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The Relative Influence of Density and Climate on the Demography of a Subalpine Ground Squirrel Population

Permanent Link: http://ufdc.ufl.edu/UFE0042252/00001

Material Information

Title: The Relative Influence of Density and Climate on the Demography of a Subalpine Ground Squirrel Population
Physical Description: 1 online resource (80 p.)
Language: english
Creator: Kneip, Eva
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: demography, density, dynamics, environmental, external, golden, lateralis, population, spermophilus, squirrel, stochastic
Interdisciplinary Ecology -- Dissertations, Academic -- UF
Genre: Interdisciplinary Ecology thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In the context of global climate change, understanding the causes and consequences of oscillations in populations is a central objective for ecologists. We utilized long-term (1990-2009) field data to investigate the influence of population size and extrinsic environmental factors on the demographic parameters of golden-mantled 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 ?1 pups) was higher 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, with a mean of 4.81 (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, ranging from 0.445 to 1.244, and was below replacement (? < 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, ?s was 0.912 suggesting an 8.8% annual population decline. This result was less than the deterministic growth rate of the mean matrix, ?M (0.944) but it was similar to the overall deterministic growth rate (?=0.905, 95% CI: 0.812-0.998) which was based on pooled data. As a result of lower-level elasticity analysis, the deterministic population growth rate was most sensitive to proportionate changes in adult survival. All three measures of stochastic elasticity indicated that ?s 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 density-independent model. When density-dependence 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 quasi-extinction of this population.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Eva Kneip.
Thesis: Thesis (M.S.)--University of Florida, 2010.
Local: Adviser: Oli, Madan K.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042252:00001

Permanent Link: http://ufdc.ufl.edu/UFE0042252/00001

Material Information

Title: The Relative Influence of Density and Climate on the Demography of a Subalpine Ground Squirrel Population
Physical Description: 1 online resource (80 p.)
Language: english
Creator: Kneip, Eva
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: demography, density, dynamics, environmental, external, golden, lateralis, population, spermophilus, squirrel, stochastic
Interdisciplinary Ecology -- Dissertations, Academic -- UF
Genre: Interdisciplinary Ecology thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In the context of global climate change, understanding the causes and consequences of oscillations in populations is a central objective for ecologists. We utilized long-term (1990-2009) field data to investigate the influence of population size and extrinsic environmental factors on the demographic parameters of golden-mantled 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 ?1 pups) was higher 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, with a mean of 4.81 (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, ranging from 0.445 to 1.244, and was below replacement (? < 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, ?s was 0.912 suggesting an 8.8% annual population decline. This result was less than the deterministic growth rate of the mean matrix, ?M (0.944) but it was similar to the overall deterministic growth rate (?=0.905, 95% CI: 0.812-0.998) which was based on pooled data. As a result of lower-level elasticity analysis, the deterministic population growth rate was most sensitive to proportionate changes in adult survival. All three measures of stochastic elasticity indicated that ?s 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 density-independent model. When density-dependence 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 quasi-extinction of this population.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Eva Kneip.
Thesis: Thesis (M.S.)--University of Florida, 2010.
Local: Adviser: Oli, Madan K.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042252:00001


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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 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 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 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, 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 GOLDEN-MANTLED
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, DENSITY-DEPENDENT AND -INDEPENDENT FACTORS................70

D LITTER SIZE MODELS TESTING FOR THE EFFECTS OF INTRINSINC,
DENSITY-DEPENDENT 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

3-1 Regression coefficients for logit-transformed survival and logit-transformed
breeding probability (BP) for the golden-mantled ground squirrel population in
G othic, C O ........... ....................... ............................... ..........55

3-2 Elasticities of stochastic population growth rate (As) to mean (Esl), variance
(Eso), and both mean and variance (Es) of matrix elements.. ........................... 55

3-3 The number of juvenile and adult female golden-mantled ground squirrels
that immigrated to our study site in Gothic, CO ............................................. 56









LIST OF FIGURES


Figure page

2-1 Annual variation in the population size of the GMGS for the period 1990-
2008. Total and age- and sex-specific numbers of squirrels are presented .......32

2-2 Model-averaged 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

2-3 Relationship between previous year's 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 logit-
transform ed survival rate.. ........................................................................... .. 57

