Metapopulation Dynamics of Yellow-Bellied Marmots

METAPOPULATION DYNAMICS OF YELLOW-BELLIED MARMOTS


By

SEYFI ARPAT OZGUL













A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2006

































Copyright 2005

by

Seyfi Arpat Ozgul

































This thesis is dedicated to two geologists, Necdet and Aynur Ozgul, for their love and
support in my endeavor to follow in their footsteps as a scientist.















ACKNOWLEDGMENTS

I am indebted to Madan K. Oli for his excellent mentorship, guidance and

friendship throughout my graduate education. His contribution to the quality of my

research and to my development as an ecologist has been invaluable. He has been a

perfect role model, and I can only hope to guide my future students as well as he has

guided me. I owe special gratitude to Kenneth B. Armitage for including me in this

amazing research, and for sharing his deep knowledge and admiration of yellow-bellied

marmots. He, Daniel T. Blumstein, and Dirk H. VanVuren have given their skillful

support to my research and have helped it along from start to finish. I also thank my other

committee members, Graeme C. Cumming, Robert D. Holt, and Kathryn E. Sieving.

During my graduate education, I have learned a lot from their advice and guidance on my

research, and from the courses they have taught. The faculty, students, and staff of the

Department of Wildlife Ecology and Conservation and the Rocky Mountain Biological

Laboratory have greatly enriched my experience as a graduate student. I am also grateful

to the following individuals, all of whom, in one way or another, have been generous

with their comments, help, inspiration or encouragement: Anne Bronikowsky, Jim

Nichols, Jim Hines, Julien Martin, Ian Fiske, Matt Trager, Jeff Hostetler, Justyn Stahl,

Ania Mikos, Elina Garrison, Melissa Moyer, Jeremy Dixon, SaifNomani, Janell Brush,

Kara Youngentob, Gabby Hyrcyshyn, Toshinori Okuyama, and my siblings Baran, Doga,

and Koray Ozgul. Finally, this work would not have been possible without the dedicated

help of all the "marmoteers" who have participated in this long term fieldwork.















TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S ................................................................................................. iv

LIST OF TABLES .................. .................. ................. ............ ............ .. viii

LIST OF FIGURES ......... ......................... ...... ........ ............ ix

ABSTRACT ........ .............. ............. ...... .......... .......... xi

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

B ack g rou n d ...................................... ............................... ... .......... ...... .
O bj ectives ............................................................... .. ... ...... ......... 4
S tu d y S y ste m ................................................................................................................6

2 EFFECTS OF PATCH QUALITY AND NETWORK STRUCTURE ON PATCH
OCCUPANCY DYNAMICS OF A YELLOW-BELLIED MARMOT
M E T A P O PU L A T IO N ....................................................................... .....................9

Intro du action ...................................... ................................................ 10
M materials and M methods ....................................................................... .................. 12
Stu dy A rea an d Sp ecies .......................................................................... ...... 12
M odel Structure .................................... .......................... ... ........ .14
Param eter Estim ation........................................................... ............... 16
M odel Sim ulation .................. .......... .................................................. 17
A dequacy of the SPO M .......................................................... ............... 18
R e su lts ................... ...................................... .................... ................2 0
Param eter E stim ation ............................................... ...... ........................ 20
M odel Sim ulation ...................................................... ... .. ........ ...... 2 1
A dequacy of the SPOM .......................................................... ............... 24
D iscu ssio n ...................................... ................................................. 2 5

3 SPATIOTEMPORAL VARIATION IN AGE-SPECIFIC SURVIVAL RATES
OF THE YELLOW-BELLIED MARMOT........................................................40

In tro d u ctio n ...................................... ................................................ 4 1
M materials and M methods ....................................................................... ..................43
Stu dy A rea an d Sp ecies .......................................................................... ......4 3









Field M ethods and Data....................... ............... ............ ............... 43
Capture-Mark-Recapture (CMR) Analysis ............... ............................... 44
R e su lts .................. ....... .. ... ........ .................... ................ ................ 4 8
Spatiotemporal Variation in Overall Survival Rates....................................48
Age Structure and Spatiotemporal Variation in Age-Specific Survival Rates....48
Effect of Environm ental Factors ................................. ..................................... 50
Influence on Population Growth Rate..... .......... ....................................... 51
D iscu ssio n ...................................... ................................................. 52

4 SPATIOTEMPORAL VARIATION IN THE REPRODUCTIVE PARAMETERS
OF THE YELLOW-BELLIED MARMOT.............................................................64

In tro d u ctio n ...................................... ................................................ 6 5
M materials and M methods ....................................................................... ..................67
Study A rea and Species ......................................................... .............. 67
F ield M ethods and D ata......................................................................... ... ..... 68
Components of Reproduction.............................................. 68
Effect of Environmental and Social Factors......................................................70
Influence on Population Growth Rate..... .......... ....................................... 71
R esults............... ..... ... ..... ........ ............ .............. ............... ............ 72
Survival, Recapture, and Breeding Probability ....................................... 72
L hitter Size ..................... ......... ................................ ............ 73
Effects of Environmental and Social Factors.................. .....................................73
Influence on Population Growth Rate..... .......... ....................................... 74
D iscu ssio n ...................................... ................................................. 7 5

5 THE INFLUENCE OF LOCAL DEMOGRAPHIC PROCESSES ON THE
REGIONAL DYNAMICS OF A YELLOW-BELLIED MARMOT
M E T A P O PU L A T IO N ..................................................................... .....................86

In tro du ctio n ...................................... ................................................ 8 7
M materials and M methods ....................................................................... ..................90
Study A rea and Species ......................................................... .............. 90
F field M eth od s .................................................................................. 9 1
Local Population D ynam ics ........................................ .......................... 91
M etapopulation D ynam ics........................................................ ............... 94
Results .................. ..... ............ ............. ............... 98
Local Population D ynam ics ........................................ .......................... 98
M etapopulation D ynam ics........................................................ ............... 99
Discussion .......................... ..............................101

6 C O N C L U SIO N .......... .................................................................. ......... ... .... 113

APPENDIX

A ANALYSIS OF SPATIAL AND TEMPORAL VARIATION IN OVERALL
APPARENT ANNUAL SURVIVAL RATES ...............................................117









B EFFECT OF ENVIRONMENTAL COVARIATES ON THE SPATIAL AND
TEMPORAL VARIATION IN AGE-SPECIFIC SURVIVAL RATES .................. 118

C ENVIRONMENTAL COVARIATES FOR THE COMPONENTS OF
R E P R O D U C T IO N ........................................ .......... ................. ..........................119

D ELASTICITY ANALYSIS OF LOCAL POPULATION DYNAMICS................ 122

L IST O F R E F E R E N C E S ...................................................................... ..................... 124

BIOGRAPHICAL SKETCH ............................................................. ............... 137














LIST OF TABLES
Table p

2-1. Models and subfunction definitions used in SPOMSIM. ......................................31

2-2. Markov Chain Monte Carlo estimates of the parameters for the best stochastic
patch occupancy m odel .......................................................................... 32

2-3. Definition of robust design occupancy models used for modeling colonization
and extinction probabilities...................... ....... ............................. 33

2-4. Number of parameters, Akaike's Information Criterion corrected for small
sample size, deviances, and model likelihood for the robust design occupancy
models fitted to the yellow-bellied marmot data.. ....................................... ....... 34

3-1. Analysis of the age structure and spatial variation in age-specific apparent
survival rates for the yellow-bellied marmot............................ .... ...............58

3-2. Analysis of temporal variation in age-specific apparent survival rates for the
yellow -bellied m arm ot. ........................... ...... .............. ....................... 59

3-3. Analysis of temporal and spatial variation in the growth rate of the entire
population and adult segment of the population..................................................60

4-1. Analysis of state-specific apparent survival, recapture, and transition rates for the
yellow -bellied m arm ot ............ .................................................... .................. .. 80

4-2. Analysis of the spatial, temporal, and age-specific variation in litter size for the
y ellow -b ellied m arm ot ............ .................................................... .................. ... 8 1

4-3. Analysis of the temporal and spatial variation in growth rate of the adult segment
of the population. .................................... ......................................82

A-1. Analysis of spatial and temporal variation in overall apparent annual survival
rates for the yellow-bellied marmot. ......................... .. .............. ................... 117

B-1. A table showing the effect of environmental covariates on the spatial and
temporal variation in age-specific survival rates. ................................................ 118

C-1. List of covariates used during the analysis of the effect of environmental factors
on the breeding probabilities and on litter size of the yellow-bellied marmot. ......121














LIST OF FIGURES
Figure page

2-1. The structure of the yellow-bellied marmot metapopulation in Colorado...............35

2-2. Yearly proportions of occupied patches, empty patches, and patches with
unknown occupancy status, for the period between 1990 and 2002......................36

2-3. Predicted patch occupancy in 1000 replicate simulations of the yellow-bellied
marmot metapopulation using the parameterized stochastic patch occupancy
m o d e l ............................ ........... ... ...................................................3 7

2-4. Predicted patch occupancy in 1000 replicate simulations when the quality of
colony sites was reduced by 20%, and when 1, 2, 3, and 4 highest quality colony
sites were excluded from the network. ................................................. .......... 38

2-5. Predicted patch occupancy in 1000 replicate simulations for the northern and
southern netw works ......................... ........................ .. .... ..... .. ............39

3-1. The spatial structure of the yellow-bellied marmot metapopulation in Colorado,
U.S.A. Seventeen sites are grouped into four colonies (River, Gothic, Marmot
Meadow and Picnic) and four satellite groups (south, west, east, and north
satellites)..................................................... ......... ..................... 61

3-2. Spatial variation in annual adult, yearling, and juvenile survival rates...................62

3-3. Temporal variation in annual adult, yearling and juvenile survival rates from
1 9 7 6 to 2 0 0 3 ................................ ......... ..... ............... ................ 6 3

4-1. The life cycle graph for the yellow bellied marmot, with three life history states
(yearling, non-reproductive adult and reproductive adult)............... ............... 83

4-2. Site-specific estimates of transition rates from yearling, non-reproductive adult,
and reproductive adult states to the reproductive adult state, and site-specific
estimates of litter size and the realized growth rate of the adult population............84

4-3. Temporal variation in transition rates from non-reproductive adult and
reproductive adult states to reproductive adult state with two years lag, and
temporal variation in the litter size with one year lag, and the realized growth
rate of the adult segment of the population ..................................................85

5-1. The life cycle graph for the yellow bellied marmot, with four life history stages:
juvenile, yearling, pre-reproductive adult, and reproductive adult ........................106









5-2. Elasticity of the projected population growth rate to the vital rates...................... 107

5-3. Elasticity of the stochastic population growth rate to the mean values of the vital
rate s.. .................................................................................... 1 0 8

5-4. The covariances of the projection matrix elements among sites, and the
contributions of the covariances to the variation in projected growth rates among
site s .............................................................................................. 10 9

5-5. The covariances of the vital rates among sites, and the contributions of the
covariances to the variation in projected growth rates among sites......................110

5-6. Proportional influence of the demography in each of the 17 sites on
metapopulation growth rate, calculated as the sums of the diagonal blocks of the
elasticity matrix........ ........ ......... .... ........ .................. 111

5-7. Proportional influence of each vital rate and the dispersal rate on XMp ................12















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

METAPOPULATION DYNAMICS OF YELLOW-BELLIED MARMOTS

By

Seyfi Arpat Ozgul

May 2006

Chair: Madan K. Oli
Major Department: Wildlife Ecology and Conservation

Many biological populations inhabit spatially heterogeneous landscapes, and the

spatial heterogeneity often has important effects on population dynamics. However, very

few empirical studies on long-lived vertebrates have thoroughly investigated the effect of

spatial heterogeneity on population dynamics. Using 42 years of field data, I investigated

the factors and processes that influenced the dynamics and persistence of a yellow-bellied

marmot metapopulation in Colorado, USA.

Using a simple patch occupancy model, I investigated the relative influence of

particular sites on metapopulation dynamics. A few colony sites were the major drivers of

metapopulation dynamics, and regional persistence was highly sensitive to changes in the

quality of these sites. Nonetheless, satellite sites also made a significant contribution to

the long-term persistence of the metapopulation.

Using capture-mark-recapture (CMR) modeling approach, I investigated the

spatiotemporal variation in demographic rates and its influences on local population

dynamics. Survival and reproductive rates exhibited both spatial and temporal variation,









but the pattern of variation significantly differed among vital rates. Vital demographic

rates that were the components of recruitment into the adult population (survival of

young animals, litter size and breeding probability) exhibited a greater degree of variation

over space and time than other vital rates, and were the main demographic factors driving

the temporal fluctuations in population dynamics.

Using a stage-structured matrix model, I investigated the demographic causes of

the spatial variation in local population dynamics. Variation in the survival of the young

animals and that of reproductive adults made the largest contributions to the observed

spatial variation in population growth rate. Using a vector-permutation matrix approach, I

developed a matrix metapopulation model, and investigated the relative influence of local

demographic rates and the dispersal rate on regional population dynamics.

Metapopulation dynamics mainly depended on a few colony sites, and the

metapopulation growth rate was highly sensitive to changes in the demography of these

high quality sites. The relative influence of dispersal on metapopulation growth rate was

lower than that of the demographic rates. Most commonly used models of

metapopulation dynamics emphasize the importance of regional processes, but do not

explicitly consider the role of within-population demographic processes. However, my

results underscore the need for the explicit consideration of the local demographic

processes for understanding the dynamics and persistence of demographically and

spatially structured populations.














CHAPTER 1
INTRODUCTION

Background

Several wildlife populations are influenced by multiple environmental factors that

vary over space and time (Orzack and Tuljapurkar 1989, Tuljapurkar 1990, Post et al.

1997). It has become increasingly apparent that the spatial structure of populations often

has important effects on population dynamics (Andrewartha and Birch 1954, Levins

1969, Hanski 1999), and investigating these effects may be critical to understanding the

dynamics of these populations (Pulliam 1988, Kareiva 1990, Hanski and Simberloff

1997, Stacey et al. 1997, Tilman and Kareiva 1997, Akcakaya 2000b, Fagan et al. 2001).

Ecologists and conservation biologists are increasingly relying on spatially-structured

population models to address the influence of spatial heterogeneity on population

dynamics (e.g., Lankester et al. 1991, Lahaye et al. 1994, Akcakaya and Sjorgen-Gulve

2000, Hokit et al. 2001). Although there are still gaps between theory and practice,

several studies utilizing metapopulation (i.e., a set of local populations connected through

dispersal) approaches have been moderately successful in explaining and predicting

wildlife population dynamics in fragmented landscapes (e.g., Hanski et al. 1995,

Moilanen et al. 1998).

The various methods of representing space, tracking populations and individuals,

dealing with environmental variability, and describing dispersal have generated a variety

of metapopulation models that differ in generality and realism (Kareiva 1990, Hanski

1999, Akcakaya and Sjorgen-Gulve 2000). Some of these models are data intensive, and









the lack of adequate data has precluded the application of more complex models.

For many threatened species, data to parameterize complex models are often lacking, and

simpler modeling approaches are the only option.

The presence-absence of a species at a particular site is the simplest form of data

that can be collected during ecological field studies (Hanski 1994b). A class of

metapopulation models that require only the presence-absence data are the patch

occupancy models (reviewed in Hanski 1999). Despite the limitations of occupancy

models, their simplicity and generality allow several important ecological questions to be

addressed (Sjorgen-Gulve and Hanski 2000). Although adequate description of

metapopulation dynamics might require more complex models, it is important to know

what we can learn about the dynamics and persistence of a spatially structured population

by analyzing these simple models. In certain situations, simple models may be as

informative as more complex models and may yield similar results (Hokit et al. 2001,

Lopez and Pfister 2001). However, there are very few comparisons of different modeling

approaches applied to the same populations (but see Hokit et al. 2001).

Simple metapopulation models (e.g., patch occupancy models) emphasize the role

of regional processes, such as dispersal and synchrony among local populations, but do

not explicitly consider the role of local demographic processes, such as survival and

reproductive rates, density dependence and temporal trends in these vital rates. However,

local demographic processes can be important determinants of metapopulation dynamics

(e.g., Burgman et al. 1993, Lahaye et al. 1994). Spatial variation in population dynamics

is a consequence of local differences in demographic parameters (Caswell 2000, Oli and

Armitage 2004, Bruna and Oli 2005). Also, the dispersal of individuals among local









populations is often dependent on demographic processes (Bowler and Benton 2005,

Matthysen 2005). However, consideration of local demographic processes usually

requires more data than is required by simple models (Akcakaya 2000a). As a result, very

few studies of long-lived species have thoroughly investigated spatiotemporal variability

in local demographic rates and its influence on population dynamics.

The relative significance of local and regional processes on population persistence

is an important question from both theoretical and practical perspectives. A group of

models, matrix metapopulation models (i.e., structured metapopulation models), attempts

to incorporate local demographic processes and regional processes into modeling

population dynamics across multiple sites (Akcakaya 2000a, Hunter and Caswell in

press). These models form the basis of several published population viability analyses

(PVA's, reviewed in Boyce 1992, Akcakaya 2000b, Beissinger and McCullough 2002).

