Stratified capture-recapture estimation of the size of a closed population

This paper considers the estimation of the size of a closed population in a stratified capture-recapture experiment using the stratified Petersen-Lincoln model introduced by Darroch (1961, Biometrika 48, 241-260). A generalization of Darroch's model where the tagging or the recovery probabilities depend on explanatory variables possibly related to the capture mechanism is proposed. A simple scoring algorithm for the estimation of the nuisance parameters (i.e., the vectors of tagging and of recovery probabilities and the matrix for the distribution of the units in the capture-recapture area) is derived. This algorithm is based on a new closed-form expression for the inverse of the Fisher information matrix of the conditional likelihood for the estimation of the nuisance parameters. Large sample tests for the tagging and the recovery probabilities are obtained. Pooling of adjacent recovery strata with equal capture probabilities is proposed as a method for getting accurate estimators of the size of the population. Conditional and unconditional estimators of the size of the population are proposed. Analyses of data on smelt migration illustrate the methodology presented in this paper.