3-2 Annual variation in the deterministic population growth rate with 95% Cl for
female golden-mantled ground squirrels during 1990-2007..............................58

3-3 Elasticity of projected population growth rate A to proportional changes in the
lower level vital rates of the overall m atrix A..................................................... 59

3-4 Frequency distribution of population size in 50 years including only the
effects of environm ental stochasticity................................................................. 60

3-5 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 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 golden-mantled 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 long-term (1990-2009) field data to investigate the influence of population size

and extrinsic environmental factors on the demographic parameters of golden-mantled

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 1-8 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 year-to-year 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: 0.812-0.998) which was based on pooled data. As a result of

lower-level 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 density-independent model. When density-dependence 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 quasi-extinction 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

human-induced (Pimm et al. 1995; Rosser and Mainka 2002). The combined effects of

landscape modification, resource-exploitation, invasive species introduction, and

accelerated greenhouse-gas production greatly alter the biosphere (Krauss et al.; Lee

and Jetz 2008; Rosser and Mainka 2002). Increased greenhouse-gas 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, climate-induced 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 density-dependence (DD) in the dynamics of a

temporally oscillating vertebrate population. The relative importance 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 studied the demographic consequences of DD and environmental

variability by utilizing a demographic data set from a 19-year (1990-2008) study on a

golden-mantled 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 golden-mantled ground squirrel data consisted of long-term, capture-mark-

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

golden-mantled 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 age-specific 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 density-dependence and environmental stochasticity 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

focuses on the population dynamic consequences of density-dependence 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 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 (Clutton-Brock 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), population-level 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 golden-mantled 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. 2-1). The long-term

(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 age-specific survival rates, breeding 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









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 13-ha

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 snow-melt 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 long-tailed weasels (Mustela

frenata).

Field Methods

For 20 consecutive years (1990-2009), GMGS were live-trapped augmented by

almost daily observations during the active season (May to late August). Squirrels were

trapped during late May-early June, for the annual census and marking of the resident

population; late June-mid 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 single-door Tomahawk live-traps (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 long-tailed 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 age-classes (juvenile: [<1yr olds]; adults: [>1yr olds]),

and estimated and modeled the state-specific 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 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









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 over-dispersion 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

(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 time-dependent 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 (Nt-1) 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 age-specific 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 model-averaged estimate of sex- and age-specific 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. Zero-truncated 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

age-classes (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. 2-1).

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 age-specific 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-specific

differences remained constant over time (Figure. 2-2).

Direct and Delayed Density-Dependence (DD) for Survival

The analysis of the effect of current (Nt) and previous year's (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









survival (3=-0.011, 95% CI: -0.015, -0.006) of squirrels of both sexes and age classes

(Figure. 2-3a-d). We note that models 2-7 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 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 (Nt-1) 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 Nt-1 (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. 2-4a).

Age, Sex, and Time Effects for BP

There was strong evidence for age-specific (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. 2-4b). 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). 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 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 sex-specific

variation on survival. Previous studies have also demonstrated the impact of age and

sex on survival rates of high-elevation 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.

2-4a). 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 age-specific 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 adult 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 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 same-year 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 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 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 same-year 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 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, high-altitude 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 multi-mammate rats (Mastomys natalensis), while the negative impact of

delayed DD in our GMGS population was consistent in all age- and 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.









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 density-dependent and density-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 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
7-S


1990 1993 1996 1999 2002 2005 2008


Year

Figure 2-1. Annual variation in the population size of the GMGS for the period 1990-
2008. Total and age- and sex-specific numbers of squirrels are presented.









00
0


A II
AF l



-













1990 1995 2000 2005

Year

Figure 2-2. Model-averaged annual survival estimates with SE for adult (AF) and
juvenile (JF) female, and adult (AM) and juvenile (JM) male GMGS during
1990-2007. All unique models from Table 2-1 a and 2-1b 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 2-3. 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 2-4. Breeding probability and distribution of litter size of golden-mantled ground
squirrels. A) Percentage of yearling and older 2yrs of age) females that
successfully weaned at least 1 pup during 1990-2008., B) Distribution of litter
size during the study period (1990-2008).


