Individual heterogeneity and capture–recapture models: what, why and how?

Variation between and within individuals in life history traits is ubiquitous in natural populations. When affecting fitness-related traits such as survival or reproduction, individual heterogeneity plays a key role in population dynamics and life history evolution. However, it is only recently that properly accounting for individual heterogeneity when studying population dynamics of free-ranging populations has been made possible through the development of appropriate statistical models. We aim here to review case studies of individual heterogeneity in the context of capture–recapture models for the estimation of population size and demographic parameters with imperfect detection. First, we define what individual heterogeneity means and clarify the terminology used in the literature. Second, we review the literature and illustrate why individual heterogeneity is used in capture–recapture studies by focusing on the detection of life-history tradeoffs, including senescence. Third, we explain how to model individual heterogeneity in capture–recapture models and provide the code to fit these models (https://github.com/oliviergimenez/indhet_in_CRmodels). The distinction is made between situations in which heterogeneity is actually measured and situations in which part of the heterogeneity remains unobserved. Regarding the latter, we outline recent developments of random-effect models and finite-mixture models. Finally, we discuss several avenues for future research.

[1]  Roger Pradel,et al.  Hidden survival heterogeneity of three Common eider populations in response to climate fluctuations , 2017, The Journal of animal ecology.

[2]  Emmanuelle Cam,et al.  Wolf in sheep's clothing: Model misspecification undermines tests of the neutral theory for life histories , 2017, Ecology and evolution.

[3]  G. White,et al.  Population abundance estimation with heterogeneous encounter probabilities using numerical integration , 2017 .

[4]  J. Gaillard,et al.  Evidence of reduced individual heterogeneity in adult survival of long‐lived species , 2016, Evolution; international journal of organic evolution.

[5]  J. Gaillard,et al.  Cohort variation in individual body mass dissipates with age in large herbivores , 2016 .

[6]  L. Aubry,et al.  The Conundrum of Heterogeneities in Life History Studies. , 2016, Trends in ecology & evolution.

[7]  H. Weimerskirch,et al.  Variation in the age of first reproduction: different strategies or individual quality? , 2016, Ecology.

[8]  G. R. Hepp,et al.  Effects of current reproductive success and individual heterogeneity on survival and future reproductive success of female Wood Ducks , 2016, The Auk.

[9]  H. Weimerskirch,et al.  Paternal but not maternal age influences early-life performance of offspring in a long-lived seabird , 2016, Proceedings of the Royal Society B: Biological Sciences.

[10]  Daniel Manrique-Vallier,et al.  Bayesian population size estimation using Dirichlet process mixtures , 2016, Biometrics.

[11]  Shen-Ming Lee,et al.  Estimation in closed capture–recapture models when covariates are missing at random , 2016, Biometrics.

[12]  E. Postma,et al.  Successful by Chance? The Power of Mixed Models and Neutral Simulations for the Detection of Individual Fixed Heterogeneity in Fitness Components , 2016, The American Naturalist.

[13]  Jean-Michel Gaillard,et al.  What shapes fitness costs of reproduction in long-lived iteroparous species? A case study on the Alpine ibex. , 2016, Ecology.

[14]  G. Nicholls,et al.  Bayesian analysis of Jolly-Seber type models; incorporating heterogeneity in arrival and departure , 2015, 1512.05170.

[15]  Jessica H Ford,et al.  Modelling latent individual heterogeneity in mark-recapture data with Dirichlet process priors , 2015, 1511.07103.

[16]  J. Laake,et al.  Multivariate State Hidden Markov Models for Mark-Recapture Data , 2015, bioRxiv.

[17]  Alexander Plum,et al.  Heterogeneity in unemployment state dependence , 2015 .

[18]  J. Kapfer,et al.  Recouping Lost Information when Mark-Recapture Data are Pooled: A Case Study of Milksnakes (Lampropeltis triangulum) in the Upper Midwestern United States , 2015 .

[19]  T. Piersma,et al.  An ontogenetic perspective on individual differences , 2015, Proceedings of the Royal Society B: Biological Sciences.

[20]  J. Gaillard,et al.  Quantifying the influence of measured and unmeasured individual differences on demography. , 2015, The Journal of animal ecology.

[21]  J. Gaillard,et al.  Early and adult social environments have independent effects on individual fitness in a social vertebrate , 2015, Proceedings of the Royal Society B: Biological Sciences.

[22]  W. Link,et al.  Individual Heterogeneity in Growth and Age at Sexual Maturity: A Gamma Process Analysis of Capture–Mark–Recapture Data , 2015 .

[23]  Hein Putter,et al.  Dynamic frailty models based on compound birth-death processes. , 2015, Biostatistics.

