Minimum chi-square method for estimating population size in capture-recapture experiments

• Published in: PloS one Vol. 18; no. 10; p. e0292622
• Main Authors: Zheng, Yuyan, Mao, Yongfei, Tsao, Min, Cowen, Laura L. E
• Format: Journal Article
• Language: English
• Published: San Francisco Public Library of Science 12.10.2023; Public Library of Science (PLoS)
• Subjects: Aquatic birds; Binomial distribution; Capture-recapture studies; Chi-square test; Chi-square tests; Confidence intervals; Estimation; Evaluation; Goodness of fit; Methods; People and places; Physical Sciences; Population biology; Population number; Population statistics; Probability; Probability distribution; Random variables; Research and Analysis Methods; Statistical analysis; Canada
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0292622

Closed population capture-recapture estimation of population size is difficult under heterogeneous capture probabilities. We introduce the minimum chi-square method which can handle multi-occasion capture-recapture data. It complements likelihood methods with elements that can lead to confidence intervals and assessment of goodness-of-fit. We conduct a comprehensive study on the minimum chi-square method for estimating the size of a closed population using multiple-occasion capture-recapture data under heterogeneous capture probability. We also develop two different bootstrap techniques that can be combined with any underlying estimator, be it the minimum chi-square estimator or a likelihood estimator, to perform useful inference for estimating population size. We present a simulation study on the minimum chi-square method and apply it to analyze white stork multiple capture-recapture data. Under certain conditions, the chi-square method outperforms the likelihood based methods.