120

100


30
25
S20-
o
15
10
5
0


r









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 long-term demographic predictions (Kalisz and McPeek 1993, Boyce

et al. 2006). It is generally believed that both endogenous (density-dependent; DD) and

exogenous (density-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 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 long-term 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 long-term 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 golden-mantled 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 19-year study, our discrete population of GMGS exhibited

substantial fluctuation in population size (Kneip et al. In review). This long-term

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

abundance of the GMGS population. Our 5-step 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 long-term

population growth rate; and (5) project the probability of quasi-extinction 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 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).

The golden-mantled ground squirrel is an asocial and diurnal species that occurs

at a broad range of elevations (~1000-4000m 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

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 forbss and grasses).

Snow-melt 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 live-trapped 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, animals were observed daily and trapped

opportunistically to capture and mark all new immigrants and refresh marks on

residents.

Single-door Tomahawk live-traps (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 dye-marked 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 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 golden-mantled ground squirrels.









There was evidence for the effect of sex on survival (Kneip et al. In review), so we used

female-only 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 (=lyr olds) and older femaleskyr olds) (Kneip et al. In review). The

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 age-structured matrix population model for both

deterministic and stochastic analysis. The age of last reproduction was chosen because

out of 326 known-age female squirrels only 1 had a maximum life span longer than 6

years. The form of the age-structured population projection matrix including lower-level

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

(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 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 age-specific fecundity and









survival probability. Age-specific 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 year-specific deterministic models. For the overall or

time-invariant model, a projection matrix A was obtained from a single estimate of the

vital rates based on capture-mark-recapture data collected during the entire study

period (1990-2008). For the year-specific model, a separate population projection matrix

At was compiled for each year t using age-specific 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 year-specific

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 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

age-specific survival rates, but not in breeding probability or litter size (Kneip et al. In









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 simulation-based 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 one-step 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-) (3-2)
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 stable-age

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:

1=
+e-(Ppo+PpN*n) (3-3)

BP = 1 (3-4)
l+e-(PBPo+PBPN*n) (3-4)

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 age-class

and all values are reported in Table 3-1. 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









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 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 age-specific time-dependent model and

the best age-specific DD model (calculated at the population density for that year)









(Figure 3-1). 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) (3-5)

Because the additive logistic regression coefficients for each age-class 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 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 quasi-extinction was estimated at various levels of quasi-extinction

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 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

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: 0.812-0.998). The year-to-year population









growth rate was highly variable as At ranged between 0.445 and 1.244 (Figure. 3-2).

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 lower-level 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. 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, 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 year-old 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 3-2).

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 3-4. 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. 3-4).

Density Dependence and Environmental Stochasticity

According 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

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 logit-transformed survival estimates computed by the best DD and time-

dependent models for adult and juvenile females are depicted in Figure 3-1 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 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









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, several 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 analysis (Morris and Doak 2002, Kendall and Wittmann 2010).

Environmental stochasticity tends to destabilize population dynamics, cause random

population fluctuations, reduce long-term population growth rate, and increase

extinction risk (Coulson et al. 2000, Kendall 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 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

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 24 squirrels in 1999 and 2000 to 140 in 2005, almost a 6-fold 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

density-dependence 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 long-term, 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 stochastic 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 50-year 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 re-bounced 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 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 2000-2002 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 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, when 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 (Figure. 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

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 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









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

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. 3-1) to explain the effects of ES in our

combined DD and ES models (Figure. 3-6).

Our 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.









This may be reduced by the regulatory effect of density-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 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 3-1. Regression coefficients for logit-transformed survival and logit-transformed
breeding probability (BP) for the golden-mantled 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 3-2. 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 3-3. The number of juvenile and adult female golden-mantled 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 3-1. Relationship between annual population density and the age-specific logit-
transformed survival rate. a) adult and b) juvenile female golden-mantled
ground squirrels between 1990 and 2007. Filled circles represent the yearly
logit-transformed survival estimates from the full time-dependent 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.




































1990 1992 1994 1996 1998 2000 2002


2004 2006


2008


Year
Figure 3-2. Annual variation in the deterministic population growth rate with 95% Cl for
female golden-mantled ground squirrels during 1990-2007.


