Generalized Behavioral Response Models For Capture-Recapture Experiments And Model Selection

The primary purpose of capture-recapture studies is to estimate the population size of wild lives. In the present paper, we propose four new behavioral response models for capture-recapture experiments in discrete time and closed populations. In this framework, a conditional-likelihood method is used to estimate the population size and the asymptotic normality of the estimators is proved.The four models are: Generalized Behavioral Response Models ( GM b), which is a generalization of the three existing models, i.e. , M b Model and two Markov Chain Models, can deal with the situations when the pattern of animals'memory for trap is unknown. The sub-models of GM b, Long Term Model M b( LTM b) and Short Term Model M b( STM b), are more effective when animals'memory for trap lasts for a long or short time. Model selection to get the best model can be easily done by changing the special parameters in these two models. The fourth is the Exponential Behavioral Response Model ( ExpM b), which is similar with Ebbinghaus'forgetting curve in psychology, behaves well when animals'memory for trap is deteriorating exponentially.At last, six groups of simulation experiments in different cases of animals'memory patterns are represented and the results of all seven models are reported to examine the performance of the proposed models. We discuss thoroughly how to make model selections in different situations by Akaike Information Criterion. The simulation results show that our four models can make better estimates for population size, and can be widely used in various situations.