[24]  J. Gaillard,et al.  Early-late life trade-offs and the evolution of ageing in the wild , 2015, Proceedings of the Royal Society B: Biological Sciences.

[25]  Competitive release modifies the impacts of hydrologic alteration for a partially migratory stream predator , 2015 .

[26]  S. T. Buckland,et al.  Analysing Mark–Recapture–Recovery Data in the Presence of Missing Covariate Data Via Multiple Imputation , 2015 .

[27]  Y. Jiao,et al.  Use of PIT tags to assess individual heterogeneity of laboratory-reared juveniles of the endangered Cumberlandian combshell (Epioblasma brevidens) in a mark–recapture study , 2015, Ecology and evolution.

[28]  D. Lusseau,et al.  Estimating spatial, temporal and individual variability in dolphin cumulative exposure to boat traffic using spatially explicit capture–recapture methods , 2015 .

[29]  Mevin B. Hooten,et al.  A guide to Bayesian model selection for ecologists , 2015 .

[30]  J. Rotella,et al.  Female Weddell seals show flexible strategies of colony attendance related to varying environmental conditions. , 2015, Ecology.

[31]  G. Gauthier,et al.  To breed or not: a novel approach to estimate breeding propensity and potential trade‐offs in an Arctic‐nesting species , 2014 .

[32]  J. Vaupel,et al.  Unobserved population heterogeneity , 2014 .

[33]  J. Gaillard,et al.  Methods for studying cause‐specific senescence in the wild , 2014 .

[34]  Giacomo Tavecchia,et al.  Bayesian model selection: The steepest mountain to climb , 2014 .

[35]  J. Gaillard,et al.  Fitness consequences of environmental conditions at different life stages in a long-lived vertebrate , 2014, Proceedings of the Royal Society B: Biological Sciences.

[36]  N. G. Best,et al.  The deviance information criterion: 12 years on , 2014 .

[37]  M. Meredith,et al.  Survival in macaroni penguins and the relative importance of different drivers: individual traits, predation pressure and environmental variability , 2014, The Journal of animal ecology.

[38]  K. Evans,et al.  Climate change and annual survival in a temperate passerine: partitioning seasonal effects and predicting future patterns , 2014 .

[39]  Thierry Chambert,et al.  Use of posterior predictive checks as an inferential tool for investigating individual heterogeneity in animal population vital rates , 2014, Ecology and evolution.

[40]  N. Ahmad State Dependence in Unemployment , 2014 .

[41]  C. Paddy Farrington,et al.  A time-varying shared frailty model with application to infectious diseases , 2014 .

[42]  J. Gaillard,et al.  A standardized approach to estimate life history tradeoffs in evolutionary ecology , 2014 .

[43]  Sophia Rabe-Hesketh,et al.  Handling initial conditions and endogenous covariates in dynamic/transition models for binary data with unobserved heterogeneity , 2014 .

[44]  Aki Vehtari,et al.  Understanding predictive information criteria for Bayesian models , 2013, Statistics and Computing.

[45]  William L. Kendall,et al.  Life-history tradeoffs and reproductive cycles in Spotted Owls , 2014 .

[46]  Olivier Gimenez,et al.  Known unknowns in an imperfect world: incorporating uncertainty in recruitment estimates using multi-event capture–recapture models , 2013, Ecology and evolution.

[47]  J. Lebreton,et al.  Individual heterogeneity in black brant survival and recruitment with implications for harvest dynamics , 2013, Ecology and evolution.

[48]  Jeffrey L. Laake,et al.  marked: an R package for maximum likelihood and Markov Chain Monte Carlo analysis of capture–recapture data , 2013 .

[49]  J. Rotella,et al.  Individual heterogeneity in reproductive rates and cost of reproduction in a long-lived vertebrate , 2013, Ecology and evolution.

[50]  Roger Pradel,et al.  Estimating demographic parameters from capture–recapture data with dependence among individuals within clusters , 2013 .

[51]  J. Andrew Royle,et al.  Looking for a needle in a haystack: inference about individual fitness components in a heterogeneous population , 2013 .

[52]  Res Altwegg,et al.  Revisiting the Effect of Capture Heterogeneity on Survival Estimates in Capture-Mark-Recapture Studies: Does It Matter? , 2013, PloS one.

[53]  H. Weimerskirch,et al.  Fisheries Bycatch as an Inadvertent Human-Induced Evolutionary Mechanism , 2013, PloS one.

[54]  Erik J. Blomberg,et al.  Seasonal reproductive costs contribute to reduced survival of female greater sage‐grouse , 2013 .

[55]  M. Vavra,et al.  Life-history strategies of North American elk: trade-offs associated with reproduction and survival , 2013 .

