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Metapopulation Dynamics of Yellow-Bellied Marmots

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METAPOPULATION DYNAMICS OF YELLOW-BELLIED MARMOTS By SEYFI ARPAT OZGUL A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006

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Copyright 2005 by Seyfi Arpat Ozgul

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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.

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iv ACKNOWLEDGMENTS I am indebted to Madan K. Oli for his excellent mentorship, guidance and friendship throughout my gradua te education. His contributio n 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, Robe rt D. Holt, and Kathryn E. Sieving. During my graduate education, I have learne d a lot from their advice and guidance on my research, and from the courses they have ta ught. The faculty, student s, and staff of the Department of Wildlife Ecology and Conser vation 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, Saif Nomani, Janell Brush, Kara Youngentob, Gabby Hyrcyshyn, Toshinori O kuyama, 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.

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v TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES...........................................................................................................viii LIST OF FIGURES...........................................................................................................ix ABSTRACT.......................................................................................................................xi CHAPTER 1 INTRODUCTION........................................................................................................1 Background...................................................................................................................1 Objectives.....................................................................................................................4 Study System................................................................................................................6 2 EFFECTS OF PATCH QUALITY AND NETWORK STRUCTURE ON PATCH OCCUPANCY DYNAMICS OF A YELLOW-BELLIED MARMOT METAPOPULATION..................................................................................................9 Introduction.................................................................................................................10 Materials and Methods...............................................................................................12 Study Area and Species.......................................................................................12 Model Structure...................................................................................................14 Parameter Estimation...........................................................................................16 Model Simulation................................................................................................17 Adequacy of the SPOM.......................................................................................18 Results........................................................................................................................ .20 Parameter Estimation...........................................................................................20 Model Simulation................................................................................................21 Adequacy of the SPOM.......................................................................................24 Discussion...................................................................................................................25 3 SPATIOTEMPORAL VARIATION IN AGE-SPECIFIC SURVIVAL RATES OF THE YELLOW-BELLIED MARMOT................................................................40 Introduction.................................................................................................................41 Materials and Methods...............................................................................................43 Study Area and Species.......................................................................................43

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vi Field Methods and Data.......................................................................................43 Capture-Mark-Recapture (CMR) Analysis.........................................................44 Results........................................................................................................................ .48 Spatiotemporal Variation in Overall Survival Rates...........................................48 Age Structure and Spatiotemporal Varia tion in Age-Specific Survival Rates....48 Effect of Environmental Factors.........................................................................50 Influence on Population Growth Rate.................................................................51 Discussion...................................................................................................................52 4 SPATIOTEMPORAL VARIATION IN THE REPRODUCTIVE PARAMETERS OF THE YELLOW-BELLIED MARMOT................................................................64 Introduction.................................................................................................................65 Materials and Methods...............................................................................................67 Study Area and Species.......................................................................................67 Field Methods and Data.......................................................................................68 Components of Reproduction..............................................................................68 Effect of Environmenta l and Social Factors........................................................70 Influence on Population Growth Rate.................................................................71 Results........................................................................................................................ .72 Survival, Recapture, and Breeding Probability...................................................72 Litter Size............................................................................................................73 Effects of Environmenta l and Social Factors......................................................73 Influence on Population Growth Rate.................................................................74 Discussion...................................................................................................................75 5 THE INFLUENCE OF LOCAL DE MOGRAPHIC PROCESSES ON THE REGIONAL DYNAMICS OF A YELLOW-BELLIED MARMOT METAPOPULATION................................................................................................86 Introduction.................................................................................................................87 Materials and Methods...............................................................................................90 Study Area and Species.......................................................................................90 Field Methods......................................................................................................91 Local Population Dynamics................................................................................91 Metapopulation Dynamics...................................................................................94 Results........................................................................................................................ .98 Local Population Dynamics................................................................................98 Metapopulation Dynamics...................................................................................99 Discussion.................................................................................................................101 6 CONCLUSION.........................................................................................................113 APPENDIX A ANALYSIS OF SPATIAL AND TEMPORAL VARIATION IN OVERALL APPARENT ANNUAL SURVIVAL RATES.........................................................117

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vii B EFFECT OF ENVIRONMENTAL CO VARIATES ON THE SPATIAL AND TEMPORAL VARIATION IN AGESPECIFIC SURVIVAL RATES..................118 C ENVIRONMENTAL COVARIATES FOR THE COMPONENTS OF REPRODUCTION...................................................................................................119 D ELASTICITY ANALYSIS OF LOCAL POPULATION DYNAMICS..................122 LIST OF REFERENCES.................................................................................................124 BIOGRAPHICAL SKETCH...........................................................................................137

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viii LIST OF TABLES Table page 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 model.............................................................................................32 2-3. Definition of robust design occupancy models used for modeling colonization and extinction probabilities.......................................................................................33 2-4. Number of parameters, Akaikes In formation Criterion corrected for small sample size, deviances, and model like lihoods for the robust design occupancy models fitted to the yellow -bellied marmot data......................................................34 3-1. Analysis of the age structure and sp atial variation in age-specific apparent survival rates for the yellow-bellied marmot............................................................58 3-2. Analysis of temporal variation in ag e-specific apparent survival rates for the yellow-bellied marmot..............................................................................................59 3-3. Analysis of temporal and spatial vari ation in the growth rate of the entire population and adult segment of the population.......................................................60 4-1. Analysis of state-specific apparent su rvival, recapture, and transition rates for the yellow-bellied marmot..............................................................................................80 4-2. Analysis of the spatial, temporal, and age-specific vari ation in litter size for the yellow-bellied marmot..............................................................................................81 4-3. Analysis of the temporal and spatial va riation in growth rate of the adult segment of the population.......................................................................................................82 A-1. Analysis of spatial and temporal va riation in overall apparent annual survival rates for the yellow-bellied marmot........................................................................117 B-1. A table showing the effect of envi ronmental covariates on the spatial and temporal variation in agespecific survival rates....................................................118 C-1. List of covariates used during the anal ysis of the effect of environmental factors on the breeding probabilities and on litter size of the yellow-bellied marmot.......121

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ix LIST OF FIGURES Figure page 2-1. The structure of the yellow-belli ed marmot metapopulation in Colorado...............35 2-2. Yearly proportions of occupied pa tches, empty patches, and patches with unknown occupancy status, for the period between 1990 and 2002........................36 2-3. Predicted patch occupancy in 1000 rep licate simulations of the yellow-bellied marmot metapopulation using the parame terized stochastic patch occupancy model........................................................................................................................37 2-4. Predicted patch occupancy in 1000 rep licate 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 re plicate simulations for the northern and southern networks....................................................................................................39 3-1. The spatial structure of the yellowbellied marmot metapopulation in Colorado, U.S.A. Seventeen sites are grouped into four colonies (Riv er, Gothic, Marmot Meadow and Picnic) and four satellit e groups (south, west, east, and north satellites)...................................................................................................................61 3-2. Spatial variation in a nnual adult, yearling, and ju venile survival rates....................62 3-3. Temporal variation in annual adult, yearling and juvenile survival rates from 1976 to 2003.............................................................................................................63 4-1. The life cycle graph for the yellow belli ed marmot, with three life history states (yearling, non-reproductive adu lt 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 transiti on rates from non-reproductive adult and reproductive adult states to reproductiv e 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 segm ent 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

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x 5-2. Elasticity of the projected populatio n growth rate to the vital rates.......................107 5-3. Elasticity of the stochastic population gr owth rate to the mean values of the vital rates........................................................................................................................108 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 sites.........................................................................................................................109 5-5. The covariances of the vital rates among sites, and the contributions of the covariances to the variation in pr ojected 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 vi tal rate and the dispersal rate on MP.................112

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xi Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 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 spatia lly heterogeneous landscapes, and the spatial heterogeneity often has important effects on population dynamics. However, very few empirical studies on long-li ved vertebrates have thoroughly investigated the effect of spatial heterogeneity on population dynamics. Us ing 42 years of field data, I investigated the factors and processes that influenced the dynamics and pe rsistence 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 persisten ce was highly sensitive to changes in the quality of these sites. Nonetheless, satellite sites also made a signi ficant contribution to the long-term persistenc e of the metapopulation. Using capture-mark-recapture (CMR) m odeling approach, I investigated the spatiotemporal variation in demographic rates and its influences on local population dynamics. Survival and reproductive rates exhi bited both spatial and temporal variation,

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xii but the pattern of variation significantly differed among vital rates. Vital demographic rates that were the components of recruitm ent into the adult popul ation (survival of young animals, litter size and breeding probabili ty) exhibited a greater degree of variation over space and time than other vital rates, a nd were the main demographic factors driving the temporal fluctuati ons in population dynamics. Using a stage-structured matrix model, I investigated the demographic causes of the spatial variation in local population dynamics. Variati on in the survival of the young animals and that of reproductive adults made the largest contribu tions to the observed spatial variation in population growth rate. Us ing a vector-permutation matrix approach, I developed a matrix metapopulation model, and i nvestigated 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 sensi tive to changes in the demography of these high quality sites. The relati ve influence of dispersal on metapopulation growth rate was lower than that of the demographic ra tes. Most commonly used models of metapopulation dynamics emphasize the importan ce of regional processes, but do not explicitly consider th e role of within-population demogr aphic processes. However, my results underscore the need for the explic it consideration of th e local demographic processes for understanding the dynamics a nd persistence of demographically and spatially structured populations.

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1 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 dynami cs (Andrewartha and Birch 1954, Levins 1969, Hanski 1999), and investigating these effe cts may be critical to understanding the dynamics of these populations (Pulliam 1988, Kareiva 1990, Hanski and Simberloff 1997, Stacey et al. 1997, Tilman and Kareiv a 1997, Akakaya 2000b, Fagan et al. 2001). Ecologists and conservation biologists are in creasingly 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, Akakaya and Sjorgen-Gulve 2000, Hokit et al. 2001). Although there are st ill gaps between theory and practice, several studies utiliz ing metapopulation (i.e., a set of lo cal populations connected through dispersal) approaches have been moderate ly successful in explaining and predicting wildlife population dynamics in fragment ed landscapes (e.g., Hanski et al. 1995, Moilanen et al. 1998). The various methods of representing sp ace, tracking populations and individuals, dealing with environmental va riability, and describing disper sal have generated a variety of metapopulation models that differ in gene rality and realism (Kareiva 1990, Hanski 1999, Akakaya and Sjorgen-Gulve 2000). Some of these models are data intensive, and

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2 the lack of adequate data has precluded the application of more complex models. For many threatened species, data to paramete rize complex models are often lacking, and simpler modeling approach es are the only option. The presence-absence of a species at a partic ular 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 pers istence 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 ve ry few comparisons of different modeling approaches applied to the same popu lations (but see Hokit et al. 2001). Simple metapopulation models (e.g., patch occupancy models) emphasize the role of regional processes, such as dispersa l and synchrony among local populations, but do not explicitly consider the role of local de mographic processes, such as survival and reproductive rates, density dependence and tempor al trends in these v ital rates. However, local demographic processes can be importa nt 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, th e dispersal of individuals among local

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3 populations is often dependent on demogr aphic processes (Bowler and Benton 2005, Matthysen 2005). However, consideration of local demographic processes usually requires more data than is required by simple models (Akakaya 2000a). As a result, very few studies of long-lived species have thorough ly investigated spatiotemporal variability in local demographic rates and it s influence on population dynamics. The relative significance of local and regi onal processes on population persistence is an important question from both theoreti cal and practical pers pectives. A group of models, matrix metapopulation models (i.e., st ructured metapopulation models), attempts to incorporate local demographic proce sses and regional processes into modeling population dynamics across multiple sites (Akakaya 2000a, Hunter and Caswell in press). These models form the basis of seve ral published populati on viability analyses (PVA's, reviewed in Boyce 1992, Akakaya 2000b, Beissinger and McCullough 2002). Recent developments in matrix metapopulati on models have provided a framework for using the analytical approach es to matrix analysis (e.g., sensitivity and elasticity analyses) for metapopulation models (Hunter and Caswell in pre ss). This approach provides an analytical fram ework for investigating the relative influence of local demography and dispersal on metapopulation dy namics. However, even simple matrix metapopulation models are data intensive and thus difficult to parameterize for most species; there are very few studies that pr ovide 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 demogra phic processes on the dynamics of spatially structured populations, partic ularly for long-lived species.

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4 Objectives In this doctoral research, I investigated the factors and processes that influence the dynamics and persistence of a yellow-bellied marmot meta population 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 (ra dio-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 an imals in several discrete habitat patches provided adequate data for a rigorous ex amination of metapopulation dynamics using models with different degrees of sophisti cation. My specific object ives were (1) to investigate the relative influence of partic ular sites and site quality on metapopulation persistence, (2) to investigate the spatial heterogeneity in demographic rates and its influence on population dynamics, (3) to determ ine the relative influence of demographic rates and the dispersal rate on the meta population 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 (Cha pters 2-5), and a general conc lusion chapter (Chapter 6). In Chapter 2, I parameterized and analy zed a stochastic patch occupancy model (Moilanen 2004), and investigated the relative influen ce of particular sites, site quality, network characteristics, and regi onal stochasticity on the pers istence of the yellow-bellied marmot metapopulation. In chapters 3 and 4, I investigated th e 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-

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5 structured Cormack-Jolly-Seber model (Leb reton et al. 1992, Lebreton et al. 1993) and long-term capture-mark-recapture (CMR) da ta. 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 Casw ell 2002) and age-specific litter sizes using a general linear model. In both chapters, I also te sted a series of hypotheses concerning the effects of key environmental and social factors on the observed variation in each vital rate. Furthermore, using a Pr adel's reverse-time CMR model (Pradel 1996, Nichols and Hines 2002), I modeled the realized population growth ra te 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. Us ing 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 popul ation dynamics of the yellow-bellied marmot. Next, using a vector permutation matrix appr oach (Hunter and Caswell in pr ess) and the dispersal data, I developed a matrix metapopulation model th at connected the local population dynamics via dispersal. Using this dem ographically and spatially struct ured model, I investigated the relative influence of local demographic rates and the dispersa l rate on metapopulation dynamics. Finally, Chapter 6 provides a general conc lusion of the results presented in the previous chapters. This research aimed to pr ovide a better understa nding of the local and

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6 regional processes that u nderlay the dynamics of the yellow-bellied marmot metapopulation, and to provide insights into th e utility of different modeling approaches. The Study System The yellow-bellied marmot ( Marmota flaviventris ) is a large, diurnal, burrowdwelling rodent, widely distri buted 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-te rm study of marmots in the Upper East River Valley (2900 m above sea level, 38 57' N 106 59' W), near the Rocky Mountain Biological Laboratory, Gunnison County, Colo rado (Armitage 1991, Schwartz et al. 1998). Distribution of marmots in the East Ri ver Valley is patchy and closely associated with the local mosaic of meadow and fo rest vegetation. Marmots typically occupy meadows associated with talus and large boul ders, where they build their burrow systems (Svendsen 1974). These distinct habitat patches vary in size ra nging 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 fema le, her litter, and sometimes an adult male. Large and higher quality patc hes (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 ol d), and young (Armitage 1991, 1998). A marmots circannual cycle has two phase s, the active period (approximately 5 months) and hibernation (approx. 7 months), th at entail, sequentially, emergence from the burrow, reproduction, growth, preparation for hibernation, immergence into burrow, and hibernation (Armitage 1991). The circannual cycl e 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 tw o years of age. This is

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7 probably the major factor leading to soci ality in marmots (Armitage 1981). Marmots produce a litter of 1 to 8 young that appear above ground ar ound late June. Most young marmots remain and hibernate at their natal site. Most of the disp ersal 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 empt y 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 st rongly 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 repr oduction in subordinate females (Armitage 1989, 2003c, Oli and Armitage 2003). Survival and reproduction seem to be aff ected by the length of the active season, which varies from year to year (Armita ge 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 aw ay 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 bi ology of yellow-bellied marmots in Gothic, Colorado, is described in detail by Arm itage (1991, 2002). Although a great deal is

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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.

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9 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 partic ular site is the simplest form of data that can be collected during ecological fiel d 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 signi ficance of particular patches and the influence of site qualit y, network characteristics, and regional stochasticity on the metapopulati on persistence. Persistence of the yellow-bellied marmot metapopulation was strongly dependent on the hi gh 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 re gional persistence. However, lower quality satellite sites also made a significa nt contribution to long-term metapopulation persistence, especially wh en regional stochasticity was high. The northern network of the marmot metapopulat ion was more stable compared to the southern network, and the persistence of th e 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 stochast ic patch occupancy models can provide important insights into metapopulation dynamics using data that are easy to collect.

