Robust Design and the Use of Auxiliary Variables in Estimating Population Size for an Open Population

We consider the problem of estimating the population size for an open population where the data are collected over secondary periods within primary periods according to a robust design suggested by Pollock (1982, Journal of Wildlife Management46, 757–760). A conditional likelihood is used to estimate the parameters associated with a generalized linear model in which the capture probability is assumed to have a logistic form depending on individual covariates. A Horvitz -Thompson-type estimator is used to estimate the population size for each primary period and the survival probabilities between primary periods. The asymptotic properties of the proposed estimators are investigated through simulation and are found to perform well. A data set for such a robust design of a small-mammal capture-recapture study conducted at Dummy Bottom within Browns Park National Wildlife Refuge is analyzed.