[56]  Roland Langrock,et al.  MAXIMUM LIKELIHOOD ESTIMATION OF MARK-RECAPTURE-RECOVERY MODELS IN THE PRESENCE OF CONTINUOUS COVARIATES , 2012, 1211.0882.

[57]  Jeffrey L. Laake,et al.  RMark : an R Interface for analysis of capture-recapture data with MARK , 2013 .

[58]  N. Dingemanse,et al.  Quantifying individual variation in behaviour: mixed-effect modelling approaches. , 2013, The Journal of animal ecology.

[59]  R. Pradel,et al.  Breeding Experience Might Be a Major Determinant of Breeding Probability in Long-Lived Species: The Case of the Greater Flamingo , 2012, PloS one.

[60]  W. Kendall,et al.  Extreme weather and experience influence reproduction in an endangered bird. , 2012, Ecology.

[61]  Roger Pradel,et al.  Estimating demographic parameters using hidden process dynamic models. , 2012, Theoretical population biology.

[62]  J. Gaillard,et al.  Modeling reproductive trajectories of roe deer females: fixed or dynamic heterogeneity? , 2012, Theoretical population biology.

[63]  F. Jiguet,et al.  The interaction between reproductive cost and individual quality is mediated by oceanic conditions in a long-lived bird. , 2012, Ecology.

[64]  Eric Marboutin,et al.  Assessing individual heterogeneity using model selection criteria: how many mixture components in capture–recapture models? , 2012 .

[65]  O. Gimenez,et al.  ASSESSING ADAPTIVE PHENOTYPIC PLASTICITY BY MEANS OF CONDITIONAL STRATEGIES FROM EMPIRICAL DATA: THE LATENT ENVIRONMENTAL THRESHOLD MODEL , 2012, Evolution; international journal of organic evolution.

[66]  U. Steiner,et al.  Neutral theory for life histories and individual variability in fitness components , 2012, Proceedings of the National Academy of Sciences.

[67]  Lucile Marescot,et al.  Bias in estimation of adult survival and asymptotic population growth rate caused by undetected capture heterogeneity , 2012 .

[68]  B. Faivre,et al.  Testing hypotheses in evolutionary ecology with imperfect detection: capture-recapture structural equation modeling. , 2012, Ecology.

[69]  Ruth King,et al.  A review of Bayesian state-space modelling of capture–recapture–recovery data , 2012, Interface Focus.

[70]  J. Gaillard,et al.  Senescence in natural populations of animals: Widespread evidence and its implications for bio-gerontology , 2013, Ageing Research Reviews.

[71]  B. Kendall,et al.  Demographic heterogeneity impacts density-dependent population dynamics , 2012, Theoretical Ecology.

[72]  Tim Coulson,et al.  Modeling Effects of Environmental Change on Wolf Population Dynamics, Trait Evolution, and Life History , 2011, Science.

[73]  Roger Pradel,et al.  Capture–recapture population growth rate as a robust tool against detection heterogeneity for population management , 2011 .

[74]  R. Choquet,et al.  The Forms and Fitness Cost of Senescence: Age-Specific Recapture, Survival, Reproduction, and Reproductive Value in a Wild Bird Population , 2011, The American Naturalist.

[75]  D. Oro,et al.  Natural ‘poor start’ does not increase mortality over the lifetime , 2011, Proceedings of the Royal Society B: Biological Sciences.

[76]  R. Pradel,et al.  Effects of age, territoriality and breeding on survival of Bonelli's Eagle Aquila fasciata , 2011 .

[77]  B. Kendall,et al.  Demographic heterogeneity, cohort selection, and population growth. , 2011, Ecology.

[78]  Once Poor, Always Poor? Do Initial Conditions Matter? Evidence from the ECHP , 2011 .

[79]  M. Collopy,et al.  Correlates of Survival in Swainson's Hawks Breeding in Northern California , 2011 .

[80]  Samuel J. Gershman,et al.  A Tutorial on Bayesian Nonparametric Models , 2011, 1106.2697.

[81]  Derek E. Lee Effects of environmental variability and breeding experience on northern elephant seal demography , 2011 .

[82]  M. Sköld,et al.  Individual heterogeneity and senescence in silvereyes on Heron Island. , 2011, Ecology.

[83]  S. Schreiber,et al.  Why intraspecific trait variation matters in community ecology. , 2011, Trends in ecology & evolution.

[84]  Roger Pradel,et al.  Studying the reproductive skipping behavior in long-lived birds by adding nest inspection to individual-based data. , 2011, Ecological applications : a publication of the Ecological Society of America.

[85]  Individual differences in reproductive costs examined using multi-state methods. , 2011, The Journal of animal ecology.

