Estimating abundance: a non parametric mark recapture approach for open and closed systems

We present a novel, non-parametric, frequentist approach for capture-recapture data based on a ratio estimator, which offers several advantages. First, as a non-parametric model, it does not require a known underlying distribution for parameters nor the associated assumptions, eliminating the need for post-hoc corrections or additional modeling to account for heterogeneity and other violated assumptions. Second, the model explicitly deals with dependence of trials by considering trials to be dependent; therefore, cluster sampling is handled naturally and additional adjustments are not necessary. Third, it accounts for ordering, utilizing the fact that a system with a small population will have a greater frequency of recaptures “early” in the survey work compared to an identical system with a larger population. We provide mathematical proof that our estimator attains asymptotic minimum variance under open systems. We apply the model to a data set of bottlenose dolphins (Tursiops truncatus) and compare results to those from classic closed models. We show that the model has an impressive rate of convergence and demonstrate that there’s an inverse relationship between population size and the proportion of the population that need to be sampled, while achieving the same degree of accuracy for abundance estimates. The model is flexible and can apply to ecological situations as well as other situations that lend themselves to capture recapture sampling.