Applications and extensions of Chao's moment estimator for the size of a closed population.

This article revisits Chao's (1989, Biometrics45, 427-438) lower bound estimator for the size of a closed population in a mark-recapture experiment where the capture probabilities vary between animals (model M(h)). First, an extension of the lower bound to models featuring a time effect and heterogeneity in capture probabilities (M(th)) is proposed. The biases of these lower bounds are shown to be a function of the heterogeneity parameter for several loglinear models for M(th). Small-sample bias reduction techniques for Chao's lower bound estimator are also derived. The application of the loglinear model underlying Chao's estimator when heterogeneity has been detected in the primary periods of a robust design is then investigated. A test for the null hypothesis that Chao's loglinear model provides unbiased abundance estimators is provided. The strategy of systematically using Chao's loglinear model in the primary periods of a robust design where heterogeneity has been detected is investigated in a Monte Carlo experiment. Its impact on the estimation of the population sizes and of the survival rates is evaluated in a Monte Carlo experiment.