[86]  Olivier Gimenez,et al.  Frailty in state-space models: application to actuarial senescence in the Dipper. , 2011, Ecology.

[87]  P. Thompson,et al.  Static and dynamic expression of life history traits in the Northern Fulmar (Fulmarus glacialis). , 2011, Oikos.

[88]  D. Koons,et al.  Drivers of age-specific survival in a long-lived seabird: contributions of observed and hidden sources of heterogeneity. , 2011, The Journal of animal ecology.

[89]  Byron J. T. Morgan,et al.  Individual heterogeneity in recapture probability and survival estimates in cheetah , 2011 .

[90]  David Borchers,et al.  A non-technical overview of spatially explicit capture–recapture models , 2012, Journal of Ornithology.

[91]  Victoria Prowse Modeling Employment Dynamics With State Dependence and Unobserved Heterogeneity , 2011, SSRN Electronic Journal.

[92]  Ruth King,et al.  Continuous Covariates in Mark‐Recapture‐Recovery Analysis: A Comparison of Methods , 2010, Biometrics.

[93]  Joachim M. Buhmann,et al.  Infinite mixture-of-experts model for sparse survival regression with application to breast cancer , 2010, BMC Bioinformatics.

[94]  T. Clutton‐Brock,et al.  Individuals and populations: the role of long-term, individual-based studies of animals in ecology and evolutionary biology. , 2010, Trends in ecology & evolution.

[95]  O Gimenez,et al.  Combining capture–recapture data and pedigree information to assess heritability of demographic parameters in the wild , 2010, Journal of evolutionary biology.

[96]  Olivier Gimenez,et al.  INVESTIGATING EVOLUTIONARY TRADE‐OFFS IN WILD POPULATIONS OF ATLANTIC SALMON (SALMO SALAR): INCORPORATING DETECTION PROBABILITIES AND INDIVIDUAL HETEROGENEITY , 2010, Evolution; international journal of organic evolution.

[97]  Kenneth H Pollock,et al.  Open Capture–Recapture Models with Heterogeneity: II. Jolly–Seber Model , 2010, Biometrics.

[98]  A. Wienke Frailty Models in Survival Analysis , 2010 .

[99]  E. Bignal,et al.  Parent age, lifespan and offspring survival: structured variation in life history in a wild population. , 2010, The Journal of animal ecology.

[100]  D. Tallmon,et al.  Strong influence of microhabitat on survival for an intertidal snail, Nucella lima , 2010, Hydrobiologia.

[101]  Alessio Farcomeni,et al.  Reference Bayesian methods for recapture models with heterogeneity , 2010 .

[102]  John M. Maniscalco,et al.  High Natality Rates of Endangered Steller Sea Lions in Kenai Fjords, Alaska and Perceptions of Population Status in the Gulf of Alaska , 2010, PloS one.

[103]  O Gimenez,et al.  Individual heterogeneity in studies on marked animals using numerical integration: capture-recapture mixed models. , 2010, Ecology.

[104]  D. Nussey,et al.  What is individual quality? An evolutionary perspective. , 2010, Trends in ecology & evolution.

[105]  Roger Pradel,et al.  Importance of Accounting for Detection Heterogeneity When Estimating Abundance: the Case of French Wolves , 2010, Conservation biology : the journal of the Society for Conservation Biology.

[106]  Roger Pradel,et al.  Capture–recapture models with heterogeneity to study survival senescence in the wild , 2010 .

[107]  A. Millon,et al.  Pulsed resources affect the timing of first breeding and lifetime reproductive success of tawny owls. , 2010, The Journal of animal ecology.

[108]  S. Orzack,et al.  Dynamic heterogeneity and life history variability in the kittiwake. , 2010, The Journal of animal ecology.

[109]  Roger Pradel,et al.  Estimating Population Growth Rate From Capture–Recapture Data in Presence of Capture Heterogeneity , 2010 .

[110]  Kenneth G. Manton,et al.  Methods For Comparing The Mortality Experience of Heterogeneous Populations , 1981, Demography.

[111]  J. Vaupel,et al.  The impact of heterogeneity in individual frailty on the dynamics of mortality , 1979, Demography.

[112]  Thomas Lenormand,et al.  Estimating and Visualizing Fitness Surfaces Using Mark-Recapture Data , 2009, Evolution; international journal of organic evolution.

[113]  H. Caswell Stage, age and individual stochasticity in demography , 2009 .

[114]  A. Lescroël,et al.  Effects of individual quality, reproductive success and environmental variability on survival of a long-lived seabird. , 2009, The Journal of animal ecology.

[115]  J. Bêty,et al.  Costs of reproduction in a long-lived bird: large clutch size is associated with low survival in the presence of a highly virulent disease , 2009, Biology Letters.