Recent developments in matrix metapopulation models have provided a framework for

using the analytical approaches to matrix analysis (e.g., sensitivity and elasticity

analyses) for metapopulation models (Hunter and Caswell in press). This approach

provides an analytical framework for investigating the relative influence of local

demography and dispersal on metapopulation dynamics. However, even simple matrix

metapopulation models are data intensive and thus difficult to parameterize for most

species; there are very few studies that provide sufficient data on all the demographic

rates in multiple sites and the dispersal rates among sites. Therefore, little is known about

the relative importance of local demographic processes on the dynamics of spatially

structured populations, particularly for long-lived species.









Objectives

In this doctoral research, I investigated the factors and processes that influence the

dynamics and persistence of a yellow-bellied marmot metapopulation in the upper East

River Valley, Colorado. Long-term research by Dr. K. B. Armitage and his colleagues at

the Rocky Mountain Biological Laboratory has yielded 41 years of demographic

(trapping) data and 10 years of dispersal (radio-telemetry) data from several colonies

(Van Vuren 1990, Armitage 1991, Schwartz et al. 1998, Armitage and Schwartz 2000).

The long-term study of individually-identified animals in several discrete habitat patches

provided adequate data for a rigorous examination of metapopulation dynamics using

models with different degrees of sophistication. My specific objectives were (1) to

investigate the relative influence of particular sites and site quality on metapopulation

persistence, (2) to investigate the spatial heterogeneity in demographic rates and its

influence on population dynamics, (3) to determine the relative influence of demographic

rates and the dispersal rate on the metapopulation dynamics, and (4) to compare the

utility of two metapopulation models with different degrees of complexity. This

dissertation is organized into six chapters: a general introduction chapter (Chapter 1),

four manuscript chapters (Chapters 2-5), and a general conclusion chapter (Chapter 6).

In Chapter 2, I parameterized and analyzed a stochastic patch occupancy model

(Moilanen 2004), and investigated the relative influence of particular sites, site quality,

network characteristics, and regional stochasticity on the persistence of the yellow-bellied

marmot metapopulation.

In chapters 3 and 4, I investigated the spatiotemporal variation in local

demographic processes and its influence on the local population dynamics. In Chapter 3,

I investigated the spatiotemporal variation in age-specific survival rates using an age-









structured Cormack-Jolly-Seber model (Lebreton et al. 1992, Lebreton et al. 1993) and

long-term capture-mark-recapture (CMR) data. In Chapter 4, I investigated the

spatiotemporal variation in the components of reproduction; I analyzed stage-specific

breeding probabilities using a multistate CMR model (Hestbeck et al. 1991, Brownie et

al. 1993, Williams et al. 2001, Fujiwara and Caswell 2002) and age-specific litter sizes

using a general linear model. In both chapters, I also tested a series of hypotheses

concerning the effects of key environmental and social factors on the observed variation

in each vital rate. Furthermore, using a Pradel's reverse-time CMR model (Pradel 1996,

Nichols and Hines 2002), I modeled the realized population growth rate for each site and

examined population dynamic consequences of the spatiotemporal variation in each vital

rate.

Chapters 3 and 4 provide robust and detailed estimates of survival and reproductive

rates for each local population. Using these estimates, I parameterized a stage structured

matrix model for each site in Chapter 5, and investigated the demographic causes of

spatial variation in local population dynamics of the yellow-bellied marmot. Next, using a

vector permutation matrix approach (Hunter and Caswell in press) and the dispersal data,

I developed a matrix metapopulation model that connected the local population dynamics

via dispersal. Using this demographically and spatially structured model, I investigated

the relative influence of local demographic rates and the dispersal rate on metapopulation

dynamics.

Finally, Chapter 6 provides a general conclusion of the results presented in the

previous chapters. This research aimed to provide a better understanding of the local and









regional processes that underlay the dynamics of the yellow-bellied marmot

metapopulation, and to provide insights into the utility of different modeling approaches.

The Study System

The yellow-bellied marmot (Marmotaflaviventris) is a large, diurnal, burrow-

dwelling rodent, widely distributed in the mountainous region of the western United

States (Frase and Hoffmann 1980). This research was based on data collected by K. B.

Armitage and his colleagues during a long-term study of marmots in the Upper East

River Valley (2900 m above sea level, 380 57' N 1060 59' W), near the Rocky Mountain

Biological Laboratory, Gunnison County, Colorado (Armitage 1991, Schwartz et al.

1998). Distribution of marmots in the East River Valley is patchy and closely associated

with the local mosaic of meadow and forest vegetation. Marmots typically occupy

meadows associated with talus and large boulders, where they build their burrow systems

(Svendsen 1974). These distinct habitat patches vary in size ranging from satellite sites as

small as 0.01 ha, to colony sites as large as 7.2 ha. Small and lower quality patches

(satellite sites) are typically occupied by a single adult female, her litter, and sometimes

an adult male. Large and higher quality patches (colony sites) are occupied by one or

more matrilines, each typically consisting of one male, two or more closely related adult

females, yearlings (1-year old), and young (Armitage 1991, 1998).

A marmot's circannual cycle has two phases, the active period (approximately 5

months) and hibernation (approx. 7 months), that entail, sequentially, emergence from the

burrow, reproduction, growth, preparation for hibernation, immergence into burrow, and

hibernation (Armitage 1991). The circannual cycle is a major constraint on individual

growth and population dynamics, because the short active season limits reproduction to a

single annual litter and delays reproductive maturity until two years of age. This is









probably the major factor leading to sociality in marmots (Armitage 1981). Marmots

produce a litter of 1 to 8 young that appear above ground around late June. Most young

marmots remain and hibernate at their natal site. Most of the dispersal takes place among

yearlings; almost all of the yearling males and half of the yearling females disperse

beyond their natal site (Schwartz et al. 1998).

Population re-establishment can occur when daughters are recruited into their natal

colonies or an immigrant occupies an empty burrow. Immigration occurs when deceased

residents are not replaced by recruits from within the colony. Matrilineal groups can

exclude potential immigrants, thus securing the site for their progeny (Armitage 2003c).

Thus, the nature of population turnover is strongly influenced by the social system. The

major cost of living in a matrilineal group is reproductive suppression; the dominant,

reproductive females tend to suppress the reproduction in subordinate females (Armitage

1989, 2003c, Oli and Armitage 2003).

Survival and reproduction seem to be affected by the length of the active season,

which varies from year to year (Armitage and Downhower 1974). The main agent of

winter mortality is unsuccessful hibernation, and the main agent of summer mortality is

predation (Van Vuren 1990). The number of males does not substantially affect the

fecundity rates. Yearling males are chased away by the adult male; hence their dispersal

is inevitable. Social tolerance of adults seems to be critical in female dispersal; females

disperse earlier when rates of aggression are high and remain longer when they are low.

Yearlings may assess the probability of future reproductive success and decide to remain

or disperse (Armitage 1991). Detailed biology of yellow-bellied marmots in Gothic,

Colorado, is described in detail by Armitage (1991, 2002). Although a great deal is






8


known about their biology and social system, the relative role of local and regional

processes in determining the dynamics and persistence of the yellow-bellied marmot

metapopulation is unknown.














CHAPTER 2
EFFECTS OF PATCH QUALITY AND NETWORK STRUCTURE ON PATCH
OCCUPANCY DYNAMICS OF A YELLOW-BELLIED MARMOT
METAPOPULATION

The presence/absence of a species at a particular site is the simplest form of data

that can be collected during ecological field studies. We used 13 years (1990-2002) of

survey data to parameterize a stochastic patch occupancy model for a metapopulation of

the yellow-bellied marmot in Colorado, and investigated the significance of particular

patches and the influence of site quality, network characteristics, and regional

stochasticity on the metapopulation persistence. Persistence of the yellow-bellied marmot

metapopulation was strongly dependent on the high quality colony sites, and persistence

probability was highly sensitive to small changes in the quality of these sites. A relatively

small number of colony sites was ultimately responsible for the regional persistence.

However, lower quality satellite sites also made a significant contribution to long-term

metapopulation persistence, especially when regional stochasticity was high. The

northern network of the marmot metapopulation was more stable compared to the

southern network, and the persistence of the southern network depended heavily on the

northern network. Although complex models of metapopulation dynamics may provide a

more accurate description of metapopulation dynamics, such models are data-intensive.

Our study, one of the very few applications of stochastic patch occupancy models to a

mammalian species, suggests that stochastic patch occupancy models can provide

important insights into metapopulation dynamics using data that are easy to collect.









Introduction

Many biological populations occupy spatially heterogeneous environments, and

there is a growing realization that spatially-mediated processes (e.g., dispersal, habitat

connectivity) are vital for the regional persistence of populations. Ecologists are

increasingly relying on metapopulation theory to understand the influence of spatial

heterogeneity on dynamics and persistence of biological populations (e.g., Lankester et

al. 1991, Lahaye et al. 1994, Akcakaya and Atwood 1997, Hokit et al. 2001).

The presence/absence of a species at a particular site is the simplest form of data

that can be collected during ecological field studies (Hanski 1994b). A class of

metapopulation models that capitalizes on such data is the stochastic patch occupancy

models (SPOMs). The theory of SPOMs has been well developed, and these models have

received much practical application (Moilanen and Hanski 1998, Hanski 1999, Moilanen

1999, Moilanen and Cabeza 2002). SPOMs assume that suitable habitat occurs in discrete

patches surrounded by unsuitable matrix and that occupancy of each patch is determined

by local colonization and extinction events. These turnover events are assumed to depend

on factors such as patch area (a proxy for local population size), spatial arrangement of

patches, dispersal ability of the species, and spatially correlated environmental

stochasticity (regional stochasticity). These assumptions are reasonable for many

biological populations inhabiting highly fragmented landscapes, where only a small

portion of the landscape often provides suitable habitat (Hanski and Ovaskainen 2003).

An important question that can be addressed using SPOMs is: what is the relative

significance of particular patches or networks (patch groups) for patch occupancy

dynamics? Intuitively, low quality patches that are poorly connected to other patches will

have lesser influence on metapopulation dynamics than high quality patches that are well









connected. However, low quality patches may, under certain conditions, significantly

influence regional dynamics (Brown 1969, Gill et al. 2001). If there is no significant

contribution of the low quality patches, metapopulation dynamics may depend only on

the high quality patches, and the interactions between high and low quality patches may

resemble source-sink (Pulliam 1988, Pulliam and Danielson 1991) or mainland-island

dynamics (Schoener 1991). The importance of a particular patch (or network) can be

investigated by comparing simulated patch occupancy dynamics with and without that

patch (or network). Previous studies have observed that persistence of a particular patch

network may depend on the presence of other networks (e.g., Moilanen et al. 1998).

SPOMs have mostly been used to model the metapopulation dynamics of large

invertebrates or small vertebrates. The preference for small-bodied habitat specialists is

dictated by the criteria of regional persistence as a classical metapopulation: high rate of

population increase, short generation time, and high habitat specificity (Murphy et al.

1990, Hanski 1999). However, some mammal populations that occupy discrete habitat

patches also exhibit characteristics of metapopulations, and SPOMs can be applied to

such populations as well (e.g., Moilanen et al. 1998).

A mammal species that meets the assumptions of the SPOMs is the yellow-bellied

marmot, Marmotaflaviventris (Audubon & Bachman 1841). Yellow-bellied marmots

occupy discrete habitat patches that vary in quality (Svendsen 1974), and populations can

go locally extinct and be recolonized by individuals from surrounding patches (Svendsen

1974, Armitage 2003b). Although there is a gradient from low quality to high quality

sites, marmot habitats can be grouped into two major quality types: (1) colony (high

quality), and (2) satellite (low quality) sites. The persistence of the metapopulation is









believed to be dependent mainly on the colony sites, but the relative influence of colony

and satellite sites on the marmot metapopulation dynamics is unknown.

In this study, we used long term (1990-2002) patch occupancy data and a SPOM to

investigate metapopulation dynamics of yellow-bellied marmots in the Upper East River

Valley near the Rocky Mountain Biological Laboratory, Colorado (hereafter referred to

as Colorado). Specifically, we investigated the relative influence of particular sites, site

quality, network characteristics, and regional stochasticity on the persistence of the

yellow-bellied marmot metapopulation.

Materials and Methods

Study Area and Species

The yellow-bellied marmot is a large, diurnal, burrow-dwelling rodent, widely

distributed in the mountainous region of the western United States (Frase and Hoffmann

1980). Marmots typically occupy meadows with talus and large boulders, under which

they dig their burrow systems (Svendsen 1974). The distribution of marmots in Colorado

is patchy (Fig. 2-1) and is closely associated with the local mosaic of meadow and forest

vegetation. The distinct habitat patches vary in size, ranging from 0.01 ha to 7.2 ha (K. B.

Armitage, unpublished data). However, the density of marmots varied remarkably among

sites, and local patch area does not necessarily represent the local population size

(Armitage and Schwartz 2000). We use the term "site quality" to describe the combined

effect of multiple environmental factors (including patch area) on local population size.

Satellite sites (lower quality patches) are typically occupied by a single adult female, her

litter, and sometimes an adult male. Colony sites (higher quality patches) are occupied by

one or more matrilines, each typically consisting of one male, two or more closely related

adult females, yearlings (1 year old), and young (Armitage 1991, 1998).









Typically, all yearling males and about half of the yearling females disperse (Van

Vuren 1990, Schwartz et al. 1998). Recolonization occurs when an immigrant occupies

an empty habitat patch. Matrilineal groups can exclude potential immigrants unless all

individuals die and the habitat patch is empty, thus reducing the chance of a 'true' rescue

effect (Armitage 1991, 2003b). Local extinction occurs when a matriline dies out or

deserts a site. However, local turnover events can be concealed by the immediate

occupation of an empty site by immigrants, thus creating an 'apparent' rescue effect. The

detailed biology of yellow-bellied marmots in Colorado is described by Armitage (1991,

2002).

Although the number of patches in the yellow-bellied marmot metapopulation in

Colorado is smaller than that observed in some studies, our study system meets the four

conditions of regional persistence as a metapopulation (Murphy et al. 1990, Hanski et al.

1995). First, marmots live in spatially discrete habitat patches. Their burrow systems are

typically located in open meadow patches with rocky outcrops (Svendsen 1974).

Philopatric marmots rarely go >50 m away from burrows because of the predation risk.

Second, all local populations face the risk of local extinction in the absence of a rescue

effect. The average population size of the largest colony is approximately 20 animals, and

local extinction is possible due to predation, disease, environmental and demographic

stochasticity or catastrophes. Third, the probability of survival during dispersal decreases

with the distance moved (Van Vuren 1990). Therefore, low survival of the long-distance

dispersers can result in a distance-dependent dispersal. Finally, the local population

dynamics are sufficiently asynchronous (Armitage and Downhower 1974, Armitage

1977, 2003b, Oli and Armitage 2004). Asynchrony in local population dynamics









increases the probability that an extinct local population is reestablished, or a declining

population is rescued by dispersers from other local populations (Hanski et al. 1995).

Therefore, the yellow-bellied marmot system provides one of the few examples of

naturally occurring mammalian metapopulations to which SPOMs can be applied (e.g.,

Bryant 1998, Moilanen et al. 1998, Stephens et al. 2002).

Model Structure

We used Program SPOMSIM (Moilanen 2004) to parameterize and simulate a

SPOM for the yellow-bellied marmot metapopulation. SPOMSIM is a computational

modeling tool designed for the parameterization and analysis of SPOMs. In SPOMSIM,

subfunctions can be chosen for describing the dispersal kernel, connectivity function,

colonization probability, extinction probability, and rescue effect (Moilanen 2004).

The shape of the dispersal kernel is important only when the metapopulation

consists of several small networks that are far from each other, which was not the case in

our system. Therefore, we used the simple negative exponential function for describing

the dispersal kernel:

D(d a) = exp(-ad) (1)

where d, is the distance between patches i andj, and a is the distribution parameter of the

dispersal distances (/ a= average dispersal distance).

For the connectivity function, we used the subfunction that includes the effect of

local patch area (patch quality in this study) on connectivity:

S,(t) = Ai c O, (t)DAc (2)


where 0,(t) is the occupancy status of each patch at time t, D is the dispersal kernel (Eq.









1), and A, is the quality of patch i. Parameter b scales emigration, and parameter c scales

immigration as a function of patch quality (Moilanen and Nieminen 2002).

Moilanen (2004) recommends that the choice of the colonization function be based

on the biology of the studied species. Because marmot colonies typically contain only

few individuals, we used the subfunction that includes the Allee effect in colonization

(Hanski 1994b):

[S, (t)]2
C, (t) [ ]2 (3)
[S, (t)]2 + 2

where S,(t) is the connectivity of patch i at time t (Eq. 2), andy is a model parameter.

For the extinction function, we used two alternative subfunctions, one that was

used in the incidence function model (IFM) and the other in spatially realistic Levin's

model (SRLM):


E, = (IFM) (4)


Ax
E= 1- exp| | (SRLM) (5)


where / is the extinction probability of a patch of unit size, and parameter x scales the

extinction risk as a function of patch area (for a discussion see Foley 1997).

The rescue effect can be included in the SPOM, and it essentially decreases the

extinction probabilities of well-connected patches. We used the generalized version of the

rescue effect function to determine the strength of the rescue effect:

E (t) = min{l, (1 C,(t))R E } (6)

where parameter R determines the strength of the rescue effect.









