UFDC Home  myUFDC Home  Help 



Full Text  
METAPOPULATION DYNAMICS OF YELLOWBELLIED 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 yellowbellied 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 YELLOWBELLIED 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 AGESPECIFIC SURVIVAL RATES OF THE YELLOWBELLIED 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 CaptureMarkRecapture (CMR) Analysis ............... ............................... 44 R e su lts .................. ....... .. ... ........ .................... ................ ................ 4 8 Spatiotemporal Variation in Overall Survival Rates....................................48 Age Structure and Spatiotemporal Variation in AgeSpecific 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 YELLOWBELLIED 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 YELLOWBELLIED 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 AGESPECIFIC 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 21. Models and subfunction definitions used in SPOMSIM. ......................................31 22. Markov Chain Monte Carlo estimates of the parameters for the best stochastic patch occupancy m odel .......................................................................... 32 23. Definition of robust design occupancy models used for modeling colonization and extinction probabilities...................... ....... ............................. 33 24. 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 yellowbellied marmot data.. ....................................... ....... 34 31. Analysis of the age structure and spatial variation in agespecific apparent survival rates for the yellowbellied marmot............................ .... ...............58 32. Analysis of temporal variation in agespecific apparent survival rates for the yellow bellied m arm ot. ........................... ...... .............. ....................... 59 33. Analysis of temporal and spatial variation in the growth rate of the entire population and adult segment of the population..................................................60 41. Analysis of statespecific apparent survival, recapture, and transition rates for the yellow bellied m arm ot ............ .................................................... .................. .. 80 42. Analysis of the spatial, temporal, and agespecific variation in litter size for the y ellow b ellied m arm ot ............ .................................................... .................. ... 8 1 43. Analysis of the temporal and spatial variation in growth rate of the adult segment of the population. .................................... ......................................82 A1. Analysis of spatial and temporal variation in overall apparent annual survival rates for the yellowbellied marmot. ......................... .. .............. ................... 117 B1. A table showing the effect of environmental covariates on the spatial and temporal variation in agespecific survival rates. ................................................ 118 C1. List of covariates used during the analysis of the effect of environmental factors on the breeding probabilities and on litter size of the yellowbellied marmot. ......121 LIST OF FIGURES Figure page 21. The structure of the yellowbellied marmot metapopulation in Colorado...............35 22. Yearly proportions of occupied patches, empty patches, and patches with unknown occupancy status, for the period between 1990 and 2002......................36 23. Predicted patch occupancy in 1000 replicate simulations of the yellowbellied marmot metapopulation using the parameterized stochastic patch occupancy m o d e l ............................ ........... ... ...................................................3 7 24. 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 25. Predicted patch occupancy in 1000 replicate simulations for the northern and southern netw works ......................... ........................ .. .... ..... .. ............39 31. The spatial structure of the yellowbellied 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 32. Spatial variation in annual adult, yearling, and juvenile survival rates...................62 33. Temporal variation in annual adult, yearling and juvenile survival rates from 1 9 7 6 to 2 0 0 3 ................................ ......... ..... ............... ................ 6 3 41. The life cycle graph for the yellow bellied marmot, with three life history states (yearling, nonreproductive adult and reproductive adult)............... ............... 83 42. Sitespecific estimates of transition rates from yearling, nonreproductive adult, and reproductive adult states to the reproductive adult state, and sitespecific estimates of litter size and the realized growth rate of the adult population............84 43. Temporal variation in transition rates from nonreproductive 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 51. The life cycle graph for the yellow bellied marmot, with four life history stages: juvenile, yearling, prereproductive adult, and reproductive adult ........................106 52. Elasticity of the projected population growth rate to the vital rates...................... 107 53. Elasticity of the stochastic population growth rate to the mean values of the vital rate s.. .................................................................................... 1 0 8 54. 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 55. The covariances of the vital rates among sites, and the contributions of the covariances to the variation in projected growth rates among sites......................110 56. 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 57. 