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 3-3. 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 3-4. 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
density-dependent 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 3-5. 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 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
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 density-independent 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 (GET-1]
- Z) E8+D( ET-1)
* 3) E8+D*oIiprmK mft (GET-1)
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(GET-1]
/ *" ^^ 1)ES ET-51
2) ES-DD IEIET-S)
.-. 3) ES-DDm-mn lfbl (iET-5)


a

~ i

-Ii
a3
-
C- &


Time
Figure 3-6. Probability of quasi extinction under various scenarios of environmental
stochasticity, density-dependence, and differing levels of quasi-extinction
threshold for the golden-mantled 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 year's 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.









CHAPTER 4
CONCLUSION

To decipher the population and species-level consequences of anticipated climate

change, 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 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 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 change. 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 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 golden-mantled ground squirrels.

Current and previous summer rainfall negatively influenced juvenile survival and









yearling breeding probability, respectively. Therefore, I concluded that precipitation; a

density-independent, 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 long-term 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 golden-mantled 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 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 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 age-specific apparent survival rates for the golden-mantled 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 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 DENSITY-DEPENDENT AND
-INDEPENDENT FACTORS

Models testing for the effect of a) current (Nt) and previous (Nt-i) 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 golden-

mantled 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 models are shown for parts a and b.

No. Model A AICc AICc wi npar
(a)
1 0(age + sex + Nt-I) 0.00 2047.27 0.199 4
2 0(sex + age Nt-1) 0.84 2048.10 0.131 5
3 P(age + sex + Nt + Nt-i) 0.95 2048.22 0.123 5
4 0(age + sex Nt-_) 1.14 2048.41 0.112 5
5 0((age + sex) Nt-1) 1.74 2049.01 0.083 6
6 P(sex + age Nt-1 + Nt) 1.77 2049.04 0.082 6
7 P(age + sex + Nt Nt-1) 1.94 2049.20 0.075 6
8 P(age + sex Nt_ + Nt) 2.10 2049.37 0.070 6
9 0((age + sex) Nt-1 + Nt) 2.67 2049.94 0.052 7
10 0(sex + age Nt + Nt-1) 2.75 2050.02 0.050 6
11 0((age + sex) Nt + Nt-1) 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 + raint-i: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 + raint-i:A + bgt_-:A) 1.02 2061.15 0.142 7
4 0(sex + age raint + raint-i: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 + raint-i:A + bgt + bgt-i:A) 2.91 2063.04 0.055 8









9 P(sex + age raint + bgt + bgt-_:A)
10 P(sex + age + raint + raint-i: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 + raint-i:A)
8 P(sex + age raint + raint-i: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 + Nt-1)
2 P(sex + age raint + pred + Nt-1)
3 P(sex + age raint + raint-_-A + Nt-1)
4 P(sex + age raint + raint-_-A + Nt-I + pred)
5 P(age + sex + Nt-1)
6 P(age + sex + Net- + pred)
7 P(age + sex + Net- + raint-iA)
8 P(age + sex + Net- + raint-_-A + pred)
9 P(sex + age raint + pred)
10 P(sex + age raint + raint-i:A + pred)
11 P(age + sex + raint-i:A + pred)
12 P(sex + age + pred)
13 P(sex + age raint + raint-i:A)
14 P(sex + age raint)
15 P(sex + age + time)
16 O(sex + age + raint-i: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 (Nt-1) 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,
DENSITY-DEPENDENT AND -INDEPENDENT FACTORS

Models testing for the effect of a) age and time; b) current (Nt) and previous (Nt-i)

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 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 + Nt-i) 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 + Nt-1) 1.51 289.18 0.114 5
6 W(age + Nt *Nt-1) 2.31 289.98 0.076 5
7 W(age + Nt-i *Nt) 2.31 289.98 0.076 5
8 W(age) 8.28 295.96 0.004 2
9 W(age + Nt-i) 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 *raint-i + pred) 1.41 280.98 0.322 5
3 W(age + raint-i) 8.01 287.57 0.012 3
4 W(age + raint.- + pred) 8.91 288.47 0.008 4
5 W(age *pred + raint-i) 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 (Nt-i)

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 golden-mantled 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 Nt-1) 1.28 532.78 0.180 4
3 LS (.) 1.29 532.79 0.179 1
4 LS (Nt-I) 1.37 532.87 0.172 2
5 LS (Nt + Nt-1) 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 (bgt-1 + pred) 2.31 535.11 0.070 3
9 LS (age + bgt-1) 2.64 535.44 0.059 3
10 LS (bgt-1 *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 (bgt-1 + Nt) 0.52 532.02 0.171 3
3 LS (.) 1.29 532.79 0.116 1









