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Scientific Report

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



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.


Richard A. Hinrichsen, Rishi Sharma, and Timothy R. Fisher


Hinrichsen, R.A., R. Sharma, and T.R. Fisher. 2012. Precision and Accuracy of Estimators of the Proportion of Hatchery-Origin Spawners. Transactions of the American Fisheries Society 141:437-454.


Aug 19th, 2011

Report No.


Media Type

Journal Article

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