Hierarchial mark–recapture models: a framework for inference about demographic processes

The development of sophisticated mark–recapture models over the last four decades has provided fundamental tools for the study of wildlife populations, allowing reliable inference about population sizes and demographic rates based on clearly formulated models for the sampling processes. Mark–recapture models are now routinely described by large numbers of parameters. These large models provide the next challenge to wildlife modelers: the extraction of signal from noise in large collections of parameters. Pattern among parameters can be described by strong, deterministic relations (as in ultrastructural models) but is more flexibly and credibly modeled using weaker, stochastic relations. Trend in survival rates is not likely to be manifest by a sequence of values falling precisely on a given parametric curve; rather, if we could somehow know the true values, we might anticipate a regression relation between parameters and explanatory variables, in which true value equals signal plus noise. Hierarchical models provide a useful framework for inference about collections of related parameters. Instead of regarding parameters as fixed but unknown quantities, we regard them as realizations of stochastic processes governed by hyperparameters. Inference about demographic processes is based on investigation of these hyperparameters. We advocate the Bayesian paradigm as a natural, mathematically and scientifically sound basis for inference about hierarchical models. We describe analysis of capture–recapture data from an open population based on hierarchical extensions of the Cormack–Jolly–Seber model. In addition to recaptures of marked animals, we model first captures of animals and losses on capture, and are thus able to estimate survival probabilities ???? (i.e., the complement of death or permanent emigration) and per capita growth rates f (i.e., the sum of recruitment and immigration rates). Covariation in these rates, a feature of demographic interest, is explicitly described in the model.