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10 Introduction Many biological populations occupy spat ially heterogeneous environments, and there is a growing realizati on that spatially-mediated pro cesses (e.g., dispersal, habitat connectivity) are vita l for the regional persistence of populations. Ecologists are increasingly relying on meta population 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, Akakaya and Atwood 1997, Hokit et al. 2001). The presence/absence of a species at a partic ular 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 be en well developed, and these models have received much practical application (M oilanen 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 extinc tion 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 (region al stochasticity). These assu mptions are reasonable for many biological populations inhabi ting highly fragmented landscapes, where only a small portion of the landscape often provides suitab le habitat (Hanski and Ovaskainen 2003). An important question that can be addre ssed using SPOMs is: what is the relative significance of particular pa tches 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

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11 connected. However, low quality patches ma y, 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 st udies have observed that persis tence of a particular patch network may depend on the presence of othe r networks (e.g., Moilanen et al. 1998). SPOMs have mostly been used to model the metapopulation dynamics of large invertebrates or small vertebra tes. The preference for small-b odied habitat specialists is dictated by the criteria of regional persisten ce as a classical metapopul ation: high rate of population increase, short generation time, and high habitat specificity (Murphy et al. 1990, Hanski 1999). However, some mammal po pulations that occupy discrete habitat patches also exhibit characteristics of me tapopulations, 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, Marmota flaviventris (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 i ndividuals from surroundi ng patches (Svendsen 1974, Armitage 2003b). Although there is a grad ient from low quality to high quality sites, marmot habitats can be grouped into two major quality t ypes: (1) colony (high quality), and (2) satellite (low quality) sites. The persiste nce of the metapopulation is

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12 believed to be dependent mainly on the colony si tes, 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 yellowbellied marmots in the Upper East River Valley near the Rocky Mountain Biological Laboratory, Colora do (hereafter referred to as Colorado). Specifically, we investigated the relative influence of particular sites, site quality, network characteristics, and regiona l stochasticity on th e persistence of the yellow-bellied marmot metapopulation. Materials and Methods Study Area and Species The yellow-bellied marmot is a large, diurnal, burrow-dwel ling rodent, widely distributed in the mountainous region of the western United States (Frase and Hoffmann 1980). Marmots typically occupy meadows w ith 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 de nsity of marmots varied remarkably among sites, and local patch area does not necessarily repres ent the local population size (Armitage and Schwartz 2000). We use the term "site quality" to de scribe the combined effect of multiple environmental factors (including patch area) on local population size. Satellite sites (lower quality patches) are typi cally occupied by a single adult female, her litter, and sometimes an adult male. Colony s ites (higher quality patc hes) are occupied by one or more matrilines, each typically consisti ng of one male, two or more closely related adult females, yearlings (1 year old), and young (Armitage 1991, 1998).

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13 Typically, all yearling males and about half of the yearling females disperse (Van Vuren 1990, Schwartz et al. 1998). Recolonizatio n 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 extincti on occurs when a matriline dies out or deserts a site. However, lo cal turnover events can be concealed by the immediate occupation of an empty site by immigrants, t hus creating an apparent rescue effect. The detailed biology of yellow-bellied marmots in Colorado is described by Armitage (1991, 2002). Although the number of patche s 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 meta population (Murphy et al 1990, Hanski et al. 1995). First, marmots live in sp atially discrete ha bitat patches. Thei r burrow systems are typically located in open meadow patches with ro cky outcrops (Svendsen 1974). Philopatric marmots rarely go >50 m away fr om burrows because of the predation risk. Second, all local populations face the risk of lo cal extinction in the absence of a rescue effect. The average population size of the larg est colony is approximately 20 animals, and local extinction is possible due to predati on, disease, environmental and demographic stochasticity or catastr ophes. Third, the probability of su rvival during dispersal decreases with the distance moved (Van Vuren 1990). Ther efore, low survival of the long-distance dispersers can result in a distance-depe ndent dispersal. Fina lly, the local population dynamics are sufficiently asynchronous (Armitage and Downhower 1974, Armitage 1977, 2003b, Oli and Armitage 2004). Asynchro ny in local population dynamics

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14 increases the probability that an extinct local population is reestablished, or a declining population is rescued by dispersers from ot her local populations (H anski et al. 1995). Therefore, the yellow-bellied marmot syst em 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 meta population. 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 probabi lity, and rescue effect (Moilanen 2004). The shape of the dispersal kernel is important only when the metapopulation consists of several small networks that are fa r from each other, which was not the case in our system. Therefore, we used the simple negative exponential function for describing the dispersal kernel: (,)exp() ijijDdd (1) where dij is the distance between patches i and j and is the distribution parameter of the dispersal distances ( 1/ = average dispersal distance). For the connectivity function, we used th e subfunction that incl udes the effect of local patch area (patch quality in this study) on connectivity: ()()cb iijj jiStAOtDA (2) where Oj(t) is the occupancy status of each patch at time t D is the dispersal kernel (Eq.

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15 1), and Ai is the quality of patch i Parameter b scales emigration, and parameter c scales immigration as a function of patch qua lity (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 th e subfunction that includes the Allee effect in colonization (Hanski 1994b): 2 22[()] () [()]i i iSt Ct Sty (3) where Si(t) is the connectivity of patch i at time t (Eq. 2), and y is a model parameter. For the extinction function, we used tw o alternative subfunctions, one that was used in the incidence function model (IFM) a nd the other in spatially realistic Levins model (SRLM): i x iE A (IFM) (4) 1exp i x iE A (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 th e SPOM, and it essentially decreases the extinction probabilities of wellconnected patches. We used th e generalized version of the rescue effect function to determine the strength of the rescue effect: ()min{1,(1())}R iiiEtCtE (6) where parameter R determines the strength of the rescue effect.

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16 Different models with alternative comb inations of connectivity and extinction functions were parameterized and the most parsimonious model was identified using Akaikes Information Criterion corrected for small samples, AICc (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 occupa ncy 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 indi cate local population si ze. This indicator is based on the assumption that as the patch area increases, local population size increases, hence the local ex tinction risk decreases. Pa tch area is preferred by many authors, because estimating area is generally easier than estima ting 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 th an was patch area. Where possible, independent estimation of m odel parameters is preferable in order to reduce the number of parameters to be es timated from site occupancy data (Hanski 1999). Parameter of the dispersal kernel was estim ated using independent dispersal data, while the remaining model parameters (b, c, y, x, and R) were estimated from the

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17 site occupancy data using the Markov Chain Monte Carlo method (Moilanen 1999). Analysis of local population dynamics duri ng the last 40 years did not reveal any significant trend in population si zes (Schwartz et al. 1998, Sc hwartz and Armitage 2003, Oli and Armitage 2004). Therefore, it was r easonable to assume th at the yellow-bellied marmot metapopulation was at a st ochastic quasi-equilibrium. Model Simulation Metapopulation dynamics were simulated using the most parsimonious model which was selected based on AICc as described above. Each scenario was simulated 1000 times for 100 years. Model predictions incl uded changes in average proportion of occupied patches and proportion of simula ted replicates that survived throughout 100 years, and average metapopulation life time (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 aver age 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) satell ite sites excluded, (3) original configuration. Predictions of alternative models on metapopulation persiste nce 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 me tapopulation can be divided into two networks, the northern and the southern ne twork, which are separated by areas of unsuitable habitat. The most parsimonious mode l was used to simulate three alternative scenarios: (1) northern networ k, (2) southern network, a nd (3) entire network. The

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18 predictions of altern ative models on metapopulation persis tence were compared to assess the significance of compar tmentalization among sites (e.g., Moilanen et al. 1998). Significance of regional stochasticity. Spatial correlation in environmental stochasticity (regional stochasticity) can heavily in fluence metapopulation persistence (Hanski and Ovaskainen 2003). Regional stocha sticity is included in SPOMSIM based on log-normal variation in patch area, which creates a yearly synchronous variation in both extinction and colonization rates (Moila nen 2004). The standard deviation () 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 ( = 0.1 & 0.2) and analyzed the sensitivity of model predictions to regional stochasticity. Adequacy of the SPOM We used the robust design occupancy m odeling approach (MacKenzie et al. 2002, MacKenzie et al. 2003) to investigate the ade quacy 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 () and the rate at which unocc upied sites are recolonized (). We used program MARK V 4.0 (White and Burnham 1999) to implement the robust design occupancy model with parameters (proportion of sites occupied), (probability of an occupied site becoming unoccupied), (probability of an unoccupied site becoming occupied), and (detection probability on a visit to the si te) (MacKenzie et al. 2002, MacKenzie et al. 2003). Robust design occupancy models implemented in pr ogram MARK provides more flexibility in modeling recolonization and extinction probabi lities, and allows comparison of several alternative model structures th at are not included in SPOMSIM.

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19 Program MARK can be used to estimate time-specific rates of extinction and colonization, and time-varying individual cova riates can be used to incorporate sitespecific information into the model. We es timated the siteand time-specific extinction and colonization rates for 21 sites for 13 y ears using the most parsimonious SPOM. We used these estimates as time-varying site covariates for estimating and parameters using MARK. Years for which the occupanc y 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 th e site was not occupied) in our occupancy history, and set our detection probability parameter () 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 AICc for model comparison, and for the identification of the most parsimonious model in the candidate model se t. Candidate models differed in the way parameters and were modeled. We used four alternative model structures for modelling extinction rate, First, we modelled as a constant rate {(.)}. Second, we modelled as a time-specific rate and let it vary among years {(t)}. Third, we let vary among sites and used site qualit y 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 st ructures for modelling recolonization rate, Similar to we initially modelled as a constant {(.)} and a time-specific {(t)} rate. Then, we let vary among sites and through ti me, and used the colonization { (C)} and connectivity { (S)} parameters estimated from SPOM as time-varying site covariates. We expect the models in which the time-vary ing site covariates (estimated from SPOM)

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20 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 fr om 90 radio-instrumented marmots (Van Vuren 1990) to estimate the dispersal kernel parameter, The average dispersal distance was 2.087 km, and was estimated as the inverse of the average dispersal distance ( = 1/(2.087) = 0.479). To evaluate the robustness of our estimate, we set as a free parameter in SPOMSIM, and estimated it from patch occupancy data. This method gave an estimate of 0.337, which was slightly sm aller than our independent estimate. These estimates indicated fairly high dispersal ability which was consistent with previous field observations (Van Vuren 1990). We perfor med simulations using both values of and found that the qualitative conclusions re mained unchanged. Here, the independent estimate of (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 AICc weights to select the best mode l 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) fo r describing the dispersal kernel ( fixed at 0.479). Connectivity function that included the e ffect of local patch quality (Eq. 2). Colonization function with the Allee effect in colonization (Eq. 3).

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21 Extinction function from th e original IFM (Eq. 4). Rescue effect with parameter R (strength of the rescue e ffect) fixed at 1.0 (Eq. 6). The differences in AICc values between the best m odel (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 include d the effect of local patch quality on connectivity by incl uding the model component Ai c (in Eq. 2). Despite the small differences in AICc values, we used model with the smallest AICc value (model # 5) for simulating metapopulation dynamics. Pa rameter 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: Moilan en 2004), indicating th at local extinction probability decreased rather quickly with increasing popul ation 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) pa tches were 0.78, 0.08 and 0.02, respectively. Incidentally, value of x estimated for the yellow-bellied marmots was very close to the one estimated for the American pika, Ochotona princeps (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. Scali ng of immigration with patch quality was in the typical range (c < 0.5), indicating that local patch quality had a significant influence on the immi gration 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

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22 estimates given in Table 2-2. For all simu lations, the average proportion of occupied patches and the proportion of surviving simulation replicat es were reported for two different levels of regional stochasticity ( = 0.1 and = 0.2). As expected, simulations of the entire network showed equilibrium dynamics at the lower regional stochasticity, and higher regi onal stochasticity did no t 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 stabilit y, 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 stoc hasticity was low, 12% of the simulated replicates went extinct within 100 years, whereas 20% went extinct when regional stochasticity was high. In the ab sence of the satellite sites, av erage persistence time of the metapopulation decreased from infinity to 2481 years. Absence of colony sites significantly altered the overall metapopulation persistence. Even at the lowe r level of regional stochasticit y, 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 onl y 12 satellite sites was only 10 years. To evaluate the sensitivity of patch occ upancy dynamics to changes in the quality of colony sites, we gradually reduced the qua lity 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 persisten ce. The proportion of

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23 occupied patches declined to 60% at th e 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 si mulated replicates pers isted at the end of 100 years, whereas, at higher regional stochast icity, only 80% persisted (Fig. 2-4A). This 20% reduction in the quality of colony s ites resulted in a decrease in average metapopulation life time from infinity to 3254 years. These results indicated that persis tence 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 qualit y sites on metapopulati on 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 una ffected by the absence of the two best quality sites (Fig. 2-4B,C). Howe ver, in the absence of the best three sites, site occupancy gradually declined to 42%, and 15% of the si mulated replicates went extinct within 100 years (Fig. 2-4B,C). In the absence of th e best four sites, the metapopulation was no longer persistent; the proportion of occupied patches rapidly declin ed, and only 45% of the simulated replicates persis ted for 100 years (Fig. 2-4B,C). We used connectivity-based clustering anal ysis available in SPOMSIM to test for the existence of hierarchical network st ructure of the metapopulation in terms of connectivity between networks (Moilanen 2004). This analysis revealed the existence of two networks: upper-valley (northern) and lo wer-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 dynami cs of these two networks. The metapopulation

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24 in the northern network was more stable than the southern network. The proportion of occupied patches in the northern network di d 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 th e simulated replicates survived till the end of 100 years (Fig. 2-5B). We repeated our simulations using va lues sampled from the 95% confidence interval of parameter estimates, and each rep licate was run with the new set of parameter values. Our previous results remained unchange d, indicating that our results were fairly robust to small changes in the parameter values. Adequacy of the SPOM To investigate the adequacy of SPOM fo r the yellow-bellied marmot system, we compared a set of candidate models us ing 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 resu lted in poor model likelihoods (Table 24). Models with constant colonization and extinction rates had higher likelihoods compared to time-specific models that ignored site-specific differences. Model likelihoods were significantly improved wh en timeand site-specific extinction probabilities estimated using the SPOM were included as covariates. The models that included connectivity or coloni zation parameters as covariat es did not significantly differ from constant colonization rate models (first three models in Table 2-4). Nonetheless, two models with SPOM-predic ted colonization rates were among the best models. These findings indicated the adequ acy of the SPOM for modeling the dynamics of the yellowbellied marmot metapopulation.

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25 Discussion Our study suggests that (1) persistenc e of the yellow-bellied marmot metapopulation strongly depends on the co lony sites. (2) Overall metapopulation persistence was highly sensitive to small cha nges 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 th e 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 th at colony sites are occupied by matrilines that may persist for many generations (Armitage and Downhower 1974, Armitage and Schwartz 2000, Armitage 2003b). Increased ma triline sizes improve the persistence of the local population by affecting survival and net reproductive rate (Armitage and Schwartz 2000, Armitage 2003b). Consistent wi th these observations, our results suggest that colony sites are the ma jor drivers of the yellow-b ellied marmot metapopulation dynamics, and that the quality of these sites was especially importan t; a small decline in site quality resulted in a si gnificant decline in metapopulation persistence. Also, a small number of colony sites might be ultima tely responsible for the metapopulation persistence. The dependence of metapopulation persistence on a small number of high quality sites has been suggested to be a genera l rule in long-lived species (Harrison 1991, Schoener 1991), and has been observed in American pika, Ochotona princeps (Moilanen et al. 1998), a species that shares similar life-hi story characteristics. These results emphasize the importance of local site quality and of environmental factors that may influence local site quality, for metapopulation persistence.

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26 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 explic itly considered in the st ochastic patch occupancy modeling approach; however, local population dynamics are a ssumed to be insignificant and generally overlooked (Hanski 1999). Gi ven that the yellow-bellied marmot metapopulation persistence is highly sensitive to changes in the quality of a few colony sites, a complete understanding of marm ot metapopulation dynamics likely requires consideration of factors and processes that influence the dynamics of local populations. Overall, however, SPOM provided a reasonab le 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 persiste nce, our results sugge st that lower quali ty satelli te sites may also contribute markedly to the long-term persistence of the yellow-bellied marmot metapopulation. The risk of metapopulation ex tinction increases in the absence of the satellite sites, especially when the fluctu ations in site qualities are regionally synchronous. Although satellite sites are much lo wer 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

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27 sites locally go extinct. Observed importance of lower quality sites for the regional dynamics suggests that the yellow-bellied marm ot 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 metapopulati on in which the extinctionrecolonization 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 southe rn 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 site s; 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 pers istence 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 in cluding the effect of local patch area in SPOMs significantly improved the connectivit y 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 alternat ive models including the origin al IFM, which ignored the effect of local patch quality on connec tivity (Hanski 1994b). To investigate the differences between the predictions of the SPO M used in this study and IFM, we repeated

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28 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 metapopulati on persistence. In the absen ce 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 connect ivity 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 populatio ns outside the study area. However, this assumption is unlikely to be correct. Base d 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 in side 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 outsi de of the study area can result in an overestimation of colonization ab ility, hence in an overestim ation of regional persistence (Moilanen 2002). It is also important to not e 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 intr insic extinction rates, dispersal distances and colonization ability (Moilanen 2002). Therefor e, our measures of persistence are not conservative, and should be interpreted with caution.

