Abstract
Hidden Markov models (HMMs) are being widely used in the field of ecological modeling, however determining the number of underlying states in an HMM remains a challenge. Here we examine a special case of capture-recapture models for open populations, where some animals are observed but it is not possible to ascertain their state (partial observations), whilst the other animals' states are assigned without error (complete observations). We propose a mixture test of the underlying state structure generating the partial observations, which assesses whether they are compatible with the set of states observed in the complete observations. We demonstrate the good performance of the test using simulation and through application to a data set of Canada Geese.
Highlights
Besides its known use for the estimation of the size of a closed population (Pledger, 2000; Yang and Chao, 2005; Bartolucci and Pennoni, 2007) originating in the work of Otis et al (1978), capturerecapture is a widely used technique to follow the dynamics of open animal populations (Cormack, 1964; Williams et al, 2002)
In this paper we focus on a special case of multievent models, where, at a given occasion, the state cannot be ascertained for a proportion of the observed animals, leading to partial observations, whilst the underlying states are directly observable for the other observed animals
We show that if partial observations are generated only by the directly observable states, the number of animals partially observed at a given occasion i and re-observed later in a known state, follows a conditional multinomial distribution, which is a mixture of the conditional multinomial distributions followed by the number of animals released at occasion i in the observable states
Summary
Reviewed by: Mahendra Mariadassou, Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, France. Specialty section: This article was submitted to Models in Ecology and Evolution, a section of the journal Frontiers in Ecology and Evolution. Hidden Markov models (HMMs) are being widely used in the field of ecological modeling, determining the number of underlying states in an HMM remains a challenge. We examine a special case of capture-recapture models for open populations, where some animals are observed but it is not possible to ascertain their state (partial observations), whilst the other animals’ states are assigned without error (complete observations). We propose a mixture test of the underlying state structure generating the partial observations, which assesses whether they are compatible with the set of states observed in the complete observations.
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