Different models with alternative combinations of connectivity and extinction

functions were parameterized and the most parsimonious model was identified using

Akaike's Information Criterion corrected for small samples, AIC, (Burnham and

Anderson 2002, Grimm et al. 2004).

Parameter Estimation

SPOMs can be parameterized with survey data from a single year; however, data

from several years provide more robust estimates of parameters (Moilanen 1999). A

long-term study in Colorado has provided occupancy data for most sites; however, some

sites were not surveyed every year (Armitage 1991, Schwartz et al. 1998). We used data

from 21 known sites surveyed between 1990 and 2002 to parameterize the SPOMs, as

this period provided the most complete occupancy information (Fig. 2-2).

In SPOMs, patch area is often used to indicate local population size. This indicator

is based on the assumption that as the patch area increases, local population size

increases, hence the local extinction risk decreases. Patch area is preferred by many

authors, because estimating area is generally easier than estimating local population size

or other measures of patch quality. However, the density of marmots varied remarkably

among sites. We used the average number of adult females per site (conditional on

occupied years) as a measure of patch quality, because it was a more accurate measure of

local population size than was patch area.

Where possible, independent estimation of model parameters is preferable in order

to reduce the number of parameters to be estimated from site occupancy data (Hanski

1999). Parameter a of the dispersal kernel was estimated using independent dispersal

data, while the remaining model parameters (b, c, y, /, x, and R) were estimated from the









site occupancy data using the Markov Chain Monte Carlo method (Moilanen 1999).

Analysis of local population dynamics during the last 40 years did not reveal any

significant trend in population sizes (Schwartz et al. 1998, Schwartz and Armitage 2003,

Oli and Armitage 2004). Therefore, it was reasonable to assume that the yellow-bellied

marmot metapopulation was at a stochastic quasi-equilibrium.

Model Simulation

Metapopulation dynamics were simulated using the most parsimonious model

which was selected based on AIC, as described above. Each scenario was simulated 1000

times for 100 years. Model predictions included changes in average proportion of

occupied patches and proportion of simulated replicates that survived throughout 100

years, and average metapopulation lifetime (Hanski 1994b, Moilanen et al. 1998).

Influence of site quality and network structure. We classified each habitat patch

either as a colony site or a satellite site based on the average number of adult females.

Nine sites that had > 1 adult female on average were designated as colony sites, and 12

sites that had < 1 adult female on average as satellite sites.

Using the most parsimonious model, we simulated three alternative scenarios: (1)

colony sites excluded, (2) satellite sites excluded, (3) original configuration. Predictions

of alternative models on metapopulation persistence were compared to assess the relative

influence of colony and satellite sites on the overall metapopulation dynamics (e.g.,

Hanski 1994a).

The Colorado yellow-bellied marmot metapopulation can be divided into two

networks, the northern and the southern network, which are separated by areas of

unsuitable habitat. The most parsimonious model was used to simulate three alternative

scenarios: (1) northern network, (2) southern network, and (3) entire network. The









predictions of alternative models on metapopulation persistence were compared to assess

the significance of compartmentalization among sites (e.g., Moilanen et al. 1998).

Significance of regional stochasticity. Spatial correlation in environmental

stochasticity (regional stochasticity) can heavily influence metapopulation persistence

(Hanski and Ovaskainen 2003). Regional stochasticity is included in SPOMSIM based on

log-normal variation in patch area, which creates a yearly synchronous variation in both

extinction and colonization rates (Moilanen 2004). The standard deviation (o) of this

variation quantifies the level of synchrony. The level of regional stochasticity could not

be directly estimated; therefore, we used two levels of regional stochasticity (o = 0.1 &

0.2) and analyzed the sensitivity of model predictions to regional stochasticity.

Adequacy of the SPOM

We used the robust design occupancy modeling approach (MacKenzie et al. 2002,

MacKenzie et al. 2003) to investigate the adequacy of the SPOM used for simulations of

the yellow-bellied marmot system. The robust design occupancy model uses occupancy

data and provides a framework for estimating the rate at which occupied sites go extinct

(E) and the rate at which unoccupied sites are recolonized (y). We used program MARK

V 4.0 (White and Burnham 1999) to implement the robust design occupancy model with

parameters Vr(proportion of sites occupied), e (probability of an occupied site becoming

unoccupied), y (probability of an unoccupied site becoming occupied), and p (detection

probability on a visit to the site) (MacKenzie et al. 2002, MacKenzie et al. 2003). Robust

design occupancy models implemented in program MARK provides more flexibility in

modeling recolonization and extinction probabilities, and allows comparison of several

alternative model structures that are not included in SPOMSIM.









Program MARK can be used to estimate time-specific rates of extinction and

colonization, and time-varying individual covariates can be used to incorporate site-

specific information into the model. We estimated the site- and time-specific extinction

and colonization rates for 21 sites for 13 years using the most parsimonious SPOM. We

used these estimates as time-varying site covariates for estimating E and parameters

using MARK. Years for which the occupancy status was unknown were treated as

missing values. Because we did not have >1 sample occasion per year, we assumed that

there were no false zeros (indicating that the site was not occupied) in our occupancy

history, and set our detection probability parameter (p) to 1.0. Considering the

conspicuousness of the presence of marmots at a given site and the high intensity of

observation efforts, we believe that this is a reasonable assumption.

We used AIC, for model comparison, and for the identification of the most

parsimonious model in the candidate model set. Candidate models differed in the way

parameters E and were modeled. We used four alternative model structures for

modelling extinction rate, e. First, we modelled e as a constant rate {E(.)}. Second, we

modelled e as a time-specific rate and let it vary among years { (t)}. Third, we let

E vary among sites and used site quality as a constant site covariate { (Q)}. Finally, we

used the extinction rate estimated from SPOM as a time-varying site covariate { (E)}.

We also used four alternative model structures for modelling recolonization rate, y

Similar to E, we initially modelled yas a constant {y(.)} and a time-specific {y(t)} rate.

Then, we let y vary among sites and through time, and used the colonization {y(C)} and

connectivity {y(S)} parameters estimated from SPOM as time-varying site covariates.

We expect the models in which the time-varying site covariates (estimated from SPOM)









were used as predictors of extinction and recolonization rates to be more parsimonious

than the time-specific or constant recolonization and extinction rate models.

Results

Parameter Estimation

We used independent dispersal data from 90 radio-instrumented marmots (Van

Vuren 1990) to estimate the dispersal kernel parameter, a. The average dispersal distance

was 2.087 km, and a was estimated as the inverse of the average dispersal distance (a=

1/(2.087) = 0.479). To evaluate the robustness of our estimate, we set a as a free

parameter in SPOMSIM, and estimated it from patch occupancy data. This method gave

an estimate of 0.337, which was slightly smaller than our independent estimate. These

estimates indicated fairly high dispersal ability, which was consistent with previous field

observations (Van Vuren 1990). We performed simulations using both values of a, and

found that the qualitative conclusions remained unchanged. Here, the independent

estimate of a (0.479) was used for parameterizing the dispersal subfunction and

simulation of alternative scenarios. The remaining model parameters were estimated

using the 13 year occupancy data (Fig. 2-2) and the Markov Chain Monte Carlo

estimation technique provided in SPOMSIM.

We used AIC, weights to select the best model from a set of 8 candidate models

(Table 2-1). The most parsimonious model (model #5 in Table 2-1) included the

following subfunctions:

* Negative exponential function (Eq. 1) for describing the dispersal kernel (a fixed at
0.479).

* Connectivity function that included the effect of local patch quality (Eq. 2).

* Colonization function with the Allee effect in colonization (Eq. 3).









* Extinction function from the original IFM (Eq. 4).

* Rescue effect with parameter R (strength of the rescue effect) fixed at 1.0 (Eq. 6).

The differences in AIC, values between the best model (model # 5) and other

alternative models were more than 2 except in two cases: model # 1 (original IFM) and

model # 7 (Table 2-1). The model structure of the best model (model # 5) differed from

that of original IFM (model # 1) in that model # 5 included the effect of local patch

quality on connectivity by including the model component A," (in Eq. 2). Despite the

small differences in AIC, values, we used model with the smallest AIC, value (model #

5) for simulating metapopulation dynamics. Parameter values of the most parsimonious

model are given in Table 2-2.

Scaling of extinction risk with patch quality, parameter x, was in the higher end of

the typical range (0.5 < x < 1.5: Moilanen 2004), indicating that local extinction

probability decreased rather quickly with increasing population size. The intrinsic

extinction probabilities for the smallest (0.3 adult females on average), average (1.3 adult

females) and largest (3.8 adult females) patches were 0.78, 0.08 and 0.02, respectively.

Incidentally, value ofx estimated for the yellow-bellied marmots was very close to the

one estimated for the American pika, Ochotonaprinceps (Moilanen et al. 1998).

Scaling of emigration with patch quality was weak (b < 0.2), indicating that quality

of a patch did not substantially influence the emigration rate. Scaling of immigration with

patch quality was in the typical range (c < 0.5), indicating that local patch quality had a

significant influence on the immigration rates (Moilanen 2004).

Model Simulation

The patch occupancy dynamics of the yellow-bellied marmot metapopulation was

simulated using the most parsimonious model (model #5 in Table 2-1) with the parameter









estimates given in Table 2-2. For all simulations, the average proportion of occupied

patches and the proportion of surviving simulation replicates were reported for two

different levels of regional stochasticity (c-= 0.1 and o= 0.2).

As expected, simulations of the entire network showed equilibrium dynamics at the

lower regional stochasticity, and higher regional stochasticity did not have a significant

effect on long-term metapopulation persistence (Fig. 2-3A). To understand the influence

of site quality on metapopulation persistence, we simulated sites of each quality type

separately. The average proportion of occupied patches in nine colony sites showed a

rapid decline followed by a long period of stability, in the absence of satellite sites (Fig.

2-3B). Despite their lower quality, satellite sites seemed to contribute to the overall

metapopulation persistence. When regional stochasticity was low, 12% of the simulated

replicates went extinct within 100 years, whereas 20% went extinct when regional

stochasticity was high. In the absence of the satellite sites, average persistence time of the

metapopulation decreased from infinity to 2481 years.

Absence of colony sites significantly altered the overall metapopulation

persistence. Even at the lower level of regional stochasticity, the proportion of occupied

patches declined very rapidly to zero within 30 years. None of the simulated replicates

survived past 40 years in the absence of the colony sites (Fig. 2-3C). Average persistence

time of the metapopulation that included only 12 satellite sites was only 10 years.

To evaluate the sensitivity of patch occupancy dynamics to changes in the quality

of colony sites, we gradually reduced the quality of each colony site, and simulated patch

occupancy dynamics using the new values. Our simulations showed that a 20% decline in

quality of colony sites significantly affected regional persistence. The proportion of









occupied patches declined to 60% at the end of 100 years at the lower regional

stochasticity, whereas, it declined to 46% at the higher regional stochasticity (Fig. 2-4A).

At lower regional stochasticity, 96% of the simulated replicates persisted at the end of

100 years, whereas, at higher regional stochasticity, only 80% persisted (Fig. 2-4A). This

20% reduction in the quality of colony sites resulted in a decrease in average

metapopulation life time from infinity to 3254 years.

These results indicated that persistence of the yellow-bellied marmot

metapopulation in Colorado heavily depended on the quality of a few colony sites. To

analyze the influence of these high quality sites on metapopulation persistence, we

repeated the simulations by excluding one, two, three, and four of the highest quality sites

(Fig. 2-1). Simulations with the low level of regional stochasticity showed that the

metapopulation persistence was relatively unaffected by the absence of the two best

quality sites (Fig. 2-4B,C). However, in the absence of the best three sites, site occupancy

gradually declined to 42%, and 15% of the simulated replicates went extinct within 100

years (Fig. 2-4B,C). In the absence of the best four sites, the metapopulation was no

longer persistent; the proportion of occupied patches rapidly declined, and only 45% of

the simulated replicates persisted for 100 years (Fig. 2-4B,C).

We used connectivity-based clustering analysis available in SPOMSIM to test for

the existence of hierarchical network structure of the metapopulation in terms of

connectivity between networks (Moilanen 2004). This analysis revealed the existence of

two networks: upper-valley (northern) and lower-valley (southern) networks (Fig. 2-1),

which was also consistent with our biological understanding of the marmot system. Thus,

we examined the differences in the dynamics of these two networks. The metapopulation









in the northern network was more stable than the southern network. The proportion of

occupied patches in the northern network did not decline during 100 years of simulations

either under low or high regional stochasticity levels (Fig. 2-5A). On the other hand, the

southern network was very unstable, and the proportion of occupied patches frequently

declined to zero (Fig. 2-5B). Very few of the simulated replicates survived till the end of

100 years (Fig. 2-5B).

We repeated our simulations using values sampled from the 95% confidence

interval of parameter estimates, and each replicate was run with the new set of parameter

values. Our previous results remained unchanged, indicating that our results were fairly

robust to small changes in the parameter values.

Adequacy of the SPOM

To investigate the adequacy of SPOM for the yellow-bellied marmot system, we

compared a set of candidate models using the robust design occupancy modeling

approach (Tables 2-3 and 2-4). In general, including time-specific, but not site-specific,

variation in colonization and extinction rates resulted in poor model likelihood (Table 2-

4). Models with constant colonization and extinction rates had higher likelihood

compared to time-specific models that ignored site-specific differences. Model

likelihood were significantly improved when time- and site-specific extinction

probabilities estimated using the SPOM were included as covariates. The models that

included connectivity or colonization parameters as covariates did not significantly differ

from constant colonization rate models (first three models in Table 2-4). Nonetheless,

two models with SPOM-predicted colonization rates were among the best models. These

findings indicated the adequacy of the SPOM for modeling the dynamics of the yellow-

bellied marmot metapopulation.









Discussion

Our study suggests that (1) persistence of the yellow-bellied marmot

metapopulation strongly depends on the colony sites. (2) Overall metapopulation

persistence was highly sensitive to small changes in number and quality of colony sites.

(3) Lower quality sites contributed to the long-term persistence of the yellow-bellied

marmot metapopulation, especially when the regional stochasticity was high. (4) The

northern network was more stable compared to the southern network, and the persistence

of the southern network strongly depended on the northern network.

Previous studies indicated that colony sites generally are more persistent than

satellite sites mainly because of the fact that colony sites are occupied by matrilines that

may persist for many generations (Armitage and Downhower 1974, Armitage and

Schwartz 2000, Armitage 2003b). Increased matriline sizes improve the persistence of

the local population by affecting survival and net reproductive rate (Armitage and

Schwartz 2000, Armitage 2003b). Consistent with these observations, our results suggest

that colony sites are the major drivers of the yellow-bellied marmot metapopulation

dynamics, and that the quality of these sites was especially important; a small decline in

site quality resulted in a significant decline in metapopulation persistence. Also, a small

number of colony sites might be ultimately responsible for the metapopulation

persistence. The dependence of metapopulation persistence on a small number of high

quality sites has been suggested to be a general rule in long-lived species (Harrison 1991,

Schoener 1991), and has been observed in American pika, Ochotonaprinceps (Moilanen

et al. 1998), a species that shares similar life-history characteristics. These results

emphasize the importance of local site quality, and of environmental factors that may

influence local site quality, for metapopulation persistence.









Local population sizes of yellow-bellied marmots can fluctuate remarkably over

time (Armitage and Downhower 1974, Schwartz et al. 1998, Oli and Armitage 2004).

These fluctuations can occur at a local scale due to factors such as predation (Van Vuren

2001, Armitage 2004), or at the regional scale due to regional fluctuations in

environmental conditions (Armitage 1994, 2003b). Regional factors influencing local

population dynamics are explicitly considered in the stochastic patch occupancy

modeling approach; however, local population dynamics are assumed to be insignificant

and generally overlooked (Hanski 1999). Given that the yellow-bellied marmot

metapopulation persistence is highly sensitive to changes in the quality of a few colony

sites, a complete understanding of marmot metapopulation dynamics likely requires

consideration of factors and processes that influence the dynamics of local populations.

Overall, however, SPOM provided a reasonable description of the dynamics of the

marmot metapopulation.

Although the colony sites rarely went extinct during our study period, there remains

a possibility that factors such as predation, disease, and demographic stochasticity can

cause local extinctions of colony sites in the long-term. Despite the high importance of

colony sites for regional persistence, our results suggest that lower quality satellite sites

may also contribute markedly to the long-term persistence of the yellow-bellied marmot

metapopulation. The risk of metapopulation extinction increases in the absence of the

satellite sites, especially when the fluctuations in site qualities are regionally

synchronous. Although satellite sites are much lower in quality than colony sites, they

create a buffer effect (Brown 1969, Gill et al. 2001) by increasing connectivity among

colony sites and providing temporary sources of recolonization when surrounding colony









sites locally go extinct. Observed importance of lower quality sites for the regional

dynamics suggests that the yellow-bellied marmot system is not a perfect mainland-island

system as suggested for other long-lived species (Harrison 1991, Schoener 1991), and it

shows characteristics of a metapopulation in which the extinction-recolonization

dynamics play an important role. Ignoring the relative role of satellite sites and

considering only dynamics of colony sites can lead to underestimation of metapopulation

extinction probability.

