Full Open Population Capture–Recapture Models With Individual Covariates

Traditional analyses of capture–recapture data are based on likelihood functions that explicitly integrate out all missing data. We use a complete data likelihood (CDL) to show how a wide range of capture–recapture models can be easily fitted using readily available software JAGS/BUGS even when there are individual-specific time-varying covariates. The models we describe extend those that condition on first capture to include abundance parameters, or parameters related to abundance, such as population size, birth rates or lifetime. The use of a CDL means that any missing data, including uncertain individual covariates, can be included in models without the need for customized likelihood functions. This approach also facilitates modeling processes of demographic interest rather than the complexities caused by non-ignorable missing data. We illustrate using two examples, (i) open population modeling in the presence of a censored time-varying individual covariate in a full robust design, and (ii) full open population multi-state modeling in the presence of a partially observed categorical variable. Supplemental materials for this article are available online.

[1]  '. R.Pradel.  Utilization of Capture-Mark-Recapture for the Study of Recruitment and Population Growth Rate , 2001 .

[2]  Joseph Hilbe,et al.  Bayesian Analysis for Population Ecology , 2009 .

[3]  A. Brix.  Bayesian Data Analysis, 2nd edn , 2005 .

[4]  D. Rubin.  INFERENCE AND MISSING DATA , 1975 .

[5]  William A. Link,et al.  Posterior model probabilities computed from model-specific Gibbs output , 2010, 1012.0073.

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

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

[8]  William A. Link,et al.  Bayesian Inference: With Ecological Applications , 2009 .

[9]  Darryl I. MacKenzie,et al.  Flexible hierarchical mark-recapture modeling for open populations using WinBUGS , 2009, Environmental and Ecological Statistics.

[10]  Søren Feodor Nielsen,et al.  Inference and Missing Data: Asymptotic Results , 1997 .

[11]  D. Pe,et al.  HETEROGENEITY AND MODEL UNCERTAINTY IN BAYESIANREGRESSION , 1999 .

[12]  Roger Pradel,et al.  A Proposal for a Goodness‐of‐Fit Test to the Arnason‐Schwarz Multisite Capture‐Recapture Model , 2003, Biometrics.

[13]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[14]  Richard J. Barker,et al.  Joint analysis of mark—recapture, resighting and ring-recovery data with age-dependence and marking-effect , 1999 .

[15]  J Andrew Royle,et al.  Analysis of Capture–Recapture Models with Individual Covariates Using Data Augmentation , 2008, Biometrics.

[16]  Trevor Hastie,et al.  The Elements of Statistical Learning , 2001 .

[17]  Richard J. Barker,et al.  A Further Step Toward the Mother-of-All-Models: Flexibility and Functionality in the Modeling of Capture–Recapture Data , 2009 .

[18]  S. Brooks,et al.  On the Bayesian Estimation of a Closed Population Size in the Presence of Heterogeneity and Model Uncertainty , 2007, Biometrics.

[19]  Kenneth H. Pollock,et al.  Goodness-of-fit tests for open capture―recapture models , 1985 .

[20]  R. Huggins.  On the statistical analysis of capture experiments , 1989 .

[21]  Kenneth H. Pollock,et al.  Design and Analysis Methods for Fish Survival Experiments Based on Release-Recapture. , 1988 .

[22]  Carl J. Schwarz,et al.  A General Methodology for the Analysis of Capture-Recapture Experiments in Open Populations , 1996 .

[23]  James E. Hines,et al.  ESTIMATION OF SEX-SPECIFIC SURVIVAL FROM CAPTURE-RECAPTURE DATA WHEN SEX IS NOT ALWAYS KNOWN , 2004 .

[24]  J. Andrew Royle,et al.  Hierarchical Modeling and Inference in Ecology: The Analysis of Data from Populations, Metapopulations and Communities , 2008 .

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

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

[27]  Evan G. Cooch,et al.  Multistate capture–recapture analysis under imperfect state observation: an application to disease models , 2009 .

[28]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[29]  J. Andrew Royle,et al.  Analysis of Multinomial Models With Unknown Index Using Data Augmentation , 2007, Journal of Computational and Graphical Statistics.

[30]  Jerome A Dupuis,et al.  A Bayesian Approach to the Multistate Jolly–Seber Capture–Recapture Model , 2007, Biometrics.

[31]  William A Link,et al.  Model weights and the foundations of multimodel inference. , 2006, Ecology.

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

[33]  Eric R. Ziegel,et al.  The Elements of Statistical Learning , 2003, Technometrics.

[34]  Byron J. T. Morgan,et al.  Bayesian Animal Survival Estimation , 2000 .

[35]  David A. Elston,et al.  Mark-recapture with occasion and individual effects: Abundance estimation through Bayesian model selection in a fixed dimensional parameter space , 2005 .

[36]  R King,et al.  Analyzing Complex Capture–Recapture Data in the Presence of Individual and Temporal Covariates and Model Uncertainty , 2008, Biometrics.

[37]  Richard A. Parker,et al.  WinBUGS for population ecologists: bayesian modeling using markov chain Monte Carlo methods , 2009 .

[38]  Matthew R. Schofield,et al.  Hierarchical capture-recapture models , 2007 .

[39]  William A Link,et al.  Modeling Association among Demographic Parameters in Analysis of Open Population Capture–Recapture Data , 2005, Biometrics.

[40]  J. Dupuis.  Bayesian estimation of movement and survival probabilities from capture-recapture data , 1995 .

[41]  Andrew Gelman,et al.  General methods for monitoring convergence of iterative simulations , 1998 .

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

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

[44]  M. Conroy,et al.  Analysis and Management of Animal Populations , 2002 .

[45]  W. Wong,et al.  The calculation of posterior distributions by data augmentation , 1987 .

[46]  Ruth King,et al.  Bayesian model discrimination for multiple strata capture‐recapture data , 2002 .

[47]  Matthew R. Schofield,et al.  Incorporating Genotype Uncertainty into Mark–Recapture‐Type Models For Estimating Abundance Using DNA Samples , 2009, Biometrics.

[48]  Richard J. Barker,et al.  A unified capture-recapture framework , 2008 .

[49]  K. Pollock.  A Capture-Recapture Design Robust to Unequal Probability of Capture , 1982 .

[50]  Steven C. Amstrup,et al.  Estimation of population size using open capture-recapture models , 2001 .