[116]  Martijn van de Pol,et al.  A simple method for distinguishing within- versus between-subject effects using mixed models , 2009, Animal Behaviour.

[117]  R. O’Hara,et al.  A review of Bayesian variable selection methods: what, how and which , 2009 .

[118]  Mollie E. Brooks,et al.  Generalized linear mixed models: a practical guide for ecology and evolution. , 2009, Trends in ecology & evolution.

[119]  Roger Pradel,et al.  The Stakes of Capture–Recapture Models with State Uncertainty , 2009 .

[120]  Michael J. Conroy,et al.  Application of Capture–Recapture to Addressing Questions in Evolutionary Ecology , 2009 .

[121]  Roger Pradel,et al.  Program E-Surge: A Software Application for Fitting Multievent Models , 2009 .

[122]  F. Pelletier,et al.  Age-dependent relationship between horn growth and survival in wild sheep. , 2009, The Journal of animal ecology.

[123]  S. Orzack,et al.  Dynamic heterogeneity in life histories. , 2009, Ecology letters.

[124]  J. Gaillard,et al.  Individual variation in reproductive costs of reproduction: high-quality females always do better. , 2009, The Journal of animal ecology.

[125]  Shirley Pledger,et al.  Using Mixtures to Model Heterogeneity in Ecological Capture‐Recapture Studies , 2008, Biometrical journal. Biometrische Zeitschrift.

[126]  R. Pradel,et al.  THE COST OF REPRODUCTION AND EXPERIENCE-DEPENDENT VITAL RATES IN A SMALL PETREL. , 2008, Ecology.

[127]  Byron J. T. Morgan,et al.  A new mixture model for capture heterogeneity , 2008 .

[128]  Roger Pradel,et al.  The Risk of Flawed Inference in Evolutionary Studies When Detectability Is Less than One , 2008, The American Naturalist.

[129]  N. Chelgren,et al.  Fidelity and breeding probability related to population density and individual quality in black brent geese Branta bernicla nigricans. , 2008, The Journal of animal ecology.

[130]  M. Bester,et al.  Seasonal survival and the relative cost of first reproduction in adult female southern elephant seals , 2008 .

[131]  J Andrew Royle,et al.  Web-based Supplementary Materials for “ Modeling Individual Effects in the Cormack-Jolly-Seber Model : A State-space Formulation ” , 2010 .

[132]  J. Gaillard,et al.  Measuring senescence in wild animal populations: towards a longitudinal approach , 2008 .

[133]  Roger Pradel,et al.  Is heterogeneity of catchability in capture–recapture studies a mere sampling artifact or a biologically relevant feature of the population? , 2008, Population Ecology.

[134]  Byron J. T. Morgan,et al.  A new method for analysing discrete life history data with missing covariate values , 2008 .

[135]  A. Mysterud,et al.  Heterogeneity in individual quality overrides costs of reproduction in female reindeer , 2008, Oecologia.

[136]  A. Yashin,et al.  Model of hidden heterogeneity in longitudinal data. , 2008, Theoretical population biology.

[137]  David Kapland,et al.  An overview of Markov chain methods for the study of stage-sequential developmental processes. , 2008, Developmental psychology.

[138]  J. Gaillard,et al.  Lifetime reproductive success and composition of the home range in a large herbivore. , 2007, Ecology.

[139]  R. Pradel,et al.  Population dynamics in a long-lived seabird: I. Impact of breeding activity on survival and breeding probability in unbanded king penguins. , 2007, The Journal of animal ecology.

[140]  Olivier Gimenez,et al.  State-space modelling of data on marked individuals , 2007 .

[141]  O. Ovaskainen,et al.  Age-dependent survival analyzed with Bayesian models of mark-recapture data. , 2007, Ecology.

[142]  J. Rotella,et al.  Evaluation of reproductive costs for Weddell seals in Erebus Bay, Antarctica. , 2007, The Journal of animal ecology.

[143]  D J Spiegelhalter,et al.  Flexible random‐effects models using Bayesian semi‐parametric models: applications to institutional comparisons , 2007, Statistics in medicine.

[144]  H. Weimerskirch,et al.  Environmental variation and experience-related differences in the demography of the long-lived black-browed albatross. , 2007, The Journal of animal ecology.

[145]  Gerard J. van den Berg,et al.  The Unobserved Heterogeneity Distribution in Duration Analysis , 2007 .

[146]  David B Dunson,et al.  Bayesian Semiparametric Dynamic Frailty Models for Multiple Event Time Data , 2006, Biometrics.

[147]  D. Duffie,et al.  Frailty Correlated Default , 2006 .