Patch occupancy dynamics in two networks indicated that the northern network

was more stable and likely to persist longer than the southern network. Moreover, in the

absence of the northern network the southern network was unlikely to persist. The

observed difference between the persistence of the two networks was largely due to the

difference in the number of higher quality sites; the northern network included 6 colony

sites, whereas the southern network included only 3 colony sites. This observation is

consistent with our results that the number and quality of colony sites were the most

important factors affecting regional persistence of the yellow-bellied marmot

metapopulation. These findings emphasize the importance of a few sites that act as a

connection between the two networks for metapopulation persistence.

Moilanen and Nieminen (2002) found that including the effect of local patch area

in SPOMs significantly improved the connectivity measure. In our study, the model that

included the effect of local patch quality in the connectivity measure had a slightly better

likelihood compared to alternative models including the original IFM, which ignored the

effect of local patch quality on connectivity (Hanski 1994b). To investigate the

differences between the predictions of the SPOM used in this study and IFM, we repeated









the simulations with the parameterized IFM. Simulation results were qualitatively very

similar to those of our original SPOM, but IFM predicted a higher contribution of

satellite sites to metapopulation persistence. In the absence of satellite sites, IFM

predicted substantially lower persistence of colony sites compared to those predicted by

the SPOM used in this study. Including local patch quality in the estimation of the

connectivity parameter increased the connectivity of higher quality sites, hence the

overall persistence of the colony sites as well as of the entire metapopulation.

We assumed that the yellow-bellied marmot metapopulation was a discrete

metapopulation with no connections to populations outside the study area. However, this

assumption is unlikely to be correct. Based on 10 years of radiotelemetry study (Van

Vuren 1990) and 41 years of intensive survey (Armitage 1991, Schwartz et al. 1998), we

are confident that all major marmot sites inside or within close proximity of our study

area are included in our analyses. However, immigration into and emigration out of the

study metapopulation did occur (Van Vuren 1990). Ignoring the connectivity of the

yellow-bellied marmot metapopulation to outside of the study area can result in an

overestimation of colonization ability, hence in an overestimation of regional persistence

(Moilanen 2002). It is also important to note that we assumed a detection probability of

1.0 during our analyses; however, it may be an unrealistic assumption for some of the

remote satellite sites that have been surveyed less frequently. False zeros in these sites

can result in slight overestimation of the intrinsic extinction rates, dispersal distances and

colonization ability (Moilanen 2002). Therefore, our measures of persistence are not

conservative, and should be interpreted with caution.









Finally, we utilized the robust design occupancy modeling approach to test the

adequacy of the SPOM used for simulations of the yellow-bellied marmot system. We

found that colonization and extinction events varied among sites; thus, an important

assumption of the classical metapopulation model (Levins 1969) was not appropriate for

the yellow-bellied marmot metapopulation. Considering site-specific connectivity

measures and extinction probabilities estimated using the SPOM significantly improved

the likelihood of the resulting model. Therefore, we believe that the SPOM adequately

described the site occupancy dynamics of the yellow-bellied marmot metapopulation.

Our study is one of the first studies to use the robust design occupancy modeling

approach to test the adequacy of a SPOM. We suggest that this approach could be utilized

rather easily in other studies as well.

Behavioral interactions among individuals can influence population dynamics of

social organisms (Grimm et al. 2003). The yellow-bellied marmot is a socially complex

species (Blumstein and Armitage 1999, Armitage and Schwartz 2000), and an accurate

description of the dynamics of marmot metapopulations may thus necessitate models that

can incorporate behavioral interactions among individuals. However, models that allow

explicit consideration of behavioral interactions (e.g., individual-based models) are

structurally complex and data-intensive. Although models that consider behavioral

interactions should be preferred when data are available to parameterize such models, it is

important to know what we can learn about dynamics and persistence of a population by

analyzing models with simple data requirements. For many species, data to parameterize

more complex models are usually lacking and simple models like SPOMs or robust

design patch occupancy models are the only option. Ovaskainen and Hanski's (2004)









findings that SPOMs adequately mimic the behavior of more complex models are

encouraging to those who lack detailed demographic and behavioral data to parameterize

individual-based models. Patch occupancy models are frequently applied to modeling

metapopulation dynamics of many invertebrates (e.g., Kuussaari et al. 1996, Wahlberg et

al. 1996, Appelt and Poethke 1997, Biedermann 2000, Kindvall 2000), but the

application of such models to avian or mammalian metapopulations are clearly

underrepresented (see Moilanen et al., 1998 for an exception). This study provides one of

the very few applications of SPOMs as well as robust design occupancy models to study

the dynamics and persistence of mammalian metapopulations.

In conclusion, this study demonstrated that the dynamics of yellow-bellied marmot

metapopulation mainly depended on a few colony sites, and the regional persistence was

highly sensitive to changes in the quality of these sites. Nonetheless, satellite sites made

an important contribution to the long-term persistence of the yellow-bellied marmot

metapopulation. Given the high sensitivity of metapopulation persistence to local

population size, future studies of the yellow-bellied marmot metapopulation should also

consider local population dynamics. Nonetheless, our analyses based on simple site

occupancy data provided an adequate description and several useful insights regarding

the dynamics and persistence of the yellow-bellied marmot metapopulation.









Table 2-1. Models and subfunction definitions used in SPOMSIM, and Akaike's
Information Criterion values corrected for small sample size (AICc), number
of parameters (#par) and model likelihood. Connectivity function parameter c
was fixed at "0" for the models without the effect of local patch, and it was set
as a "free" parameter for the models with the effect of local patch. "IFM" is
extinction probability function used in the original incidence function model,
and "SELM" is the one used in the spatially explicit Levin's model.
Subfunction for the rescue effect was modeled with R (strength of the rescue
effect) fixed at "1", and R set as a "free" parameter during parameter
estimation.

Model c Extinction probability R AIC, AAIC, # par Model likelihood

1 0 IFM 1 161.4 0.8 5 0.670
2 0 IFM Free 162.8 2.2 6 0.333
3 0 SELM 1 162.7 2.1 5 0.350
4 0 SELM Free 164.7 4.1 6 0.129
5 Free IFM 1 160.6 0.0 6 1.000
6 Free IFM Free 162.6 2.0 7 0.368
7 Free SELM 1 161.4 0.8 6 0.670
8 Free SELM Free 163.5 2.9 7 0.235









Table 2-2. Markov Chain Monte Carlo estimates of the parameters for the best stochastic
patch occupancy model (model #5 in Table 2-1). The 95% confidence
intervals for the parameters that are independently estimated are given as
"fixed". The a is the dispersal function parameter, b and c are the
connectivity function parameters, y is the colonization function parameter, u
and x are the extinction function parameters, and R is the rescue effect
function parameter.
Model parameters Estimates 95% CI
a 0.479 fixed
b 0.056 0.000 0.283
c 0.351 0.088 0.398
y 6.579 6.579 8.570
u 0.127 0.094 0.128
x 1.465 1.445 -1.859
R 1 fixed









Table 2-3. Definition of robust design occupancy models used for modeling colonization
(y) and extinction (s) probabilities.
Notation Biological significance
E (.) constant extinction rate
E (t) time-specific extinction rate
e (Q) extinction rate with site quality as a constant site covariate
E (E) extinction rate with extinction* as a time-varying site covariate
y(.) constant colonization rate
y(t) time-specific colonization rate
y(C) colonization rate with colonization* as a time-varying site covariate
y(S) colonization rate with connectivity* as a time-varying site covariate
Estimated using the parameterized stochastic patch occupancy model.









Table 2-4. Number of parameters (#Par), Akaike's Information Criterion corrected for
small sample size (AICc), deviances, and model likelihood for the robust
design occupancy models fitted to the yellow-bellied marmot data. Parameters
E and 7 are the extinction and colonization rates, respectively. Initial
occupancy rate ('F) was estimated as a constant rate, and detection probability
(p) was set to 1 in all models. For model definitions see Table 2-3.


Deviance
143.7
148.1
144.5
150.1
154.4
150.8
165.3
166.2
170.5
149.3
151.6


AAIC,
0
0.5
0.8
6.3
6.8
7
17.8
18.7
19.7
123.9
126.2


Model likelihood
1.00
0.75
0.67
0.04
0.03
0.03
0
0
0
0
0


Model
E(E) y(S)
E(E) (.)
E(E) (C)
e(Q) y(S)
E(Q) 0(.)
e(Q) (C)
E(.) y(S)
(.) y(C)
E(.) 7(.)
E(.) (t)
E(t) (.)


# Par
5
4
5
5
4
5
4
4
3
14
14


AIC,
158.4
158.9
159.2
164.7
165.2
165.4
176.2
177.1
178.1
282.3
284.6





























2


1


0
0


Northern Network


4

42

*'


Southern Network


*3


IiL~2J


East-west distance (km)

Figure 2-1. The structure of the yellow-bellied marmot metapopulation in Colorado.
Diameters of circles are proportional to the estimated quality of each site.
Four highest quality sites are indicated with numbers. The figure also shows
the division of the metapopulation into northern and southern networks.









100


unknown

empty




occupied


Year


Figure 2-2. Yearly proportions of occupied patches, empty patches, and patches with
unknown occupancy status, for the period between 1990 and 2002.


,~,~:~~~~~Ps~b~'~"~p~









1.0 ------ --- -



0.4 -- -
P0.6
0.4









-2 sAites
1.0 -



P 0.



0.4






0.2
C
0 20 40 60 80 100
Year

Figure 2-3. Predicted patch occupancy in 1000 replicate simulations of the yellow-bellied
marmot metapopulation using the parameterized stochastic patch occupancy
model. Confidence intervals (95%) for the proportion of occupied patches in
all sites (A), colony sites only (B), and satellite sites only (C) are given as
solid lines. Proportion of surviving replicates for all sites (A), in only colony
sites (B), and in only satellite sites (C) are given as dashed lines. Simulation
results with regional stochasticity set at 0-= 0.1 are shown as black lines, and
for c= 0.2 are shown as gray lines.










1.0
0.8
P 0.6
0.4
0.2


1.0
0.8
P 0.6
0.4
0.2


1.0
0.8
P 0.6
0.4
0.2


All sites
----------------------






A

Colony sites


-- --


Satellite sites


0 20 40 60 80 100
Year

Figure 2-4. Predicted patch occupancy in 1000 replicate simulations (A) when the quality
of colony sites was reduced by 20%, and (B, C) when 1, 2, 3, and 4 highest
quality colony sites were excluded from the network. These sites are indicated
in Fig. 2-1. Confidence intervals (95%) for the proportion of occupied patches
are given as solid lines. Proportion of surviving replicates are given as dashed
lines. Simulation results with regional stochasticity set at 0 = 0.1 are shown as
black lines, and for a= 0.2 are shown as gray lines.















1.0
0.8
P0.6
0.4
0.2



1.0
0.8
P 0.6
0.4
0.2


Upper-valley network


Lower-valley network


0 20 40 60 80 100
Year

Figure 2-5. Predicted patch occupancy in 1000 replicate simulations for the northern and
southern networks. Confidence intervals (95%) for the proportion of occupied
patches in the northern (A) and the southern (B) network are given as solid
lines. Proportion of surviving replicates in the northern (A) and the southern
(B) network are given as dashed lines. Simulation results with regional
stochasticity set at = 0.1 are shown as black lines, and for = 0.2 are shown
as gray lines.


- ---- ---A--

A














CHAPTER 3
SPATIOTEMPORAL VARIATION IN AGE-SPECIFIC SURVIVAL RATES OF THE
YELLOW-BELLIED MARMOT

Spatiotemporal variation in age-specific survival rates can profoundly influence

population dynamics, but few studies of vertebrates have thoroughly investigated both

spatial and temporal variability in age-specific survival rates. We used 28 years (1976 -

2003) of capture-mark-recapture (CMR) data from 17 locations to parameterize an age-

structured Cormack-Jolly-Seber model, and investigated spatial and temporal variation in

age-specific annual survival rates of yellow-bellied marmots (Marmotaflaviventris).

Survival rates varied both spatially and temporally, with survival of younger animals

exhibiting the highest degree of variation. Juvenile survival rates (mean SE) varied

from 0.52 0.05 to 0.78 0.10 among sites and from 0.15 0.14 to 0.89 0.06 over

time. Adult survival rates varied from 0.62 0.09 to 0.80 + 0.03 among sites, but did not

vary significantly over time. We used reverse-time CMR models to estimate the realized

population growth rate (k), and to investigate the influence of the observed variation in

age-specific survival rates on X. The realized growth rate of the population closely

covaried with, and was significantly influenced by, spatiotemporal variation in juvenile

survival rate. High variability in juvenile survival rates over space and time clearly

influenced the dynamics of our study population, and is also likely to be an important

determinant of the spatiotemporal variation in the population dynamics of other mammals

with similar life history characteristics.









Introduction

Populations inhabiting spatially heterogeneous landscapes are influenced by

multiple environmental factors that vary over space and time (Orzack and Tuljapurkar

1989, Tuljapurkar 1990, Post et al. 1997). Such spatiotemporal variation in

environmental factors can cause differences in vital demographic rates, and these

differences can significantly influence the dynamics, regulation, and persistence of

populations (Kareiva 1990, Pulliam and Danielson 1991, Tilman and Kareiva 1997).

Survival is a crucial demographic parameter influencing population growth rate,

and thus the population dynamics, of many populations (Stearns 1992, Pfister 1998,

Heppell et al. 2000, Saether and Bakke 2000, Oli and Dobson 2003), and it can be

influenced by spatiotemporal variation in factors such as weather, habitat quality, disease,

competition and predation (e.g., Jorgenson et al. 1997, Coulson et al. 1999, Coulson et al.

2000, Farand et al. 2002). Although several studies have examined the causes and

population dynamic consequences of temporal variation in survival (e.g., Francis 1995,

Saether 1997, Coulson et al. 2000, Blums et al. 2002, Oli and Armitage 2004), less

attention has been paid to the influence of spatial heterogeneity on this important

demographic parameter. Nonetheless, a significant spatial variation in survival has been

reported for a number of species. For example, Coulson et al. (1999) observed spatial

differences in survival rates among local populations of Soay sheep (Ovis aries). Waser

et al. (1995) attributed spatial differences in survival of dwarf mongooses (Helogale

parvula) to variation in habitat quality. Several studies on ground squirrels have reported

elevational variation in the demographic parameters (Bronson 1979, Zammuto and Millar

1985, Dobson and Oli 2001, Gillis et al. 2005). However, the population dynamic

consequences of such variation have rarely been addressed.









Survival rates of many long-lived species vary by age; individuals of different ages

often respond differentially to changes in environmental factors. In general, survival rates

of young animals are generally lower than those of adults, and also are expected to be

more variable over space and time (e.g., Fowler and Smith 1981, Douglas and Leslie

1986, Clutton-Brock et al. 1987, Gaillard et al. 1998, Portier et al. 1998, Doherty et al.

2004). Older individuals are typically less severely affected by spatiotemporal changes,

and their survival rates are expected to be less variable. Elucidating the interactive effects

of extrinsic and intrinsic factors (e.g., age, stage) on survival rates is important for a

thorough understanding of the dynamics, regulation, and persistence of populations.

However, simultaneous examinations of both spatial and temporal variation in extrinsic

factors, and their influence on age-specific survival rates, have been rare (but see Ringsby

et al. 1999, Saether et al. 1999, Graham and Lambin 2002). This is due primarily to the

difficulty in collecting demographic data over large spatial and temporal scales.

Consequently, spatiotemporal variations in age-specific survival rates of long-lived

species remain poorly understood.

We used data from a long-term study of the yellow-bellied marmot (Marmota

flaviventris) to investigate the spatiotemporal variation in age-specific survival rates.

Using an age-structured Cormack-Jolly-Seber (CJS) model, we analyzed 28 years of

capture-mark-recapture (CMR) data from 17 discrete habitat patches within our study

site. We estimated age-specific survival rates, and examined both spatial and temporal

variation in these rates. We also tested a series of hypotheses concerning the effects of

key environmental factors on the observed variation in survival rates. Finally, using a

Pradel's reverse-time CMR model, we estimated the realized population growth rate, and









investigated the influence of the observed variation in age-specific survival rates on the

realized population growth rate, and hence on the dynamics of the yellow-bellied marmot

population.

Materials and Methods

Study Area and Species

The yellow-bellied marmot is a large, diurnal, burrow-dwelling rodent, occupying

montane regions of the western North America (Frase and Hoffmann 1980, Armitage

2003a). Our study area is located in the Upper East River Valley near the Rocky

Mountain Biological Laboratory, Gothic, Colorado (38 57' N, 1060 59' W). The

marmots in our study area occupy 17 discrete habitat patches (Fig. 3-1). The elevation of

marmot sites varies from 2700 to 3100 m above sea level. Habitat characteristics vary

within and between sites from rolling grassy meadows to steeper talus slopes (Svendsen

1974). These distinct habitat patches vary in size and quality, ranging from satellite sites

as small as 0.01 ha, to colony sites as large as 7.2 ha. Colony sites are occupied by one or

more matrilines, each typically consisting of one or more adult females, yearlings, and

juveniles with an adult male defending one or more matrilines, whereas, satellite sites are

typically occupied by a single adult female, her litter, and sometimes an adult male

(Armitage 1991, 1998). The biology of yellow-bellied marmots in Colorado is described

in detail by Armitage (1991, 2003a).

