Overdispersion in the Estimation of Salmon Escapements by Mark–Recapture Surveys and Its Related Factors

Abstract

The Petersen method, a well-known mark–recapture method, is frequently used in the estimation of escapement of Pacific salmon Oncorhynchus spp. Robust estimates and associated variances can be obtained when the underlying assumptions of this method are met. However, in field surveys, it is often difficult to meet these assumptions because wild animals are often not randomly distributed. When the sampling variance of the estimator exceeds its binomial variance (resulting in overdispersion), the Petersen model underestimates variance. We assessed the occurrence of overdispersion in the mark–recapture data collected to estimate the escapements of Masu Salmon Oncorhynchus masou in a river in northern Japan in 1998 and 1999. The dispersion parameters estimated from 2-year data were 2.89 and 2.51 for males and 1.45 and 1.52 for females, indicating that overdispersion occurred in all cases. The magnitude of overdispersion for males exceeded that for females, probably related to differences in the postspawning behaviors of the sexes, as represented by the changes of the sex ratio of Masu Salmon recovered on the spawning grounds. In this paper, we propose a simple procedure to detect the occurrence of overdispersion in multiple-recovery mark–recapture data.

Received February 8, 2015; accepted November 3, 2015

ACKNOWLEDGMENTS

The field survey was conducted with the assistance of researchers from the Salmon and Freshwater Fisheries Research Institute, Hokkaido Research Organization (formerly the Hokkaido Fish Hatchery), as a part of a research project on the production of Masu Salmon in the Atsuta River. We thank Tatsuya Takami, Mitsuhiro Nagata, Katsumi Takeuchi, Hajime Omori, Kiyoshi Kasugai, Naoyuki Misaka, Hirofumi Hayano, Mahito Miyamoto, and Kei-ichi Sugiwaka for their assistance with data collection. Invaluable comments from anonymous reviewers are appreciated.