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29 Finally, we utilized the robust design o ccupancy modeling approach to test the adequacy of the SPOM used for simulations of the yellow-bellied marmot system. We found that colonization and ex tinction events varied among sites; thus, an important assumption of the classical metapopulation mo del (Levins 1969) was not appropriate for the yellow-bellied marmot metapopulation. Considering site-s pecific connectivity measures and extinction probabilities estimated using the SPOM significantly improved the likelihood of the resulting model. Theref ore, we believe that the SPOM adequately described the site occupancy dynamics of the yellow-bellied ma rmot 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 individua ls can influence population dynamics of social organisms (Grimm et al. 2003). The ye llow-bellied marmot is a socially complex species (Blumstein and Armitage 1999, Ar mitage and Schwartz 2000), and an accurate description of the dynamics of marmot metapopulations may t hus necessitate models that can incorporate behavioral in teractions among individuals. Ho wever, models that allow explicit consideration of beha vioral interactions (e.g., individual-based models) are structurally complex and data-intensive. A lthough models that consider behavioral interactions should be preferred when data ar e 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 requireme nts. 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 Hanskis (2004)

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30 findings that SPOMs adequately mimic the behavior of more complex models are encouraging to those who lack detailed demogr aphic 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 we ll as robust design occ upancy 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 th ese 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 pers istence to local population size, future studies of the yello w-bellied marmot meta population should also consider local population dynamics. Nonetheles s, our analyses based on simple site occupancy data provided an adequate descri ption and several useful insights regarding the dynamics and persistence of the yellow-bellied marmot metapopulation.

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31 Table 2-1. Models and subfunction defin itions used in SPOMSIM, and Akaikes Information Criterion values corrected for small sample size (AICc), number of parameters (#par) and model likel ihoods. Connectivity f unction parameter c was fixed at for the mode ls 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 Levins model. Subfunction for the rescue effect was m odeled with R (strength of the rescue effect) fixed at , and R set as a free parameter during parameter estimation. Model c Extinction probabilityR AICc AICc# par Model likelihood 1 0 IFM 1 161.40.8 5 0.670 2 0 IFM Free162.82.2 6 0.333 3 0 SELM 1 162.72.1 5 0.350 4 0 SELM Free164.74.1 6 0.129 5 Free IFM 1 160.60.0 6 1.000 6 Free IFM Free162.62.0 7 0.368 7 Free SELM 1 161.40.8 6 0.670 8 Free SELM Free163.52.9 7 0.235

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32 Table 2-2. Markov Chain Monte Ca rlo estimates of the paramete rs 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 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 parametersEstimates95% 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

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

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34 Table 2-4. Number of parameters (#Par), Akaikes Information Criterion corrected for small sample size (AICc), deviances, and model likelihoods for the robust design occupancy models fitted to the yellow-bellied marmot data. Parameters and are the extinction and colonizati on rates, respectively. Initial occupancy rate ( was estimated as a constant rate, and detection probability () was set to 1 in all models. For model definitions see Table 2-3. Model # ParAICc DevianceAICcModel likelihood (E) (S) 5 158.4143.7 0 1.00 (E) (.) 4 158.9148.1 0.5 0.75 (E) (C) 5 159.2144.5 0.8 0.67 (Q) (S) 5 164.7150.1 6.3 0.04 (Q) (.) 4 165.2154.4 6.8 0.03 (Q) (C) 5 165.4150.8 7 0.03 (.) (S) 4 176.2165.3 17.8 0 (.) (C) 4 177.1166.2 18.7 0 (.) (.) 3 178.1170.5 19.7 0 (.) (t) 14 282.3149.3 123.9 0 (t) (.) 14 284.6151.6 126.2 0

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

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

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37 Figure 2-3. Predicted patch occupancy in 1000 replicate simulations of the yellow-bellied marmot metapopulation using the parame terized stochastic patch occupancy model. Confidence intervals (95%) for th e proportion of occupied patches in all sites (A), colony sites only (B), and satellite si tes only (C) are given as solid lines. Proportion of surviving replic ates 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 = 0.1 are shown as black lines, and for = 0.2 are shown as gray lines.

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38 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 replic ates 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.

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39 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 sout hern (B) network ar e given as solid lines. Proportion of surviving replicates in the northern (A ) and the southern (B) network are given as dashed line s. Simulation results with regional stochasticity set at = 0.1 are shown as black lines, and for = 0.2 are shown as gray lines.

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40 CHAPTER 3 SPATIOTEMPORAL VARIATION IN AGESPECIFIC SURVIVAL RATES OF THE YELLOW-BELLIED MARMOT Spatiotemporal variation in age-specific survival rates can profoundly influence population dynamics, but few studi es of vertebrates have t horoughly investigated both spatial and temporal variability in age-specific su rvival rates. We used 28 years (1976 2003) of capture-mark-recapture (CMR) data from 17 locations to parameterize an agestructured Cormack-Jolly-Seber model, and inve stigated spatial and temporal variation in age-specific annual survival ra tes of yellow-bellied marmots (Marmota flaviventris). Survival rates varied both spatially and te mporally, 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 mode ls to estimate the realized population growth rate ( ), and to investigate the influe nce of the observed variation in age-specific survival rates on 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 dynami cs of other mammals with similar life history characteristics.

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41 Introduction Populations inhabiting spatially heter ogeneous 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 th e dynamics, regulation, and persistence of populations (Kareiva 1990, Pulliam and Da nielson 1991, Tilman and Kareiva 1997). Survival is a crucial demographic para meter influencing population growth rate, and thus the population dyna mics, of many populations (Stearns 1992, Pfister 1998, Heppell et al. 2000, Sther and Bakke 2000, Oli and Dobson 2003), and it can be influenced by spatiotemporal variation in fact ors such as weather, ha bitat 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, Sther 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 significa nt spatial variation in survival has been reported for a number of species. For exampl e, Coulson et al. (1999) observed spatial differences in survival rates among local populations of Soay sheep (Ovis aries). Waser et al. (1995) attributed sp atial differences in surv ival of dwarf mongooses (Helogale parvula) to variation in habitat quality. Severa l 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.

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42 Survival rates of many long-lived species vary by age; individuals of different ages often respond differentially to changes in enviro nmental 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 affect ed by spatiotemporal changes, and their survival rates are expected to be le ss 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, regul ation, and persistence of populations. However, simultaneous examinations of both sp atial and temporal variation in extrinsic factors, and their influence on age-specific surviv al rates, have been rare (but see Ringsby et al. 1999, Sther 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 vari ation 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 rate s, and examined both spatial and temporal variation in these rates. We also tested a series of hypotheses con cerning the effects of key environmental factors on the observed vari ation in survival rates. Finally, using a Pradels reverse-time CMR model, we estimat ed the realized population growth rate, and

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43 investigated the influence of the observed vari ation in age-specific survival rates on the realized population growth ra te, 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-dwel ling rodent, occupying montane regions of the western North Amer ica (Frase and Hoffmann 1980, Armitage 2003a). Our study area is located in the U pper East River Valley near the Rocky Mountain Biological Laboratory, Gothic, Colorado (38 57 N, 106 59 W). The marmots in our study area occupy 17 discrete ha bitat patches (Fig. 31). 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 st eeper 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-be llied marmots in Colorado is described in detail by Armitage (1991, 2003a). Field Methods and Data From 1962 to 2003, yellow-bellied marmot s were live-trapped and individually marked using numbered ear tags (details in Armitage 1991). Animal identification number, sex, mass and reproduc tive condition were recorded for each animal. Trapping concurrently occurred in 17 sites kno wn to be occupied by marmots.

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44 Four variables were used as site-speci fic 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 el evation towards the northwest. Marmot sites on the west side of the East River Valley have steeper slopes facing northeast (38o-98o), whereas sites on the east side are located on gradually inclined meadows generally facing southwest (183o-280o). Seven time-specific climatic variables were used as temporal covariates in the CMR analyses: (1) length of the growing s eason (number of days between first bare ground and the first killing frost), (2) annual precipitation (cm), a nd (3) monthly mean summer (MayAugust) temperature (oC) 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 we re obtained from Rocky Mount ain Biological Laboratory, Gothic. Mean monthly temperature during the active season (May-August) ranged from 9.7 11.9 Co, and annual precipitation ranged fr om 38.6 86.6 cm. For a detailed description of time-specific climatic f actors, 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 prov ided 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 ag es were known exactly. Sixty-nine known dispersers that moved among sites (identifie d based on trapping data) were excluded from

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45 the analyses. Seventeen sites were grouped in to eight categories on the basis of site quality and location (Fig. 3-1). Four major co lony sites were consid ered separately: (1) Picnic, (2) River (two adjacent sites were gr ouped into one), (3) Marmot Meadow and (4) Gothic. Satellite sites were typically occ upied by few individuals. We assumed that survival rates of marmots o ccupying adjacent satell ite sites that share similar habitat characteristics (e.g., size, aspect, elevation) we re similar. Therefore, satellite sites were grouped with respect to their lo cation: (5) north sa tellites, (6) west satellites, (7) east satellites and (8) south satellites. We implemented the CMR models usi ng 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 () and recapture rates (), and to investigate the spatial and temporal variati on in these rates. We used Program UCARE V2.02 (Choquet et al. 2003) to test the goodne ss-of-fit of the CJS model. We used Akaikes Information Criterion, corrected for small sample size, (AICc) for model comparison, and for the identification of th e most parsimonious model from a candidate model set (Burnham and Anderson 2002). Model comparison was based on the differences in AICc values, AICc. We used AICc weight as a measure of relative support for each model. The underlying process standard deviation () of the estimated parameters over space (or time) was used as an estimate of the spatial (or temporal) variation. The was estimated using the variance components procedure implemented in Program MARK, which is an extension of th e procedure described in Burnham et al. (1987).

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46 The CMR analyses proceeded in a stepwise fashion. In preliminary analyses, we tested for site and time effects on overall surv ival rates. We then proceeded to determine the appropriate age structure for our study population. Previo us demographic studies of yellow-bellied marmots have used 2 or more age classes (Schwart z et al. 1998, Oli and Armitage 2004). Thus, we parameterized and compared the following models with alternative age structures: no ag e structure, two age classes (j uveniles: 0-1 yr ; adults: >1 yr), three age classes (juveniles: 0-1 yr, year lings: 1-2 yrs, and adu lts: >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 mode ls 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 ar e generally less variab le 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 th e site effect. Next, using the most parsimonious model, we investigated the temporal variation in ageand site-specific survival rates. We considered the additive and interactive effects of site and time on agespecific survival rates (Williams et al. 2001). We note that the order in which site and time effects were included in the model did no t influence the results of model selection; testing for the time effect first, and then tes ting for the site effect resulted in the same final models. To investigate the effect of s ite quality on spatiotemporal variation in agespecific survival rates, we fu rther 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 spatia l and temporal variation in age-specific

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47 survival rates. We tested fo r the effects of each covariate by modeling the logits of agespecific survival rates as a lin ear function of a site-specific or temporal covariate. Each temporal covariate was scaled to range betw een 0 and 1. If the 95% confidence interval for the slope parameter ( ) did not include 0, th e relationship was considered statistically significant (Williams et al. 2001). Because we only had data on a subset of the environmental factors that could have influen ced 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 Pradels 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 (). RELEASE Tests 2+3 (implemented in Program MARK) were used for assessing goodness-of-fit of the Pradels model. Spatial and temporal variation in was examined as described for the CJS models. Because Pradels models do not allow for age effect (Franklin 2001), estimates of could be biased due to unaccounted differences in age-specific survival rates. Th erefore, we also estimated and modeled the realized growth rate of the adult (>2 yrs) segment of the population, a nd investigated the relative influence of the spatial and temporal varia tion in age-specific survival rates on adult population growth rate (ad). To assess the relative importance of age-specific survival rates to ad, we modeled ad directly as a function of these rates (N ichols and Hines 2002, Nichols et al. 2003). Specifically, we asked: which age-specific su rvival rate most closely covaried (over space and time) with ad? We used site-specific estimates of age-specific survival rates as

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48 a covariate for site effect on ad, and time-specific estimates as a covariate for time effect on ad. We used the slope parameter () to relate the variation in the vital rate to variation in ad (Nichols et al. 2003). Results Spatiotemporal Variation in Overall Survival Rates Our general CJS model, (t s) (t s), fit the data with a slight under-dispersion (2 150 = 120.2, P = 0.965). There was strong support fo r significant variation in the overall (i.e., age structure i gnored) annual survival rates both among sites and through time (Table A-1). However, site and time effects were additive, and there was no evidence for interactive effects. The most pa rsimonious 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 st udied 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-1). The recapture rate was 0.98 for these th ree colony sites and 0.79 for the fourth colony site (Gothic). R ecapture rates for the north, west, east, and south satellites were 0.91, 0.85, 0.69, and 0.94, respectively. Age Structure and Spatiotemporal Vari ation 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, wh ereas there was less support for site effect in adult survival rates (mode l #6 in Table 3-1). However, these two models (models #2 & #6) did not differ significantly ( AICc < 3), and we chose to continue our analysis with

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49 the model including site effect in all three age classes (model #2 in Table 3-1). Juvenile survival rates were relatively low in three co lony 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). Yearlin g 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 satelli te sites (0.64; 95% CI: 0.57, 0.71) (Fig. 3-2A). Adult survival ra tes were generally high er 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 ( = 0.11). Spatial variation in juvenile survival ( = 0.08) was slightly lower than in yearling survival, but higher than in adult survival rates ( = 0.04). Analysis of recapture rates with age stru cture 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 eff ect 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 a dult survival rates (m odel #3 in Table 3-2). Grouping sites into two quality types (colony an d satellite sites) resulted in a more parsimonious model for the adult and juvenile survival rates. The model with separate

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50 adult survival rates for col ony and satellite sites (model #18 in Table 3-2) was more parsimonious than the model with separate adul t survival rates for each of the eight sites (model #10 in Table 3-2), indicating that the ob served spatial variati on in adult survival rates was due primarily to differences betw een satellite and colony sites. Juvenile survival rates varied spatially but not temporally in satellite sites, whereas they exhibited substantial temporal variation ( = 0.20) in the colony sites (model #18 in Table 3-2; Fig. 3-3C). A model with a similar support (AICc < 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), whic h was biologically more plausible, as the base model for evaluating the eff ect of environmental covariates. Effect of Environmental Factors Preceding analyses revealed temporal vari ation in juvenile survival rates, and spatial variation in the survival rates of a ll three age-classes. T hus, we examined the influence of temporal and site-specific covari ates on juvenile surviv al rates and of sitespecific covariates on the yearling and adu lt survival rates (see Table B-1 for model details). Site-specific variation in juvenile survival rates was positively influenced by the aspect ( = 0.41; 95% CI: 0.03, 0.79) and ne gatively influenced by elevation ( = -0.24; 95% CI: -0.47, -0.01) of each site. Site-speci fic variation in yearling survival rates was positively influenced by the elevation ( = 0.26; 95% CI: 0.01 0.51). Site-specific variation in adult survival rates was pos itively influenced by the average group size ( = 0.13; 95% CI: 0.00, 0.27). Temporal variation in juvenile survival rates in colonies was negatively influenced by the leng th of permanent snow cover ( = -3.09; 95% CI: -5.37, 0.85).