[148]  G. E. Woolfenden,et al.  Consequences of heterogeneity in survival probability in a population of Florida scrub-jays. , 2006, The Journal of animal ecology.

[149]  S. Verhulst,et al.  Age‐Dependent Traits: A New Statistical Model to Separate Within‐ and Between‐Individual Effects , 2006, The American Naturalist.

[150]  C J Schwarz,et al.  An Extension of the Cormack–Jolly–Seber Model for Continuous Covariates with Application to Microtus pennsylvanicus , 2006, Biometrics.

[151]  C. Guinet,et al.  Age‐specific survival and reproductive performances in fur seals: evidence of senescence and individual quality , 2006 .

[152]  A. N. Arnason,et al.  The estimation of population size, migration rates and survival in a stratified population , 1973, Researches on Population Ecology.

[153]  A. N. Arnason,et al.  Parameter estimates from mark-recapture experiments on two populations subject to migration and death , 1972, Researches on Population Ecology.

[154]  R. Gadagkar Nothing in Biology Makes Sense Except in the Light of Evolution , 2005 .

[155]  Shirley Pledger,et al.  The Performance of Mixture Models in Heterogeneous Closed Population Capture–Recapture , 2005, Biometrics.

[156]  Roger Pradel,et al.  Multievent: An Extension of Multistate Capture–Recapture Models to Uncertain States , 2005, Biometrics.

[157]  Renate Meyer,et al.  Bayesian inference for recurrent events data using time-dependent frailty. , 2005, Statistics in medicine.

[158]  Sujit K. Ghosh,et al.  Bayesian capture-recapture analysis and model selection allowing for heterogeneity and behavioral effects , 2005 .

[159]  H. Weimerskirch,et al.  ENVIRONMENTAL CONDITIONS AND BREEDING EXPERIENCE AFFECT COSTS OF REPRODUCTION IN BLUE PETRELS , 2005 .

[160]  Roger Pradel,et al.  Joint modelling of breeding and survival in the kittiwake using frailty models , 2005 .

[161]  Anatoli I. Yashin,et al.  HIDDEN FRAILTY : MYTHS AND REALITY by , 2005 .

[162]  J. Nichols,et al.  Individual quality, survival variation and patterns of phenotypic selection on body condition and timing of nesting in birds , 2005, Oecologia.

[163]  M. Efford Density estimation in live‐trapping studies , 2004 .

[164]  Emmanuelle Cam,et al.  Dispersal and individual quality in a long lived species , 2004 .

[165]  Roger Pradel,et al.  Influence of food availability on demography and local population dynamics in a long-lived seabird , 2004, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[166]  Modelling the effects of environmental and individual variability when measuring the costs of first reproduction , 2004 .

[167]  W. Link Individual heterogeneity and identifiability in capture-recapture models , 2004 .

[168]  A. Roulin,et al.  Female colour polymorphism covaries with reproductive strategies in the tawny owl Strix aluco , 2003 .

[169]  W. Link Nonidentifiability of Population Size from Capture‐Recapture Data with Heterogeneous Detection Probabilities , 2003, Biometrics.

[170]  J. Norris,et al.  Capture-Recapture Models with Heterogeneity : I . Cormack-Jolly-Seber Model , 2003 .

[171]  E. Bignal,et al.  Age‐specific reproductive performance in red‐billed choughs Pyrrhocorax pyrrhocorax: patterns and processes in a natural population , 2003 .

[172]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[173]  D. Peart,et al.  Dealing with death data: individual hazards, mortality and bias , 2003 .

[174]  J. Hines,et al.  Long‐term fitness consequences of early conditions in the kittiwake , 2003 .

[175]  James E. Hines,et al.  ADJUSTING MULTISTATE CAPTURE–RECAPTURE MODELS FOR MISCLASSIFICATION BIAS: MANATEE BREEDING PROPORTIONS , 2003 .

[176]  Bruce E. Lyon,et al.  Individual variation in prey selection by sea otters: patterns, causes and implications , 2003 .

[177]  Martyn Plummer,et al.  JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling , 2003 .

[178]  Andreas Wienke,et al.  Frailty Models , 2003 .

[179]  B. Kendall,et al.  Variation among Individuals and Reduced Demographic Stochasticity , 2002, Conservation biology : the journal of the Society for Conservation Biology.

[180]  James E. Hines,et al.  Influence of behavioural tactics on recruitment and reproductive trajectory in the kittiwake , 2002 .

[181]  Carl J. Schwarz,et al.  Modelling heterogeneity of survival in band-recovery data using mixtures , 2002 .

[182]  J. Nichols Discussion comments on: 'Occam's shadow: Levels of analysis in evolutionary ecology-- where to next?' by Cooch, Cam and Link , 2002 .