Field Methods and Data

From 1962 to 2003, yellow-bellied marmots were live-trapped and individually

marked using numbered ear tags (details in Armitage 1991). Animal identification

number, sex, mass and reproductive condition were recorded for each animal. Trapping

concurrently occurred in 17 sites known to be occupied by marmots.









Four variables were used as site-specific covariates in the CMR analyses: (1)

elevation (m), (2) aspect (slope direction: 1 = southwest, 0 = northeast), (3) slope

(degrees), and (4) the average number of adult females per site. The Upper East River

Valley stretches in a southeast-northwest direction, gaining elevation towards the

northwest. Marmot sites on the west side of the East River Valley have steeper slopes

facing northeast (38-98), whereas sites on the east side are located on gradually inclined

meadows generally facing southwest (183-280).

Seven time-specific climatic variables were used as temporal covariates in the

CMR analyses: (1) length of the growing season (number of days between first bare

ground and the first killing frost), (2) annual precipitation (cm), and (3) monthly mean

summer (May-August) temperature (C) were obtained from Crested Butte Weather

Station (National Oceanic and Atmospheric Administration), approximately 10 km south

of the study area, whereas (4) duration of permanent snow cover (days), (5) annual

amount of snow fall (cm), (6) Julian date of first permanent snow pack, and (7) Julian

date of first bare ground were obtained from Rocky Mountain Biological Laboratory,

Gothic. Mean monthly temperature during the active season (May-August) ranged from

9.7 11.9 C, and annual precipitation ranged from 38.6 86.6 cm. For a detailed

description of time-specific climatic factors, see Schwartz & Armitage (2005).

Capture-Mark-Recapture (CMR) Analysis

Although our study spanned 42 years (1962-2003), we analyzed data from the last

28 years (1976-2003), because this period provided the most comprehensive CMR data

for the entire region. We used data from 860 resident females; all of these females were

captured and marked as pups and their ages were known exactly. Sixty-nine known

dispersers that moved among sites (identified based on trapping data) were excluded from









the analyses. Seventeen sites were grouped into eight categories on the basis of site

quality and location (Fig. 3-1). Four major colony sites were considered separately: (1)

Picnic, (2) River (two adjacent sites were grouped into one), (3) Marmot Meadow and (4)

Gothic. Satellite sites were typically occupied by few individuals. We assumed that

survival rates of marmots occupying adjacent satellite sites that share similar habitat

characteristics (e.g., size, aspect, elevation) were similar. Therefore, satellite sites were

grouped with respect to their location: (5) north satellites, (6) west satellites, (7) east

satellites and (8) south satellites.

We implemented the CMR models using Program MARK (White and Burnham

1999). We used an age-structured CJS model (Lebreton et al. 1992, Lebreton et al. 1993)

to estimate and model age-specific apparent survival (4) and recapture rates (p), and to

investigate the spatial and temporal variation in these rates. We used Program UCARE

V2.02 (Choquet et al. 2003) to test the goodness-of-fit of the CJS model. We used

Akaike's Information Criterion, corrected for small sample size, (AICc) for model

comparison, and for the identification of the most parsimonious model from a candidate

model set (Burnham and Anderson 2002). Model comparison was based on the

differences in AIC, values, AAICc. We used AIC, weight as a measure of relative support

for each model. The underlying process standard deviation (C) of the estimated

parameters over space (or time) was used as an estimate of the spatial (or temporal)

variation. The o was estimated using the variance components procedure implemented in

Program MARK, which is an extension of the procedure described in Burnham et al.

(1987).









The CMR analyses proceeded in a stepwise fashion. In preliminary analyses, we

tested for site and time effects on overall survival rates. We then proceeded to determine

the appropriate age structure for our study population. Previous demographic studies of

yellow-bellied marmots have used 2 or more age classes (Schwartz et al. 1998, Oli and

Armitage 2004). Thus, we parameterized and compared the following models with

alternative age structures: no age structure, two age classes (juveniles: 0-1 yr; adults: >1

yr), three age classes (juveniles: 0-1 yr, yearlings: 1-2 yrs, and adults: >2 yrs), and four

age classes (juveniles: 0-1 yr, yearlings: 1-2 yrs, sub-adults: 2-3 yrs, and adults: >3 yrs).

Although our data did not permit analysis of models with >4 age-classes, we believe that

the range of age structure considered here is adequate because, in many species of

mammals, survival rates of older animals are generally less variable than those of

younger animals (Gaillard et al. 1998, Schwartz et al. 1998). We also investigated the

spatial variation in age-specific survival rates by testing for the site effect. Next, using the

most parsimonious model, we investigated the temporal variation in age- and site-specific

survival rates. We considered the additive and interactive effects of site and time on age-

specific survival rates (Williams et al. 2001). We note that the order in which site and

time effects were included in the model did not influence the results of model selection;

testing for the time effect first, and then testing for the site effect resulted in the same

final models. To investigate the effect of site quality on spatiotemporal variation in age-

specific survival rates, we further grouped eight sites into two major quality types (colony

and satellite sites), and tested for time and site effects.

Using the most parsimonious model, we examined the potential influence of

environmental covariates on observed spatial and temporal variation in age-specific









survival rates. We tested for the effects of each covariate by modeling the logits of age-

specific survival rates as a linear function of a site-specific or temporal covariate. Each

temporal covariate was scaled to range between 0 and 1. If the 95% confidence interval

for the slope parameter (0) did not include 0, the relationship was considered statistically

significant (Williams et al. 2001). Because we only had data on a subset of the

environmental factors that could have influenced survival rates, we did not attempt to

develop a predictive model with multiple environmental covariates. Instead, our goal was

to identify the environmental factors that potentially influenced age-specific survival

rates, so we considered the influence of each environmental covariate separately.

We used a Pradel's reverse-time CMR model (Pradel 1996) to estimate and model

the realized population growth rate, and to investigate time and site specific population

growth rates (X). RELEASE Tests 2+3 (implemented in Program MARK) were used for

assessing goodness-of-fit of the Pradel's model. Spatial and temporal variation in k was

examined as described for the CJS models. Because Pradel's models do not allow for age

effect (Franklin 2001), estimates of k could be biased due to unaccounted differences in

age-specific survival rates. Therefore, we also estimated and modeled the realized growth

rate of the adult (>2 yrs) segment of the population, and investigated the relative

influence of the spatial and temporal variation in age-specific survival rates on adult

population growth rate (kad).

To assess the relative importance of age-specific survival rates to Xad, we modeled

Xad directly as a function of these rates (Nichols and Hines 2002, Nichols et al. 2003).

Specifically, we asked: which age-specific survival rate most closely covaried (over

space and time) with kad? We used site-specific estimates of age-specific survival rates as









a covariate for site effect on kad, and time-specific estimates as a covariate for time effect

on kad. We used the slope parameter (3) to relate the variation in the vital rate to variation

in Xad (Nichols et al. 2003).

Results

Spatiotemporal Variation in Overall Survival Rates

Our general CJS model, ) (t s) p (t s), fit the data with a slight under-dispersion

(X150 = 120.2, P = 0.965). There was strong support for significant variation in the

overall (i.e., age structure ignored) annual survival rates both among sites and through

time (Table A-i). However, site and time effects were additive, and there was no

evidence for interactive effects. The most parsimonious model included site effect, but no

time effect, on recapture rates. Three colony sites (River, Picnic, and Marmot Meadow)

were the largest and the most intensively studied sites. Constraining the recapture rates

for these three sites to have the same value resulted in a more parsimonious model

(model #16 in Table A-i). The recapture rate was 0.98 for these three colony sites and

0.79 for the fourth colony site (Gothic). Recapture rates for the north, west, east, and

south satellites were 0.91, 0.85, 0.69, and 0.94, respectively.

Age Structure and Spatiotemporal Variation in Age-Specific Survival Rates

Among the candidate models with different age structures, the three age-class

model was the most parsimonious (model #2 in Table 3-1). Among the three age-class

models, the most parsimonious model indicated that the survival rate of juveniles and

yearlings varied significantly among sites, whereas there was less support for site effect

in adult survival rates (model #6 in Table 3-1). However, these two models (models #2 &

#6) did not differ significantly (AAICc < 3), and we chose to continue our analysis with









the model including site effect in all three age classes (model #2 in Table 3-1). Juvenile

survival rates were relatively low in three colony sites, Picnic (0.54; 95% CI: 0.46, 0.62),

Marmot Meadow (0.53; 95% CI: 0.43, 0.63), and Gothic (0.52; 95% CI: 0.42, 0.62),

whereas they were the highest in east (0.78; 95% CI: 0.52, 0.92) and south satellite sites

(0.75; 95% CI: 0.60, 0.86) (Fig. 3-2C). Yearling survival rates were the lowest in Marmot

Meadow (0.30; 95% CI: 0.19, 0.45) and south satellites (0.33; 95% CI: 0.20, 0.48), and

the highest in east satellites (0.78; 95% CI: 0.40, 0.95) (Fig. 3-2B). Adult survival rates

were higher in colony sites (0.76; 95% CI: 0.72, 0.80) than in satellite sites (0.64; 95%

CI: 0.57, 0.71) (Fig. 3-2A). Adult survival rates were generally higher than juvenile and

yearling survival rates in colony sites; however, there was no apparent trend in satellite

sites. The greatest spatial variation was observed in the survival of yearlings (o = 0.11).

Spatial variation in juvenile survival (c = 0.08) was slightly lower than in yearling

survival, but higher than in adult survival rates (c = 0.04).

Analysis of recapture rates with age structure revealed that the model with the

modified site effect (s) remained the most parsimonious recapture rate model. Thus, we

used the three age-class model with site effect for all age classes as the base survival

model and the modified site effect model as the base recapture model (model #2 in Table

3-1) for all subsequent analyses.

Next, we tested for temporal variation in the age-specific survival rates for each

site. The best model structure included the additive effect of time on juvenile survival

rates, and no time effect on yearling or adult survival rates (model #3 in Table 3-2).

Grouping sites into two quality types (colony and satellite sites) resulted in a more

parsimonious model for the adult and juvenile survival rates. The model with separate









adult survival rates for colony and satellite sites (model #18 in Table 3-2) was more

parsimonious than the model with separate adult survival rates for each of the eight sites

(model #10 in Table 3-2), indicating that the observed spatial variation in adult survival

rates was due primarily to differences between satellite and colony sites. Juvenile

survival rates varied spatially but not temporally in satellite sites, whereas they exhibited

substantial temporal variation (o = 0.20) in the colony sites (model #18 in Table 3-2; Fig.

3-3C). A model with a similar support (AAIC, < 3; model #19 in Table 3-2) indicated

additive effects of time and site on juvenile survival rates within the colonies. We used

this final model (model #19 in Table 3-3), which was biologically more plausible, as the

base model for evaluating the effect of environmental covariates.

Effect of Environmental Factors

Preceding analyses revealed temporal variation in juvenile survival rates, and

spatial variation in the survival rates of all three age-classes. Thus, we examined the

influence of temporal and site-specific covariates on juvenile survival rates and of site-

specific covariates on the yearling and adult survival rates (see Table B-l for model

details). Site-specific variation in juvenile survival rates was positively influenced by the

aspect (P = 0.41; 95% CI: 0.03, 0.79) and negatively influenced by elevation (3 = -0.24;

95% CI: -0.47, -0.01) of each site. Site-specific variation in yearling survival rates was

positively influenced by the elevation (3 = 0.26; 95% CI: 0.01, 0.51). Site-specific

variation in adult survival rates was positively influenced by the average group size (3 =

0.13; 95% CI: 0.00, 0.27). Temporal variation in juvenile survival rates in colonies was

negatively influenced by the length of permanent snow cover (3 = -3.09; 95% CI: -5.37, -

0.85).









Influence on Population Growth Rate

Goodness-of-fit test indicated that the general Pradel's model for the entire

population fit the data poorly (X2151 = 422.7, P < 0.001). We, thus, used a variance

inflation factor (c = 2.79) in parameter estimation and model-selection (White and

Burnham 1999, Burnham and Anderson 2002). We used the model structure for survival

and recapture rates {( (t+s) p (s)} identified during the preliminary analysis, and

estimated the spatial and temporal variation in the realized annual population growth rate,

k. The most parsimonious model indicated only site effect on X (model #2 in Table 3-3).

Site-specific estimates of k ranged from 0.96 (95% CI: 0.90, 0.99) to 1.09 (95% CI: 1.05,

1.13); estimated realized population growth rates were less than 1.0 in two satellite sites

(north and west satellites; Fig. 3-2E). Time-specific estimates of X ranged from 0.65

(95% CI: 0.45, 0.81) to 1.49 (95% CI: 0.93, 2.05) (Fig. 3-3E).

The general Pradel's model for the adult segment of the population fit the data with

a slight under-dispersion (X256 = 27.6, P = 0.999). We used the model structure for adult

survival and recapture rates {4ad col (.) ,ad sat (.) P (s)} identified previously, and

estimated the spatial and temporal variation in the annual realized adult population

growth rate, kad. The most parsimonious model indicated additive effects of site and time

on kad (model #8 in Table 3-3). Further grouping of sites into colony and satellites

resulted in a more parsimonious model. Parameter kad varied only spatially in satellite

sites, whereas it varied only temporally in colony sites (model #10 in Table 3-3). A

model with a similar support indicated additive effects of time and site on kad within the

colonies (model #11 in Table 3-3). Site-specific estimates of Xad ranged from 0.92 (95%

CI: 0,86, 0.99) to 1.07 (95% CI: 1.03, 1.11); Xad was less than 1.0 only in north and west









satellite sites (Fig. 3-2D). Annual estimates of kadin colony sites ranged from 0.28 (95%

CI: 0.19, 0.47) to 1.83 (95% CI: 1.20, 2.30); Xad exhibited substantial temporal

fluctuations (Fig. 3-3D).

Because of the poor fit of the general Pradel's model (i.e., model for overall

population growth rate, k) to data, we conducted additional analyses focusing on the adult

segment of the population. The Xad covaried most closely with juvenile survival rates

over space (Fig. 3-2) as well as over time with a one year lag (Fig. 3-3). Spatial variation

in Xad was significantly influenced by among-site variation in juvenile survival rates (3 =

0.36; 95% CI: 0.14, 0.58; model #12 in Table 3-3), but not by that in yearling (P = -0.03,

95% CI: -0.19, 0.12; model #13 in Table 3-3) or adult (P = 0.17; 95% CI: -0.43, 0.77;

model #14 in Table 3-3) survival rates. Temporal variation in Xad was significantly

influenced by temporal variation in juvenile survival rates of the preceding year (3 =

0.76, 95% CI: 0.39, 1.12; model #15 in Table 3-3) and yearling survival rates (3 = 0.40,

95% CI: 0.02, 0.79; model #16 in Table 3-3), but not by that in adult survival rates (3 = -

0.44, 95% CI: -1.08, 0.19; model #17 in Table 3-3).

Discussion

Spatiotemporal variation in vital demographic rates is a common phenomenon in

animal populations, and such variation can have important population dynamic

consequences. However, rigorous investigations into population dynamic consequences

of spatiotemporal variation in age-specific vital rates require data at large spatial and

temporal scales. Consequently, there have been relatively few studies that explicitly

considered both sources of variation. Our long-term study of individually-identified

animals in several discrete habitat patches provided adequate data for a rigorous









examination of spatiotemporal patterns in age-specific survival rates of yellow-bellied

marmots and their population dynamic consequences.

In general, overall survival rates of yellow-bellied marmots varied both spatially

and temporally. Detailed analysis of age-specific survival rates indicated that the pattern

of variation differed among age classes. The most appropriate age structure was the three

age-class model: juveniles (0-1 yr), yearlings (1-2 yrs) and adults (>2), suggesting that

the survival rates significantly differed among these three age classes. Previous studies on

other ground squirrels reported higher survival rates for adults, and lower rates for young

animals (Bronson 1979, Farand et al. 2002). Survival rates of adult yellow-bellied

marmots in Colorado were generally higher than those of the younger age classes;

however, this trend was consistent only in high quality colony sites. There was no

significant difference between the adult and juvenile survival rates in the lower quality

satellite sites. Hence, our results indicate that differences in habitat quality can

differentially affect age-specific survival rates in sciurid rodent populations. Yearling

survival rates were, in general, lower than adult and juvenile survival rates. We note,

however, that the estimated survival rates were apparent, rather than true, survival rates.

Yearling marmots are much more likely to disperse than juveniles or adults (Van Vuren

1990, Van Vuren and Armitage 1994). As a result, estimates of yearling survival rates

were confounded by permanent emigration out of the study area, and therefore, are likely

to be underestimated.

Spatial variation in survival rates was observed in all three age classes; however,

the degree of spatial variation differed among age classes. The spatial variation in the

survival rate of younger animals was greater than that of adults, and it was influenced by









the aspect and the elevation of each site. Juvenile survival rates on southwest facing

slopes were higher than those on northeast facing slopes. Aspect of each site determines

the amount of exposure to sunlight and duration of snow cover, which in turn, determines

the length of the active season and hibernation period at a given site. These factors have

been suggested as important determinants of juvenile survival (Van Vuren and Armitage

1991). Bronson (1979) reported no effect of elevation on the survival of juvenile golden-

mantled ground squirrels (Spermophilus lateralis), whereas survival of juvenile marmots

was negatively associated with elevation in our study population. Survival of the

juveniles did not differ significantly between satellite and colony sites (see also Lenihan

and VanVuren 1996); they were actually higher in two satellite sites (Fig. 3-2C). Juvenile

survival rates are likely to be affected by differences in microclimate owing mostly to the

differences in aspect and elevation among sites (Armitage 1994).