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51 Influence on Population Growth Rate Goodness-of-fit test indicate d that the general Pradels model for the entire population fit the data poorly (2 151 = 422.7, P < 0.001). We, thus, used a variance inflation factor ( = 2.79) in parameter estimation and model-selection (White and Burnham 1999, Burnham and A nderson 2002). We used the model structure for survival and recapture rates { (t+s) (s')} identified during the pr eliminary analysis, and estimated the spatial and temporal variation in the realized annual population growth rate, The most parsimonious model indicated only site effect on (model #2 in Table 3-3). Site-specific estimates of 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. 32E). Time-specific estimates of ranged from 0.65 (95% CI: 0.45, 0.81) to 1.49 (95% CI: 0.93, 2.05) (Fig. 3-3E). The general Pradels model for the adult se gment of the population fit the data with a slight under-dispersion (2 56 = 27.6, P = 0.999). We used the model structure for adult survival and recapture rates {ad_col (.) ad_sat (.) (s')} identified previously, and estimated the spatial and temporal variati on in the annual realized adult population growth rate, ad. The most parsimonious model indicated additive effects of site and time on ad (model #8 in Table 3-3). Further grouping of sites into colony and satellites resulted in a more parsimonious model. Parameter ad 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 ad within the colonies (model #11 in Table 3-3) Site-specific estimates of ad ranged from 0.92 (95% CI: 0,86, 0.99) to 1.07 (95% CI: 1.03, 1.11); ad was less than 1.0 only in north and west

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52 satellite sites (Fig. 3-2D ). Annual estimates of ad in colony sites ranged from 0.28 (95% CI: 0.19, 0.47) to 1.83 (95% CI: 1.20, 2.30); ad exhibited substantial temporal fluctuations (Fig. 3-3D). Because of the poor fit of the general Pradels model (i.e., model for overall population growth rate, ) to data, we conducted additiona l analyses focusing on the adult segment of the population. The ad covaried most closely with juvenile survival rates over space (Fig. 3-2) as well as over time with a one year lag (Fig. 33). Spatial variation in ad was significantly influenced by among-site variation in juvenile survival rates ( = 0.36; 95% CI: 0.14, 0.58; model #12 in Tabl e 3-3), but not by that in yearling ( = -0.03, 95% CI: -0.19, 0.12; model #13 in Table 3-3) or adult ( = 0.17; 95% CI: -0.43, 0.77; model #14 in Table 3-3) survival rates. Temporal variation in ad was significantly influenced by temporal variation in juven ile survival rates of the preceding year ( = 0.76, 95% CI: 0.39, 1.12; model #15 in Table 3-3) and yearling survival rates ( = 0.40, 95% CI: 0.02, 0.79; model #16 in Table 3-3), but not by that in adult survival rates ( = 0.44, 95% CI: -1.08, 0.19; model #17 in Table 3-3). Discussion Spatiotemporal variation in vital dem ographic rates is a common phenomenon in animal populations, and such variation can have important population dynamic consequences. However, rigorous investiga tions into population dynamic consequences of spatiotemporal variation in age-specific vi tal rates require data at large spatial and temporal scales. Consequently, there have b een relatively few studies that explicitly considered both sources of variation. Our long-term study of individua lly-identified animals in several discrete habitat patche s provided adequate data for a rigorous

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53 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 mo st appropriate age st ructure was the three age-class model: juveniles (0-1 yr), yearlings (1-2 yrs) and adults (>2), suggesting that the survival rates sign ificantly differed among these three age classes. Previous studies on other ground squirrels reported higher survival rates for ad ults, and lower rates for young animals (Bronson 1979, Farand et al. 2002). Su rvival rates of adult yellow-bellied marmots in Colorado were generally highe r 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 juve nile survival rates in the lower quality satellite sites. Hence, our results indicat e that differences in habitat quality can differentially affect age-speci fic survival rates in sciuri d 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 disp erse 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 th erefore, are likely to be underestimated. Spatial variation in survival rates was obs erved 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 th an that of adults, and it was influenced by

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54 the aspect and the elevation of each site. Juvenile survival rates on southwest facing slopes were higher than those on northeast faci ng 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 gi ven site. These factors have been suggested as important determinants of juvenile survival (Van Vuren and Armitage 1991). Bronson (1979) reported no eff ect of elevation on the surv ival of juvenile goldenmantled 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 si tes (see also Lenihan and VanVuren 1996); they were ac tually higher in two satellite sites (Fig. 3-2C). Juvenile survival rates are likely to be affected by di fferences in microclimate owing mostly to the differences in aspect and eleva tion 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., ad equate hibernation opportunity, protection from predation, higher food availability) ar e 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 w ith those of Armitage and Schwartz (2000) that average group size positively influenced th e survival rate of a dult animals. Zammuto and Millar (1985) and Bronson ( 1979) indicated that adult su rvival rates were higher at higher elevations for some ground squirrel popula tions. Gillis et al. (2005), on the other

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55 hand, reported that annual survival ra tes 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 st udy 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 fo r 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 wa s 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 su ch variation (Schwartz and Armitage 2005). Multiple environmental and social factors may act synergistically to influence survival rates of marmots in our metapopulation, and th e individual or combined effect of a few factors cannot account for the observed variatio n. 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

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56 entire population ( ) and of the adult segment of the population ( ad) followed a pattern that primarily reflected site-specific differe nces in juvenile survival rates. Modeling ad as a function of age-specific survival rates revealed that spatial variation in ad was significantly influenced by surviv al of juveniles but not of ye arlings or adults. Likewise, ad closely covaried over time with survival of juveniles with one y ear time lag. Because survival of yearlings and adults did not va ry significantly over time, it seems reasonable to conclude that most of the observed tempor al variation in population growth rate was due primarily to temporal variation in surviv al of juveniles. Thes e results suggest that spatial and temporal variation in populati on dynamics of yellow-bellied marmots was strongly influenced by spatiotemporal va riation in juvenile survival rates. It has been suggested that vital demogr aphic rates with th e greatest potential influence on population growth rate tend to exhibit the least tem poral (or spatial) variability (Cairns 1992, Gaillard et al. 1998, Pfister 1998, Gaillard et al. 2000). In yellow-bellied marmots, the projected populat ion growth rate is highly sensitive to variation in juvenile surviv al rates (Oli and Armitage 2004). However, we found that, among all age-specific survival rates, surviv al of juveniles was the most variable over space and time. This variation heavily influe nced the dynamics of our study population; site-specific and temporal vari ation in population growth rate closely covaried with, and primarily reflected spatiotemporal variation in survival of juveniles. Thus, the high variability in juvenile surviv al rates over space and time cl early 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

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57 classes has been reported for other long-lived vertebrate spec ies (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 j uveniles is more variab le over space and time than that of older animals. Spatial and temporal variation in juvenile survival rates strongly influenced the variati on in the growth rates of our study population. Given the high variability in survival rates of younge r 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 t horoughly 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 surv ival on the population dynamics of some longlived vertebrates (e.g., Doak et al. 1994, Caswell et al. 1999, Gaillard et al. 2000), suggesting that the generality of our conclu sions may be limited to species with lifehistories similar to the yellow-bellied marmot.

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58 Table 3-1. Analysis of the age structure and spatial variation in age-specific apparent survival rates for the yellow-bellie d marmot, using Cormack-Jolly-Seber models. Akaikes Information Criterion corrected for small sample size (AICc), differences in AICc values (AICc), AICc 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 ageclass model). Symbols are: = apparent annual survival rate, = annual recapture rate, s = site effect, and s' = modified site effect. A period (.) indicates constant value of the parame ter. The most parsimonious models are highlighted in bold. No. Model AICc AICc AICc Weights #p 1 juv (s) ad (s) (s')* 2666.1745.89 0.000 22 2 juv ( s ) yrl ( s ) ad ( s ) ( s' )** 2622.63 2.35 0.170 30 3 juv (s) yrl (s) sub-ad (s) ad (s) (s')***2633.1312.85 0.001 38 4 juv (.) yrl (s) ad (s) (s')** 2625.485.20 0.041 23 5 juv (s) yrl (.) ad (s) (s')** 2626.286.00 0.027 236 juv ( s ) yrl ( s ) ad ( ) ( s' )** 2620.28 0.00 0.549 23 7 juv (s) yrl (s) ad (.) (s)**2622.71 2.43 0.163 25 8 juv (s) yrl (s) ad (s) (s)**2625.09 4.80 0.050 32 9 juv (s) yrl (s) sub-ad (.) ad (.) (s')***2622.322.03 0.152 24 10 juv (s) ad (.) (s')*2674.8354.55 0.000 15 11 juv (s) yrl (.) ad (.) (s')**2623.543.26 0.082 16 2 age-class model ** 3 age-class model *** 4 age-class model

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59 Table 3-2. Analysis of temporal variation in age-specific apparent survival rates for the yellow-bellied marmot, using age stru ctured 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 th e subscripts. Other symbols are defined in Table 3-1. The most pa rsimonious models are highlighted in bold. No. Model AICc AICc AICc Weights #p 1 juv ( s ) yrl ( s ) ad ( s ) ( s' ) 2622.6334.25 0.000 30 2 juv ( t ) yrl ( s ) ad ( s ) ( s' ) 2613.0224.64 0.000 49 3 juv ( t + s ) yrl ( s ) ad ( s ) ( s' ) 2607.2618.88 0.000 56 4 juv ( t s ) yrl ( s ) ad ( s ) ( s' ) 2655.4167.03 0.000 179 5 juv ( t + s ) yrl ( t ) ad ( s ) ( s' ) 2624.9236.54 0.000 73 6 juv ( t + s ) yrl ( t + s ) ad ( s ) ( s' ) 2628.0039.62 0.000 80 7 juv ( t + s ) yrl ( s ) ad ( t ) ( s' ) 2627.0038.62 0.000 73 8 juv ( t + s ) yrl ( s ) ad ( t + s ) ( s' ) 2627.8239.44 0.000 80 9 juv_col ( t ) juv_sat ( t ) yrl ( s ) ad ( s ) ( s' ) 2602.6114.23 0.000 68 10 juv_col ( t ) juv_sat ( s ) yrl ( s ) ad ( s ) ( s' ) 2598.7210.35 0.003 52 11 juv_col ( s ) juv_sat ( t ) yrl ( s ) ad ( s ) ( s' ) 2625.6237.24 0.000 46 12 juv_col ( t ) juv_sat (.) yrl ( s ) ad ( s ) ( s' ) 2599.2910.91 0.002 49 13 juv_col ( t + s ) juv_sat ( s ) yrl ( s ) ad ( s ) ( s' ) 2599.0610.68 0.002 55 14 juv_col ( t ) juv_sat ( s ) yrl_col ( s ) yrl_sat (.) ad ( s ) ( s' ) 2602.3313.95 0.000 49 15 juv_col ( t ) juv_sat ( s ) yrl_col (.) yrl_sat ( s ) ad ( s ) ( s' ) 2600.1511.77 0.001 49 16 juv_col ( t ) juv_sat ( s ) yrl ( s ) ad_col ( s ) ad_sat (.) ( s' ) 2592.504.12 0.062 49 17 juv_col ( t ) juv_sat ( s ) yrl ( s ) ad_col (.) ad_sat ( s ) ( s' ) 2594.586.20 0.022 49 18 juv_col ( t ) juv_sat ( s ) yrl ( s ) ad_col (.) ad_sat (.) ( s' ) 2588.380.00 0.486 46 19 juv_col ( t + s ) juv_sat ( s ) yrl ( s ) ad_col (.) ad_sat (.) ( s' ) 2588.670.29 0.421 49

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60 Table 3-3. Analysis of temporal and spatial variation in the growth rate of the entire population () and adult (animals >2 yrs ol d) segment of the population (ad), using Pradels reverse-time models Site-specific covariates for ad are juvenile (juvs), yearling (yrls), and adult (ads) survival rates, and temporal covariate for ad are juvenile survival rate of the previous year (juvt-1), 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. No. Model AICc AICc AICc Weights #p Entire population: 1 ( t+s ) ( s' ) (.) 2994.6313.92 0.001 41 2 ( t+s ) ( s' ) ( s ) 2982.241.53 0.318 48 3 ( t+s ) ( s' ) ( t ) 2994.6413.93 0.001 67 4 ( t+s ) ( s' ) ( t+s ) 2980.710.00 0.681 74 Adult segment of the population: 5 ad_col (.) ad_sat (.) ( s' ) ad (.) 2183.3667.29 0.000 9 6 ad_col (.) ad_sat (.) ( s' ) ad ( s ) 2162.9846.91 0.000 16 7 ad_col (.) ad_sat (.) ( s' ) ad ( t ) 2158.9742.90 0.000 35 8 ad_col (.) ad_sat (.) ( s' ) ad ( t+s ) 2127.7211.65 0.003 42 9 ad_col (.) ad_sat (.) ( s' ) ad_col ( t ) ad_sat ( t ) 2140.5124.44 0.000 36 10 ad_col (.) ad_sat (.) ( s' ) ad_col ( t ) ad_sat ( s ) 2120.584.51 0.090 37 11 ad_col (.) ad_sat (.) ( s' ) ad_col ( t+s ) ad_sat ( s ) 2122.196.12 0.040 42 12 ad_col (.) ad_sat (.) ( s' ) ad_col ( t+juvs) ad_sat ( juvs) 2116.070.00 0.857 35 13 ad_col (.) ad_sat (.) ( s' ) ad_col ( t+yrls) ad_sat ( yrls) 2126.4610.39 0.005 35 14 ad_col (.) ad_sat (.) ( s' ) ad_col ( t+ads) ad_sat ( ads) 2126.3310.25 0.005 35 15 ad_col (.) ad_sat (.) ( s' ) ad_col ( juvt-1+s ) ad_sat ( s ) 2151.9935.91 0.000 17 16 ad_col (.) ad_sat (.) ( s' ) ad_col ( yrlt+s ) ad_sat ( s ) 2161.0144.94 0.000 17 17 ad_col (.) ad_sat (.) ( s' ) ad_col ( adt+s ) ad_sat ( s ) 2163.2147.14 0.000 17

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61 Figure 3-1. The spatial structure of th e 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).

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62 Figure 3-2. Spatial variati on in annual (A) adult (ad), (B) yearling (yrl), and (C) juvenile (juv) 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 (ad) and (F) entire population (). Mean values and standard errors were estimated us ing model #6 and model #2 in Table 3-3, respectively.

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63 Figure 3-3. Temporal varia tion in annual (A) adult (ad), (B) yearling (yrl) and (C) juvenile (juv) survival rates from 1976 to 2003. Mean values (s olid 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 (ad) with one year lag, and (E) entire population (). Mean values (solid line) a nd 95% confidence intervals (gray shade) were estimated using the model #10 and model #3 in Table 3-3, respectively.

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64 CHAPTER 4 SPATIOTEMPORAL VARIATION IN TH E REPRODUCTIVE PARAMETERS OF THE YELLOW-BELLIED MARMOT Spatiotemporal variation in reproductive rates is a common phenomenon in many wildlife populations, but popul ation dynamic consequences of spatial and temporal variability in different components of repr oduction (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 (Marmota flaviventris), and its influence on the real ized population growth rate. Specifically, we estimated and modeled the litt er size, and the probability of breeding the following year of the yearling (i.e., pr e-reproductive), non-reproductive adult and reproductive adult females. The breeding probabilities of the non-reproductive and reproductive adults and the litter size vari ed 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 e nvironmental and social factors on the observed variation in each component of re production. We used a reverse-time CMR model to investigate the influence of co mponents of reproduction on the realized population growth rate. The litter size and the breeding probability of the nonreproductive adults had a significant influen ce on the realized population growth rate. Our results indicate that the re cruitment into the adult segmen t of the populat ion is likely

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65 to be the critical component of the po pulation dynamics of the yellow-bellied marmots and other mammals with sim ilar life history characteristics. Introduction Many species live in discrete habitat patche s that occur either naturally or due to human-caused fragmentation of once contiguou s habitats (Hanski and Ovaskainen 2003, Hanski and Gaggiotti 2004) Habitat patches may experience different sets of environmental conditions, such as resour ce availability, pred ation pressure, and microclimatic conditions. Additionally, envi ronmental conditions in each habitat patch may change over time. Such spatiotemporal va riation in environmental factors can cause differences in vital demographic rates over time and space, and these differences can significantly influence the dynami cs, regulation, and persiste nce of populations (Kareiva 1990, Pulliam and Danielson 1991, Tilman and Kareiva 1997). Reproduction is an important life history tra it that can be partic ularly sensitive to spatiotemporal variation in the environment (Roff 1992, Stearns 1992, Heppell et al. 2000, Caswell 2001). Changes in the environmen tal 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., Sther 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. Therefor e, a thorough understanding of population dynamics over space and time requires a de tailed understanding of spatiotemporal variation in reproductive rates, and of environmental and/or so cial factors that can cause such variation.

