Model selection and model robustness for population size estimation in 2-sample capture-recapture studies

Two-sample capture-recapture studies are commonly used in the epidemiologic and ecological literature. Most of these studies have been limited to analysis using the Lincoln-Petersen estimator, especially in epidemiologic studies. We examine the use of the Lincoln-Petersen estimator and 2 alternative closed-population methods: Huggins' conditional likelihood method and Pledger's likelihood method with mixtures. We assessed the ability of Akaike information criterion (AIC) to perform model selection when time, behavioral effects, or heterogeneity are present in capture probabilities. In addition, we examined the effects of model misspecification on estimates of population size. An extensive simulation study found that these models are not robust to misspecification and that AIC was not capable of selecting the correct model with 2 capture occasions.