Parameterexpanded data augmentation for Bayesian analysis of capture–recapture models
 J. Andrew Royle,
 Robert M. Dorazio
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Data augmentation (DA) is a flexible tool for analyzing closed and open population models of capture–recapture data, especially models which include sources of hetereogeneity among individuals. The essential concept underlying DA, as we use the term, is based on adding “observations” to create a dataset composed of a known number of individuals. This new (augmented) dataset, which includes the unknown number of individuals N in the population, is then analyzed using a new model that includes a reformulation of the parameter N in the conventional model of the observed (unaugmented) data. In the context of capture–recapture models, we add a set of “all zero” encounter histories which are not, in practice, observable. The model of the augmented dataset is a zeroinflated version of either a binomial or a multinomial base model. Thus, our use of DA provides a general approach for analyzing both closed and open population models of all types. In doing so, this approach provides a unified framework for the analysis of a huge range of models that are treated as unrelated “black boxes” and named procedures in the classical literature. As a practical matter, analysis of the augmented dataset by MCMC is greatly simplified compared to other methods that require specialized algorithms. For example, complex capture–recapture models of an augmented dataset can be fitted with popular MCMC software packages (WinBUGS or JAGS) by providing a concise statement of the model’s assumptions that usually involves only a few lines of pseudocode. In this paper, we review the basic technical concepts of data augmentation, and we provide examples of analyses of closedpopulation models (M _{0}, M _{ h }, distance sampling, and spatial capture–recapture models) and openpopulation models (Jolly–Seber) with individual effects.
 Bled F, Royle JA, Cam E (2010) Hierarchical modeling of an invasive spread: case of the Eurasian collareddove Streptopelia decaocto in the USA. Ecol Appl (in press)
 Bonner, S, Schwarz, C (2006) An extension of the Cormack Jolly Seber model for continuous covariates with application to Microtus pennsylvanicus. Biometrics 62: pp. 142149 CrossRef
 Borchers, DL, Efford, MG (2008) Spatially explicit maximum likelihood methods for capture–recapture studies. Biometrics 64: pp. 377385 CrossRef
 Burnham, KP, Overton, WS (1978) Estimation of the size of a closed population when capture probabilities vary among animals. Biometrika 65: pp. 625633 CrossRef
 Converse SJ, Royle JA (2010) Dealing with incomplete and variable detectability in multiyear, multisite monitoring of ecological populations. In: Design and analysis of longterm ecological monitoring studies (in press)
 Cooch, E, White, G (2001) Using MARK: a gentle introduction. Cornell University, Ithaca
 Coull, BA, Agresti, A (1999) The use of mixed logit models to reflect heterogeneity in capture–recapture studies. Biometrics 55: pp. 294301 CrossRef
 Crosbie, SF, Manly, BFJ (1985) Parsimonious modelling of capture–markrecapture studies. Biometrics 41: pp. 385398 CrossRef
 Dorazio, RM, Royle, JA (2003) Mixture models for estimating the size of a closed population when capture rates vary among individuals. Biometrics 59: pp. 350363 CrossRef
 Dorazio, RM, Royle, JA (2005) Estimating size and composition of biological communities by modeling the occurrence of species. J Am Stat Assoc 100: pp. 389398 CrossRef
 Dorazio, RM, Royle, JA, Soderstrom, B, Glimskar, A (2006) Estimating species richness and accumulation by modeling species occurrence and detectability. Ecology 87: pp. 842854 CrossRef
 Dorazio, RM, Kéry, M, Royle, JA, Plattner, M (2010) Models for inference in dynamic metacommunity systems. Ecology 91: pp. 24662475 CrossRef
 Dupuis, JA, Schwarz, CJ (2007) A Bayesian approach to the multistate JollySeber capture–recapture model. Biometrics 63: pp. 10151022 CrossRef
