Estimating the Hatchery Fraction of a Natural Population: A Bayesian Approach

Abstract

There is strong and growing interest in estimating the proportion of hatchery fish that are in a natural population (the hatchery fraction). In a sample of fish from the relevant population, some are observed to be marked, indicating their origin as hatchery fish. The observed proportion of marked fish is usually less than the actual hatchery fraction, since the observed proportion is determined by the proportion originally marked, differential survival (usually lower) of marked fish relative to unmarked hatchery fish, and rates of mark retention and detection. Bayesian methods can work well in a setting such as this, in which empirical data are limited but for which there may be considerable expert judgment regarding these values. We explored a Bayesian estimation of the hatchery fraction using Monte Carlo–Markov chain methods. Based on our findings, we created an interactive Excel tool to implement the algorithm, which we have made available for free.

Received March 30, 2011; accepted June 21, 2011

ACKNOWLEDGMENTS

Gerow is thankful to the University of Hawaii at Hilo for hosting his sabbatical visit, during which this project was moved forward. Any use of trade names is for descriptive purposes only and does not imply endorsement of the U.S. Government. We thank reviewers of an earlier draft, Charles Snow and Kenneth Tiffan, for their comments that quite improved the paper; one anonymous reviewer in particular offered useful suggestions for eliciting priors and other suggestions for improving the model.

Notes

The tool is available at Gerow’s Web site, www.statsalive.com.