Estimating the Size of a Population Through Repeated Sampling: A Survey Sampling View on Capture-Recapture Procedures

Capture-recapture methods estimate the size of an elusive population based on repeated partial observations. In closed populations, estimators are typically constructed by modeling either the probability of capture frequencies or entire capture histories of observed units. This paper introduces a survey sampling approach to capture-recapture modeling. By framing capture occasions as sample draws, we begin with an explicit assumption on the sampling design, such as simple random sampling or, in the case of this paper, PPS sampling, allowing population size estimators to be tailored to the data collection methods of a given experiment or study. We model individual inclusion probabilities, accommodating latent heterogeneity, and variable sample sizes-the latter of which is often overlooked in current research-and show that the resulting estimator shares many similarities with current methods. To evaluate the proposed estimator, we present a novel simulation framework that generates unequal probability samples, providing unique insights into the estimator's performance under varying sampling effort and heterogeneity assumptions. The results of our simulations and applications to 14 benchmark datasets demonstrate that our method performs competitively, matching the accuracy of well-established estimators.