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 YELLOWBELLIED 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 longlived 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 yellowbellied 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 longterm persistence of the metapopulation. Using capturemarkrecapture (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 stagestructured 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 vectorpermutation 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 withinpopulation 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 spatiallystructured population models to address the influence of spatial heterogeneity on population dynamics (e.g., Lankester et al. 1991, Lahaye et al. 1994, Akcakaya and SjorgenGulve 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 SjorgenGulve 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 presenceabsence 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 presenceabsence 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 (SjorgenGulve 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 longlived 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 longlived species. Objectives In this doctoral research, I investigated the factors and processes that influence the dynamics and persistence of a yellowbellied marmot metapopulation in the upper East River Valley, Colorado. Longterm 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 (radiotelemetry) data from several colonies (Van Vuren 1990, Armitage 1991, Schwartz et al. 1998, Armitage and Schwartz 2000). The longterm study of individuallyidentified 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 25), 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 yellowbellied 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 agespecific survival rates using an age structured CormackJollySeber model (Lebreton et al. 1992, Lebreton et al. 1993) and longterm capturemarkrecapture (CMR) data. In Chapter 4, I investigated the spatiotemporal variation in the components of reproduction; I analyzed stagespecific breeding probabilities using a multistate CMR model (Hestbeck et al. 1991, Brownie et al. 1993, Williams et al. 2001, Fujiwara and Caswell 2002) and agespecific 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 reversetime 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 yellowbellied 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 yellowbellied marmot metapopulation, and to provide insights into the utility of different modeling approaches. The Study System The yellowbellied 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 longterm 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 (1year 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 reestablishment 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 yellowbellied 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 yellowbellied marmot metapopulation is unknown. CHAPTER 2 EFFECTS OF PATCH QUALITY AND NETWORK STRUCTURE ON PATCH OCCUPANCY DYNAMICS OF A YELLOWBELLIED 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 (19902002) of survey data to parameterize a stochastic patch occupancy model for a metapopulation of the yellowbellied 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 yellowbellied 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 longterm 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 dataintensive. 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 spatiallymediated 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 sourcesink (Pulliam 1988, Pulliam and Danielson 1991) or mainlandisland 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 smallbodied 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 yellowbellied marmot, Marmotaflaviventris (Audubon & Bachman 1841). Yellowbellied 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 (19902002) 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, 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 yellowbellied marmot metapopulation. Materials and Methods Study Area and Species The yellowbellied marmot is a large, diurnal, burrowdwelling 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. 21) 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 yellowbellied marmots in Colorado is described by Armitage (1991, 2002). Although the number of patches in the yellowbellied 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 longdistance dispersers can result in a distancedependent 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 yellowbellied 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 yellowbellied 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 wellconnected 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 longterm 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. 22). 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 yellowbellied marmot metapopulation was at a stochastic quasiequilibrium. 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 yellowbellied 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 lognormal 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 yellowbellied 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 timespecific rates of extinction and colonization, and timevarying individual covariates can be used to incorporate site specific information into the model. We estimated the site and timespecific extinction and colonization rates for 21 sites for 13 years using the most parsimonious SPOM. We used these estimates as timevarying 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 timespecific 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 timevarying 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 timespecific {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 timevarying site covariates. We expect the models in which the timevarying site covariates (estimated from SPOM) were used as predictors of extinction and recolonization rates to be more parsimonious than the timespecific or constant recolonization and extinction rate models. Results Parameter Estimation We used independent dispersal data from 90 radioinstrumented 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. 22) 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 21). The most parsimonious model (model #5 in Table 21) 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 21). 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 22. 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 yellowbellied 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 yellowbellied marmot metapopulation was simulated using the most parsimonious model (model #5 in Table 21) with the parameter estimates given in Table 22. 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 longterm metapopulation persistence (Fig. 23A). 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. 23B). 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. 23C). 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. 24A). 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. 24A). 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 yellowbellied 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. 21). 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. 24B,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. 24B,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. 