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66 Reproduction can be considered as bei ng composed of two parts: breeding probability and number of offs pring produced (Lebreton et al 1990, Nichols et al. 1994). The probability that an indi vidual 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, Br yant 2005). Spatiotemporal variation in breeding probability can cause spatiotempor al variation in population dynamics even when average litter or clutch size remains relatively st able. Although spatiotemporal variation in litter (or clutch) size or fecundity rates have been examined for some species (e.g., Bronson 1979, Jarvinen 1993, Sther et al. 1999, Coulson et al. 2000, Gaillard et al. 2000, Chamberlain and Crick 2003, Trembl ay et al. 2003), variation in breeding probability over space and time, and population dynamic consequences of such variations have received much less attention. Discer ning the population dynamic consequences of spatiotemporal variation in reproductive parameters necessitates simultaneous examination of variation in both component s of reproduction (i.e ., breeding probability and number of offspring produced). Howe ver, few studies have simultaneously considered spatial and temporal variati on in both components of reproduction or investigated population dynamic cons equences of such variation. Our objective was to investigate the sp atiotemporal variation in breeding probability and litter si ze, and to examine the population dynamic consequences of such variation in the yellow-bellied marmot (Marmota flaviventris). We applied multistate capture-mark-recapture (CMR) models to 43 ye ars (1962 2004) of data from 17 discrete habitat patches, and examined both spatia l and temporal variation in the breeding probability. We also investigated the spatial a nd temporal variation in litter size; this,

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67 combined with spatiotemporal variation in breeding probability, enabled us to discern which component of reproduction varied over sp ace or time. We also tested a series of hypotheses concerning the effects of key e nvironmental and social factors on the observed variation in each component. Fina lly, using a Pradel 's reverse-time CMR model, we estimated and modeled the reali zed population growth rate, and examined population dynamic consequences of the spa tiotemporal variation in components of reproduction. Materials and Methods Study Area and Species The yellow-bellied marmot is a large, diurnal, burrow-dwel ling rodent, occupying montane regions of the western North Amer ica (Frase and Hoffmann 1980, Armitage 2003a). The study was conducted in the Uppe r East River Valley near the Rocky Mountain Biological Laboratory, Gothic, Colorado (38 57 N, 106 59 W). The marmots in our study area occupy discrete habi tat 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 st eeper talus slopes (Svendsen 1974, Blumstein et al. in press) These distinct habitat patc hes 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, yearli ngs, and juveniles, wher eas 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-bell ied marmot first breeds at 2 years of age, less than a quarter of 2-year-old females reproduce, a nd the median age of first reproduction is 3

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68 years (Schwartz et al. 1998). The biology of yellow-bellied marmots in Colorado is described in detail by Armitage (1991, 2003a). Field Methods and Data From 1962 to 2004, yellow-bellied marmot s were live-trapped and individually marked using numbered ear tags (details in Armitage 1991). Animal identification number, sex, mass and reproduc tive 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 th ese 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 fema les that were captured as juveniles were known exactly, whereas ages fo r other females were estimated based on body mass ( 2 kg = yearling, > 2 kg = adult, Arm itage et al. 1976). Li tter size was the number of weaned young that em erged 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 probabi lity 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 st atus (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

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69 year) states. We used the multistate CMR m odel (Hestbeck et al. 1991, Brownie et al. 1993, Williams et al. 2001, Fujiwara and Casw ell 2002) implemented in Program MARK (White and Burnham 1999) to estimate and m odel state-specific survival, recapture, and transition rates. The transition rate xy 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 stat e to the reproductive state: 13 (probability of a yearling breeding the following year as a two year-old conditional on survival), 23 (probability of a non-reproductive adult breed ing the following year cond itional on survival), and 33 (probability of a reproductive adult breed ing again the following year conditional on survival) (Fig. 4-1). Hereafter, we will us e "the breeding probabil ity" to indicate "the probability of breeding the following year conditional on survival", for simplicity. Both yearling recapture (1) and yearling to yearling transition rates (11) 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 (21) and reproductive to yearling state (31), which were biologically impossible, were al so fixed to zero. Transitions 12, 22, and 32 are complements of 13, 23, and 33, respectively (e.g., 32 = 1 33). We used Program UCARE V2.02 (Choquet et al. 2003) to test the goodness-of-fit of the general multistate mode l. We used quasi-likelihood adjusted Akaikes Information Criterion, corrected for small sample size (QAICc) for model comparison, and for the identification of the most parsimonious mode l from a candidate model set (Burnham and Anderson 2002). Model comparison was based on the differences in QAICc values, QAICc. We used QAICc weight as a measure of relati ve support for each model. There was no significant temporal variation in the surv ival or recapture rates of the yearling or

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70 adult marmots (Ozgul et al. in press-a). Theref ore, 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-reproductiv e adults and reproductive adults. Fi nally, we tested for both site and time effects on state-specific trans ition rates (i.e., breed ing probabilities). We used a general linear model (GLM) to test for spatial and temporal variation in the litter size. Analysis of ag e effects on litter size re vealed that two age-class (2 year old, and older females) model was the most parsimonious model, a result consistent with earlier findings that two y ear 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 e nvironmental and social factors on breeding probabilities and litter size. We considered the influence of th ree sets of covariates that can potentially influence components of reproduc tion: (1) site-specifi c, (2) climatic, and (3) social factors (Appendix C, Table C-1). 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 c ovariates. The influence of the aforementioned covariates on the litter size was examined si milarly by modeling the l itter size as a linear function of each of the site-spe cific, climatic, or social c ovariates. Because we only had

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71 data on a subset of the environmental and so cial factors that c ould have influenced reproductive parameters, we considered the infl uence of each covariat e separately. If the 95% confidence interval for the slope parameter ( ) did not include 0, the relationship was considered statistically significant (Williams et al. 2001). Influence on Population Growth Rate We used Pradels reverse-time CMR m odel (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 (). RELEASE Tests 2+3 (implemented in Program MARK) were used for assessing goodness-of-fit of the Pradels model. Previous analysis (Ozgul et al. in pressa) indicated a poor fit of th e general Pradels model (i.e., model for overall population growth rate, ) to data. Therefore, we conducted our analyses focusing on the growth rate of the adult ( 2 yrs) segment of the population ( ad). Spatial and tem poral variation in ad was examined as described for the multistate models. To assess the relative importance of different components of repr oduction to adult population growth rate, we modeled ad directly as a function of these rates (Nichols and Hine s 2002, Nichols et al. 2003). Specifically, we asked: which components of reproduction significantly influenced spatial and temporal variation in ad? We used site-specific es timates of transition rates and litter size as covariates to test for site effect on ad, and time-specific estimates as covariates to test for time effect on ad. Each component of re production would influence the adult segment of the population with a ti me lag. Time-specific estimates of the transition rates were included with a two year lag (e.g., 23 during 1996-97 period would influence ad during 1998-99), whereas those of the litter size were included with a one

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72 year lag (e.g., litter size during 1996 would influence ad during 1997-98). We used the slope parameter () to relate the variation in th e vital rate to variation in ad (Nichols et al. 2003). Results Survival, Recapture, and Breeding Probability The goodness-of-fit test of the general mu ltistate model indicated a slight overdispersion (2 111 = 121.4, P = 0.24). Thus, we used the calculated value of the overdispersion parameter ( = 1.09) for parameter estimati on 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 adul ts, and site effect on the recapture rates of non-reproductive adults. Recapture rates (mean SE) for nonreproductive 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. R ecapture rate for nonreproductive adults in satellite sites was 0.62 0.05. The su rvival rates for yearlings (0.46 0.03) and reproductive a dults (0.76 0.02) were cons tant, whereas survival rates of non-reproductive adults varied among sites. Survival rate of non-re productive 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 a nd temporal variation in each transition rate. The most parsimonious model indicated no spa tial or temporal variation in 13 (0.25 0.03). However, it is important to note that 13 was inestimable for the majority of the sampling periods. The parameter 23 did not vary over time, but sh owed spatial variation ranging from 0.31 0.05 (River) to 0.59 0.14 (Marmot Meadow) (Fig. 4-2). The parameter 33

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73 exhibited both spatial and temporal variation. It varied from 0.47 0.06 (Satellites) to 0.82 0.07 (Marmot Meadow) among sites (F ig. 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 th e three transition rates (Table 4-1). Litter Size The most parsimonious model for litter size in cluded the additive effects of site and age, but no time effect (model #4 in Table 42). Estimates of litte r 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 lowe r 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 ( AICc = 3.48). Effects of Environmental and Social Factors We examined the influence of environmen tal and social factors on each transition rate using the most parsimonious model id entified above (model #22 in Table 4-1). Among the site-specific factors considered (Appendix C), the aspect significantly influenced 23 ( = -0.64, 95% CI: -1.06, -0.22) and 33 ( = 0.61, 95% CI: 1.21, 0.01); breeding probability was lower for non-repr oductive adults and higher for reproductive adults in southwest facing sites than in northeast facing sites. The parameter 23 was positively influenced by elevation ( = 0.44, 95% CI: 0.12, 0.77). Among social factors (Appendix C), residency status significantly influenced 23 ( = 0.61, 95% CI: 0.16, 1.06); probability of breeding was higher fo r resident non-reproductive females than immigrant non-reproductive females. The parameter 23 was positively influenced by the average group size ( = 0.26, 95% CI: 0.10, 0.42) a nd the relative number of adults ( =

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74 0.46, 95% CI: 0.11, 0.80). The parameter 13 was negatively influenced by the relative number of yearlings ( = -0.75, 95% CI: -1.14, -0.36) and the relative number of adults ( = -0.50, 95% CI: -0.69, -0.31) present in the site. Parameter 33 was negatively influenced by the principal components representing the severity of the preceding winter ( = -0. 31, 95% CI: -0.02, -0.60) an d the onset of the present summer ( = -0.34, 95% CI: -0.03, -0.64), and it was positively influenced by the principal component representing preci pitation during the previous summer ( = 0.41, 95% CI: 0.69, 0.12) (Appendix C). We examined the influence of environmenta l 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 ( = 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 factor s significantly influenced litter size. Influence on Population Growth Rate The general Pradels model for the adult se gment of the population fit the data with a slight underdispersion (2 118 = 52.2, P = 0.999). We used the most parsimonious model identified for the adult survival and recapture rates {ad (s) (s)}, and modeled the spatial and temporal variation in the annua l realized adult population growth rate, ad. The most parsimonious model indicated onl y the time effect, but no site effect, on ad (model #2 in Table 4-3). A model with less suppo rt indicated additive effects of time and site on ad (model #1 in Table 4-3) Annual estimates of ad ranged from 0.54 0.05 (1983) to 1.68 0.23 (2003) indicating substan tial temporal fluctuations (Fig. 4-3). The ad was positively influenced by the temporal variation in 23 ( = 0.28, 95% CI: 0.04,

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75 0.51) and litter size ( = 0.65, 95% CI: 0.37, 0.94), but not by that in 33 ( = -0.01, 95% CI: 0.18, -0.20). We did not include 13 in this analysis, because 13 was not estimable for the majority of the periods. The ad ranged from 1.01 0.01 (Marmot Meadow) to 1.04 0.01 (Gothic), but did not vary signifi cantly among sites (Fig. 4-1). Thus, variation in some reproductive parameters over space di d not contribute substantially to spatial variation in ad. 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 spatio temporal variation in reproduction and its demographic consequences requir es data at large spatial a nd temporal scales. Our long term study of yellow-bellied marmots provided sufficient data for a thorough investigation of the spatiotemporal varia tion in different com ponents of reproduction. Specifically, we addressed the following que stions: Which compone nts of reproduction varied over time and among sites? Which e nvironmental or social factors potentially influenced the observed variation? And, finally, what are the population dynamic consequences of the observed variat ions in these demographic rates? Components of reproduction in yellow-bellie d marmots exhibited both spatial and temporal variation. However, the degr ee of variation differed among different components of reproduction. The breeding proba bility 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 probabi lity of the non-repr oductive adults showed significant spatial, but not temporal, va riation. However, it was alwa ys higher than the breeding

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76 probability of the yearlings, indicating si gnificant effect of age on the breeding probability. The breeding probability of the re productive adults showed both spatial and temporal variation. Nonetheless, it was ge nerally higher than the breeding probability of the non-reproductive adults, indica ting that females that have reproduced in a given year are also more likely to reproduce the followi ng year. The litter si ze varied among sites and between two age classes. Two year old fe males, which are all first time breeders, generally have smaller litters compared to ol der 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 pres s-a). Yet, our study revealed that the survival of non-reproductive adults was generally lower than that of re productive adults. There was no evidence that reproduction was costly as measured by change s in either the surv ival rate or the probability of breeding the following year (Nichols et al. 1994). Contrary to the predictions of life history th eory (Stearns 1992), reproductive females generally survived better, and also were more likely to breed the following year compared to nonreproductive females (see also Oli and Armitage 2003). Several environmental and social factor s can act simultaneously to influence components of reproduction in mammals (e.g., Cl utton-Brock et al. 1987, Stenseth et al. 1996, Leirs et al. 1997, Couls on et al. 2000). We found that different components of reproduction in yellow-bellied marmots we re influenced by different sets of environmental or social factors. The breedi ng probability of the re productive adults and litter size were influenced mostly by the climatic factors, whereas the breeding

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77 probabilities of the yearlings and non-reprodu ctive 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 c onsistent with earlier studies suggesting that reproduc tive suppression might play a dominant role in causing delayed age of first repr oduction (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 nonreproductive resident adult had significantly higher probability of breeding than a nonreproductive immigrant. Group size had a positive effect on this breeding probability, indicating social enhancement of reproducti on (Armitage 1998, Armitage and Schwartz 2000). Environmental factors that significantly in fluenced the breeding probability of the reproductive adults included precipitation du ring the previous summe r, winter severity, and early summer environmental conditions. All of these factors can potentially influence the physical condition of a fema le, 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 as pect 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 so cial conditions. A cha nge in the breeding probability of the reproductive adults is lik ely to be a consequence of the trade-off between somatic and reproductive efforts in reaction to a change in environmental

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78 conditions (Stearns 1992, Oli 1999). This inte rpretation is strongly supported by studies of other species of marmots in which reprodu ctive skipping occurs because females are unable to gain sufficient mass to both surv ive 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 nort heast 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 gr owth rate is a resu lt of variation in vital demographic rates. Give n that components of reproducti on varied over time and/or space, we asked how these variations influen ced the population growth rate. The realized growth rate of the adult segment of the population ( ad) showed significant fluctuations during the study period (see also Ozgul et al. in press-a). Among all reproductive parameters, litter size and th e breeding probability of the non-reproductive adults significantly influenced th e temporal variation in ad. The observed spatial or temporal variation in the breeding probability of th e reproductive adults did not significantly influence the observed variation in ad. 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 p opulation 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 Oz gul et al. (in press-a) indicate that litter size and juvenile survival, abetted by the breeding probability of the non-reproductive

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79 adults, are likely to be the main demographic factors drivi ng the dynamics of the yellowbellied marmot population. Thes e vital rates (survival of you ng 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 sp ace 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 th e yellow-bellied marmot (Armitage 1973, 2003b), and other species with simila r life history characteristics. We conclude that components of repr oduction 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 nonreproductive 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.

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80 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 adjust ed Akaikes Information Criterion corrected for small sample size (QAICc), QAICc weights and number of parameters (#p) are given for each mode l. Each age class is indicated as a subscript: yearling (1), non-reproductive adult (2), and reproductive adult (3). Symbols are: = apparent annual survival rate, = annual recapture rate, xy = 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 1, 11, 21, and 31 are fixed at 0. Parameters 12, 22, and 32 are complements of 13, 23, and 33, respectively (e.g., 22 = 1 23). No. Survival model Recapture model Transition model QAICc QAICc Weights #p 1 1 ( s ) 2 ( s ) 3 ( s ) 2 ( s ) 3 ( s ) 13 ( s ) 23 ( s ) 33 ( s ) 36.04 0.000 37 2 1 ( s ) 2 ( s ) 3 ( s ) 2 ( cs ) 3 ( s ) 13 ( s ) 23 ( s ) 33 ( s ) 43.76 0.000 36 3 1 ( s ) 2 ( s ) 3 ( s ) 2 (.) 3 ( s ) 13 ( s ) 23 ( s ) 33 ( s ) 42.95 0.000 35 4 1 ( s ) 2 ( s ) 3 ( s ) 2 ( s ) 3 ( cs ) 13 ( s ) 23 ( s ) 33 ( s ) 34.03 0.000 36 5 1 ( s ) 2 ( s ) 3 ( s ) 2 ( s ) 3 (.) 13 ( s ) 23 ( s ) 33 ( s ) 32.65 0.000 35 6 1 ( cs ) 2 ( s ) 3 ( s ) 2 ( s ) 3 (.) 13 ( s ) 23 ( s ) 33 ( s ) 31.83 0.000 32 7 1 (.) 2 ( s ) 3 ( s ) 2 ( s ) 3 (.) 13 ( s ) 23 ( s ) 33 ( s ) 30.49 0.000 31 8 1 (.) 2 ( cs ) 3 ( s ) 2 ( s ) 3 (.) 13 ( s ) 23 ( s ) 33 ( s ) 34.35 0.000 28 9 1 (.) 2 (.) 3 ( s ) 2 ( s ) 3 (.) 13 ( s ) 23 ( s ) 33 ( s ) 45.02 0.000 27 10 1 (.) 2 ( s ) 3 ( cs ) 2 ( s ) 3 (.) 13 ( s ) 23 ( s ) 33 ( s ) 25.76 0.000 28 11 1 (.) 2 ( s ) 3 (.) 2 ( s ) 3 (.) 13 ( s ) 23 ( s ) 33 ( s ) 26.41 0.000 27 12 1 (.) 2 ( s ) 3 (.) 2 ( s ) 3 (.) 13 ( cs ) 23 ( s ) 33 ( s ) 20.58 0.000 24 13 1 (.) 2 ( s ) 3 (.) 2 ( s ) 3 (.) 13 (.) 23 ( s ) 33 ( s ) 20.62 0.000 23 14 1 (.) 2 ( s ) 3 (.) 2 ( s ) 3 (.) 13 (.) 23 ( cs ) 33 ( s ) 31.39 0.000 20 15 1 (.) 2 ( s ) 3 (.) 2 ( s ) 3 (.) 13 (.) 23 (.) 33 ( s ) 30.51 0.000 19 16 1 (.) 2 ( s ) 3 (.) 2 ( s ) 3 (.) 13 (.) 23 ( s ) 33 ( cs ) 23.99 0.000 20 17 1 (.) 2 ( s ) 3 (.) 2 ( s ) 3 (.) 13 (.) 23 ( s ) 33 (.) 26.51 0.000 19 18 1 (.) 2 ( s ) 3 (.) 2 ( s ) 3 (.) 13 ( t ) 23 ( s ) 33 ( s ) 25.62 0.000 50 19 1 (.) 2 ( s ) 3 (.) 2 ( s ) 3 (.) 13 (.) 23 ( t ) 33 ( s ) 56.01 0.000 57 20 1 (.) 2 ( s ) 3 (.) 2 ( s ) 3 (.) 13 (.) 23 ( s + t ) 33 ( s ) 48.08 0.000 61 21 1 (.) 2 ( s ) 3 (.) 2 ( s ) 3 (.) 13 (.) 23 ( s ) 33 ( t ) 12.69 0.002 51 22 1 (.) 2 ( s ) 3 (.) 2 ( s ) 3 (.) 13 (.) 23 ( s ) 33 ( s + t ) 0.00 0.998 55

