On the estimation of population sizes in capture–recapture experiments

This work considers a nested mark–recapture experiment with two levels of sampling: within each primary sampling period of an open population model, there are secondary capture occasions to estimate the size of the population at that primary period. This scheme is known as Pollock’s robust design. Two sources of information are then available to estimate the population size for a primary period: the within and the between primary period data. This work proves that the population size estimators derived from these two sources are asymptotically independent for a large class of closed population models. In this context, the robust design maximum likelihood estimator of population size is shown to be asymptotically equivalent to a weighted sum of the estimators for the open population Jolly–Seber model (Jolly, 1965; Seber, 1965) and for the closed population model. This article shows that the weighted estimator is more efficient than the moment estimator of Kendall et al. (1995). A closed form expression for the efficiency associated with this estimator is given and evaluated in a Monte Carlo study and in a numerical example about the estimation of the size of dolphin populations discussed by Santostasi et al. (2016).