24B,C). We used connectivitybased 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: uppervalley (northern) and lowervalley (southern) networks (Fig. 21), 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. 25A). On the other hand, the southern network was very unstable, and the proportion of occupied patches frequently declined to zero (Fig. 25B). Very few of the simulated replicates survived till the end of 100 years (Fig. 25B). 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 yellowbellied marmot system, we compared a set of candidate models using the robust design occupancy modeling approach (Tables 23 and 24). In general, including timespecific, but not sitespecific, 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 timespecific models that ignored sitespecific differences. Model likelihood were significantly improved when time and sitespecific 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 24). Nonetheless, two models with SPOMpredicted 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 yellowbellied 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 longterm persistence of the yellowbellied 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 yellowbellied 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 longlived species (Harrison 1991, Schoener 1991), and has been observed in American pika, Ochotonaprinceps (Moilanen et al. 1998), a species that shares similar lifehistory 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 yellowbellied 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 yellowbellied 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 longterm. Despite the high importance of colony sites for regional persistence, our results suggest that lower quality satellite sites may also contribute markedly to the longterm persistence of the yellowbellied 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 yellowbellied marmot system is not a perfect mainlandisland system as suggested for other longlived species (Harrison 1991, Schoener 1991), and it shows characteristics of a metapopulation 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 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 yellowbellied 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 yellowbellied 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 yellowbellied 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 yellowbellied 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 yellowbellied marmot metapopulation. Considering sitespecific 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 yellowbellied 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 yellowbellied 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., individualbased models) are structurally complex and dataintensive. 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 individualbased 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 yellowbellied 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 longterm persistence of the yellowbellied marmot metapopulation. Given the high sensitivity of metapopulation persistence to local population size, future studies of the yellowbellied 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 yellowbellied marmot metapopulation. Table 21. 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 22. Markov Chain Monte Carlo estimates of the parameters for the best stochastic patch occupancy model (model #5 in Table 21). 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 23. Definition of robust design occupancy models used for modeling colonization (y) and extinction (s) probabilities. Notation Biological significance E (.) constant extinction rate E (t) timespecific extinction rate e (Q) extinction rate with site quality as a constant site covariate E (E) extinction rate with extinction* as a timevarying site covariate y(.) constant colonization rate y(t) timespecific colonization rate y(C) colonization rate with colonization* as a timevarying site covariate y(S) colonization rate with connectivity* as a timevarying site covariate Estimated using the parameterized stochastic patch occupancy model. Table 24. 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 yellowbellied 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 23. 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 Eastwest distance (km) Figure 21. The structure of the yellowbellied 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 22. 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 23. Predicted patch occupancy in 1000 replicate simulations of the yellowbellied 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 24. 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. 21. 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 Uppervalley network Lowervalley network 0 20 40 60 80 100 Year Figure 25. 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 AGESPECIFIC SURVIVAL RATES OF THE YELLOWBELLIED MARMOT Spatiotemporal variation in agespecific survival rates can profoundly influence population dynamics, but few studies of vertebrates have thoroughly investigated both spatial and temporal variability in agespecific survival rates. We used 28 years (1976  2003) of capturemarkrecapture (CMR) data from 17 locations to parameterize an age structured CormackJollySeber model, and investigated spatial and temporal variation in agespecific annual survival rates of yellowbellied 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 reversetime CMR models to estimate the realized population growth rate (k), and to investigate the influence of the observed variation in agespecific 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 longlived 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, CluttonBrock 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 agespecific 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 agespecific survival rates of longlived species remain poorly understood. We used data from a longterm study of the yellowbellied marmot (Marmota flaviventris) to investigate the spatiotemporal variation in agespecific survival rates. Using an agestructured CormackJollySeber (CJS) model, we analyzed 28 years of capturemarkrecapture (CMR) data from 17 discrete habitat patches within our study site. We estimated agespecific 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 reversetime CMR model, we estimated the realized population growth rate, and investigated the influence of the observed variation in agespecific survival rates on the realized population growth rate, and hence on the dynamics of the yellowbellied marmot population. Materials and Methods Study Area and Species The yellowbellied marmot is a large, diurnal, burrowdwelling 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. 