4 LS (bgt-1 *Nt) 1.50 533.00 0.105 4
5 LS (bgt-1) 2.00 533.50 0.082 2
6 LS (bgt-1 + Nt + pred) 2.09 533.59 0.078 4
7 LS (pred) 2.71 534.21 0.057 2
8 LS (bgt-1 Nt + pred) 3.14 534.65 0.046 5
9 LS (age) 3.16 534.66 0.046 2
10 LS (bgt-1 + pred) 3.60 535.11 0.037 3
11 LS (bgt-1 pred + Nt) 4.04 535.54 0.029 5
12 LS (bgt-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.









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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 Chicago-based 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

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, non-profit, 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 Florida, Gainesville in Dr. Madan Oli's population ecology lab in 2008.

Her thesis focuses on the demography of a golden-mantled ground squirrel population

occupying a dynamic subalpine habitat. Furthermore, her research interest includes the

population dynamics and conservation of mammalian predator species.





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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

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2 2010 va Kneip

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3 To my mom, dad, and grandparents

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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.

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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

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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, DENSITY-DEPENDENT AND -INDEPENDENT FACTORS .................................... 72 LIST OF REFERENCES ................................................................................................... 74 BIOGRAPHICAL SKETCH ................................................................................................ 80

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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

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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 1990-2007. ................................ 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

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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 long-term (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

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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.

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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 human-induced (Pimm et al. 1995; Rosser and Mainka 2002) The combined effects of landscape modification, resource exploitation, invasive species introduction, and accelerated greenhouse-gas production greatly alter t he biosphere (Krauss et al.; Lee and Jetz 2008; Rosser and Mainka 2002). Increased greenhouse-gas 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, climate-induced 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

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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 (1990-2008) 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

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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 age-specific 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.

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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

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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) population-level 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

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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

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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 long-tailed weasels ( Mustela frenata). Field M ethods For 20 consecutive years (1990-2009), 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 June-mid 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 single-door 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

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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.

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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 age-classes (juvenile: [<1yr olds] ; adult s: [ 1yr olds] ), and estimated and modeled the state-specific 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

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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 time-dependent 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,

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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 age-specific 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. Zero-truncated 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 age-classes ( yearling [=1yr olds] and older [ yr olds] females ) for the reproductive

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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 age-specific 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

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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 2-7 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

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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.

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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

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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

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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 age-specific 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

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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

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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).

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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.

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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.

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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.

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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 2-1a and 2 -1 b were included for model averaging

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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.

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35 A B Figure 24. Breeding probability and distribution of litter size of golden-mantled 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)

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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 long-term 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

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37 variability is critical since these pertur bations are likely to influence the long-term 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

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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 long-term 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 5-step 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.

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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).

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40 Field Methods GMGS were live-trapped 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 live-traps (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.

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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 age-structured 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 age-structured 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

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42 survival probability. Age-specific 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 capture-mark -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 age-specific 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 age-specific survival rates, but not in breeding probability or litter size (Kneip et al. In

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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 one-step 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

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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 age-class 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

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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 age-specific time dependent model and the best age -specific DD model (calculated at the population density for that year)

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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 age-class 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

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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 3-2). 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

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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

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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 6-fold difference The

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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

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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 2000-2002 and 2007, immigration occurred in 6 out of 8 years.

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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

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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.

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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.

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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

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56 Table 3 3. The number of juvenile and adult female golden-mantled 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

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57 Figure 31. Relationship between annual population density and the age-specific 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 time-dependent 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.

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58 Figure 32. Annual variation in the deterministic population growth rate with 95% CI for female goldenmantled ground squirrels during 1990 -2007

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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.

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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.

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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.

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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.

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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

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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 long-term 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 -

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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.

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66 APPENDIX A SURVIVAL MODELS TEST ING FOR THE EFFECTS OF SEX, AGE, AND TIM E Analysis of age-specific 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.

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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

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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,

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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

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70 APPENDIX C BREEDING PROBABILITY MODELS TESTING FOR T HE EFFECTS OF INTRIN SIC, DENSITY-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 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

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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.

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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

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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.

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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.