A case study of green tree frog population size estimation by repeated capture–mark–recapture method with individual tagging: a parametric bootstrap method vs Jolly–Seber method

Abstract

This paper deals with estimation of a green tree frog population in an urban setting using repeated capture–mark–recapture (CMR) method over several weeks with an individual tagging system which gives rise to a complicated generalization of the hypergeometric distribution. Based on the maximum likelihood estimation, a parametric bootstrap approach is adopted to obtain interval estimates of the weekly population size which is the main objective of our work. The method is computation-based; and programming intensive to implement the algorithm for re-sampling. This method can be applied to estimate the population size of any species based on repeated CMR method at multiple time points. Further, it has been pointed out that the well-known Jolly–Seber method, which is based on some strong assumptions, produces either unrealistic estimates, or may have situations where its assumptions are not valid for our observed data set.

Keywords:

• generalized hypergeometric distribution
• parametric bootstrap
• point estimation
• interval estimation
• coverage probability

Mathematics Subject Classification :

• primary 62F03
• secondary 62E17

Acknowledgements

We would like to thank an anonymous referee, an Associate Editor and the Editor for many helpful comments and suggestions which have helped in improving presentation of our work. N. Pal and A.S. Ackleh were supported by the National Science Foundation Grants no. DMS–0718465 and DUE–0531915.