rain t 1 :A + N t 1 ) 1.62 2040.77 0.19 7 7 4 ( sex + age rain t + rain t 1 :A + N t 1 + pred ) 2.94 2042.09 0.10 1 8 5 ( age + sex + N t 1 ) 8.26 2047.41 0.007 4 6 ( age + sex + N t 1 + pred ) 8.78 2047.93 0.005 5 7 ( age + sex + N t 1 + rain t 1 :A ) 9. 12 2048. 27 0.00 5 5 8 ( age + sex + N t 1 + rain t 1 :A + pred ) 9.53 2048.68 0.004 6 9 ( sex + age rain t + pred ) 13.86 2053.01 0.000 6 10 ( sex + age rain t + rain t 1 :A + pred ) 14.63 2053.78 0.000 7 11 ( age + sex + rain t 1 :A + pred ) 19.66 205 8 .8 1 0.000 5 12 ( sex + age + pred ) 20.70 2059.85 0.000 4 13 ( sex + age rain t + rain t 1 :A ) 20.98 2060.13 0.000 6 14 ( sex + age rain t ) 21.90 2061.05 0.000 5 15 ( sex + age + time ) 23.13 2062.28 0.000 20 16 (sex + age + rain t 1 :A ) 30.11 2069.26 0.000 4 17 ( sex + age ) 31.99 2071.14 0.000 3 For symbols and table content descriptions, refer to Table 1 footnotes The following variable notations are used: current ( Nt) and previous ( Nt 1) population size, PAGE 69 69 current ( raint) and previous ( raint 1) summer rain fall, current ( bgt) and previous (i) first day of bare ground, and predation ( pred). In addition, the effects of previous year's rain fall and previous first day of bare ground on survival were only relevant to adult animals. Hence, we analyzed the effects of these parameters only for the adult segment of the population. Notation for thes e parameters therefore are: raint 1:A and bgt 1:A respectively PAGE 70 70 APPENDIX C BREEDING PROBABILITY MODELS TESTING FOR T HE EFFECTS OF INTRIN SIC, DENSITYDEPENDENT AND INDEPENDENT FACTORS Models testing for the effect of a) age and time ; b) current ( Nt) and previous ( Nt 1) year's population size; c) environmental factors including predation; and d) the relative and synergistic effects of the best intrinsic, density dependent, and environmental factors on breeding probability of the golden mantled ground squirrel population in Gothic, CO using logistic regression. In all analyses, the most parsimonious models are bold. No. Model AICc w i npar (1 ) 1 0.00 295.96 1.000 2 2 37.11 333.07 0.000 1 3 time ) 52.75 348.71 0.000 19 ( 2 ) 1 t ) 0.00 287.67 0.242 3 2 t + N t 1 ) 0.31 287.98 0.207 4 3 t ) 0.93 288.60 0.152 4 4 t 1 + N t ) 1.32 288.99 0.125 5 5 t + N t 1 ) 1.51 289.18 0.114 5 6 t N t 1 ) 2.31 289.98 0.076 5 7 t 1 N t ) 2.31 289.98 0.076 5 8 8.28 295.96 0.004 2 9 t 1 ) 8.86 296.54 0.003 3 10 t 1 ) 9.84 297.51 0.002 4 ( 3 ) 1 t 1 ) 0.00 279.56 0.652 4 2 t 1 + pred) 1.41 280.98 0.322 5 3 t 1 ) 8.01 287.57 0.012 3 4 t 1 + pred) 8.91 288.47 0.008 4 5 t 1 ) 9.79 289.35 0.005 5 6 t ) 13.46 293.02 0.001 4 7 t ) 14.92 294.49 0.000 3 PAGE 71 71 No. Model AICc wi npar 8 16.39 295.96 0.000 2 9 t 1 ) 17.38 296.94 0.000 4 10 17.92 297.49 0.000 3 11 18.00 297.56 0.000 4 12 t ) 18.34 297.90 0.000 3 13 t 1 ) 18.35 297.91 0.000 3 14 t) 20.33 299.89 0.000 4 ( 4 ) 1 t 1 + N t ) 0.00 279.34 0.511 5 2 t 1) 0.22 279.56 0.457 4 3 t ) 8.33 287.67 0.008 3 4 16.61 295.96 0.000 2 For symbols and table content descriptions, refer to Table 2 footnotes The symbol refers to breeding probability. PAGE 72 72 APPENDIX D LITTER SIZE MODELS T ESTING FOR THE EFFEC TS OF INTRINSIC, DEN SITY DEPENDENT AND INDEPENDENT FACTORS Models testing for the effect of a) age and time ; b) current ( Nt) and previous ( Nt 1) year's population size; c) environmental factors including predation; and d) the relative and synergistic effects of the best intrinsic, density dependent, and en vironmental factors on litter size for the golden mantled ground squirrel population in Gothic, CO using Poisson regression. In all analyses, the most parsimonious models are bold. No. Model AIC w i npar ( 1 ) 1 LS (.) 