The use of auxiliary variables in capture-recapture modelling: an overview

I review the use of auxiliary variables in capturerecapture models for estimation of demographic parameters (e.g. capture probability, population size, survival probability, and recruitment, emig ration and immigration numbers). I focus on what has been done in current research and what still needs to be done. Typically in the literature, covariate modelling has made capture and survival probabilities functions of covariates, but there are good reasons also to make other parameters functions of covariates as well. The types of covariates considered include environmental covariates that may vary by occasion but are constant over animals, and individual animal covariates that are usually assumed constant over time. I also discuss the diý culties of using time-dependent individual animal covariates and some possible solutions. Covariates are usually assumed to be measured without er ror, and that may not be realistic. For closed populations, one approach to modelling heterogeneity in capture probabilities uses observable individual covariates and is thus related to the primary purpose of this paper. The now standard HugginsAlho approach conditions on the captured animals and then uses a generalized HorvitzThompson estimator to estimate population size. This approach has the advantage of simplicity in that one does not have to specify a distribution for the covariates, and the disadvantage is that it does not use the full likelihood to estimate population size. Alternately one could specify a distribution for the covariates and implement a full likelihood approach to inference to estimate the capture function, the covariate probability distribution, and the population size. The general JollySeber open model enables one to estimate capture probability, population sizes, survival rates, and birth numbers. Much of the focus on modelling covariates in program MARK has been for survival and capture probability in the CormackJollySeber model and its generalizations (including tag-return models). These models condition on the number of animals marked and released. A related, but distinct, Correspondence: Kenneth H. Pollock, Department of Statistics, North Carolina State University, Raleigh NC 27695 8203 , USA. E-mail: [email protected] ISSN 0266-476 3 print; 1360-053 2 online/02/010085-18 © 2002 Taylor & Francis Ltd DOI: 10.1080 /0266476