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81 Table 4-2. Analysis of the spat ial, temporal, and age-specific variation in litter size for the yellow-bellied marmot, using a general linear model. Akaikes Information Criterion corrected for small sample size (AICc), differences in AICc (AICc), 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. No. Model AICc AICc AICc Weights Degrees of 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

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82 Table 4-3. Analysis of the temporal and spat ial variation in growth rate of the adult (animals 2 yrs old) segment of the population (ad), using Pradels reversetime models. Site-specific covariates for ad are site-specific estimates of litter size (litters), and site-specific transition ra tes from non-reproductive adult (s 23) and reproductive adult (s 33) states to reproductive adult state. Temporal covariates for ad are annual estimates of litter size (littert), and time-specific transition rates from yearling (t 13), non-reproductive adult (t 23), and reproductive adult (t 33) states to reproductive adu lt state. Other symbols are defined in Table 4-1. No. Model AICc AICc AICc Weights #p 1 (s) (s) ad (s+t) 4456.17 4.19 0.043 56 2 (s) (s) ad (t) 4451.98 0.00 0.351 52 3 (s) (s) ad (s) 4517.21 65.23 0.000 15 4 (s) (s) ad (.) 4512.99 61.01 0.000 11 5 (s) (s) ad (t 23) 4509.69 57.71 0.000 12 6 (s) (s) ad (t 33) 4515.03 63.05 0.000 12 7 (s) (s) ad (littert) 4495.72 43.74 0.000 12 8 (s) (s) ad (s 13+t) 4453.91 1.93 0.134 53 9 (s) (s) ad (s 23+t) 4453.30 1.31 0.182 53 10 (s) (s) ad (s 33+t) 4453.86 1.88 0.137 53 11 (s) (s) ad (litters+t) 4453.65 1.66 0.153 53

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83 Figure 4-1. The life cycle graph for the yello w bellied marmot, with three life history states (yearling, non-reproductive adult and reproductive adult). Transition rates are denoted as xy = probability of moving from state x to state y, conditional on surviving the period in state x. Transitions 12, 22, and 32 are complements of 13, 23, and 33 (e.g., 22 = 1 23). 1 Yearling 3 Reproductive Adult 2 Non-reproductive Adult 1 2 13 23 3 2 2 2 33

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84 Figure 4-2. Site-specific estimates (mean SE) of transition rates from (A) yearling (13), (B) non-reproductive adult (23), and (C) reproductive adult (33) 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 (ad). Mean values and standard errors were estimated using model #4 in Ta ble 4-2 and model #3 in Table 4-3, respectively.

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85 Figure 4-3. Temporal varia tion in transition rates from (A) non-reproductive adult (23) and (B) reproductive adult (33) states to reproductiv e adult state with two years lag. Mean values (solid line) a nd 95% confidence intervals (gray shade) were estimated using model #19 and model #21 in Table 4-1, respectively. Temporal variation in (C) th e litter size with one year lag, and (D) the realized growth rate of the adult segment of the population (ad). The gaps in 4A and 4B indicate that these parameters were not estimable for those years. Mean values and 95% confidence intervals we re estimated using model #3 in Table 4-2, and model #2 in Table 4-3, respectively.

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86 CHAPTER 5 THE INFLUENCE OF LOCAL DEMOGR APHIC 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 interactio ns among local populations (i.e., dispersal). However, few studies of long-li ved vertebrates have empirically investigated the relative importance of local demography and disper sal on regional popul ation dynamics. We investigated the dynamics of a spatially structured population of the yellow-bellied marmot in Colorado, USA using data colle cted from 17 local populat ions over 43 years. Local projected population growth rates ra nged from 0.85 to 1.04, and varied among sites. Retrospective analysis of life-table response experiment s revealed that variation in yearling survival, followed by variations in the survival of juveniles and reproductive adults made the largest contri butions to the spatial variati on in population growth rates. Using a vec-permutation matrix approach, we developed a matrix metapopulation model and investigated the relative influence of lo cal demographic rates and the dispersal rate on metapopulation dynamics. Prospective elas ticity analysis revealed that the metapopulation growth rate was most sensitiv e 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 change s in the demographic rates of these sites. These results

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87 underscore the need for the explicit c onsideration of the local demographic processes for understanding the dynamics a nd persistence of demographically and spatially structured populations. Introduction Spatial heterogeneity is a common fe ature of wildlife populations, and can influence dynamics and pe rsistence of popula tion at local and regional scales (Andrewartha and Birch 1954, Levins 1969, Hans ki 1999). It has been suggested that a complete understanding of the population dyna mics necessitates an understanding of the influence of spatial processes (Pulliam 1988, Kareiva 1990, Tilman and Kareiva 1997). Consequently, both theoretical ecologist s and conservation bi ologists 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, Akakaya and Atwood 1997, Hokit et al. 2001). Although ther e are still gaps between theory and practice, metapopulation models have been moderately successful in explaining and predicting population dynamics in fragme nted landscapes (Hanski 1999, Akakaya and Sjorgen-Gulve 2000, Sjorge n-Gulve and Hanski 2000). Several models with varying degrees of complexity have been developed to investigate the dynamics of spatially structur ed populations (for a review see Akakaya and Sjorgen-Gulve 2000). However, detailed demographic data at multiple sites are difficult to collect; consequently, most em pirical studies of metapopulation dynamics have used simple models that do not require detailed demographic data (e.g., stochastic patch occupancy models, logistic regressi on 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-

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88 population demographic processes on the dynami cs and persistence of populations at regional scales. Ironically, regi onal 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, O li and Armitage 2004, Bruna and Oli 2005). Moreover, dispersal is strongly dependent on local demographic processes such as population density (Bowler and Benton 2005, Ma tthysen 2005). However, consideration of local population dynamics often requires more data than those required by simpler models (Akakaya 2000a). As a result very few studies, pa rticularly of long-lived vertebrates, have investigated the relativ e 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 's (Caswell 2000, Oli and Armita ge 2004, Bruna and Oli 2005). However, a thorough understanding of metapopulation dynamics also requires information on the regional processes such as dispersal of individu als. Dispersal connects otherwise disjunct populations inhabiting different sites, and spatial correlation in demographic rates can link the fates of separate popul ations (Hanski 1998, Morris and Doak 2002). Investigating the relative influence of demographic a nd regional processes on the dynamics and persistence of populations requires models that simu ltaneously consider local demographic processes as we ll as regional processes. A group of models, matrix metapopul ation models (i.e. spatially and demographically structured models), inco rporate local demographic processes and

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89 regional processes in modeling the populati on dynamics across multiple sites (Akakaya 2000a). These models form the basis of se veral spatially-explicit population viability analyses, which have proven to be useful in conservation biology (for reviews see Akakaya 2000b, Beissinger and McCullough 20 02, Akakaya et al. 2004). However, most of these studies are based on model si mulations, as predicting future changes in population size often prevents the use of analytical met hods (Morris and Doak 2002). Recent developments in matrix metapopulation models (i.e., multi-site matrix models) allows estimating metapopulation growth rates and evaluating the absolute or proportional sensitivity of meta population growth rate to mo del parameters (Hunter and Caswell in press). Using a special permutati on matrix called the vec-permutation matrix, Hunter and Caswell (in press) show how to construct a metapopulation model from a simple block-diagonal formulation of the de mographic and dispersal processes. Their approach provides an analytical framework for the perturbation analysis of metapopulation models that simultaneously c onsiders local demographic processes as well as dispersal am ong local populations. In this study, we used a stage-structur ed matrix population model to investigate the spatial variation in population dynamics of a yellow-bellied marmot (Marmota flaviventris) metapopulation in East River Valley, Colorado. First, we used a random design life-table response experiment analysis to identify the key demographic rates that made the largest contributions to the observed spatial variation in po pulation growth rate (). Next, using the recently developed vecpermutation matrix a pproach (Hunter and Caswell in press), we developed a matrix metapopulation model that connected the local population dynamics via dispersal. Finally, usi ng a prospective pertur bation analysis of

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90 the matrix metapopulation model, we investigat ed the relative influence of demographic rates and the dispersal rate on the metapopulation growth rate (MP), and evaluated the relative influence of each site to MP. Materials and Methods Study Area and Species The yellow-bellied marmot is a large, diurnal, burrow-dwel ling rodent, occupying montane regions of the western North Amer ica (Frase and Hoffmann 1980, Armitage 2003a). This study was conducted in the U pper East River Valley near the Rocky Mountain Biological Laboratory, Gothic, Colorado (38 57 N, 106 59 W). The marmots in our study area occupied discrete habi tat patches that varied in size and quality (Armitage 1991, 1998). We identified 17 distinct sites (hereafter, sit es) within the study area, and grouped these sites into 8 categories on the basis of site quality and location (for details see Ozgul et al. in press-a). Four ma jor colonies, which were higher quality sites, were considered separately: (1) Picnic, (2) Ri ver (two sites), (3) Marmot Meadow and (4) Gothic. Satellite sites, which were lower quality sites, were grouped with respect to their location: (5) north satellites (2 sites), (6) west satellites (2 sites), (7 ) east satellites (4 sites) and (8) south satellites (4 sites). Previous studies have shown that surviv al and reproductive rates of individual marmots differed among life-history stages (Armitage and Downhower 1974, Schwartz et al. 1998, Oli and Armitage 2004, Ozgul et al. in press-a, Ozgul et al. in review). Also, a vast majority of dispersers are yearlings, a nd about 45% of yearling females disperse out of natal sites (Armitage 1984, Van Vuren 1990). The biology of yellow-bellied marmots in Colorado is described in detail by Armitage (1991, 2003a).

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91 Field Methods From 1962 to 2004, yellow-bellied marmot s were live-trapped and individually marked using numbered ear tags (details in Armitage 1991). Animal identification number, sex, mass and reproduc tive condition were recorded for each animal. Trapping concurrently occurred in 17 sites known to be occupied by marmots. Ages for the females that were captured as juven iles 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 estimated as the number of weaned young that emerged from the natal burrows (Schwartz et al. 1998, Oli and Armitage 2004). Local Population Dynamics We used a post-breeding census, stage-stru ctured matrix model to investigate the local population dynamics at each site. We modeled only the female segment of the population, because it was difficult to estimate fecundity for males. We considered two age and two stage classes. The two age classe s were juveniles (0-1 yr) and the yearlings (1-2 yrs). Adult marmots ( 2 yrs) were divided into two reproductive stages: prereproductive adults ( 2 yrs and have not reproduced ye t) and reproductive adults ( 2 yrs and have reproduced right before the census). This stage structure is depicted as a lifecycle graph (Fig. 5-1), which can be expre ssed in population projec tion matrix form as: 0/2/2/2 000 0(1)(1)0 0yyypparra j yypp yypprSlsSlsSls S SS SSS where Sx = the probability of an individual in state x surviving until the following year's census, x = the probability of an individual in stage x breeding the following year (just

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92 before the next census) conditional on survival, and lsx= average litter size of a female in stage x. Because this model is based on postbreeding census and br eeding takes place just before the next census, all stages except the juvenile stage have a non-zero probability of breeding before the next census (Fig. 5-1). The parameters Sj and Sy were estimated for each site using an age-structured Cormack-Jolly-Seber model (Ozgul et al. in press-a), whereas the parameters Sp, Sr, y, p and r were estimated for each site using a multistate capture-mark-recapture (CMR) model (Ozgul et al. in review). Parameter estimates were based on maximu m likelihood CMR analysis of long-term trapping data, and were undertak en in coordination with the development of this model. The litter sizes were estimated for each site us ing a general linear model (Ozgul et al. in press-a); litter size differed onl y between the yearling females (lsy) and older females (lsa) (Schwartz et al. 1998). Because the sex ratios of the litter were even (Armitage 1991, 2002), we divided the litter size by two to es timate the number of female offspring per female. The model structure given above is sli ghtly different than the model used for parameter estimation in Ozgul et al. (in review). The prereproductive stage in our model includes only those adult females that have not yet reproduced (nulliparous females), whereas the non-reproductive stage in Ozgul et al. (in review) includes the prereproductive adults and also thos e adults that have reproduce d before, but not this year. This was because the available data limited the estimable parameters to only two adult stages. As a result, we used the parameter estimates of the non-reproductive stage from Ozgul et al. (in review) to parameterize the pre-reproductive stage in our model.

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93 For each site, the projected population growth rate () was estimated as the dominant eigenvalue of the population proj ection matrix. We estimated covariance among demographic variables using data from the entire study period, and estimated approximate variance of using the series approximati on method (i.e. "delta method", Caswell 2001). We investigated the sensitivity of to proportional changes in the elements of the population projection matrix for each site (de Kroon et al 2000, Caswell, 2001 #31). As some of the projection matrix elements are functions of the same vital rates (Si, i, lsi), we also calculated lower-leve l elasticities for each site (C aswell 2001). The details of the elasticity analysis are given in Appendix D. We also used stochastic simulations to estimate the elasticity of stochastic population growth rate (s) to vital rates (Morris and Doak 2002). By perturbing each mean, variance, or covariance of the vital rates one at a time, we simulated the model long enough to arrive at a good estimate of s, and then estimated the elasticity as s s x x E x , s newsoriginal s neworiginalxxx where x is the entity (mean, variance, or covarian ce of the vital rates) being perturbed, and s x is the sensitivity of s to x (Morris and Doak 2002). We estimated the process variance by discounting the sampling vari ance using White's (2000) method. We assumed that the correlations am ong vital rates were identical for all s ites, and estimated the correlations using the mean annual values for the entire populat ion during the last 27

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94 years. We assumed that survival and breedi ng probabilities were beta distributed, and litter size was lognormally distributed (Mor ris and Doak 2002). In each simulation we generated correlated vital rate s using the estimated correlati on matrix (Morris and Doak 2002). We used a 5% change in each rate and simulated population dynamics for 500 years with 500 replicates. Next, we used a random design life-table response experiment (LTRE) analysis to investigate the actual contribu tion of the covariation among demographic parameters to observed spatial variation in (Caswell 2001): (,)ijkl ijkl ijklVCovaa aa where Cov(aij,akl) is the covariance of pr ojection matrix elements aij and akl, and sensitivities were evaluated at the mean matr ix. We also calculated the contributions to V() in terms of lower-level parameters xi. In this case the variance V() was calculated as: (,)ij ij klVCovxx x x where the sensitivities were evaluated at the mean value of the parameter (Caswell 2001). Metapopulation Dynamics We used Hunter & Caswell's (in press) vec-permutation matrix approach to model the metapopulation dynamics by combining de mographic and dispersal data from 17 sites. Their method provides a technique to formulate the metapopulation projection matrix using a similar approach to the formulation of a singl e population projection matrix. In a single population projection matrix the number of columns (or rows) is equal to the number of stage classes within a si ngle population, whereas in a metapopulation

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95 projection matrix, the number of columns is equal to the number of local populations x the number of stage classes. To facilita te the formulation of the metapopulation projection matrix, Hunter & Ca swell (in press) decomposes the projection matrix into two major components: the demography matrix and the dispersal matrix. We assumed that demography and dispersal occurred se quentially within the projection interval; demographic changes occurred within each site and then dispersal redistributed individuals among sites. Th e corresponding metapopulation pr ojection equation can be written as: 11 1717 1 1 T ttt t NNAnn P P B nn where Nt is the metapopulation vector at time t, written in terms of stage distributions within each site, and ni is the population vector of the ith site. The matrix product A = PT M P B is the metapopulation projection matr ix (Hunter and Caswell in press). B is the block-diagonal matrix for demography: 1 2 1700 00 00 K K B K where the ith diagonal block Ki is a 4x4 demographic projection matrix for site i. M is the block-diagonal matrix for dispersal: 1 2 3 4000 000 000 000 L L M L L,

