New capture-recapture models of behavioral response for estimating the size of a closed animal population.

Capture-recapture (CRC) experiments conducted over discrete time points motivate the development of models characterizing animal behavioral responses to facilitate estimating sizes of closed animal populations. We propose a multinomial distribution-based CRC modeling framework allowing for flexibly incorporating behavioral response patterns. In the proposed modeling framework, behavioral patterns of animals are reflected by specifying desirable constraints among conditional probabilities used to parameterize overall probabilities of different capture histories. We explicitly introduce various sets of crucial constraints which encode interpretable assumptions of behavioral patterns and lead to a unique estimate of the animal population size. Bias corrections and Bayesian credible intervals previously designed for disease surveillance are adapted to accommodate sparse CRC data which are commonly encountered in ecological studies. The proposed method incorporating minimal constraints is demonstrated to provide comparatively robust estimates in real data applications and simulation studies. To improve estimation when data are sparse, we also illustrate the use of Akaike's information criterion (AIC) to potentially justify additional noncrucial modeling constraints.