 Durban, JW, Elston, DA (2005) Markrecapture with occasion and individual effects: abundance estimation through Bayesian model selection in a fixed dimensional parameter space. J Agric Biol Environ Stat 10: pp. 291305 CrossRef
 Efford, M (2004) Density estimation in livetrapping studies. Oikos 106: pp. 598610 CrossRef
 Gardner, B, Royle, JA, Wegan, MT, Rainbolt, RE, Curtis, PD (2010) Estimating black bear density using DNA data from hair snares. J Wildl Manag 74: pp. 318325 CrossRef
 Gardner B, Reppucci J, Lucherini M, Royle JA (2010b) Spatiallyexplicit inference for open populations: estimating demographic parameters from cameratrap studies. Ecology 91:3376–3383
 Gimenez, O, Rossi, V, Choquet, R, Dehais, C, Doris, B, Varella, H, Vila, JP, Pradel, R (2007) Statespace modelling of data on marked individuals. Ecol Model 206: pp. 431438 CrossRef
 Gimenez, O, Choquet, R (2010) Individual heterogeneity in studies on marked animals using numerical integration: capture–recapture mixed models. Ecology 91: pp. 148154
 Green, PJ (1995) Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82: pp. 711732 CrossRef
 Johnson, DH (1999) The insignificance of statistical significance testing. J Wildl Manag 63: pp. 763772 CrossRef
 Jolly, G (1965) Explicit estimates from capture–recapture data with both death and immigration—stochastic model. Biometrika 52: pp. 225247
 Karanth, KU (1995) Estimating tiger (Panthera tigris) populations from cameratrap data using capture–recapture models. Biol Conserv 71: pp. 333338 CrossRef
 Karanth, KU, Nichols, JD (1998) Estimation of tiger densities in India using photographic captures and recaptures. Ecology 79: pp. 28522862 CrossRef
 Karanth, K, Nichols, JD, Kumar, N, Hines, JE (2006) Assessing tiger population dynamics using photographic capture–recapture sampling. Ecology 87: pp. 29252937 CrossRef
 Kéry, M, Royle, JA Inference about species richness and community structure using speciesspecific occupancy models in the National Swiss Breeding Bird Survey MHB. In: Thomson, DL, Cooch, EG, Conroy, MJ eds. (2009) Modeling demographic processes in marked populations.. Springer, New York, pp. 639656 CrossRef
 Kéry, M, Royle, JA, Plattner, M, Dorazio, RM (2009) Species richness and occupancy estimation in communities subject to temporary emigration. Ecology 90: pp. 12791290 CrossRef
 King, R, Brooks, SP (2001) On the Bayesian analysis of population size. Biometrika 88: pp. 317336 CrossRef
 King, R, Brooks, SP (2008) On the Bayesian estimation of a closed population size in the presence of heterogeneity and model uncertainty. Biometrics 64: pp. 816824 CrossRef
 King, R, Brooks, SP, Coulson, T (2008) Analysing complex capture–recapture data in the presence of individual and temporal covariates and model uncertainty. Biometrics 64: pp. 11871195 CrossRef
 Langtimm CA, Dorazio RM, Stith BM, Doyle TJ (2010) A new aerial survey design to monitor manatee abundance for Everglades restoration. J Wildl Manag (in press)
 Lebreton, JD, Burnham, K, Clobert, J, Anderson, DR (1992) Modeling survival and testing biological hypotheses using marked animals: a unified approach with case studies. Ecol Monogr 62: pp. 67118 CrossRef
 Link, WA (2003) Nonidentifiability of population size from capture–recapture data with heterogeneous detection probabilities. Biometrics 59: pp. 11231130 CrossRef
 Link, WA, Barker, RJ (2010) Bayesian inference: with ecological applications. Academic, New York
 Liu, JS, Wu, YN (1999) Parameter expansion for data augmentation. J Am Stat Assoc 94: pp. 12641274 CrossRef
 Lunn, D, Spiegelhalter, D, Thomas, A, Best, N (2009) The BUGS project: evolution, critique and future directions (with discussion). Stat Med 28: pp. 30493082 CrossRef
 MacKenzie, DI, Nichols, JD, Lachman, GB, Droege, S, Royle, JA, Langtimm, CA (2002) Estimating site occupancy rates when detection probabilities are less than one. Ecology 83: pp. 22482255 CrossRef