0.00 532.79 0.717 1 2 LS ( age ) 1.87 534.66 0.282 2 3 LS ( time ) 13.69 546.49 0.001 19 ( 2 ) 1 LS ( N t ) 0.00 531.50 0.341 2 2 LS ( N t N t 1 ) 1.28 532.78 0.180 4 3 LS (.) 1.29 532.79 0.179 1 4 LS ( N t 1 ) 1.37 532.87 0.172 2 5 LS ( N t + N t 1 ) 1.97 533.47 0.128 3 ( 3 ) 1 LS (.) 0.00 532.79 0.222 1 2 LS ( bg t 1 ) 0.70 533.50 0.156 2 3 LS ( pred ) 1.42 534.21 0.109 2 4 LS ( age ) 1.87 534.66 0.087 2 5 LS ( bg t ) 1.92 534.71 0.085 2 6 LS ( rain t 1 ) 1.98 534.78 0.082 2 7 LS ( rain t ) 2.00 534.79 0.082 2 8 LS ( bg t 1 + pred ) 2.31 535.11 0.070 3 9 LS ( age + bg t 1 ) 2.64 535.44 0.059 3 10 LS ( bg t 1 pred ) 4.31 537.10 0.026 4 11 LS ( age bg t 1 ) 4.58 537.37 0.022 4 ( 4 ) 1 LS ( N t ) 0.00 531.50 0.221 2 2 LS ( bg t 1 + N t ) 0.52 532.02 0.171 3 3 LS (.) 1.29 532.79 0.116 1 PAGE 73 73 4 LS ( bg t 1 N t ) 1.50 533.00 0.105 4 5 LS ( bg t 1 ) 2.00 533.50 0.082 2 6 LS ( bg t 1 + N t + pred ) 2.09 533.59 0.078 4 7 LS ( pred ) 2.71 534.21 0.057 2 8 LS ( bg t 1 N t + pred ) 3.14 534.65 0.046 5 9 LS ( age ) 3.16 534.66 0.046 2 10 LS ( bg t 1 + pred ) 3.60 535.11 0.037 3 11 LS ( bg t 1 pred + N t ) 4.04 535.54 0.029 5 12 LS ( bg t 1 pred ) 5.60 537.10 0.013 4 13 LS ( time ) 14.99 546.49 0.000 19 For symbols and table content descriptions, refer to Table 2 footnotes The symbol LS refers to litter size. PAGE 74 74 LIST OF REFERENCES ANDERSON, D R 2008. Model Based Inference in the Life Sciences, 1st ed. Springer Science+Business Media, LLC, New York, NY. BAKKER, V J ET AL. 2009. Incorporating ecological drivers and uncertainty into a demographic population viability analysis for the island fox. Ecological Monographs 79: 77108. BARTELS, M A. AND D P. THOMPSON. 1993. Spermophilus lateralis Mammalian Species 440:1 8. BERNSTEIN, L ET AL. 2007. Climate change 2007: Synthesis Report. BOONSTRA, R 1994. Populationc ycles in m icrotines The s enescence h ypothesis. Evolutionary Ecology 8 : 196219. BOYCE, M S. C V. HARIDAS, C T LEE, AND N S. DEMOGRAPHY. 2006. Demography in an increasingly variable world. Trends in Ecology & Evolution 21 :141 148. BRONSON, M T 1979. Altitudinal variation in the life history of the goldenmantled ground squirrel ( Spermophilus lateralis ). Ecology 60: 272279. BURNHAM, K. P. AND D R ANDER SON. 2002. Model selection and multimodal inference: A practical information theoretic approach. Springer Verlag, New York. CASWELL, H 2001. Matrix population models: Construction, analysis, and interpretation, 2nd ed. Sinauer Associates, Sunderland, Mass achusetts. CHOQUET, R M REBOULET, J D LEBRETON, O GIMENEZ, AND R PRADEL. 2005b. U CARE 2.2 user's manual, Montpellier, France. CLUTTONBROCK, T H AND T COULSON. 2002. Comparative ungulate dynamics: the devil is in the detail. Philosophical Transactions of the Royal Society of London Series B 357:1285 1298. COULSON, T ET AL. 2001. Age, sex, density, winter weather, and population crashes in Soay sheep. Science 292: 15281531. COULSON, T ET AL. 2008. Estimating the functional form for the d ensity dependence from life history data. Ecology 89: 1661 1674. COULSON, T E J MILNERGULLAND, AND T CLUTTONBROCK. 2000. The relative roles of density and climatic variation on population dynamics and fecundity rates in three contrasting ungulate spe cies. Proceedings of the Royal Society of London Series B Biological Sciences 267: 17711779. PAGE 75 75 DEN BOER, P J AND J REDDINGIUS. 