Adult survival rates differed only between the colony and satellite sites, with

generally higher survival rates in colony sites. Colony sites, characterized by large habitat

area and more abundant resources (e.g., adequate hibernation opportunity, protection

from predation, higher food availability) are usually inhabited by large groups, whereas

satellite sites, characterized by smaller habitat area and limited resources, sustain fewer

adults (Armitage 1991, 1998). The risk of predation during the active season, and/or

mortality during hibernation, are likely to be higher in satellite sites, resulting in lower

adult survival. Our results were consistent with those of Armitage and Schwartz (2000)

that average group size positively influenced the survival rate of adult animals. Zammuto

and Millar (1985) and Bronson (1979) indicated that adult survival rates were higher at

higher elevations for some ground squirrel populations. Gillis et al. (2005), on the other









hand, reported that annual survival rates of the adult arctic ground squirrels

(Spermophilus parryii pleisus) did not vary with elevation, but noted a trade-off between

active season and over-winter survival. We did not observe a positive association

between elevation and survival of adult marmots. It is important to note that the range of

elevational gradient in our study sites was smaller than that in aforementioned studies.

The additive effect of time in the overall survival rates primarily reflected temporal

variation in juvenile survival rates; there was no support for the existence of temporal

variation in yearling or adult survival rates. A model of synchronous temporal variation

in survival rates among colony sites (i.e., the additive effects of time and space) was

supported by the data more strongly than was an asynchronous temporal variation model

(i.e., the interactive effects of time and space), suggesting that regional climatic factors

were likely to be the main cause of such variation (Schwartz and Armitage 2005).

Multiple environmental and social factors may act synergistically to influence survival

rates of marmots in our metapopulation, and the individual or combined effect of a few

factors cannot account for the observed variation. Nonetheless, our results suggest that

juvenile survival rates were mainly influenced by environmental factors that determined

the duration of snow cover, whereas survival of older animals were mostly influenced by

social factors such as group size. The precise mechanisms underlying these effects

require further study. Differential predation on adults as a function of site is strongly

implicated by previous studies (Van Vuren 2001, Blumstein et al. in press), and prior

work also suggests that predation may vary temporally (Armitage 2004).

The variation in age-specific survival rates over space and time were naturally

reflected in spatial and temporal variation in population growth rates. Growth rate of the









entire population (k) and of the adult segment of the population (Xad) followed a pattern

that primarily reflected site-specific differences in juvenile survival rates. Modeling Xad as

a function of age-specific survival rates revealed that spatial variation in ?ad was

significantly influenced by survival of juveniles but not of yearlings or adults. Likewise,

Xad closely covaried over time with survival of juveniles with one year time lag. Because

survival of yearlings and adults did not vary significantly over time, it seems reasonable

to conclude that most of the observed temporal variation in population growth rate was

due primarily to temporal variation in survival of juveniles. These results suggest that

spatial and temporal variation in population dynamics of yellow-bellied marmots was

strongly influenced by spatiotemporal variation in juvenile survival rates.

It has been suggested that vital demographic rates with the greatest potential

influence on population growth rate tend to exhibit the least temporal (or spatial)

variability (Cairns 1992, Gaillard et al. 1998, Pfister 1998, Gaillard et al. 2000). In

yellow-bellied marmots, the projected population growth rate is highly sensitive to

variation in juvenile survival rates (Oli and Armitage 2004). However, we found that,

among all age-specific survival rates, survival of juveniles was the most variable over

space and time. This variation heavily influenced the dynamics of our study population;

site-specific and temporal variation in population growth rate closely covaried with, and

primarily reflected spatiotemporal variation in survival of juveniles. Thus, the high

variability in juvenile survival rates over space and time clearly influenced the dynamics

of our study population, and is also likely to be an important determinant of the

spatiotemporal variation in the population dynamics of other mammals with similar life

history characteristics. Higher spatiotemporal variability in the survival of younger age









classes has been reported for other long-lived vertebrate species (e.g., Douglas and Leslie

1986, Clutton-Brock et al. 1987, Gaillard et al. 1998, Portier et al. 1998); however, its

effects on population dynamics were rarely addressed.

We conclude that survival rates of yellow-bellied marmots exhibit both spatial and

temporal variation, but that survival of juveniles is more variable over space and time

than that of older animals. Spatial and temporal variation in juvenile survival rates

strongly influenced the variation in the growth rates of our study population. Given the

high variability in survival rates of younger age classes, and the high sensitivity of

population dynamics to these rates in several species of mammals (Oli and Dobson

2003), future modeling attempts should thoroughly incorporate the spatiotemporal

variation in the survival of younger age classes, and carefully examine population

dynamic consequences of such variations. We note, however, that adult survival may

have a greater influence than juvenile survival on the population dynamics of some long-

lived vertebrates (e.g., Doak et al. 1994, Caswell et al. 1999, Gaillard et al. 2000),

suggesting that the generality of our conclusions may be limited to species with life-

histories similar to the yellow-bellied marmot.









Table 3-1. Analysis of the age structure and spatial variation in age-specific apparent
survival rates for the yellow-bellied marmot, using Cormack-Jolly-Seber
models. Akaike's Information Criterion corrected for small sample size
(AICo), differences in AIC, values (AAICc), AIC, weights and number of
parameters (#p) are given for each model. Age classes used for this analysis
are juvenile (juv: 0-1 yr), yearling (yr : 1-2 yr), sub-adult (sub-ad: 2-3 yr), and
adults (ad: >1 yr for 2 age-class, >2 yr for 3 age-class, and >3 yr for 4 age-
class model). Symbols are: 4 = apparent annual survival rate, p = annual
recapture rate, s = site effect, and s'= modified site effect. A period (.)
indicates constant value of the parameter. The most parsimonious models are
highlighted in bold.
AICC
No. Model AIC A AIC, C #p
Weights
1 4uv (s) 4ad (S)p (sJ 2666.17 45.89 0.000 22
2 sjuv (s) yrl (s) ad (s)p(s') 2622.63 2.35 0.170 30
3 j,v (s) yrl (s) sub-ad (S) ~d () p (s)*** 2633.13 12.85 0.001 38
4 4jv (.) )yrl () 4d (s)p(s)* 2625.48 5.20 0.041 23
5 uj, (s) y (.) d ()p(s)** 2626.28 6.00 0.027 23
6 juv (S) yrl (S)ad(.)p(S')P 2620.28 0.00 0.549 23
7 4jv (s) 4yr (s)~d (.)p(s)** 2622.71 2.43 0.163 25
8 4jU (s) byrI (s) pad () p (s)* 2625.09 4.80 0.050 32
9 (juv (s) qyr, (s) sub-ad (.) 4ad (.) (s)* 2622.32 2.03 0.152 24
10 4j, (s) ad (.)p (s* 2674.83 54.55 0.000 15
11 ,uv, (s) )r () d (.) p (s')** 2623.54 3.26 0.082 16
S2 age-class model
* 3 age-class model
S4 age-class model









Table 3-2. Analysis of temporal variation in age-specific apparent survival rates for the
yellow-bellied marmot, using age structured Cormack-Jolly-Seber models.
Three age-class model was used for these analyses: juvenile (juv : 0-1 yr),
yearlings (yrl: 1-2 yr), and adults (ad: >2 yr). Symbols are: t = time effect, t *
s = interactive effects of t and s, and t + s = additive effects of t and s. Colony
(col) and satellite (sat) groups are indicated in the subscripts. Other symbols
are defined in Table 3-1. The most parsimonious models are highlighted in
bold.
AIC
No. Model AIC A AICc #p
___Weights
1 u (s) syri (s) )ad (s) (s) 2622.63 34.25 0.000 30
2 ju, (t) yri (s) ad (s) p (s) 2613.02 24.64 0.000 49
3 ^, (t+s) ,ri (s) ad (S) p (S) 2607.26 18.88 0.000 56
4 Sv (t*s) ri (s) 1d (s) p (s) 2655.41 67.03 0.000 179
5 j, (t+s) ,i (t) ad (s) p (s) 2624.92 36.54 0.000 73
6 j v (t+s) yri (t+s) ad (s) p (s) 2628.00 39.62 0.000 80
7 juv (t+s) yri (s) 1ad (t) (s) 2627.00 38.62 0.000 73
8 uv, (t+s) ~yr (s) sad (t+s) p (s) 2627.82 39.44 0.000 80
9 jucozp (t) j vsat (t) byri (s) kad (s) p (s) 2602.61 14.23 0.000 68
10 A .coz (t) u sat (s) yrl (s) (ad (s) p (s) 2598.72 10.35 0.003 52
11 .coz (s) ju st (t) (yr (s) 1ad (s) p (s 2625.62 37.24 0.000 46
12 v coz (t) jv sat (.)yHr (s) dad (s) p (s) 2599.29 10.91 0.002 49
13 v .col (t+s) (at (s) y i (s) 1d (s) p (s) 2599.06 10.68 0.002 55
14 j .col (t) j, s (s) yl co (s) y,l at (.) ad (s)p (s) 2602.33 13.95 0.000 49
15 jv col (t) jv sat (s) yri col (.)yrI sat (s) ad (s) p (s) 2600.15 11.77 0.001 49
16 jv col (t) Wj~s(s) ri(s) d co(s) t(.)d ( p (s) 2592.50 4.12 0.062 49
17 uv col (t) sat(juvt (s) 1 (s) ad col (.)ad sat (s)p (s) 2594.58 6.20 0.022 49
18 uv_ col (t) juvsat (s) yrl (s) dad col (.)+adsat (.) p (s) 2588.38 0.00 0.486 46
19 iuv coi (t+s) i.uv sat (s) vri (s) ad col (.)ad sat (.) p (s') 2588.67 0.29 0.421 49









Table 3-3. Analysis of temporal and spatial variation in the growth rate of the entire
population (k) and adult (animals >2 yrs old) segment of the population (kad),
using Pradel's reverse-time models. Site-specific covariates for kad are
juvenile (juvs), yearling (yrls), and adult (ads) survival rates, and temporal
covariate for kad are juvenile survival rate of the previous year (juvt-l), and
yearling (yrlt) and adult (adt) survival rates of the current year. Other symbols
are defined in Tables 3-1 and 3-2. The most parsimonious models are
highlighted in bold.
AIC
No. Model AIC, A AIC, #p
c Weights
Entire population:
1 (t+s)p (s')(.) 2994.63 13.92 0.001 41
2 (t+s)p (s ') (s) 2982.24 1.53 0.318 48
3 (t+s)p (s')(t) 2994.64 13.93 0.001 67
4 (t+s) p (s') I (t+s) 2980.71 0.00 0.681 74
Adult segment of the population:
5 ad co .)d (.) p (s) ad (.) 2183.36 67.29 0.000 9
6 d co (.) d at (.) p (S) Xd (s) 2162.98 46.91 0.000 16
7 cd col (.) d t (.) (S) ad (t) 2158.97 42.90 0.000 35
8 ad col (.)ad sat (.) p (S ad (t+s) 2127.72 11.65 0.003 42
9 ad col (.) ad sat (.) p (S) ad co (t) ad sat (t) 2140.51 24.44 0.000 36
10 ad col (.) ad t (.) p (S) d co (t) ,d t (s) 2120.58 4.51 0.090 37
11 ad col () ad sat (.) (S) ad ol (t+s) ad sat () 2122.19 6.12 0.040 42
12 ad col (.) at (.) p (s') ad ol (t+juv,) ad sat (juv) 2116.07 0.00 0.857 35
13 ad co (.)d t (.) p (S) (ad ~ (t+yrl,) Xd (yrl,) 2126.46 10.39 0.005 35
14 ad co (.) ad at (.)p (S) Xad ol (t+ad,) Xad t (ad,) 2126.33 10.25 0.005 35
15 ad co (.) ad t (.) p (S)ad col (UVt- +S) ad sat (s) 2151.99 35.91 0.000 17
16 ad co ()d t (.) p (S)~ d ol (yrlt+s) ad at (s) 2161.01 44.94 0.000 17
17 ad co (.)ad sat(.)p(s) dcol (adt+s) ad sat(s) 2163.21 47.14 0.000 17






61



North swelites



MarmotPicnic East satellite
Meadow .
4-

II


0 3




o 2-
z
FI ar

1 0
North

t
South sauleee

0 1 2 3
East-west distance (km)


Figure 3-1. The spatial structure of the yellow-bellied marmot metapopulation in
Colorado, U.S.A. Seventeen sites are grouped into four colonies (River,
Gothic, Marmot Meadow and Picnic) and four satellite groups (south, west,
east, and north satellites).











T T


B


T r


IK"


' *


T T


, 000*Ot & 4 00 D Of#


-Il


t t
\4 %t4L


Figure 3-2. Spatial variation in annual (A) adult (4ad), (B) yearling (yr1), and (C) juvenile
(bju) survival rates. Mean values and standard errors were estimated using
model #2 in Table 3-1. Spatial variation in the growth rate of the (D) adult
segment of the population (kad) and (F) entire population (k). Mean values
and standard errors were estimated using model #6 and model #2 in Table 3-3,
respectively.


ad


^ad


T T


U.-


D


1.0 4.....


-I-


-I-F


E


4***00


1.0 4....


I***


9,


4


O ., p -4b,
qc"p










0.9 -A
0.7
1ad 0.5
0.3
0.1


0.7
1y, 0.5
0.3
0.1


0.7
*juv 0.5
0.3



2.0
1.5










0.5ad1 11
1.0 e eo0e e ee0







Figure 3-3. Temporal variation in annual (A) adult (,ad), (B) yearling (>yri) and (C)
juvenile (4ju) survival rates from 1976 to 2003. Mean values (solid line) and
95% confidence intervals (gray shade) were estimated using model #7, model
#5, and model #18 in Table 3-2, respectively. The gap in B indicates that the
parameter was not estimable. Temporal variation in the growth rate of the (D)
adult segment of the population (kad) with one year lag, and (E) entire
population (k). Mean values (solid line) and 95% confidence intervals (gray
shade) were estimated using the model #10 and model #3 in Table 3-3,
respectively.














CHAPTER 4
SPATIOTEMPORAL VARIATION IN THE REPRODUCTIVE PARAMETERS OF
THE YELLOW-BELLIED MARMOT

Spatiotemporal variation in reproductive rates is a common phenomenon in many

wildlife populations, but population dynamic consequences of spatial and temporal

variability in different components of reproduction (e.g., breeding probability, number of

offspring produced) remain poorly understood. We used 43 years (1962 -2004) of data

from 17 locations and capture-mark-recapture (CMR) modeling framework to investigate

the spatiotemporal variation in reproductive parameters of the yellow-bellied marmot

(Marmotaflaviventris), and its influence on the realized population growth rate.

Specifically, we estimated and modeled the litter size, and the probability of breeding the

following year of the yearling (i.e., pre-reproductive), non-reproductive adult and

reproductive adult females. The breeding probabilities of the non-reproductive and

reproductive adults and the litter size varied over space, whereas only the breeding

probability of the reproductive adults varied over time. We also tested a series of

hypotheses concerning the effects of key environmental and social factors on the

observed variation in each component of reproduction. We used a reverse-time CMR

model to investigate the influence of components of reproduction on the realized

population growth rate. The litter size and the breeding probability of the non-

reproductive adults had a significant influence on the realized population growth rate.

Our results indicate that the recruitment into the adult segment of the population is likely









to be the critical component of the population dynamics of the yellow-bellied

marmots and other mammals with similar life history characteristics.

Introduction

Many species live in discrete habitat patches that occur either naturally or due to

human-caused fragmentation of once contiguous habitats (Hanski and Ovaskainen 2003,

Hanski and Gaggiotti 2004). Habitat patches may experience different sets of

environmental conditions, such as resource availability, predation pressure, and

microclimatic conditions. Additionally, environmental conditions in each habitat patch

may change over time. Such spatiotemporal variation in environmental factors can cause

differences in vital demographic rates over time and space, and these differences can

significantly influence the dynamics, regulation, and persistence of populations (Kareiva

1990, Pulliam and Danielson 1991, Tilman and Kareiva 1997).

Reproduction is an important life history trait that can be particularly sensitive to

spatiotemporal variation in the environment (Roff 1992, Stearns 1992, Heppell et al.

2000, Caswell 2001). Changes in the environmental or social conditions can significantly

influence reproductive rates (e.g., Coulson et al. 1999, Coulson et al. 2000). Because

population growth rates are highly sensitive to changes in reproductive parameters in

many species (e.g., Saether and Bakke 2000, Oli and Dobson 2003, Oli and Armitage

2004), spatiotemporal variation in these rates can play a significant role on the dynamics

and persistence of populations. Therefore, a thorough understanding of population

dynamics over space and time requires a detailed understanding of spatiotemporal

variation in reproductive rates, and of environmental and/or social factors that can cause

such variation.









Reproduction can be considered as being composed of two parts: breeding

probability and number of offspring produced (Lebreton et al. 1990, Nichols et al. 1994).

