Estimation of population size when capture probability depends on individual states

TL;DR

This paper introduces a multi-state capture-recapture model that accounts for individual state changes and heterogeneity in capture probabilities to improve population size estimation in ecological studies.

Contribution

It generalizes existing closed population models to include multiple states and movement, providing a new likelihood expression and addressing bias issues.

Findings

The model accurately estimates population size with state-dependent movement.

Ignoring state changes leads to biased estimates.

Simulation shows the importance of accounting for heterogeneity and movement.

Abstract

We develop a multi-state model to estimate the size of a closed population from ecological capture-recapture studies. We consider the case where capture-recapture data are not of a simple binary form, but where the state of an individual is also recorded upon every capture as a discrete variable. The proposed multi-state model can be regarded as a generalisation of the commonly applied set of closed population models to a multi-state form. The model permits individuals to move between the different discrete states, whilst allowing heterogeneity within the capture probabilities. A closed-form expression for the likelihood is presented in terms of a set of sufficient statistics. The link between existing models for capture heterogeneity are established, and simulation is used to show that the estimate of population size can be biased when movement between states is not accounted for. The proposed unconditional approach is also compared to a conditional approach to assess estimation bias. The model derived in this paper is motivated by a real ecological data set on great crested newts, Triturus cristatus.