1996. Regulation and stabilization paradigms in population ecology. Chapman & Hall, London, U.K. DOBSON, F S. AND M K OLI. 2001. The demographic basis of population regulation in Columbian ground squirrels. American Naturalist 158:236 247. DOHERTY, P. F ET AL. 2004. Testing life history predictions in a longlived seabird: A population matrix approach with improved parameter estimation. Oikos 105: 606618. FERRON, J 1985. Social behavior of the goldenmantled groundsquirrel ( Spermophilus lateralis ). Journal of Zoology 63 : 25292533. FREDERIKSEN, M F DAUNT, M P. HARRIS, AND S. WANLESS. 2008. The demographic impact of extre me events: Stochastic weather drives survival and population dynamics in a long lived seabird. Journal of Animal Ecology 77 :1020 1029. GAILLARD, J M J M BOUTIN, D DELORME, G VANLAERE, P DUNCAN, AND J D LEBRETON. 1997. Early survival in roe deer: causes and consequences of cohort variation in two contrasted populations. Oecologia 112: 502513. GANNON, W L AND R S. SIKES. 2007. Guidelines of the American Society of Mammalogists for the use of wild mammals in research. Journal o f Mammalogy 88: 809823. GASCOIGNE, J L BEREC, S GREGORY, AND F COURCHAMP. 2009. Dangerously few liaisons: a review of mate finding Allee effects. Population Ecology 51 :355372. GROTAN, V. B E. SAETHER, S ENGEN, J H VAN BALEN, A C PERDECK, and M E. VISSER. 20 09. Spatial and temporal variation in the relative contribution of density dependence, climate variation and migration to fluctuations in the size of great tit populations. Journal of Animal Ecology 78 :447459. HANSKI, I H HENTTONEN, E KORPIMAKI, L OKSANEN, AND P. TURCHIN. 2001. Small rodent dynamics and predation. Ecology 82: 15051520. HARIDAS, C V. and S TULJAPURKAR. 2005. Elasticities in variable environments: Properties and implications. American Naturalist 166: 481495. HELGEN, K M F. R COLE, L E. HELGEN, AND D E WILSON. 2009. Generic revision in the holarctic ground squirrel genus Spermophilus Journal of Mammalogy 90 :270305. HONE, J AND R M SIBLY. 2002. Demographic, mechanistic and density dependent determinants of population growth rate: a case study in an avian predator. Philosophical Transactions of the Royal Society of London Series B 357: 11711177. PAGE 76 76 HORVITZ, C C and D W SCHEMSKE. 1995. Spatiotemporal variation in demographic transitions of a tropical understory herb projection matrix analysis. Ecological Monographs 65 :155192. HUGHES, L 2000. Biological consequences of global warming: is the signal already apparent? Trends in Ecology & Evolution 15: 56 61. HUNTER, C M H CASWELL, M C RUNGE, E V. REGEHR, S C AM STRUP, and I STRIRLING. 2007. Polar bears in the Southern Beaufort Sea II: demography and population growth in relation to Sea Ice Conditions. INOUYE, D W B BARR, K B. ARMITAGE, AND B. D INOUYE. 2000. Climate change is affecting altitudinal migrants and hibernating species. Proceedings of the National Academy of Sciences USA 97 :1630 1633. JENOUVRIER, S H CASWELL, C BARBRAUD, M HOLLAND, J STROEVE, AND H WEIMERSKIRCH. 2009. Demographic models and IPCC climate projections predict the decline of a n emperor penguin population. Proceedings of the National Academy USA 106: 1844 1847. JONZN, N T POPLE, J KNAPE, AND M SKLD. 2010. Stochastic demography and population dynamics in the red kangaroo Macropus rufus Journal of Animal Ecology 79: 109116. KALISZ, S and M A. MCPEEK. 1993. Extinction d ynamics, p opulationg rowth and s eed b anks a n e xample u sing an a ge s tructured a nnual. Oecologia 95 :314 320. KENDALL, B. E. and M E. WITTMANN. 2010. A s tochastic m odel for a nnual r eproductive s uccess. Amer ican Naturalist 175 :461468. KILGORE, D L AND K. B. ARMITAGE. 