The probability that an individual of reproductive age reproduces in a given breeding

season is typically less than 1.0, and this probability can vary over space or time (e.g.,

Watson and Moss 1970, Jenouvrier et al. 2003, Bryant 2005). Spatiotemporal variation in

breeding probability can cause spatiotemporal variation in population dynamics even

when average litter or clutch size remains relatively stable. Although spatiotemporal

variation in litter (or clutch) size or fecundity rates have been examined for some species

(e.g., Bronson 1979, Jarvinen 1993, Saether et al. 1999, Coulson et al. 2000, Gaillard et

al. 2000, Chamberlain and Crick 2003, Tremblay et al. 2003), variation in breeding

probability over space and time, and population dynamic consequences of such variations

have received much less attention. Discerning the population dynamic consequences of

spatiotemporal variation in reproductive parameters necessitates simultaneous

examination of variation in both components of reproduction (i.e., breeding probability

and number of offspring produced). However, few studies have simultaneously

considered spatial and temporal variation in both components of reproduction or

investigated population dynamic consequences of such variation.

Our objective was to investigate the spatiotemporal variation in breeding

probability and litter size, and to examine the population dynamic consequences of such

variation in the yellow-bellied marmot (Marmotaflaviventris). We applied multistate

capture-mark-recapture (CMR) models to 43 years (1962 2004) of data from 17 discrete

habitat patches, and examined both spatial and temporal variation in the breeding

probability. We also investigated the spatial and temporal variation in litter size; this,









combined with spatiotemporal variation in breeding probability, enabled us to discern

which component of reproduction varied over space or time. We also tested a series of

hypotheses concerning the effects of key environmental and social factors on the

observed variation in each component. Finally, using a Pradel's reverse-time CMR

model, we estimated and modeled the realized population growth rate, and examined

population dynamic consequences of the spatiotemporal variation in components of

reproduction.

Materials and Methods

Study Area and Species

The yellow-bellied marmot is a large, diurnal, burrow-dwelling rodent, occupying

montane regions of the western North America (Frase and Hoffmann 1980, Armitage

2003a). The study was conducted in the Upper East River Valley near the Rocky

Mountain Biological Laboratory, Gothic, Colorado (38 57' N, 1060 59' W). The

marmots in our study area occupy discrete habitat patches (Fig. 2-1). The elevation of

marmot sites varies from 2700 to 3100 m above sea level. Habitat characteristics vary

within and between sites from rolling grassy meadows to steeper talus slopes (Svendsen

1974, Blumstein et al. in press). These distinct habitat patches vary in size and quality,

ranging from satellite sites as small as 0.01 ha, to colony sites as large as 7.2 ha. Colony

sites are occupied by one or more matrilines, each typically consisting of one male, two

or more closely related adult females, yearlings, and juveniles, whereas satellite sites are

typically occupied by a single adult female, her litter, and sometimes an adult male

(Armitage 1991, 1998). Marmots breed shortly after emergence from hibernation

(Armitage 2003a). The yellow-bellied marmot first breeds at 2 years of age, less than a

quarter of 2-year-old females reproduce, and the median age of first reproduction is 3









years (Schwartz et al. 1998). The biology of yellow-bellied marmots in Colorado is

described in detail by Armitage (1991, 2003 a).

Field Methods and Data

From 1962 to 2004, yellow-bellied marmots were live-trapped and individually

marked using numbered ear tags (details in Armitage 1991). Animal identification

number, sex, mass and reproductive condition were recorded for each animal. Trapping

concurrently occurred in 17 sites known to be occupied by marmots. We grouped these

sites into five categories on the basis of site quality and location. Four major colony sites

were grouped separately: Picnic, River (two adjacent sites were grouped together),

Marmot Meadow, and Gothic. Satellite sites were typically occupied by few individuals.

We assumed that reproductive rates of marmots occupying these low-quality sites were

similar. Therefore, all the satellite sites were grouped together. We used data collected

from 748 females that were >1 year old. Ages for the females that were captured as

juveniles were known exactly, whereas ages for other females were estimated based on

body mass (< 2 kg = yearling, > 2 kg = adult, Armitage et al. 1976). Litter size was the

number of weaned young that emerged from the natal burrows.

Components of Reproduction

We investigated the spatial and temporal variation in two major components of

reproduction: (1) the breeding probability and (2) the litter size. Female marmots can

reproduce at 2 years of age, but the probability that 2-year old females reproduce is

generally lower than that of older females (Schwartz et al. 1998). Therefore, we

considered three life history states based on age and reproductive status (Fig. 4-1): (1)

yearling (1-2 yrs; pre-reproductive), (2) non-reproductive adult (females > 2 yrs and do

not breed in a given year) and (3) reproductive adult (females > 2 yrs and breed in a given









year) states. We used the multistate CMR model (Hestbeck et al. 1991, Brownie et al.

1993, Williams et al. 2001, Fujiwara and Caswell 2002) implemented in Program MARK

(White and Burnham 1999) to estimate and model state-specific survival, recapture, and

transition rates. The transition rate i' indicates the probability of transition from state x

to state y, conditional on surviving the period in state x. Specifically, we estimated the

transition rate from each state to the reproductive state: J13 (probability of a yearling

breeding the following year as a two year-old conditional on survival), i23 (probability of

a non-reproductive adult breeding the following year conditional on survival), and y33

(probability of a reproductive adult breeding again the following year conditional on

survival) (Fig. 4-1). Hereafter, we will use "the breeding probability" to indicate "the

probability of breeding the following year conditional on survival", for simplicity. Both

yearling recapture (pl) and yearling to yearling transition rates (Y11) were fixed to zero,

as all the yearlings either die or move to one of the adult states. Transition rates from

non-reproductive to yearling (Y21) and reproductive to yearling state (Y31), which were

biologically impossible, were also fixed to zero. Transitions i12, Y22, and x32 are

complements of Y13, Y23, and Y33, respectively (e.g., Y32 = 1 Y33).

We used Program UCARE V2.02 (Choquet et al. 2003) to test the goodness-of-fit

of the general multistate model. We used quasi-likelihood adjusted Akaike's Information

Criterion, corrected for small sample size (QAICc) for model comparison, and for the

identification of the most parsimonious model from a candidate model set (Burnham and

Anderson 2002). Model comparison was based on the differences in QAICc values,

AQAICc. We used QAICc weight as a measure of relative support for each model. There

was no significant temporal variation in the survival or recapture rates of the yearling or









adult marmots (Ozgul et al. in press-a). Therefore, we tested only for the site effect in

these rates. First, we tested for site effect on recapture rates of the non-reproductive and

reproductive adults. We then proceeded to test for site effect on the survival rate of

yearlings, non-reproductive adults and reproductive adults. Finally, we tested for both site

and time effects on state-specific transition rates (i.e., breeding probabilities).

We used a general linear model (GLM) to test for spatial and temporal variation in

the litter size. Analysis of age effects on litter size revealed that two age-class (2 year old,

and older females) model was the most parsimonious model, a result consistent with

earlier findings that two year old females generally produce smaller litters than older

females (Schwartz et al. 1998). Thus, we grouped females into two age classes for

investigating spatial and temporal variation in litter size: (1) two year old females and (2)

older females. We used AICc for model comparison, and for the identification of the most

parsimonious model (Burnham and Anderson 2002). GLM analysis was performed in

Program R (R Development Core Team 2005).

Effect of Environmental and Social Factors

Using the most parsimonious models identified in the preceding analyses, we

examined the potential influence of the environmental and social factors on breeding

probabilities and litter size. We considered the influence of three sets of covariates that

can potentially influence components of reproduction: (1) site-specific, (2) climatic, and

(3) social factors (Appendix C, Table C-l). We tested for the effect of each covariate on

the breeding probabilities by modeling the logit of each transition rate as a linear function

of the site-specific, climatic, or social covariates. The influence of the aforementioned

covariates on the litter size was examined similarly by modeling the litter size as a linear

function of each of the site-specific, climatic, or social covariates. Because we only had









data on a subset of the environmental and social factors that could have influenced

reproductive parameters, we considered the influence of each covariate separately. If the

95% confidence interval for the slope parameter (0) did not include 0, the relationship

was considered statistically significant (Williams et al. 2001).

Influence on Population Growth Rate

We used Pradel's reverse-time CMR model (Pradel 1996, Nichols and Hines 2002)

to examine the spatiotemporal variation in the realized population growth rate, and to

investigate the influence of each component of reproduction on the realized population

growth rates (k). RELEASE Tests 2+3 (implemented in Program MARK) were used for

assessing goodness-of-fit of the Pradel's model. Previous analysis (Ozgul et al. in press-

a) indicated a poor fit of the general Pradel's model (i.e., model for overall population

growth rate, k) to data. Therefore, we conducted our analyses focusing on the growth rate

of the adult (>2 yrs) segment of the population (kad). Spatial and temporal variation in Xad

was examined as described for the multistate models. To assess the relative importance of

different components of reproduction to adult population growth rate, we modeled Xad

directly as a function of these rates (Nichols and Hines 2002, Nichols et al. 2003).

Specifically, we asked: which components of reproduction significantly influenced

spatial and temporal variation in kad? We used site-specific estimates of transition rates

and litter size as covariates to test for site effect on Xad, and time-specific estimates as

covariates to test for time effect on kad. Each component of reproduction would influence

the adult segment of the population with a time lag. Time-specific estimates of the

transition rates were included with a two year lag (e.g., Y23 during 1996-97 period would

influence kad during 1998-99), whereas those of the litter size were included with a one









year lag (e.g., litter size during 1996 would influence Xad during 1997-98). We used the

slope parameter (3) to relate the variation in the vital rate to variation in had (Nichols et

al. 2003).

Results

Survival, Recapture, and Breeding Probability

The goodness-of-fit test of the general multistate model indicated a slight over-

dispersion (2111 = 121.4, P = 0.24). Thus, we used the calculated value of the over-

dispersion parameter (c = 1.09) for parameter estimation and quasi-likelihood adjustment

for model comparison. The most parsimonious model (model #22 in Table 4-1) included

a constant recapture rate of 1.00 (SE < 0.01) for the reproductive adults, and site effect on

the recapture rates of non-reproductive adults. Recapture rates (mean SE) for non-

reproductive adults in Picnic, River, Marmot Meadow, and Gothic colonies were 0.96 +

0.02, 0.88 + 0.04, 0.56 + 0.11, and 0.51 + 0.07, respectively. Recapture rate for non-

reproductive adults in satellite sites was 0.62 0.05. The survival rates for yearlings

(0.46 0.03) and reproductive adults (0.76 0.02) were constant, whereas survival rates

of non-reproductive adults varied among sites. Survival rate of non-reproductive adults in

Picnic, River, Marmot Meadow, and Gothic colonies was 0.73 0.04, 0.66 0.04, 0.40 +

0.09, and 0.60 + 0.05, respectively, and in satellite sites it was 0.50 + 0.03. Next, we

investigated the spatial and temporal variation in each transition rate. The most

parsimonious model indicated no spatial or temporal variation in J13 (0.25 0.03).

However, it is important to note that i13 was inestimable for the majority of the sampling

periods. The parameter Y23 did not vary over time, but showed spatial variation ranging

from 0.31 0.05 (River) to 0.59 0.14 (Marmot Meadow) (Fig. 4-2). The parameter Y33









exhibited both spatial and temporal variation. It varied from 0.47 0.06 (Satellites) to

0.82 0.07 (Marmot Meadow) among sites (Fig. 4-2), and from 0.11 0.11 (1991) to

0.90 + 0.10 (2003) over time (Fig. 4-3). There were no significant differences between

colonies and satellites in any of the three transition rates (Table 4-1).

Litter Size

The most parsimonious model for litter size included the additive effects of site and

age, but no time effect (model #4 in Table 4-2). Estimates of litter size ranged from 3.74

0.14 (satellites) to 5.03 0.19 (Marmot Meadow) among sites. The litter size for two

year old females (3.79 + 0.16) was slightly lower than that of older females (4.22 0.08).

The second best model (model #6 in Table 4-2) indicated only site effect, but this model

was less supported by the data (AAIC = 3.48).

Effects of Environmental and Social Factors

We examined the influence of environmental and social factors on each transition

rate using the most parsimonious model identified above (model #22 in Table 4-1).

Among the site-specific factors considered (Appendix C), the aspect significantly

influenced i23 (P = -0.64, 95% CI: -1.06, -0.22) and 33 (P = 0.61, 95% CI: 1.21, 0.01);

breeding probability was lower for non-reproductive adults and higher for reproductive

adults in southwest facing sites than in northeast facing sites. The parameter i23 was

positively influenced by elevation (3 = 0.44, 95% CI: 0.12, 0.77). Among social factors

(Appendix C), residency status significantly influenced Y23 (P = 0.61, 95% CI: 0.16,

1.06); probability of breeding was higher for resident non-reproductive females than

immigrant non-reproductive females. The parameter W23 was positively influenced by the

average group size (3 = 0.26, 95% CI: 0.10, 0.42) and the relative number of adults (3 =









0.46, 95% CI: 0.11, 0.80). The parameter Y13 was negatively influenced by the relative

number of yearlings (3 = -0.75, 95% CI: -1.14, -0.36) and the relative number of adults

(P = -0.50, 95% CI: -0.69, -0.31) present in the site. Parameter Y33 was negatively

influenced by the principal components representing the severity of the preceding winter

(P = -0. 31, 95% CI: -0.02, -0.60) and the onset of the present summer (3 = -0.34, 95%

CI: -0.03, -0.64), and it was positively influenced by the principal component

representing precipitation during the previous summer (3 = 0.41, 95% CI: 0.69, 0.12)

(Appendix C).

We examined the influence of environmental and social factors on litter size using

the most parsimonious model identified above (model #4 in Table 4-2). Litter size was

significantly influenced by the aspect (3 = 0.58, 95% CI: 0.26, 0.89); it was slightly

higher in southwest facing sites (4.45 + 0.12) than in northeast facing sites (3.89 0.11).

No other environmental or social factors significantly influenced litter size.

Influence on Population Growth Rate

The general Pradel's model for the adult segment of the population fit the data with

a slight underdispersion (2118 = 52.2, P = 0.999). We used the most parsimonious model

identified for the adult survival and recapture rates {fad (s) p (s)}, and modeled the

spatial and temporal variation in the annual realized adult population growth rate, kad.

The most parsimonious model indicated only the time effect, but no site effect, on kad

(model #2 in Table 4-3). A model with less support indicated additive effects of time and

site on kad (model #1 in Table 4-3). Annual estimates of kad ranged from 0.54 0.05

(1983) to 1.68 0.23 (2003) indicating substantial temporal fluctuations (Fig. 4-3). The

Xad was positively influenced by the temporal variation in i23 (3 = 0.28, 95% CI: 0.04,









0.51) and litter size (P = 0.65, 95% CI: 0.37, 0.94), but not by that in 33 (P = -0.01, 95%

CI: 0.18, -0.20). We did not include Y13 in this analysis, because j13 was not estimable

for the majority of the periods. The kad ranged from 1.01 0.01 (Marmot Meadow) to

1.04 0.01 (Gothic), but did not vary significantly among sites (Fig. 4-1). Thus, variation

in some reproductive parameters over space did not contribute substantially to spatial

variation in kad.

Discussion

Spatiotemporal variation in reproduction is a common phenomenon in many animal

populations, and such variation can have important demographic consequences.

However, rigorous investigation of spatiotemporal variation in reproduction and its

demographic consequences requires data at large spatial and temporal scales. Our long

term study of yellow-bellied marmots provided sufficient data for a thorough

investigation of the spatiotemporal variation in different components of reproduction.

Specifically, we addressed the following questions: Which components of reproduction

varied over time and among sites? Which environmental or social factors potentially

influenced the observed variation? And, finally, what are the population dynamic

consequences of the observed variations in these demographic rates?

Components of reproduction in yellow-bellied marmots exhibited both spatial and

temporal variation. However, the degree of variation differed among different

components of reproduction. The breeding probability of the yearlings did not exhibit

spatial or temporal variation. In general, only a quarter of the two year old females bred

successfully. The breeding probability of the non-reproductive adults showed significant

spatial, but not temporal, variation. However, it was always higher than the breeding









probability of the yearlings, indicating significant effect of age on the breeding

probability. The breeding probability of the reproductive adults showed both spatial and

temporal variation. Nonetheless, it was generally higher than the breeding probability of

the non-reproductive adults, indicating that females that have reproduced in a given year

are also more likely to reproduce the following year. The litter size varied among sites

and between two age classes. Two year old females, which are all first time breeders,

generally have smaller litters compared to older females, indicating that mother's age and

experience might influence litter size (Schwartz et al. 1998).

Spatiotemporal variation in age-specific survival rates of the yellow-bellied

marmots in Colorado and the population dynamic consequences were reported elsewhere

(Ozgul et al. in press-a). Yet, our study revealed that the survival of non-reproductive

adults was generally lower than that of reproductive adults. There was no evidence that

reproduction was costly as measured by changes in either the survival rate or the

probability of breeding the following year (Nichols et al. 1994). Contrary to the

predictions of life history theory (Stearns 1992), reproductive females generally survived

better, and also were more likely to breed the following year compared to non-

reproductive females (see also Oli and Armitage 2003).

Several environmental and social factors can act simultaneously to influence

components of reproduction in mammals (e.g., Clutton-Brock et al. 1987, Stenseth et al.