 MacKenzie, DI, Nichols, JD, Hines, JE, Knutson, MG, Franklin, AB (2003) Estimating site occupancy, colonization, and local extinction when a species is detected imperfectly. Ecology 84: pp. 22002207 CrossRef
 Nichols JD, Karanth KU (2002) Statistical concepts: assessing spatial distributions. In: Monitoring tigers and their prey: a manual for researchers, managers, and conservationists in tropical Asia. Centre for Wildlife Studies, pp 29–38
 Patil A, Huard D, Fonnesbeck CJ (2010) PyMC 2.0: Bayesian stochastic modelling in python. J Stat Softw (in press)
 Pledger S (2005) The performance of mixture models in heterogeneous closed population capture–recapture. Biometrics 61:868–873
 Pledger, S, Pollock, KH, Norris, JL (2003) Open capture–recapture models with heterogeneity: I. CormackJollySeber model. Biometrics 59: pp. 786794 CrossRef
 Pollock, K (1982) A capture–recapture design robust to unequal probability of capture. J Wildl Manag 46: pp. 757760 CrossRef
 Royle, JA (2006) Site occupancy models with heterogeneous detection probabilities. Biometrics 62: pp. 97102 CrossRef
 Royle JA (2008) Modeling individual effects in the CormackJollySeber model: a statespace formulation. Biometrics 64:364–370
 Royle, JA (2009) Analysis of capture—recapture models with individual covariates using data augmentation. Biometrics 65: pp. 267274 CrossRef
 Royle JA, Kéry M (2007) A Bayesian statespace formulation of dynamic occupancy models. Ecology 88:1813–1823
 Royle, JA, Dorazio, RM, Link, WA (2007) Analysis of multinomial models with unknown index using data augmentation. J Comput Graph Stat 16: pp. 6785 CrossRef
 Royle, JA, Dorazio, RM (2008) Hierarchical modeling and inference in ecology: the analysis of data from populations, metapopulations and communities. Academic, San Diego
 Royle JA, Gardner B (2010) Hierarchical spatial capture–recapture models for estimating density from trapping arrays. In: O'Connell AF, Nichols JD, Karanth KU (eds) Camera traps in animal ecology: methods and analyses. Springer, Berlin
 Royle, JA, Young, KV (2008) A hierarchical model for spatial capture–recapture data. Ecology 89: pp. 22812289 CrossRef
 Royle, JA, Karanth, KU, Gopalaswamy, AM, Kumar, NS (2009) Bayesian inference in camera trap studies using a class of spatial capture–recapture models. Ecology 90: pp. 32333244 CrossRef
 Schwarz, C, Arnason, A (1996) A general methodology for the analysis of capture–recapture experiments in open populations. Biometrics 52: pp. 860873 CrossRef
 Schofield, MR, Barker, RJ (2008) A unified capture–recapture framework. J Agric Biol Environ Stat 13: pp. 458477 CrossRef
 Seber, G (1965) A note on the multiplerecapture census. Biometrika 52: pp. 24959
 Tanner, MA (1996) Tools for statistical inference: methods for the exploration of posterior distributions and likelihood functions, 3rd edn. Springer, New York
 Tanner, MA, Wong, WH (1987) The calculation of posterior distributions by data augmentation. J Am Stat Assoc 82: pp. 528540 CrossRef
 Williams, BK, Nichols, JD, Conroy, MJ (2002) Analysis and management of animal populations. Academic, San Diego
 Wright, JA, Barker, RJ, Schofield, MR, Frantz, AC, Byrom, AE, Gleeson, DM (2009) Incorporating genotype uncertainty into markrecapture–type models for estimating abundance using DNA samples. Biometrics 65: pp. 833840 CrossRef
 Title
 Parameterexpanded data augmentation for Bayesian analysis of capture–recapture models
 Journal

Journal of Ornithology
Volume 152, Issue 2 Supplement, pp 521537
 Cover Date
 20120201
 DOI
 10.1007/s1033601006194
 Print ISSN
 21937192
 Online ISSN
 14390361
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Hierarchical models
 Individual covariates
 Individual heterogeneity
 Markov chain Monte Carlo
 Occupancy models
 Authors

 J. Andrew Royle ^{(1)}
 Robert M. Dorazio ^{(2)} ^{(3)}
 Author Affiliations

 1. USGS Patuxent Wildlife Research Center, Laurel, MD, 20708, USA
 2. USGS Southeast Ecological Science Center, Gainesville, FL, 32653, USA
 3. Department of Statistics, University of Florida, Gainesville, FL, 32611, USA