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 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 yellowbellied marmots in Colorado is described in detail by Armitage (1991, 2003a). Field Methods and Data From 1962 to 2003, yellowbellied marmots were livetrapped 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 sitespecific 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 southeastnorthwest direction, gaining elevation towards the northwest. Marmot sites on the west side of the East River Valley have steeper slopes facing northeast (3898), whereas sites on the east side are located on gradually inclined meadows generally facing southwest (183280). Seven timespecific 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 (MayAugust) 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 (MayAugust) ranged from 9.7 11.9 C, and annual precipitation ranged from 38.6 86.6 cm. For a detailed description of timespecific climatic factors, see Schwartz & Armitage (2005). CaptureMarkRecapture (CMR) Analysis Although our study spanned 42 years (19622003), we analyzed data from the last 28 years (19762003), 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. Sixtynine 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. 31). 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 agestructured CJS model (Lebreton et al. 1992, Lebreton et al. 1993) to estimate and model agespecific 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 goodnessoffit 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 yellowbellied 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: 01 yr; adults: >1 yr), three age classes (juveniles: 01 yr, yearlings: 12 yrs, and adults: >2 yrs), and four age classes (juveniles: 01 yr, yearlings: 12 yrs, subadults: 23 yrs, and adults: >3 yrs). Although our data did not permit analysis of models with >4 ageclasses, 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 agespecific survival rates by testing for the site effect. Next, using the most parsimonious model, we investigated the temporal variation in age and sitespecific 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 agespecific 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 sitespecific 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 agespecific survival rates, so we considered the influence of each environmental covariate separately. We used a Pradel's reversetime 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 goodnessoffit 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 agespecific 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 agespecific survival rates on adult population growth rate (kad). To assess the relative importance of agespecific 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 agespecific survival rate most closely covaried (over space and time) with kad? We used sitespecific estimates of agespecific survival rates as a covariate for site effect on kad, and timespecific 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 underdispersion (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 Ai). 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 Ai). 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 AgeSpecific Survival Rates Among the candidate models with different age structures, the three ageclass model was the most parsimonious (model #2 in Table 31). Among the three ageclass 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 31). 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 31). 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. 32C). 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. 32B). 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. 32A). 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 ageclass 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 31) for all subsequent analyses. Next, we tested for temporal variation in the agespecific 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 32). 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 32) was more parsimonious than the model with separate adult survival rates for each of the eight sites (model #10 in Table 32), 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 32; Fig. 33C). A model with a similar support (AAIC, < 3; model #19 in Table 32) indicated additive effects of time and site on juvenile survival rates within the colonies. We used this final model (model #19 in Table 33), 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 ageclasses. Thus, we examined the influence of temporal and sitespecific covariates on juvenile survival rates and of site specific covariates on the yearling and adult survival rates (see Table Bl for model details). Sitespecific 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. Sitespecific variation in yearling survival rates was positively influenced by the elevation (3 = 0.26; 95% CI: 0.01, 0.51). Sitespecific 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 Goodnessoffit 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 modelselection (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 33). Sitespecific 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. 32E). Timespecific estimates of X ranged from 0.65 (95% CI: 0.45, 0.81) to 1.49 (95% CI: 0.93, 2.05) (Fig. 33E). The general Pradel's model for the adult segment of the population fit the data with a slight underdispersion (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 33). 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 33). A model with a similar support indicated additive effects of time and site on kad within the colonies (model #11 in Table 33). Sitespecific 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. 32D). 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. 33D). 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. 32) as well as over time with a one year lag (Fig. 33). Spatial variation in Xad was significantly influenced by amongsite variation in juvenile survival rates (3 = 0.36; 95% CI: 0.14, 0.58; model #12 in Table 33), but not by that in yearling (P = 0.03, 95% CI: 0.19, 0.12; model #13 in Table 33) or adult (P = 0.17; 95% CI: 0.43, 0.77; model #14 in Table 33) 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 33) and yearling survival rates (3 = 0.40, 95% CI: 0.02, 0.79; model #16 in Table 33), but not by that in adult survival rates (3 =  0.44, 95% CI: 1.08, 0.19; model #17 in Table 33). 