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96 where the ith diagonal block Li is a column stochastic (the sum of each column is 1), 17x17 dispersal matrix for stage i. P is the 68 x 68 vec-permutation matrix, and PT is the transpose of P where P is defined as (Hunter and Caswell in press): 417 11 T ijij ij PEE where Eij is a 4 x 17 matrix with 1 in the (i,j) position and zeros elsewhere and denotes the Kronecker matrix product (Hunt er and Caswell in press). Dispersal. The majority of dispersers were yearlings (Armitage 1984, Van Vuren 1990), so we assumed that only yearlings dispersed among sites. A 10-year radiotelemetry study indicated that ~45% of the female yearlings dispersed, and that many animals dispersed outside of the study ar ea (Van Vuren 1990). In our analysis, we assumed that the Colorado metapopulation was a closed system, and that 45% of female yearlings dispersed from each site, and forced these individuals to disperse inside the metapopulation based on distances among sites. We also assumed that the survival rate of disperser yearlings were equal to that of resident yearlings [Van Vuren, 1994 #98]. These assumptions were necessary, because the dispersal matrices needed to be column stochastic. To understand the influence of dispersal rate on the metapopulation dynamics, we repeated our analyses using four additional levels of dispersal rate: two lower (25% and 35%) and two higher (55% and 65%) th an estimated dispersal rate of 45%. We estimated the distance-dependenc e of dispersal base d on the dispersal distances of 38 radio-tagged yearling marmots (Van Vuren 1990). Proportion of individuals dispersing to each distance class (i n km) was used as the dependent variable (D), and the mid-point of each distance class as the independent variable (d) in the exponential model (Akakaya and Atwood 1997, Hanski 1999):

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97 d bDae where a and b are model parameters. The parameter b is the average dispersal distance, and it was estimated at 1.44 km for female marmots (Van Vuren 1990). The model was fitted with a = 0.084 and b fixed at 1.44 km. We used the estimated D to distribute the dispersing individuals among sites. The resultin g dispersal matrix is column stochastic (the sum of each column is 1) with the probabi lity of staying at the natal site (0.55) along the diagonal. The metapopulation growth rate MP was estimated as the dominant eigenvalue of the metapopulation projection matrix A The sensitivity of the MP to changes in demography (SB) and dispersal ( SM) were calculated using results of Caswell and Trevisan (1994) and Lesnoff et al. (2003): TT BAS=PMP S TT MAS=P SBP where SA is the sensitivity matrix of the metapopulation matrix, A (Hunter and Caswell in press). In each case, the elasticity matrices were calculated as: 1BB MP EBS 1 M M MPEMS The sensitivities and elasticities relevant to demographic and dispersal parameters appear in the 4 x 4 diagonal blocks of SB and EB and the 17x17 diagonal blocks of SM and EM, respectively. The sums of the diagonal blocks of EB quantify proportional contributions of the demography in each site to MP (Hunter and Caswell in press). The

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98 sensitivity and elasticity of MP to lower-level vital rates and dispersal rates were calculated using the chain rule as described previously (Caswell 2001). Results Local Population Dynamics Local 's (mean SE) showed substantial variation among sites. It was the highest in the River colony (1.043 0.039) and the lo west in the south satellites (0.848 0.052). In general, was higher in colony sites (Picnic: 1.016 0.049, Marmot Meadow: 0.964 0.065, Gothic: 0.974 0.068) than in satellite site s (North: 0.876 0.045, West: 0.849 0.052, East: 0.907 0.059). The estimated using a single projection matrix for the entire population was 0.977 0.084, which was sim ilar to that reported by Schwartz et al. (1998) and Oli and Armitage (2004). Elasticity of to changes in the lower-level vita l rates did not vary substantially among sites (Fig. 5-2). In all sites, elastic ity of local was the highest to Sr, and the second highest to Sj and Sy (elasticity values were the same for the two rates in all sites). The summed elasticity of to the survival of the pre-reproductive classes (Sj, Sy, Sp) was very close to that of reproductive class (Sr). As for the deterministic elasticities, stochastic growth rate S had the highest elasticity to the mean values of adult survival rates in all sites (Fig. 5-3). However, elasticity of S to changes in other vital rates varied among sites. The detailed results of elastic ity analyses are given in Appendix D. The largest spatial variance was observed in the fertility of the reproductive adult stage, and it also made the largest contribution to V() (Fig. 5-4). The fertility rate of prereproductive females and its covariance with fe rtility rate of reproductive females were

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99 large, but these made ve ry small contribution to V(). Variances in the probability of transition from yearling to pre-reproductive st age and from juvenile to yearling stage had positive contributions, and the covariance between the growth from yearling to prereproductive stage and the fertility of the reproductive stage had negative contributions, to V(). We also calculated the contributions to V() in terms of lower level vital rates: Sj, Sy, Sp, Sr, y, p, r, lsy, and lsa. The largest variances and covariances were observed in lsy and lsa; however, these did not make significant contribution to V() (Fig. 5-5). The largest contribution to V() came from variances in Sy, Sa, and Sj, in that order. The covariance between yearling survival and the litter size for the adults had a negative effect on V(). Metapopulation Dynamics We analyzed the metapopulation dynamics for five different levels of dispersal rate (25%, 35%, 45%, 55%, and 65%). At the estimated 45% dispersal rate, MP was 0.971, indicating a small annual decline. This estimate was very close to the estimated using a single population matrix fo r the entire region (0.977). The MP decreased with increasing dispersal rate (Fig. 5-6). We first examined the influence of the demography in each site on MP (Fig. 5-6). At the estimated 45% dispersal rate, MP was most sensitive to demographic rates of two River colonies, which were the sites with the highest 's (Fig. 5-6C). The sum of the proportional influence of the demography of colony sites (0.933) was substantially greater than that of satellite sites (0.067). At lower dispersal levels, the two sites with the highest had a substantially greater influence on MP, than the rest of the sites had (Fig.

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100 5-6A,B). At higher dispersal levels, the two sites with the highest local 's still had the greatest influence on MP (Fig. 5-6D,E). However, as disp ersal increased the influence of the demography in other sites on MP increased significantly; at 65% dispersal, the sum of the proportional influence of col ony sites decreased to 0.803, and that of satellite sites increased to 0.197. Next, we calculated the elasticity of MP to the vital demographic rates and the dispersal rate, treating these rates as lower-lev el parameters. We summed the elasticities of the vital demographic rates across all the site s. We again used five different levels of dispersal rate and examined the elasticity of the MP to each vital rate (Fig. 5-7). The overall elasticity pattern was the sa me in all five dispersal levels; MP was most sensitive to survival rates (particularly Sr), followed by the lsa and r. As expected, MP was negatively influenced by the di spersal rate; as the proportion of yearlings dispersing from a site increased, MP decreased. However, the poten tial influence of dispersal on MP was much lower than that of the demographic rates. The elasticity of MP to dispersal was the highest at the 55% dispersal rate; higher or lower dispersal rates resulted in a decline in this elasticity value. As the dispersal rate increased from 25% to 65%, the elasticity of MP to the survival of the reproductive adults increased, and the elasticity of MP to all the other demographic rates decreased. Only the elasticity of MP to the breeding probability of the pre-reproductive adults showed a small increase at the 65% dispersal level. It is important to note that these changes in the elasticity values were small, a nd did not affect the ove rall elasticity pattern (Fig. 5-7).

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101 These results indicated that MP was heavily influenced by the demography of the colony sites with the highest growth rates, pa rticularly by the surviv al of the reproductive adults in these sites. To analyze the influence of each colony site on MP, we calculated MP by excluding one, two, three, and four of the colony sites. The MP decreased from 0.971 to 0.941 in the absence of the best site (River), and to 0.917, 0.910, and 0.886 in the absence of the best two, three and four colony sites (Picnic, Gothic, and Marmot Meadow), respectively. Discussion Consideration of local demographic pro cceses can be important for a better understanding of regional popul ation dynamics (Burgman et al. 1993, Lahaye et al. 1994), but it often requires more data than those required by simpler models (Akakaya 2000b). As a result, very few studies, particul arly of long-lived vertebrates, have investigated the influence of local po pulation dynamics in determining population dynamics at regional scales. Although the ro le of spatial hetero geneity on population dynamics is well established, the relative roles of demography and dispersal on the dynamics of population at local and regional sc ales is not well understood. Our long-term study of individually-identified animals in several discrete habitat patches has provided data necessary for a rigorous examinati on of the local population and metapopulation dynamics of yellow-bellied marmots. As a result of spatial variation in environmental factors, the survival and reproductive rates of the female yellow-bellied marmots varied among sites (Ozgul et al. in press-a, Ozgul et al. in review). Natura lly, these variations in fluenced local population dynamics, as indicated by subs tantial variation in local 's among sites. However,

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102 population growth rates in most of the site s had indicated that these populations were decreasing, and could not persis t without dispersal from the fe w high quality sites, clearly indicating the interplay between regiona l and local demographic processes. Although the demographic rates and the local 's showed spatial variation, the elasticity patterns did not vary significantly among sites; local 's had, overall, higher elasticity to the mean values of the survival rates than to thos e of reproductive rates, as is true for many long-lived sp ecies (Pfister 1998). Local 's were the most sensitive to the survival of the reproductive adults, follo wed by the survival of the two younger age classes. Caswell (2001) argued that the determin istic sensitivities, in general, were good approximations of the sensitivity values of the stochastic models. Similar to the deterministic analysis, the stochastic growth rate (S) was most sensitive to proportional changes in the survival of the reproductiv e adult. However, unlike the deterministic analysis, the elasticity pattern for the rest of the vita l rates varied significantly among sites. Juvenile and yearling survival rates a nd the breeding probability of the reproductive adults had differential influence on S among sites. These results indicate the importance of considering the temporal covariation of th e vital rates for identifying those rates that potentially influence th e population growth rate. Ozgul (in press-a) and Ozgul (in review) i nvestigated the vital rates that covaried most closely with the realized growth ra te of the adult segm ent of the population (ad). The LTRE analysis revealed that the variati on in yearling survival, followed by variation in survival of reproductive adults and juveni les made the largest contributions to the spatial variation in Although survival of female yearli ngs was not as influential as the

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103 survival of the reproductive adults, the signifi cant variation in this rate contributed the most to the variation in local 's. Survival of reproductive ad ults was generally very high in all the sites and did not show substantial variation among sites. Nonetheless, even the very small variation in this rate caused a significant variation in local 's. As predicted by theoretical studies, the most influential vital rate was buffered by the environment and showed the least amount of variation among s ites (Pfister 1998); however, even the small variation in this rate signifi cantly contributed to the spatia l variation in local dynamics. Demographic analysis of the local popul ations helped elucidate the demographic basis of spatial variation in population growth rates. However, local populations of yellow-bellied marmots in Colorado are in terconnected through dispersal, and understanding the regional dynamics requires an additional consideration of the role of dispersal. Thus, we used a recently devel oped matrix metapopulation model (Hunter and Caswell in press) to investigate the metapopulation dynamics. Although the available data allowed us to parameterize only a simple dispersal model, we used the resulting metapopulation model to perform asymptotic analyses and to inve stigate the relative influence of local demography on regional dynamics. Our results suggest that a few colony s ites are the major driv ers of the regional population dynamics; the two major col ony sites were more influential on MP compared to all the other sites. These results are consistent with those from a study based on a simple patch occupancy model (Ozgul et al (in press-b). The de pendence of regional persistence on a small number of high quality sites has been s uggested as a general rule in long-lived species (Harrison 1991, Schoener 1991, Beier 1993), and has been observed in other species that shared simila r life-history char acteristics (e.g., Ochotona princeps,

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104 Moilanen et al. 1998). The higher the of a local population, th e more likely that it served to increase MP; excluding the highest quality si tes significantly decreased MP (see also Ozgul et al. in press-b). These results emphasized the importance of local population dynamics of these few high quality s ites for regional persistence. Therefore, we also investigated the relative influence of local demographic rates and the dispersal rate on regional population dynamics. Simila r to the local population dynamics, the survival of reproductive adults, followed by th e survival of juvenile and yearlings, were the most influential vital rates on MP. As expected, the dispersal rate negatively influenced MP; however, the magnitude of th e influence of dispersal on MP was lower than that of the demographic rates. Increasi ng or decreasing the disp ersal levels did not have a significant effect on this elasticity pattern. Overall, demographic rates that were most influential on loca l population dynamics of the best qua lity sites were also the most influential vital rates on regional population dynamics. In general, lower quality sites had a very small influence on MP. At higher dispersal levels, the influence of lower quality sites on MP increased, but the overall MP decreased. These results i ndicated a mainland-island or source-sink type population dynamics (Pulliam 1988, Harrison 1989), in which the viability of the metapopulation depends on the fate of the best quality sites. However, lower quality sites had a small but meaningful contribution to the regional persistence of the ye llow-bellied marmot metapopulation (Ozgul et al. in press-b). It is important to note that our analysis of asymptotic dynamics did not address the potenti al contribution of lo wer quality sites to the regional persistence. In our model, > 1 indicated a growing local population, whereas < 1 indicated a declining local populati on; the former always increased the

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105 MP, whereas the latter decreased MP. However, no single local population is invulnerable to extinction over time. Lower quality site s can contribute to regional persistence especially when local extinctions are async hronous and balanced by local recolonization (Hanski 1999). To investigate the importance of the lower quality sites on regional persistence, one may choose an appr oach that would incl ude the environmental and demographic stochasticities, a form of density dependence in both demographic and dispersal rates, and also a level of asynchrony among local population dynamics. A simulation based approach may be necessary to include these features using a matrix metapopulation modeling framework (Morris and Doak 2002). However, such an approach requires more parameter estimat es, which may be difficult to obtain. In conclusion, the dynamics of the ye llow-bellied marmot metapopulation mainly depended on a few colony sites, and the meta population growth rate was highly sensitive to changes in the demography of these high quality sites. The re lative influence of dispersal on the 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 withinpopulation demographic processes. However, our results suggest th at local demographic processes can be at least as important as, if not more important than the regional processes in governing the dynamics and pe rsistence of the spatially structured populations of yellow-bellied marmots and othe r species that share similar life-history characteristics.

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106 Figure 5-1. The life cycle graph for the yello w bellied marmot, with four life history stages: juvenile (j), yearling (y), pre-reproductive adult (p), and reproductive adult (r). Sx denotes the probability of an individual in stage x surviving until the next census. x denotes the probability of an individual in stage x breeding right before the next censu s, conditional on survival. lsy and lsa denote the litter size for the yearling and adult stages, respectively.

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107 Figure 5-2. Elasticity (propor tional sensitivity) of the pr ojected population growth rate () to the vital rates. El asticities are given for eac h site group: (A) Picnic colony, (B) River colonies, (C) Marm ot Meadow colony and (D) Gothic colony, (E) north satellites, (F) west sate llites, (G) east satell ites and (H) south satellites. See Fig.5-1 for definitions of the vital rates.

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108 Figure 5-3. Elasticity (proporti onal sensitivity) of the stocha stic population growth rate (s) to the mean values of the vital rate s. Elasticities are given for each site group: (A) Picnic colony, (B) River colonies, (C) Marmot Meadow colony and (D) Gothic colony, (E) north sate llites, (F) west sa tellites, (G) east satellites and (H) south satellites. See Fig. 5-1 for definitions of the vital rates.

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109 Figure 5-4. (A) The covariances of the proj ection matrix elements among sites. (B) The contributions of the covariances to th e variation in projected growth rates among sites, V(). {i j} denotes the matrix element in the ith row and jth column of the projection matrix.

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110 Figure 5-5. (A) The covariance s of the vital rate s among sites. (B) The contributions of the covariances to the va riation in projected gr owth rates among sites, V(). See Fig.5-1 for definitions of the vital rates.

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111 Figure 5-6. Proportional influence of the demography in each of the 17 sites on metapopulation growth rate (MP), calculated as the sums of the diagonal blocks of the elasticity matrix, EB (see text for details). Proportional influences are given for five different levels of dispersal: (A) 25%, (B) 35%, (C) 45%, (D) 55%, and (E) 65% dispersal rate.

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112 Figure 5-7. Proportional influence of each vital rate and the dispersal rate (disp) on MP. The elacticity values for the vital dem ographic rates are summed across all the sites. Proportional influences are given for five different levels of dispersal: (A) 25%, (B) 35%, (C) 45%, (D) 55%, and (E) 65% dispersal rate. See Fig.5-1 for definitions of the vital rates.

