The Analysis of Continuous Mark-Recapture Data

Abstract

The purpose of this thesis is to develop a general methodology for the analysis of continuously sampled data from open populations. The thesis consists of four parts and one appendix. The four parts may be read independently of each other. The appendix consists of a submitted article based on the developments in Part III.

The aim of Part I is to present the major contributions to the mark-recapture methodology over the last century. It is not a complete reference to the subject, but gives the reader an introduction to mark-recapture models. In addition to the classic models, some recent development of interest is included. The introduction of Bayesian statistics to mark-recapture models is covered, in addition to the analysis of continuously sampled data from closed populations. With the ever increasing amount of models available, the need for model selection tools is grave. We look at some of the most used methods such as the Likelihood Ratio Test (LRT) and the Akaike Information Criterion in connection with mark-recapture models. For the Bayesian models, we review some of the latest developments in model selection such as the Deviance Information Criterion.

Part II addresses the challenge of analysing a set of continuously sampled markrecapture data from a Norwegian coastal cod population (the Risør data set). These data are already analysed with discrete models by Julliard et al. (2001), but it is suggested that this approach may lead to biased estimates of the survival. The approach taken in Part II is to renounce the discrete models for mark-recapture data, and to develop an new, continuous model. The analysis of this model is preformed by a Monte Carlo EM algorithm. The survival and capture estimates are presented and compared with the estimates of Julliard et al. (2001). The Risør data set contains much auxilliary information such as size at release and capture, release location and capture gear. A semi-parametric multiplicative hazard model is implemented to include some of this information.

The EM algorithm from Part II is developed further in Part III. Instead of a Monte Carlo simulation in the E step of the algorithm, an analytic solution is presented. The algorithm is developed for the discrete Cormack-Jolly-Seber(CJS) model, and shows nice convergence and stability properties for this model. An argument is then given for applying the CJS model directly to continuous data. The stability of the EM algorithm makes it suitable for such analysis. When covariate information is to be included into the analysis of continuous data, the CJS model is no longer appropriate. A semi-parametric multiplicative model for the survial and capture processes is presented as an answer to this challenge. The EM algorithm is still used for analysis. The methodology is applied to a set of continuously sampled data on the Eurpean Dipper, gathered by G. Marzolin (Marzolin (2002)). These data have been analysed discretely by Lebreton et al. (1992) (frequentistic) and by Brooks et al. (2000) (Bayesian).

One of the assumptions of the CJS model is that the sampling is done instantaneously. The aim of Part IV is to assess the consequences of violating this assumption. A simulation analysis showes that there is potential for substantial bias of the survival estimates when the sampling periods are long.