Low-risk population size estimates in the presence of capture heterogeneity

Abstract

Population estimation methods are used for estimating the size of a population from samples of individuals. In many applications, the probability of being observed in the sample varies across individuals, resulting in sampling bias. We show that in this setting, estimators of the population size have high and sometimes infinite risk, leading to large uncertainty in the population size. As an alternative, we propose estimating the population of individuals with observation probability exceeding a small threshold. We show that estimators of this quantity have lower risk than estimators of the total population size. The proposed approach is shown empirically to result in large reductions in mean squared error in a common model for capture-recapture population estimation with heterogeneous capture probabilities.