[183]  K. Erikstad,et al.  Costs of reproduction in common eiders ( Somateria mollissima ): An assessment of relationships between reproductive effort and future survival and reproduction based on observational and experimental studies , 2002 .

[184]  J. D. Lebreton,et al.  Multistate recapture models: Modelling incomplete individual histories , 2002 .

[185]  K. Pollock The use of auxiliary variables in capture-recapture modelling: An overview , 2002 .

[186]  William A. Link,et al.  Occam's shadow: Levels of analysis in evolutionary ecology--where to next? , 2002 .

[187]  W. Link,et al.  Individual Covariation in Life‐History Traits: Seeing the Trees Despite the Forest , 2002, The American Naturalist.

[188]  Carl J. Schwarz,et al.  The Jolly-seber model: More than just abundance , 2001 .

[189]  S. Leal Genetics and Analysis of Quantitative Traits , 2001 .

[190]  E. Cam,et al.  Stratification based on reproductive state reveals contrasting patterns of age‐related variation in demographic parameters in the kittiwake , 2000 .

[191]  S. Pledger Unified Maximum Likelihood Estimates for Closed Capture–Recapture Models Using Mixtures , 2000, Biometrics.

[192]  E. Cam,et al.  Apparent inferiority of first‐time breeders in the kittiwake: the role of heterogeneity among age classes , 2000 .

[193]  Marco Festa-Bianchet,et al.  AGE‐SPECIFIC SURVIVAL IN FIVE POPULATIONS OF UNGULATES: EVIDENCE OF SENESCENCE , 1999 .

[194]  Carl E. Rasmussen,et al.  The Infinite Gaussian Mixture Model , 1999, NIPS.

[195]  Gary C. White,et al.  EFFECTS OF INDIVIDUAL HETEROGENEITY IN ESTIMATING THE PERSISTENCE OF SMALL POPULATIONS , 1999 .

[196]  A. Agresti,et al.  The Use of Mixed Logit Models to Reflect Heterogeneity in Capture‐Recapture Studies , 1999, Biometrics.

[197]  K. Burnham,et al.  Program MARK: survival estimation from populations of marked animals , 1999 .

[198]  James E. Hines,et al.  Are adult nonbreeders prudent parents? The kittiwake model , 1998 .

[199]  J. Gaillard,et al.  Mass‐ and Density‐Dependent Reproductive Success and Reproductive Costs in a Capital Breeder , 1998, The American Naturalist.

[200]  J. Norris,et al.  NONPARAMETRIC MLE UNDER TWO CLOSED CAPTURE-RECAPTURE MODELS WITH HETEROGENEITY , 1996 .

[201]  A. Houston,et al.  State-dependent life histories , 1996, Nature.

[202]  F. Maytag Evolution , 1996, Arch. Mus. Informatics.

[203]  W. Koenig,et al.  Patterns and consequences of egg destruction among joint-nesting acorn woodpeckers , 1995, Animal Behaviour.

[204]  James D. Nichols,et al.  The use of multi-state capture-recapture models to address questions in evolutionary ecology , 1995 .

[205]  P. Hougaard,et al.  Frailty models for survival data , 1995, Lifetime data analysis.

[206]  Jeffrey M. Wooldridge,et al.  The Initial Conditions Problem in Dynamic, Nonlinear Panel Data Models with Unobserved Heterogeneity , 2002 .

[207]  Kenneth H. Pollock,et al.  Estimating breeding proportions and testing hypotheses about costs of reproduction with capture-recapture data , 1994 .

[208]  E. Balaban,et al.  The Differences between the Sexes , 1994 .

[209]  Kenneth P. Burnham,et al.  MODELING HETEROGENEITY IN SURVIVAL RATES OF BANDED WATERFOWL , 1993 .

[210]  Carl J. Schwarz,et al.  Estimating migration rates using tag-recovery data , 1993 .

[211]  David R. Anderson,et al.  Heterogeneous survival rates of mallards (Anas platyrhynchos) , 1992 .

[212]  J. Nichols,et al.  Statistical inference for capture-recapture experiments , 1992 .

[213]  Kenneth H. Pollock,et al.  Estimating Transition Probabilities for Stage‐Based Population Projection Matrices Using Capture‐Recapture Data , 1992 .

[214]  David R. Anderson,et al.  Modeling Survival and Testing Biological Hypotheses Using Marked Animals: A Unified Approach with Case Studies , 1992 .

[215]  D. Roff The evolution of life histories : theory and analysis , 1992 .

[216]  P. Hougaard Modelling heterogeneity in survival data , 1991, Journal of Applied Probability.

[217]  V. Kannisto Frailty and survival. , 1991, Genus.

