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.

Maximum Likelihood Estimation of the Proportion of Hatchery‐Origin Fish on Spawning Grounds Using Coded Wire Tagging and Parentage‐Based Tagging

“…Currently, several published approaches for estimating p, including Bayesian (e.g., Geiger 1994; Barber et al 2011) or frequentist (e.g., Hankin 1982;Hinrichsen et al 2012) methods of estimation are based on tagging or marking (CWTs, otolith marks, or adipose fin clips) of juveniles prior to release. Dauer et al (2009) proposed a modified mark-recapture method for iteroparous steelhead Oncorhynchus mykiss based on spawn checks (reabsorption of scales during previous freshwater migration due to high energy demands of egg or milt production, which Rideout et al (2005) identified in upriver migrating adults).…”

“…Dauer et al (2009) proposed a modified mark-recapture method for iteroparous steelhead Oncorhynchus mykiss based on spawn checks (reabsorption of scales during previous freshwater migration due to high energy demands of egg or milt production, which Rideout et al (2005) identified in upriver migrating adults). However, the method of Hinrichsen et al (2012), which was originally applied to CWT and VM data, is the only published approach that produces release-specific estimators of p and their standard errors when there are multiple hatchery releases contributing fish to the spawning grounds. In the Columbia River basin, fish originating from different source hatcheries are known to stray into the same spawning area (McClure et al 2008;Hinrichsen et al 2012).…”

“…However, the method of Hinrichsen et al (2012), which was originally applied to CWT and VM data, is the only published approach that produces release-specific estimators of p and their standard errors when there are multiple hatchery releases contributing fish to the spawning grounds. In the Columbia River basin, fish originating from different source hatcheries are known to stray into the same spawning area (McClure et al 2008;Hinrichsen et al 2012).…”

“…We chose the MLE framework because it has a well-developed theory and desirable statistical properties including asymptotic normality, function invariance, and consistency (Mood et al 1974). This MLE framework has several advantages over the generalized least-squares estimation (GLSE) used previously by Hinrichsen et al (2012). In contrast to the GLSE approach of Hinrichsen et al (2012), the MLE approach allows non-VM carcasses to be checked for tags, does not require a known sample rate, and explicitly accounts for tag and VM loss due to carcass decay, which, if ignored, can introduce bias (Mohr and Satterthwaite 2013).…”

“…In equation (1), the realized spawning ground PBT and VM fractions for hatchery fish in the absence of carcass decay were unknown, and were estimated as the PBT and VM fractions at release, respectively. This is a common assumption in tagging studies (e.g., Hankin 1982;Hinrichsen et al 2012;Satterthwaite et al 2015).…”