Abstract
Batch marking provides an important and efficient way to estimate the survival probabilities and population sizes of wild animals. It is particularly useful when dealing with animals that are difficult to mark individually. For the first time, we provide the likelihood for extended batch-marking experiments. It is often the case that samples contain individuals that remain unmarked, due to time and other constraints, and this information has not previously been analyzed. We provide ways of modeling such information, including an open N-mixture approach. We demonstrate that models for both marked and unmarked individuals are hidden Markov models; this provides a unified approach, and is the key to developing methods for fast likelihood computation and maximization. Likelihoods for marked and unmarked individuals can easily be combined using integrated population modeling. This allows the simultaneous estimation of population size and immigration, in addition to survival, as well as efficient estimation of standard errors and methods of model selection and evaluation, using standard likelihood techniques. Alternative methods for estimating population size are presented and compared. An illustration is provided by a weather-loach data set, previously analyzed by means of a complex procedure of constructing a pseudo likelihood, the formation of estimating equations, the use of sandwich estimates of variance, and piecemeal estimation of population size. Simulation provides general validation of the hidden Markov model methods developed and demonstrates their excellent performance and efficiency. This is especially notable due to the large numbers of hidden states that may be typically required.
Highlights
The standard protocol for capture–recapture studies of animals is to use individually numbered tags so that the capture history can be constructed, determining whether an individual was captured at each sampling occasion
We present hidden Markov models (HMMs) for the extended batch-mark survey incorporating both marked and unmarked individuals captured and released at each sampling occasion
Integrated modeling is employed: an open N-mixture model is used to model the information on unmarked individuals, and that likelihood component is formed using a HMM
Summary
The standard protocol for capture–recapture studies of animals is to use individually numbered tags so that the capture history can be constructed, determining whether an individual was captured at each sampling occasion. Conditional on the number of individuals released at each sample time, they developed a pseudo likelihood for the recaptured individuals They derived estimating equations to estimate survival and capture probabilities, with error estimation obtained from a sandwich estimator. The article is structured as follows: the data motivating the work are described and presented in Section 2; Section 3 lists the notation used, including model specification, and explains the relevance of HMMs; Section 4 presents the two likelihood components, corresponding to marked and unmarked individuals
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