1996, Leirs et al. 1997, Coulson et al. 2000). We found that different components of

reproduction in yellow-bellied marmots were influenced by different sets of

environmental or social factors. The breeding probability of the reproductive adults and

litter size were influenced mostly by the climatic factors, whereas the breeding









probabilities of the yearlings and non-reproductive adults were influenced mostly by

social factors. The breeding probability of yearlings is lower when the number of

yearlings and adults in the colony are larger. These results are consistent with earlier

studies suggesting that reproductive suppression might play a dominant role in causing

delayed age of first reproduction (Armitage 1999, Blumstein and Armitage 1999,

Armitage and Schwartz 2000, Armitage 2003c, Oli and Armitage 2003). The breeding

probability of the non-reproductive adults was influenced by the residency status; a non-

reproductive resident adult had significantly higher probability of breeding than a non-

reproductive immigrant. Group size had a positive effect on this breeding probability,

indicating social enhancement of reproduction (Armitage 1998, Armitage and Schwartz

2000).

Environmental factors that significantly influenced the breeding probability of the

reproductive adults included precipitation during the previous summer, winter severity,

and early summer environmental conditions. All of these factors can potentially

influence the physical condition of a female, and thus her likelihood of breeding

(Armitage 1994, 1996, Lenihan and Van Vuren 1996). The spatial variation in this

breeding probability was influenced by the aspect of marmot sites; on northeast facing

sites, where the length of the active season is shorter and the hibernation period is longer,

breeding probability of the reproductive adults was lower. Our results suggest that the

breeding probability of the females that had bred at least once is mostly governed by the

environmental conditions, rather than the social conditions. A change in the breeding

probability of the reproductive adults is likely to be a consequence of the trade-off

between somatic and reproductive efforts in reaction to a change in environmental









conditions (Stears 1992, Oli 1999). This interpretation is strongly supported by studies

of other species of marmots in which reproductive skipping occurs because females are

unable to gain sufficient mass to both survive hibernation and reproduce in the year

following reproduction (Armitage and Blumstein 2002).

Litter size was influenced by the aspect of marmot sites; sites located on southwest

facing slopes had relatively higher litter size than sites on northeast facing slopes.

Lengths of the active season and hibernation period have been suggested as important

determinants of litter size (Van Vuren and Armitage 1991, Schwartz and Armitage 2002).

Spatiotemporal variation in the population growth rate is a result of variation in

vital demographic rates. Given that components of reproduction varied over time and/or

space, we asked how these variations influenced the population growth rate. The realized

growth rate of the adult segment of the population (Xad) showed significant fluctuations

during the study period (see also Ozgul et al. in press-a). Among all reproductive

parameters, litter size and the breeding probability of the non-reproductive adults

significantly influenced the temporal variation in Xad. The observed spatial or temporal

variation in the breeding probability of the reproductive adults did not significantly

influence the observed variation in Xad. Thus, litter size and the breeding probability of

the non-reproductive adults are likely to be the major components of reproduction with

important influence on population growth rate.

Survival of younger animals and reproductive rates have been suggested to be

important drivers of population dynamics in many species of mammals (e.g., Gaillard et

al. 2000). Our results, combined with those of Ozgul et al. (in press-a), indicate that litter

size and juvenile survival, abetted by the breeding probability of the non-reproductive









adults, are likely to be the main demographic factors driving the dynamics of the yellow-

bellied marmot population. These vital rates (survival of young animals, litter size, and

breeding probability) are the components of recruitment into the adult segment of the

population. They are generally more sensitive to variation in extrinsic factors, thus

exhibit a greater degree of variation over space and time. Consequently, they play a

predominant role in the observed fluctuations in population growth rate. Therefore, we

suggest that recruitment into adult segment of the population is likely to be the critical

component of the population dynamics of the yellow-bellied marmot (Armitage 1973,

2003b), and other species with similar life history characteristics.

We conclude that components of reproduction in yellow-bellied marmots exhibit

both spatial and temporal variation, but that the pattern of variation differs among the

components. However, only litter size and the breeding probability of the non-

reproductive adults significantly influenced the realized population growth rate. The

spatiotemporal variation in the components of recruitment into the adult population is

likely to be the main demographic factor driving the dynamics of the yellow-bellied

marmot population.










Table 4-1. Analysis of state-specific apparent survival, recapture, and transition rates for
the yellow-bellied marmot using a multistate mark-recapture model.
Differences in quasi-likelihood adjusted Akaike's Information Criterion
corrected for small sample size (AQAICc), QAICc weights and number of
parameters (#p) are given for each model. Each age class is indicated as a
subscript: yearling (1), non-reproductive adult (2), and reproductive adult (3).
Symbols are: ) = apparent annual survival rate, p = annual recapture rate, i ,
= transition rate from state x to state y, s = site effect, t = time effect, s + t =
additive effects of s and t, and cs = site effect constrained to be colony or
satellite. A period (.) indicates constant value of the parameter. Parameters pi,
Y11, V21, and Y31 are fixed at 0. Parameters Y12, Y22, and Y32 are complements
of v13, Y23, and i33, respectively (e.g., Y22 = 1 23).


Survival
No.
Model
1 1 (s) 2 (S) 3 (s)
2 1 (s) (2 (S) 43 (S)
3 ;1 (s) 2 (s) 3 (s)
4 1 (s) (2 (s) 43 (s)
5 1 (s) 2 (s) 43 (s)
6 (, (cs) 2S (S) P3 (S)
7 1 (.) 2 (S) 3 (s)
8 1 (.) 2 (CS) 43 (s)
9 1 (.) 42 (.) 3 (S)
10 1 (.) (S) 3 (CS)
11 (.) 2 (S) 3 (.)
12 (.) 2 () 3 (.)
13 (.) 2 () 3 (.)
14 (.) 42 (S 3(.)
15 (.) 2 () 3 (.)
16 (.) 42 (S 3(.)
17 (.) 2 () 3 (.)
18 (.) 2 () 3 (.)
19 1 (.) 2 (S) 3 (.)
20 (.) 2 () 3 (.)
21 (.)2 () 3 (.)
22 6 (.) (s) 3(.)


Recapture
model
p2 (s) p3 (S)
p2 (cs) p3 (S)
P2 (.)P3 (S)
p2 (s) p3 (CS)
p2 (s) P3 (.)
p2 (s) P3 (.)
p2 (s) P3 (.)
p2 (s) P3 (.)
p2 (s) P3 (.)
p2 (s) P3 (.)
P2 (s) P3 (.)
P2 (s) P3 (.)
P2 (s) p3 (.)
P2 (s) P3 (.)
P2 (s) P3 (.)
P2 (s) P3 (.)
P2 (s) p3 (.)
P2 (s) P3 (.)
P2 (s) P3 (.)
P2 (s) P3 (.)
P2 (s) p3 (.)
P2 (s) P3 (.)


Transition
model
'V13 (S) 'V23 (S) 'V33 (S)
'V13 (S) 'V23 (S) 'V33 (S)
'V13 (S) 'V23 (S) 'V33 (S)
'V13 (S) 'V23 (S) 'V33 (S)
'V13 (S) 'V23 (S) 'V33 (S)
'V13 (S) 'V23 (S) 'V33 (S)
'V13 (S) 'V23 (S) 'V33 (S)
'V13 (S) 'V23 (S) 'V33 (S)
'V13 (S) 'V23 (S) 'V33 (S)
'V13 (S) 'V23 (S) 'V33 (S)
'V13 (S) 'V23 (S) 'V33 (S)
\V13 (CS) \V23 (S) \V33 (S)
'13 (.) 23 (S) \V33 (S)
V13 (.) 23 (CS) \S33 (S)
'13 (.) h23 (.) '33 (S)
V13 (.) h23 (S) '33 (CS)
'13 (.) 23 (S) \V33 (.)
V13 (t) '23 (S) '33 (S)
V13 (.) V23 (t) V33 (S)
'13 (.) 23 (S+t) \V33 (S)
'13 (.) 23 (S) '33 (t)
\13 (.) \-23 (S) W-33 (s+t)


A QAIC,
36.04
43.76
42.95
34.03
32.65
31.83
30.49
34.35
45.02
25.76
26.41
20.58
20.62
31.39
30.51
23.99
26.51
25.62
56.01
48.08
12.69
0.00


QAIC,
Weights
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.002
0.998









Table 4-2. Analysis of the spatial, temporal, and age-specific variation in litter size for
the yellow-bellied marmot, using a general linear model. Akaike's
Information Criterion corrected for small sample size (AICc), differences in
AICc (AAICc), AICc weights and degrees of freedom are given for each model.
Symbols are: year = time effect, site = site effect and age = age effect. A plus
sign (+) denotes additive effects. A period (.) indicates constant value of the
parameter.
AICc Degrees of
No. Model AICc A AICc ,Wehts freedom
Weights freedom
1 Litter size (year + site + age) 1773.73 19.06 0.000 49
2 Litter size (year + site) 1781.86 27.19 0.000 48
3 Litter size (year + age) 1806.56 51.89 0.000 45
4 Litter size (site + age) 1754.67 0.00 0.851 7
5 Litter size (year) 1812.33 57.65 0.000 44
6 Litter size (site) 1758.15 3.48 0.149 6
7 Litter size (age) 1786.02 31.35 0.000 3
8 Litter size (.) 1788.61 33.93 0.000 2








Table 4-3. Analysis of the temporal and spatial variation in growth rate of the adult
(animals > 2 yrs old) segment of the population (kad), using Pradel's reverse-
time models. Site-specific covariates for kad are site-specific estimates of litter
size (litters), and site-specific transition rates from non-reproductive adult ("'
23) and reproductive adult (Y'33) states to reproductive adult state. Temporal
covariates for Xad are annual estimates of litter size litterrt, and time-specific
transition rates from yearling ('t13), non-reproductive adult (,t23), and
reproductive adult (Yt33) states to reproductive adult state. Other symbols are
defined in Table 4-1.
AIC
No. Model AICc A AICC AC #
Weights
1 ~ (s) p (s) ad (s+t) 4456.17 4.19 0.043 56
2 4 (s)p (s) ad (t) 4451.98 0.00 0.351 52
3 4 (s)p (s) )d (s) 4517.21 65.23 0.000 15
4 (s)p (s) kad (.) 4512.99 61.01 0.000 11
5 (s)p (s) Xad (t23) 4509.69 57.71 0.000 12
6 (s) p (s) ad (t/33) 4515.03 63.05 0.000 12
7 (s) (s) ad (litter) 4495.72 43.74 0.000 12
8 (s)p (s) kad (s13+t) 4453.91 1.93 0.134 53
9 (s)p (s) kad (s23+t) 4453.30 1.31 0.182 53
10 4 (s) p (s) kad (S33+t) 4453.86 1.88 0.137 53
11 4 (s) p (s) kd (litters+t) 4453.65 1.66 0.153 53



















Yearling T32 W23


13 3
Reproductive
Adult



VW33



Figure 4-1. The life cycle graph for the yellow bellied marmot, with three life history
states (yearling, non-reproductive adult and reproductive adult). Transition
rates are denoted as 1i' = probability of moving from state x to state y,
conditional on surviving the period in state x. Transitions Y12, Y22, and Y32 are
complements of Y13, Y23, and Y33 (e.g., Y22 = 1 423).









0.9
0.7
Y13 0.5
0.3
0.1 -
0.9-
0,7

W23 0o5-
0.3
0.1 -
0.9-
0.,7
W33 0.5 "
0.3-
0.1 -
6-

0 5 4
4'

2-

1.1


a-


B






C





D





E


.0-4*


0000 6-Po


Figure 4-2. Site-specific estimates (mean + SE) of transition rates from (A) yearling
(Y13), (B) non-reproductive adult (Y23), and (C) reproductive adult (Y33) states
to the reproductive adult state. Mean values and standard errors were
estimated using model #11, model #22, and model #13 in Table 4-1,
respectively. Site-specific estimates of(D) litter size and (E) the realized
growth rate of the adult population (kad). Mean values and standard errors
were estimated using model #4 in Table 4-2 and model #3 in Table 4-3,
respectively.


J I


N











1.0


0.48


0.4

0.2 -

1.0

0.8

S0.6

0.4

0.2 -


6-
5-

4-
'
2



2.0

1.6 -

1.2 -

0.8

0.4
1974 1977 1MD0 1983 19M 1989 1992 1995 1998 2001


Figure 4-3. Temporal variation in transition rates from (A) non-reproductive adult (Y23)
and (B) reproductive adult (Y33) states to reproductive adult state with two
years lag. Mean values (solid line) and 95% confidence intervals (gray shade)
were estimated using model #19 and model #21 in Table 4-1, respectively.
Temporal variation in (C) the litter size with one year lag, and (D) the realized
growth rate of the adult segment of the population (Lad). The gaps in 4A and
4B indicate that these parameters were not estimable for those years. Mean
values and 95% confidence intervals were estimated using model #3 in Table
4-2, and model #2 in Table 4-3, respectively.














CHAPTER 5
THE INFLUENCE OF LOCAL DEMOGRAPHIC PROCESSES ON THE REGIONAL
DYNAMICS OF A YELLOW-BELLIED MARMOT METAPOPULATION

The dynamics of spatially structured populations are determined by the local

demographic processes, and by the interactions among local populations (i.e., dispersal).

However, few studies of long-lived vertebrates have empirically investigated the relative

importance of local demography and dispersal on regional population dynamics. We

investigated the dynamics of a spatially structured population of the yellow-bellied

marmot in Colorado, USA using data collected from 17 local populations over 43 years.

Local projected population growth rates ranged from 0.85 to 1.04, and varied among

sites. Retrospective analysis of life-table response experiments revealed that variation in

yearling survival, followed by variations in the survival of juveniles and reproductive

adults made the largest contributions to the spatial variation in population growth rates.

Using a vec-permutation matrix approach, we developed a matrix metapopulation model

and investigated the relative influence of local demographic rates and the dispersal rate

on metapopulation dynamics. Prospective elasticity analysis revealed that the

metapopulation growth rate was most sensitive to survival of the reproductive adults,

followed by that of the two younger age classes. The potential influence of dispersal on

the metapopulation growth rate was lower than that of the aforementioned demographic

rates. The dynamics of the yellow-bellied marmot metapopulation depended heavily on a

small number of good quality colony sites, and the metapopulation growth rate was

highly sensitive to the changes in the demographic rates of these sites. These results









underscore the need for the explicit consideration of the local demographic

processes for understanding the dynamics and persistence of demographically and

spatially structured populations.

Introduction

Spatial heterogeneity is a common feature of wildlife populations, and can

influence dynamics and persistence of population at local and regional scales

(Andrewartha and Birch 1954, Levins 1969, Hanski 1999). It has been suggested that a

complete understanding of the population dynamics necessitates an understanding of the

influence of spatial processes (Pulliam 1988, Kareiva 1990, Tilman and Kareiva 1997).

Consequently, both theoretical ecologists and conservation biologists rely on

metapopulation theory and models to understand the influence of spatial heterogeneity on

population dynamics (e.g., Lankester et al. 1991, Lahaye et al. 1994, Akcakaya and

Atwood 1997, Hokit et al. 2001). Although there are still gaps between theory and

practice, metapopulation models have been moderately successful in explaining and

predicting population dynamics in fragmented landscapes (Hanski 1999, Akcakaya and

Sjorgen-Gulve 2000, Sjorgen-Gulve and Hanski 2000).

Several models with varying degrees of complexity have been developed to

investigate the dynamics of spatially structured populations (for a review see Akcakaya

and Sjorgen-Gulve 2000). However, detailed demographic data at multiple sites are

difficult to collect; consequently, most empirical studies of metapopulation dynamics

have used simple models that do not require detailed demographic data (e.g., stochastic

patch occupancy models, logistic regression models). Such models of metapopulation

dynamics typically emphasize the role of regional processes such as dispersal and

synchrony among local populations, but they do not explicitly consider the role of within-









population demographic processes on the dynamics and persistence of populations at

regional scales. Ironically, regional processes such as dispersal can be heavily influenced

by local demography (e.g., Burgman et al. 1993, Lahaye et al. 1994, Lopez and Pfister

2001). Spatial variation in population dynamics is a consequence of local differences in

demographic parameters (Caswell 2000, Oli and Armitage 2004, Bruna and Oli 2005).

Moreover, dispersal is strongly dependent on local demographic processes such as

population density (Bowler and Benton 2005, Matthysen 2005). However, consideration

of local population dynamics often requires more data than those required by simpler

models (Akcakaya 2000a). As a result very few studies, particularly of long-lived

vertebrates, have investigated the relative role of local demographic processes in

determining metapopulation dynamics.

Retrospective demographic techniques provide an adequate framework for

identifying vital rates that contribute the most to the observed spatial variation in k's

(Caswell 2000, Oli and Armitage 2004, Bruna and Oli 2005). However, a thorough

understanding of metapopulation dynamics also requires information on the regional

processes such as dispersal of individuals. Dispersal connects otherwise disjunct

populations inhabiting different sites, and spatial correlation in demographic rates can

link the fates of separate populations (Hanski 1998, Morris and Doak 2002). Investigating

the relative influence of demographic and regional processes on the dynamics and

persistence of populations requires models that simultaneously consider local

demographic processes as well as regional processes.

A group of models, matrix metapopulation models (i.e. spatially and

demographically structured models), incorporate local demographic processes and