No abstract

Statistical inference for capture–recapture studies of open animal populations typically relies on the assumption that all emigration from the studied population is permanent. However, there are many instances in which this assumption is unlikely to be met. We define two general models for the process of temporary emigration: completely random and Markovian. We then consider effects of these two types of temporary emigration on Jolly–Seber estimators and on estimators arising from the full‐likelihood approach to robust design data. Capture–recapture data arising from Pollock’s robust design provide the basis for obtaining unbiased estimates of demographic parameters in the presence of temporary emigration, and for estimating the probability of temporary emigration. We present a likelihood‐based approach to dealing with temporary emigration that permits estimation under different models of temporary emigration and yields tests for completely random and Markovian emigration. In addition, we use the relationship between capture probability estimates based on closed and open models under completely random temporary emigration to derive three ad hoc estimators for the probability of temporary emigration. Two of these should be especially useful in situations where capture probabilities are heterogeneous among individual animals. Ad hoc and full‐likelihood estimators are illustrated for small‐mammal capture–recapture data sets. We believe that these models and estimators will be useful for testing hypotheses about the process of temporary emigration, for estimating demographic parameters in the presence of temporary emigration, and for estimating probabilities of temporary emigration. These latter estimates are frequently of ecological interest as indicators of animal movement and, in some sampling situations, as direct estimates of breeding probabilities and proportions.

The Jolly-Seber method has been the traditional approach to the estimation of demographic parameters in long-term capture-recapture studies of wildlife and fish species. This method involves restrictive assumptions about capture probabilities that can lead to biased estimates, especially of population size and recruitment. Pollock (1982, Journal of Wildlife Management 46, 752-757) proposed a sampling scheme in which a series of closely spaced samples were separated by longer intervals such as a year. For this "robust design," Pollock suggested a flexible ad hoc approach that combines the Jolly-Seber estimators with closed population estimators, to reduce bias caused by unequal catchability, and to provide estimates for parameters that are unidentifiable by the Jolly-Seber method alone. In this paper we provide a formal modelling framework for analysis of data obtained using the robust design. We develop likelihood functions for the complete data structure under a variety of models and examine the relationship among the models. We compute maximum likelihood estimates for the parameters by applying a conditional argument, and compare their performance against those of ad hoc and Jolly-Seber approaches using simulation.

Closed‐population capture–recapture methods have been used extensively in animal ecology, both by themselves and within the context of Pollock’s robust design and multistate models, to estimate various parameters of population and community dynamics. The defining assumption of geographic and demographic closure (i.e., no births, deaths, immigration, or emigration) for the duration of sampling is restrictive and is likely to be violated in many field situations. I evaluated several types of violations of the closure assumption and found that completely random movement in and out of a study area does not introduce bias to estimators from closed‐population methods, although it decreases precision. In addition, if capture probabilities vary only with time, the closed‐population Lincoln‐Petersen estimator is unbiased for the size of the superpopulation when there are only births/immigration or only deaths/emigration. However, for other cases of nonrandom movement, closed‐population estimators were biased when movement was Markovian (dependent on the presence/absence of the animal in the previous time period), when an animal was allowed one entry to and one exit from the study area, or when there was trap response or heterogeneity among animals in capture probability. In addition, the probability that an animal is present and available for capture (e.g., breeding propensity) can be estimated using Pollock’s robust design only when movement occurs at a broader temporal scale than that of sampling.

Analytical methods accounting for imperfect detection are often used to facilitate reliable inference in population and community ecology. We contend that similar approaches are needed in disease ecology because these complicated systems are inherently difficult to observe without error. For example, wildlife disease studies often designate individuals, populations, or spatial units to states (e.g., susceptible, infected, post-infected), but the uncertainty associated with these state assignments remains largely ignored or unaccounted for. We demonstrate how recent developments incorporating observation error through repeated sampling extend quite naturally to hierarchical spatial models of disease effects, prevalence, and dynamics in natural systems. A highly pathogenic strain of avian influenza virus in migratory waterfowl and a pathogenic fungus recently implicated in the global loss of amphibian biodiversity are used as motivating examples. Both show that relatively simple modifications to study designs can greatly improve our understanding of complex spatio-temporal disease dynamics by rigorously accounting for uncertainty at each level of the hierarchy.