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 agespecific 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 longterm study of individuallyidentified animals in several discrete habitat patches provided adequate data for a rigorous examination of spatiotemporal patterns in agespecific survival rates of yellowbellied marmots and their population dynamic consequences. In general, overall survival rates of yellowbellied marmots varied both spatially and temporally. Detailed analysis of agespecific survival rates indicated that the pattern of variation differed among age classes. The most appropriate age structure was the three ageclass model: juveniles (01 yr), yearlings (12 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 yellowbellied 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 agespecific 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. 32C). 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 tradeoff between active season and overwinter 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 agespecific 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 sitespecific differences in juvenile survival rates. Modeling Xad as a function of agespecific 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 yellowbellied 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 yellowbellied 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 agespecific survival rates, survival of juveniles was the most variable over space and time. This variation heavily influenced the dynamics of our study population; sitespecific 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 longlived vertebrate species (e.g., Douglas and Leslie 1986, CluttonBrock 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 yellowbellied 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 yellowbellied marmot. Table 31. Analysis of the age structure and spatial variation in agespecific apparent survival rates for the yellowbellied marmot, using CormackJollySeber 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: 01 yr), yearling (yr : 12 yr), subadult (subad: 23 yr), and adults (ad: >1 yr for 2 ageclass, >2 yr for 3 ageclass, 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) subad (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) subad (.) 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 ageclass model * 3 ageclass model S4 ageclass model Table 32. Analysis of temporal variation in agespecific apparent survival rates for the yellowbellied marmot, using age structured CormackJollySeber models. Three ageclass model was used for these analyses: juvenile (juv : 01 yr), yearlings (yrl: 12 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 31. 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 33. 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 reversetime models. Sitespecific 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 (juvtl), and yearling (yrlt) and adult (adt) survival rates of the current year. Other symbols are defined in Tables 31 and 32. 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 Eastwest distance (km) Figure 31. The spatial structure of the yellowbellied 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 32. 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 31. 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 33, respectively. ad ^ad T T U. D 1.0 4..... I IF 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 33. 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 32, 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 33, respectively. CHAPTER 4 SPATIOTEMPORAL VARIATION IN THE REPRODUCTIVE PARAMETERS OF THE YELLOWBELLIED 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 capturemarkrecapture (CMR) modeling framework to investigate the spatiotemporal variation in reproductive parameters of the yellowbellied 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., prereproductive), nonreproductive adult and reproductive adult females. The breeding probabilities of the nonreproductive 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 reversetime 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 yellowbellied marmots and other mammals with similar life history characteristics. Introduction Many species live in discrete habitat patches that occur either naturally or due to humancaused 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 yellowbellied marmot (Marmotaflaviventris). We applied multistate capturemarkrecapture (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 reversetime 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 yellowbellied marmot is a large, diurnal, burrowdwelling 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. 21). 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 yellowbellied marmot first breeds at 2 years of age, less than a quarter of 2yearold females reproduce, and the median age of first reproduction is 3 years (Schwartz et al. 1998). The biology of yellowbellied marmots in Colorado is described in detail by Armitage (1991, 2003 a). Field Methods and Data From 1962 to 2004, yellowbellied marmots were livetrapped 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 lowquality 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 2year 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. 41): (1) yearling (12 yrs; prereproductive), (2) nonreproductive 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 statespecific 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 yearold conditional on survival), i23 (probability of a nonreproductive adult breeding the following year conditional on survival), and y33 (probability of a reproductive adult breeding again the following year conditional on survival) (Fig. 41). 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 nonreproductive 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 goodnessoffit of the general multistate model. We used quasilikelihood 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 pressa). Therefore, we tested only for the site effect in these rates. First, we tested for site effect on recapture rates of the nonreproductive and reproductive adults. We then proceeded to test for site effect on the survival rate of yearlings, nonreproductive adults and reproductive adults. Finally, we tested for both site and time effects on statespecific 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 ageclass (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) sitespecific, (2) climatic, and (3) social factors (Appendix C, Table Cl). 