Covariate-Free Likelihood Ratio Confidence Interval for Abundance Based on Capture-Recapture Data

Abundance or population size is an important indicator for measuring biodiversity and has significant implications for ecological research. Without covariate capture and recapture data, the classic population size estimation methods include Chapman’s estimator and Dang et al.’s (2021) estimator, which are only applicable to the case of two captures. Their corresponding intervals are all Wald type, their coverage may be lower than confidence level, and may contain unreasonable values. To this end, we propose a likelihood estimation method for population size based on the full likelihood function. Compared to classical methods, its significant advantage is that it is not only suitable for situations with two captures, but also for scenarios with multiple captures. We constructed the global likelihood function and likelihood ratio statistic for the samples, And prove that the likelihood ratio statistic asymptotically follows a chi-square distribution with one degree of freedom, Furthermore, the maximum likelihood estimation and likelihood ratio interval estimation of population size are provided. The numerical simulation results indicate that, unlike classical estimation methods, The coverage of the likelihood ratio confidence interval we propose is always close to or higher than the confidence level, And even when the number of captures exceeds 2, it still performs satisfactorily. Finally, we found through analysis of data from the Hong Kong yellow bellied warbler that, the left endpoint of the classic Wald type interval may be lower than the observed number of individuals, which is unreasonable. In contrast, our likelihood ratio interval provides reasonable results, which confirms the widespread applicability and superiority of our likelihood ratio interval estimator.