Precision and Accuracy of Estimators of the Proportion of Hatchery-Origin Spawners

Abstract

For salmon populations in the Columbia River basin, many of which are listed under the U.S. Endangered Species Act of 1973, reliable estimation of the proportion of hatchery-origin spawners in spawning areas (p) is needed to make inferences about their status and potential for interbreeding with wild-origin adults, which may reduce the genetic fitness of subsequent generations. Despite its importance, accurate and precise techniques for estimating p are lacking, especially when there are spawner inputs from multiple hatcheries in a single spawning area. To identify hatchery-origin spawners, some hatchery releases are given visible marks, some are tagged with coded wire tags (CWTs), and some are marked in both ways. However, different marking fractions are used at different hatcheries and this complicates the problem of estimating p. To handle this situation, we derived a new generalized least-squares estimator (GLSE) of p and another, less computationally intensive estimator that uses CWT recoveries alone (SMME). We conducted Monte Carlo simulations using both estimators to compare their precision and statistical accuracy. We then applied the estimators to 2010 carcass survey data for fall Chinook salmon Oncorhynchus tshawytscha in the Hanford Reach of the Columbia River. An incremental change away from identical marking fractions for all source hatchery releases reduced precision, increased bias, and complicated estimation. The GLSE had greater precision than the SMME. Statistical bias shrank as the true spawning population size, the fraction of hatchery-origin fish, or the CWT fraction increased. The GLSE estimate of p in the Hanford Reach was 0.077, while the SMME estimate was 0.041. To maximize the accuracy and precision of the estimates of p, we recommend that identical marking fractions (preferably 100%) be used for all hatchery releases; barring this, we recommend that the CWT fractions be as large as possible.

Received April 12, 2011; accepted August 19, 2011

ACKNOWLEDGMENTS

The authors gratefully acknowledge the reviews of Charlie Paulsen, Tracy Hillman, Bruce Crawford, Michael Newsome, Craig Busack, Brian Maschhoff, Paul Hoffarth, two anonymous referees, and an associate editor. Brian Maschhoff implemented this analysis as a Web application at http://www.onefishtwofish.net. Paul Hoffarth supplied the 2010 Hanford Reach fall Chinook salmon carcass survey data. This work was supported by the Bonneville Power Administration. The views expressed in this report are solely those of the authors and are not intended to represent the views of any organizations with which the authors are affiliated.

Notes

^aNo releases corresponding to migration year 2010.

^aIn the case of the generalized least-squares estimator, this assumption is not necessary if the VM fractions are identical at all source hatcheries.

^aAn exception occurs when all but one hatchery CWT all VM releases. In this case, unmarked fish may be identified as originating at the source hatchery that did not CWT all of its VM releases. Thus, the untagged observations are in essence “tagged,” and x ₂=0. In this instance, case 3 applies rather than case 5, and p is estimable.

^aSome juveniles from this hatchery were visually marked with a visual implant elastomer tag. In this application, however, only fish that were marked with an adipose fin clip were considered visually marked.