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 sitespecific, 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 sitespecific, 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 reversetime 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 goodnessoffit 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 sitespecific estimates of transition rates and litter size as covariates to test for site effect on Xad, and timespecific 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. Timespecific estimates of the transition rates were included with a two year lag (e.g., Y23 during 199697 period would influence kad during 199899), whereas those of the litter size were included with a one year lag (e.g., litter size during 1996 would influence Xad during 199798). 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 goodnessoffit 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 quasilikelihood adjustment for model comparison. The most parsimonious model (model #22 in Table 41) included a constant recapture rate of 1.00 (SE < 0.01) for the reproductive adults, and site effect on the recapture rates of nonreproductive 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 nonreproductive adults varied among sites. Survival rate of nonreproductive 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. 42). 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. 42), and from 0.11 0.11 (1991) to 0.90 + 0.10 (2003) over time (Fig. 43). There were no significant differences between colonies and satellites in any of the three transition rates (Table 41). 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 42). 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 42) 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 41). Among the sitespecific 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 nonreproductive 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 nonreproductive females than immigrant nonreproductive 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 42). 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 43). A model with less support indicated additive effects of time and site on kad (model #1 in Table 43). Annual estimates of kad ranged from 0.54 0.05 (1983) to 1.68 0.23 (2003) indicating substantial temporal fluctuations (Fig. 43). 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. 41). 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 yellowbellied 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 yellowbellied 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 nonreproductive 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 nonreproductive 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 agespecific survival rates of the yellowbellied marmots in Colorado and the population dynamic consequences were reported elsewhere (Ozgul et al. in pressa). Yet, our study revealed that the survival of nonreproductive 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., CluttonBrock et al. 1987, Stenseth et al. 1996, Leirs et al. 1997, Coulson et al. 2000). We found that different components of reproduction in yellowbellied 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 nonreproductive 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 nonreproductive 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 tradeoff 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 pressa). Among all reproductive parameters, litter size and the breeding probability of the nonreproductive 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 nonreproductive 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 pressa), indicate that litter size and juvenile survival, abetted by the breeding probability of the nonreproductive 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 yellowbellied marmot (Armitage 1973, 2003b), and other species with similar life history characteristics. We conclude that components of reproduction in yellowbellied 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 yellowbellied marmot population. Table 41. Analysis of statespecific apparent survival, recapture, and transition rates for the yellowbellied marmot using a multistate markrecapture model. Differences in quasilikelihood 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), nonreproductive 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) W33 (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 42. Analysis of the spatial, temporal, and agespecific variation in litter size for the yellowbellied 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 43. 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. Sitespecific covariates for kad are sitespecific estimates of litter size (litters), and sitespecific transition rates from nonreproductive adult ("' 23) and reproductive adult (Y'33) states to reproductive adult state. Temporal covariates for Xad are annual estimates of litter size litterrt, and timespecific transition rates from yearling ('t13), nonreproductive adult (,t23), and reproductive adult (Yt33) states to reproductive adult state. Other symbols are defined in Table 41. 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 41. The life cycle graph for the yellow bellied marmot, with three life history states (yearling, nonreproductive 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 .04* 0000 6Po Figure 42. Sitespecific estimates (mean + SE) of transition rates from (A) yearling (Y13), (B) nonreproductive 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 41, respectively. Sitespecific 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 42 and model #3 in Table 43, 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 43. Temporal variation in transition rates from (A) nonreproductive 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 41, 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 42, and model #2 in Table 43, respectively. CHAPTER 5 THE INFLUENCE OF LOCAL DEMOGRAPHIC PROCESSES ON THE REGIONAL DYNAMICS OF A YELLOWBELLIED 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 longlived 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 yellowbellied 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 lifetable 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 vecpermutation 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 yellowbellied 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 SjorgenGulve 2000, SjorgenGulve 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 SjorgenGulve 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 longlived 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 