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113 CHAPTER 6 CONCLUSION The gap between theory and practice in ecology makes it difficult to select an appropriate modeling approach for addressi ng conservation needs of wildlife populations that live in spatially heter ogeneous landscapes. The applica tion of metapopulation models is often constrained by the lack of suffi cient data. Therefore, the majority of metapopulation studies are based on simple mode ls with fewer data requirements and on species with simple life-histor ies. In this research, I anal yzed the population dynamics of a socially complex, long-lived mammal specie s that lives in a spatially structured population. I investigated the factors and processes that in fluenced the dynamics of a yellow-bellied marmot metapopulation in Colora do using two different spatially explicit modeling approaches with different degrees of complexity. My specific objectives were (1) to investigate the relative influence of particular sites and site quality on metapopulation persistence, (2) to investigate the spatial he terogeneity 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 mode ls with different degrees of complexity. In Chapter 2, I used a stochastic patc h occupancy model and investigated the relative influence of particular sites, site quality, network charact eristics, and regional stochasticity on the persisten ce of the yellow-bellied marmot metapopulation. Results of thes analyses indicated that the dynamics of the yellow-bellied marmot metapopulation mainly depended on a few high quality sites, and the regional persistence was highly

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114 sensitive to changes in the quality of these sites. Nonetheless, I also found that the lower quality sites made a significant contri bution to the long-ter m persistence of the yellow-bellied marmot metapopulation. The im portance of lower quality sites for the metapopulation dynamics suggests that the yellowbellied marmot system is not a typical mainland-island system, but shows characte ristics of a metapopulation in which the extinctionrecolonizat ion dynamics play a significant role. These analyses, based on simple site occupancy data, provided severa l useful insights regarding the dynamics and persistence of the ye llow-bellied marmot metapopulation. However, the high sensitivity of metapopulation persistence to local population size, particularly in high quality sites, demanded a more elaborate investigation of the local demographic processes. Patch occupancy models do not consider the demographic processes within local populations. In chapters 3 and 4, I investigat ed the spatiotemporal variation in local demographic processes. Survival and repr oduction are the two majo r components of the local demographic processes, and spatiotempor al variations in these rates potentially influence both local and re gional population dynamics. Agespecific survival rates of yellow-bellied marmots exhibited both spatial and temporal variati on, but survival of younger animals was more variable over space a nd time than that of adults. Spatial and temporal variation in juvenile survival rates strongly influenced the variation in the realized population growth ra te. Also, the components of reproduction in yellow-bellied marmots exhibited both spatial and temporal variation, bu t the pattern of variation differed among the components. Only the litter size and the breeding probability of the non-reproductive adults significan tly influenced the temporal variation in the realized population growth rate. These an alyses indicated that juveni le survival a nd litter size,

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115 followed by the breeding probability of the nonreproductive adults, we re likely to be the main demographic factors driving the tempor al dynamics of the yellow-bellied marmot population. These vital rates were the compone nts of recruitment into the adult segment of the population; they were more sensitive to the variation in extr insic factors, thus exhibiting a greater degree of variation over space and time. Consequently, they play a predominant role in influencing the fluctuat ions in the realized population growth rate. Therefore, recruitment into the adult population is likely to be the critical component of the population dynamics of the yellow-bellied ma rmot and of other species with similar life history characteristics. In Chapter 5, I parameterized a stage-structured matrix model for each population, and investigated the demographi c causes of the observed sp atial variation in projected population growth rate. The survival of the reproductive adults, fo llowed by the survival of the two young age classes, was potentially the most influential demographic parameter on the local population dynamics. The variation in female yearling survival, followed by the variation in the survival of reproductiv e adults and juveniles, made the largest contributions to the observed vari ation among local population dynamics. Using a demographically and spatially st ructured matrix metapopulation model, I investigated the relative infl uence of local demographic ra tes and the dispersal rate on metapopulation dynamics. Only a small number of colony sites ultimately governed the dynamics of the yellow-bellied marmot meta population. analysis of the patch occupancy model also led to the same conclusion. Th e projected metapopulation growth rate was highly sensitive to the change s in the local demography of these high quality sites, particularly to changes in th e survival of the reproductive adults. The magnitude of the

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116 influence of dispersal on metapopulation dynamics was lower than that of the demographic rates. Interestingly, demographi c rates that were most influential on the local population dynamics of the best quality sites were also the vital rates with the greatest influence on metapopulation dynamics. Many wildlife species live in fragment ed populations, and id entifying the relative importance of local and regiona l processes is an important issue in conservation decisionmaking. Several approaches to modeling the dynamics of spatially structured populations have emphasized the importance of regional pr ocesses without explic itly considering the role of local demographic processes. Howe ver, my results have demonstrated the importance of incorporating local demographic processes for understanding the dynamics of spatially structured populations of yellowbellied marmots and othe r species that share similar life-history characteristics. In conclusi on, the findings of this research provide a thorough understanding of the population dynamics of a socially complex, long-lived mammal species that live in a sp atially structured population.

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117 APPENDIX A ANALYSIS OF SPATIAL AND TEMPORAL VARIATION IN OVERALL APPARENT ANNUAL SURVIVAL RATES Table A-1. Analysis of spatia l and temporal variation in ove rall apparent annual survival rates for the yellow-bellied marmot using Cormack-Jolly-Seber models. Akaikes Information Criterion corrected for small sample size (AICc), differences in AICc values (AICc), AICc weights and number of parameters are given for each model. Symbols are: = apparent annual survival rate, = annual recapture rate, t = time effect, s = site effect, s' = modified site effect, t*s = interactive effects of site and time, t+s = additive effects of site and time. A period (.) indicates constant value of the parameter. The most parsimonious models are highlighted in bold. no. Model AICc AICc AICc WeightsNumber of parameters 1 (.) (.) 2729.8176.22 0 2 2 (.) (s) 2684.0030.41 0 9 3 (.) (t) 2723.0569.46 0 28 4 (s) (.) 2720.9967.39 0 9 5 (s) (s) 2675.0621.46 0 16 6 (s) (t) 2715.6162.02 0 35 7 (t) (.) 2707.4053.81 0 28 8 (t) (s) 2661.587.98 0.013 35 9 (t) (t) 2712.6259.03 0 54 10 (t+s) (.) 2701.1547.56 0 35 11 (t+s) (s) 2655.682.08 0.258 42 12 (t+s) (t) 2706.4552.86 0 61 13 (t*s) (.) 2798.83145.240 217 14 (t*s) (s) 2762.83109.240 224 15 (t*s) (t) 2818.19164.600 243 16 (t+s) (s') 2653.590.00 0.729 40

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118 APPENDIX B EFFECT OF ENVIRONMENTAL CO VARIATES ON THE SPATIAL AND TEMPORAL VARIATION IN AGESPECIFIC SURVIVAL RATES Table B-1. A table showing the effect of environmental covariates on the spatial and temporal variation in age-specific surviv al rates. The base model used for the covariate analysis is juv_col (t+s) juv_sat (s) yrl (s) ad_col (.) ad_sat (.) (s') (see Table 3-2) Site-specific covariates are elevation (elev), aspect (asp), slope (slope), and average group size (size), and temporal covariates are length of the growing season (grw.ssn), duration of permanent snow cover (snw.cvr), annual snow fall (snw.fall), annual precipitation (prep), monthly mean summer temperature (temp), first Julian date of bare ground (bare), and first Julian date of permanent snow pack (snw.pck). Other symbols are defined in Table 3-2. No. Model AICc AICc Weights Number of Parameters Base models: 1 juv_col ( t ) juv_sat ( s ) yrl ( s ) ad_col (.) ad_sat (.) ( s' ) 1.77 0.122 46 2 juv_col ( t+s ) juv_sat ( s ) yrl ( s ) ad_col (.) ad_sat (.) ( s' ) 2.06 0.106 49 Spatial variation in juvenile survival: 3 juv_col ( t+elev ) juv_sat ( elev ) yrl ( s ) ad_col (.) ad_sat (.) ( s' ) 0.48 0.233 44 4 juv_col ( t+asp ) juv_sat ( asp ) yrl ( s ) ad_col (.) ad_sat (.) ( s' ) 0.00 0.297 44 5 juv_col ( t + slope ) juv_sat ( slope ) yrl ( s ) ad_col (.) ad_sat (.) ( s' ) 3.87 0.043 44 6 juv_col ( t+size ) juv_sat ( size ) yrl ( s ) ad_col (.) ad_sat (.) ( s' ) 3.90 0.042 44 Spatial variation in yearling survival: 7 juv_col ( t+s ) juv_sat ( s ) yrl ( elev ) ad_col (.) ad_sat (.) ( s' ) 3.18 0.060 43 8 juv_col ( t+s ) juv_sat ( s ) yrl ( asp ) ad_col (.) ad_sat (.) ( s' ) 4.29 0.035 43 9 juv_col ( t+s ) juv_sat ( s ) yrl ( slope ) ad_col (.) ad_sat (.) ( s' ) 7.37 0.007 43 10 juv_col ( t+s ) juv_sat ( s ) yrl ( size ) ad_col (.) ad_sat (.) ( s' ) 3.92 0.042 43 Spatial variation in adult survival: 11 juv_col ( t+s ) juv_sat ( s ) yrl ( s ) ad ( elev ) ( s' ) 11.55 0.001 49 12 juv_col ( t+s ) juv_sat ( s ) yrl ( s ) ad ( asp ) ( s' ) 10.02 0.002 49 13 juv_col ( t+s ) juv_sat ( s ) yrl ( s ) ad ( size ) ( s' ) 7.91 0.006 49 14 juv_col ( t+s ) juv_sat ( s ) yrl ( s ) ad ( slope ) ( s' ) 8.46 0.004 49 Temporal variation in juvenile survival in colony sites: 15 juv_col ( grw.ssn + s ) juv_sat ( s ) yrl ( s ) ad_col (.) ad_sat (.) ( s' ) 27.42 0.000 25 16 juv_col ( prep + s ) juv_sat ( s ) yrl ( s ) ad_col (.) ad_sat (.) ( s' ) 27.78 0.000 25 17 juv_col ( temp + s ) juv_sat ( s ) yrl ( s ) ad_col (.) ad_sat (.) ( s' ) 26.04 0.000 25 18 juv_col ( snw.cvr + s ) juv_sat ( s ) yrl ( s ) ad_col (.) ad_sat (.) ( s' ) 20.86 0.000 25 19 juv_col ( snw.fall + s ) juv_sat ( s ) yrl ( s ) ad_col (.) ad_sat (.) ( s' ) 27.61 0.000 25 20 juv_col ( snw.pck + s ) juv_sat ( s ) yrl ( s ) ad_col (.) ad_sat (.) ( s' ) 26.19 0.000 25 21 juv_col ( bare + s ) juv_sat ( s ) yrl ( s ) ad_col (.) ad_sat (.) ( s' ) 27.93 0.000 25

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119 APPENDIX C ENVIRONMENTAL COVARIATES FOR THE COMPONENTS OF REPRODUCTION Site-specific factors. We considered two site-specific factors that influence the local micro-climatic conditions: (1) elevation (m ) and the (2) aspect (i.e. slope direction: 1 = southwest, 0 = northeast). 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 (38o 98o), whereas sites on the east side are located on gra dually inclined meadows generally facing southwest (183o 280o). Climatic factors. We investigated climatic factors at three different time periods: The climatic factors of (1) the previous su mmer, (2) the previous winter, and (3) the present summer (Table C-1). We used prin cipal components analysis (Varimax rotation with Kaiser normalization) to reduce the numbe r of environmental variables in each time period to be used in subsequent analyses. We extracted two components that explained 58.3% of the variation in the previous summe r's climatic factors. The first component alone explained 29.6% of the variation, a nd it represented the overall precipitation. Summer precipitation (0.93) a nd late summer precipitation (0 .92) both loaded highly on this component. The second component expl ained 28.7% of the variation, and it represented the growing season. The Julian da te of snowmelt loaded highly negatively (0.93) and the length of the growing season loaded highly positively (0.90) on this component. We extracted one component that explained 56.8% of th e variation in the

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120 previous winter's climatic factors. This component represented the winter severity; average snow pack loaded highly positively (0.89), followed by the length of the snow pack (0.75), while average winter temperat ure loaded negatively (-0.59) on this component. We extracted one component that explained 76.7% of th e variation in the present years climatic factor s. This component represented the onset of the summer; the Julian date of snowmelt loaded highly positively (0.93), followed by the early summer precipitation (0.79), while the early summer temperature loaded highly negatively (-0.90) on this component. Social factors. We considered five social factor s: (1) Residency status of the female (resident vs. immigrant), (2 ) the average number of adult ( 2 yrs) females (i.e. average group size), and the weighted number of (3) breeding, (4) adult ( 2 yrs), and (5) yearling (1-2 yrs) females at the focal site at a given year. The weighted numbers were calculated by dividing the numbe r of individuals by the site -specific averages over 43 years.

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121 Table C-1. List of c ovariates used during the analysis of the effect of environmental factors on the breeding pr obabilities and on litter si ze of the yellow-bellied marmot. Factor Period Reference Site-specific factors: Elevation (m) constant Aspect (northeast = 0, southwest = 1) constant Previous summer's climatic factors: Summer precipitation {May-Sep} (cm) a 1962-2004 (Armitage 1994) (Salsbury and Armitage 2003) (Schwartz and Armitage 2002) Late summer precipitation {Jul-Sep} (cm) a 1962-2004(Armitage 1994) Julian date of first killing frost a 1962-2004 Late summer temperature (oC) a 1962-2004(Schwartz and Armitage 2005) Length of growing season (days) a. b 1975-2004 (Schwartz and Armitage 2002) (Schwartz and Armitage 2005) Julian date of last bare ground b 1975-2004 Julian date of snowmelt b 1975-2004 (Armitage 2003b) (Van Vuren and Armitage 1991) Previous winter's climatic factors: Average winter snow pack (cm) b 1975-2004(Inouye et al. 2000) Length of the snow pack (days) b 1975-2004(Inouye et al. 2000) Average winter temperature (oC) b 1975-2004(Schwartz and Armitage 2005) Present summer's climatic factors: Julian date of snowmelt b 1975-2004(Armitage 2003b) Early summer temperature {Apr-May} (oC) a 1962-2004(Schwartz and Armitage 2005) Early summer precipitation {Apr-May} (cm) a 1962-2004(Armitage 1994) Social factors: Residency (resident = 1 / immigrant = 0) constant Average adult population size constant Number of breeding females 1962-2004 Number of adult females 1962-2004 Number of yearlings 1962-2004

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122 APPENDIX D ELASTICITY ANALYSIS OF LOCAL POPULATION DYNAMICS Elasticity value for each matrix entry is given by the formulae (Caswell 2001): ij ij ija e a ,ii ijvw a wv where, ija is the sensitivity of to (changes in) the matrix element aij. wi and vi are the associated right and left eige nvectors corresponding to stable -stage distribution and stagespecific reproductive values, respectively. wvis the scalar product of vectors w and v. As some of the projection matrix elements are functions of the same vital rates (Si, i, lsi), we calculated lower-level elasticities for each site using the chain rule (Caswell 2001): x x e x ,ij ij ija d dxax where x is the sensitivity of to the vital rate x. Elasticity of local to changes in matrix elemen ts did not vary substantially among sites. In all the sites, elasticity of was the highest to the survival of the reproductive adults, and second high est to the survival of the j uveniles. Overall, elasticity

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123 for the fertility of the reproductive adults ra nked third in seven sites and for the growth from yearling to reproductive adult stage in one site. Elasticity of local to changes in lower-level vital rates did not vary substantially among sites either (Fig. 5-3). In a ll the sites, elas ticity of local was the highest to Sr, and the second highest to Sj and Sy (elasticity values were the same for the two rates in all the sites). Overall, elasticity for Sp ranked fourth in six sites, and for lsa in two sites. We also calculated the summed elasticity of to the survival rates for the three prereproductive classes (Sj, Sy, Sp) and compared it to that of reproductive adults (Sr). The summed elasticity of to the survival of the pre-repr oductive classes was very close to that of reproductive classes; it was slightly higher in four sites (Picnic, River, north satellites, and east satellites) and slightly lowe r in the rest of the sites (Gothic, Marmot Meadow, west satellites and south satellites). As for the deterministic elasticities, S had the highest elasticity to the mean values of adult survival rates in all sites (Fig. 5-4). However, elasticity of S to changes in other vital rates varied significantly am ong sites (Fig. 5-4). Elasticity for Sj ranked second in four sites, for Sy in two sites, and for r in two sites. Elasticity for Sp ranked third in three sites, for r in two sites, and for Sj, Sy and lsa, each in one site. Elasticity for lsa ranked fourth in three sites, for Sp in two sites, and for Sy and r, each in one site. There was a relatively low effect on S of the small changes in vari ances in and covariances among vital rates. The summed elasticity of to the survival of the pre-reproductive classes was again close to that of reproducti ve classes; it was slightly hi gher in two sites (Picnic and north satellites) and lower in the rest of the sites (River, Gothic, Marmot Meadow, west satellites, east satellites and south satellites).

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137 BIOGRAPHICAL SKETCH Arpat Ozgul was born on April 21, 1976, in Ankara, Turkey. He earned a bachelor's degree in business administration from the Bosphorus University, Istanbul, Turkey, in 1999. During his undergraduate degree, he decided to switch careers and become an ecologist. He received his master's degree in environmental sciences from the Bosphorus University in 2001. His master's thesis was on the community ecology of cave-dwelling bats in Northwes tern Turkey. In 2001, he started his PhD in wildlife ecology and conservation at the University of Florida, Gainesville, USA.


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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