Abstract
We develop a multi-state model to estimate the size of a closed population from 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 allows for heterogeneity within the capture probabilities associated with each state while also permitting individuals to move between the different discrete states. 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 is 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. Supplementary materials accompanying this paper appear online.
Highlights
The models presented within this paper focus on the estimation of the size of a closed population along with capture and transition probabilities between discrete states using real ecological capture–recapture data on a population of great crested newts Triturus cristatus
We extend the previous models for closed capture–recapture data to account for individual heterogeneity where the “state” of an individual is recorded as a discrete variable
We present the likelihood in terms of a set of minimal sufficient statistics which permits the fit of the model to be assessed using a Pearson chi-squared test
Summary
The models presented within this paper focus on the estimation of the size of a closed population along with capture and transition probabilities between discrete states using real ecological capture–recapture data on a population of great crested newts Triturus cristatus. The model we present can be considered a generalisation of the time-dependent multistate closed population model of Schwarz and Ganter (1995) to a form that includes trap dependence and heterogeneity in the capture probabilities. The CJS and AS models allow for a time dependence in the capture probabilities, with the AS model able to allow capture probabilities to be state dependent These models condition on the first capture of an individual and so are unable to estimate the total population size directly. 2, we review the construction of existing single-state closed population models in terms of sets of sufficient statistics, before introducing the likelihood function for the multistate model and considering the time-varying population size for each state in Sect.
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