Sequential capture-recapture method

Capture-recapture is a well-established sampling technique used to estimate population size and related demographic parameters such as birth, mortality, immigration, and emigration rates. Traditional methods rely on a fixed-size recapture sample. In this work, we propose a sequential capture-recapture method where individuals are sampled one by one until a fixed number of previously marked individuals is observed. We derive an unbiased estimator of the population size and establish its variance analytically. A stability-based stopping rule is also introduced to optimize the sampling effort while preserving estimation accuracy. Simulation results demonstrate that the proposed estimator outperforms classical estimators in terms of efficiency and stability. Approximate confidence intervals are also derived and empirically shown to achieve near-nominal coverage probabilities.