[218]  James D. Nichols,et al.  ESTIMATES OF MOVEMENT AND SITE FIDELITY USING MARK-RESIGHT DATA OF WINTERING CANADA GEESE' , 1991 .

[219]  Ian Newton,et al.  Lifetime Reproduction in Birds , 1990 .

[220]  K. Yasukawa Reproductive Success, T.H. Clutton-Brock (Ed.). The University of Chicago Press, Chicago (1988), ix , 1989 .

[221]  A. Chao Estimating the population size for capture-recapture data with unequal catchability. , 1987, Biometrics.

[222]  J. Sauer,et al.  Uinta Ground Squirrel Demography: Is Body Mass a Better Categorical Variable Than Age? , 1987 .

[223]  K G Manton,et al.  Alternative models for the heterogeneity of mortality risks among the aged. , 1986, Journal of the American Statistical Association.

[224]  A. J. Noordwijk,et al.  Acquisition and Allocation of Resources: Their Influence on Variation in Life History Tactics , 1986, The American Naturalist.

[225]  J. E. Cohen An uncertainty principle in demography and the unisex issue. , 1986, The American statistician.

[226]  J. D. Nichols,et al.  The role of heterogeneity in animal population dynamics , 1986 .

[227]  Gary Chamberlain,et al.  Longitudinal Analysis of Labor Market Data: Heterogeneity, omitted variable bias, and duration dependence , 1985 .

[228]  A. Yashin,et al.  Heterogeneity's ruses: some surprising effects of selection on population dynamics. , 1985, The American statistician.

[229]  D. Reznick Costs of reproduction: an evaluation of the empirical evidence , 1985 .

[230]  Philip Hougaard,et al.  Life table methods for heterogeneous populations: Distributions describing the heterogeneity , 1984 .

[231]  Gerald H. Kramer,et al.  The Ecological Fallacy Revisited: Aggregate- versus Individual-level Findings on Economics and Elections, and Sociotropic Voting , 1983, American Political Science Review.

[232]  P. Allison Discrete-Time Methods for the Analysis of Event Histories , 1982 .

[233]  Kenneth H. Pollock,et al.  Capture-Recapture Models Allowing for Age-Dependent Survival and Capture Rates , 1981 .

[234]  J. Heckman,et al.  Does Unemployment Cause Future Unemployment? Definitions, Questions and Answers from a Continuous Time Model of Heterogeneity and State Dependence. , 1980 .

[235]  Kenneth H. Pollock Capture-recapture models: A review of current methods, assumptions and experimental design , 1980 .

[236]  K. Burnham,et al.  Robust Estimation of Population Size When Capture Probabilities Vary Among Animals , 1979 .

[237]  Douglas H. Johnson Estimating Nest Success: The Mayfield Method and an Alternative , 1979 .

[238]  Byron J. T. Morgan,et al.  Modelling Heron Survival Using Weather Data , 1979 .

[239]  N. Keyfitz,et al.  Mortality in a heterogeneous population , 1979 .

[240]  David R. Anderson,et al.  Statistical inference from capture data on closed animal populations , 1980 .

[241]  Adam Iomnicki,et al.  INDIVIDUAL DIFFERENCES BETWEEN ANIMALS AND THE NATURAL REGULATION OF THEIR NUMBERS , 1978 .

[242]  James J. Heckman,et al.  A Beta-logistic Model for the Analysis of Sequential Labor Force Participation by Married Women , 1975, Journal of Political Economy.

[243]  S. Stearns Life-History Tactics: A Review of the Ideas , 1976, The Quarterly Review of Biology.

[244]  A. Carothers,et al.  The Effects of Unequal Catchability on Jolly-Seber Estimates , 1973 .

[245]  J. Emlen,et al.  Age Specificity and Ecological Theory , 1970 .

[246]  L. L. Eberhardt,et al.  Population Estimates from Recapture Frequencies , 1969 .

[247]  D. Falconer The inheritance of liability to diseases with variable age of onset, with particular reference to diabetes mellitus , 1967, Annals of human genetics.

[248]  G. Caughley Mortality Patterns in Mammals , 1966 .

[249]  M. Cody,et al.  A GENERAL THEORY OF CLUTCH SIZE , 1966, Evolution; international journal of organic evolution.

[250]  G. Seber A NOTE ON THE MULTIPLE-RECAPTURE CENSUS. , 1965, Biometrika.

[251]  G. Jolly EXPLICIT ESTIMATES FROM CAPTURE-RECAPTURE DATA WITH BOTH DEATH AND IMMIGRATION-STOCHASTIC MODEL. , 1965, Biometrika.

[252]  R. Cormack Estimates of survival from the sighting of marked animals , 1964 .