1978. Energetics of y ellow b ellied m armot p opulations. Ecology 59 : 7888. KLINGER, R 2007. Catastrophes, disturbances and density dependence: population dynamics of the spiny pocket mouse ( Heteromys desmarestianus ) in a neotropical lowland forest. Journal of Tropical Ecology 23 :507518. KNEIP, E. D H VAN VUREN, J A. HOSTETLER, and M K. OLI. In review. Relative influence of population density, climate, and predation on the demography of a subalpine species. Journal of Mammalogy. KRAUSS, J et al. Habitat fragmentation causes immediate and time delayed biodiversity loss at different trophic levels. Ecology Letters 13: 597605. KREBS, C J 1995. Two paradigms of population regulation. Wildlife Research 22 : 1 10. KREBS, C J 2002. Two complementary paradigms for analysing population dynamics. Philosophical Transactions of the Royal Society of London Series B 357: 12111219. PAGE 77 77 KRUGER, O 2007. L ongterm demographic analysis in goshawk Accipiter gentilis: the role of density dependence and stochasticity. Oecologia 152: 459471. LAAKE, J AND E. REXTAD. 2009. RMark an alternative approach to building linear models in MARK in Program MARK: a gent le introduction (E. Cooch and G. White, eds.). http://www.phidot.org/software/mark/docs/book/ LEE, T M and W JETZ. 2008. Future battlegrounds for conservation under global change. Proceeding s Of The Royal Society B Biological Sciences 275:1261 1270. LEIRS, H N C STENSETH, J D NICHOLS, J E. HINES, R VERHAGEN, AND W VERHEYEN. 1997. Stochastic seasonality and nonlinear density dependent factors regulate population size in an African rodent. Nature 389: 176180. MATLAB. 2006. Mathworks, Natick, Mass. MCLAUGHLIN, J F J J HELLMANN, C L BOGGS, AND P R EHRLICH. 2002. Climate change hastens population extinctions. Proceedings of the National Academy USA 99: 60706074. MORRIS, W F and D F DOAK. 2002. Quantitative Conservation Biology. Sinauer Associates Inc, Sunderland, MA. MORRIS, W F and D F DOAK. 2005. How general are the determinants of the stochastic population growth rate across nearby sites? Ecological Monographs 75: 11 9 137. MORRIS, W F et al. 2008. Longevity can buffer plant and animal populations against changing climatic variability. Ecology 89: 1925. MORRIS, W F S TULJAPURKAR, C V. HARIDAS, E S. MENGES, C C HORVITZ, and C A. PFISTER. 2006. Sensitivity of the population growth rate to demographic variability within and between phases of the disturbance cycle. Ecology Letters 9 :1331 1341. OLI, M K. AND K. B. ARMITAGE. 2004. Yellow bellied marmot population dynamics: Demographic mechanisms of growth and decline. Ecology 85: 24462455. OZGUL, A. K B. ARMITAGE, D T BLUMSTEIN, AND M K. OLI. 2006. Spatiotemporal variation in survival rates: Implications for population dynamics of yellow bellied marmots. Ecology 87: 10271037. OZGUL, A. L L GETZ, AND M K. OLI. 2004. Demography of fluctuating populations: Temporal and phaserelated changes in vital rates of Microtus ochrogaster. Journal of Animal Ecology 73: 201215. OZGUL, A. M K OLI, L E. OLSON, D T BLUMSTEIN, AND K. B. ARMITAGE. 2007. Spatiotemporal variation in reproductive parameters of yellow bellied marmots. Oecologia 154: 95106. PAGE 78 78 OZGUL, A. et al. In press. Coupled dynamics of body mass and population growth in response to environmental change. Nature. PARMESAN, C 2006. Ecological and evolutionary responses to recent climate change. Annual Review of Ecology Evolution and Systematics 37 :637669. PARMESAN, C and G YOHE. 2003. A globally coherent fingerprint of climate change impacts across natural systems. Nature 421: 37 42. PHILLIP S, J A. 1984. Environmental i nfluences on r eproduction in the g olden mantled g round s quirrel in The b iology of g round d welling s quirrels: a nnual c ycles, b ehavioral e cology, and s ociality (J. O. Murie and G. R. Michener, eds.). University of Nebraska Pr, Lincoln. PIMM, S L G J RUSSELL, J L GITTLEMAN, and T M BROOKS. 1995. The Future o f Biodiversity. Science 269: 347350. R DEVELOPMENT CORE TEAM. 2009. R: a language and environment for statistical computingin R Foundation for Statistical Computing. http://www.r project.org/ Vienna, Austria. REGEHR, E. V. C M HUNTER, H CASWELL, S C AMSTRUP, AND I STIRLING. 2010. Survival and breeding of polar bears in the southern Beaufort Sea in relation to sea ice. Journal of Animal Ecology 79 :117 127. ROSSER, A M and S A MAINKA. 2002. Overexploitation and species extinctions. Conservation Biology 16: 584586. ROYAMA, T 1992. Analytical population dynamics. Chapman & Hall, London, U.K. SHERMAN, P W AND M C RUNGE. 2002. Demography of a population collapse: The Northern Idaho ground squirrel ( Spermophilus brunneus brunneus ). Ecology 83: 28162831. TAMARIN, R H 1978. Population regulation. Dowden, Hutchinson & Ross, Inc., Stroudsburg, Pennsylvania. TULJAPURKAR, S. C C HORVITZ, and J B PASCARELLA. 2003. The many growth rates and elasticities of populations in random environments. American Naturalist 162:489 502. TURCHIN, P. 2003. Complex population dynamics. Princeton University Press. VAN VUREN, D H 2001. Predation on yellow bellied marmots ( Marmota flaviventris ). American Midland Naturalist 145:94 100. PAGE 79 79 VAN VUREN, D H AND K B ARMITAGE. 1991. Duration of snow cover and its influence on life history variation in yellow bellied marmots. Canadian Journal of Zoology 69: 17551758. VAN VU REN, D H 2001. Predation on yellow bellied marmots ( Marmota flaviventris ). American Midland Naturalist 145:94 100. WHITE, G C AND K. P. BURNHAM. 1999. Program MARK: Survival estimation from populations of marked animals. Bird Study 46 :120139. WILLIAMS, B K J D NICHOLS, AND M J CONROY. 2001. Analysis and management of animal populations. Academic Press, San Diego, California, USA. PAGE 80 80 BIOGRAPHICAL SKETCH Eva Kneip received a Bachelor of Business Administration degree in m anagement i nfo rmation s ystems with concentration in c omputer s cience from the University of Wisconsin in 1996. She obtained a Certificate in Conservation Biology from Columbia Universitys Center for Environmental Research and Conservation in 2004. Between 1996 and 2007 she worked in information technology consulting and financial services. Her first employer was Technology Solutions Company, a Chicagobased information technology consulting firm and in 1998 she joined Goldman Sachs Co. in New York City, as a software e ngineer. Ms. Kneip volunteered as a research assistant at various ecology related field study sites, including a population genetics project of the small Indian mongoose in Jamaica and a guenon behavior study in Kenya. She has been involved with WildMetro, a New York based nonprofit conservation organization since 2004 focusing on mammal related studies in the New York metropolitan area. In order to pursue her passion of conservation biology, Ms. Kneip began her graduate education in University of Florid a, Gainesville in Dr. Madan Olis population ecology lab in 2008 Her thesis focuses on the demography of a goldenmantled ground squirrel population occupying a dynamic subalpine habitat. Furthermore, her research interest includes the population dynamics and conservation of mammalian predator species. 