Bias and significance of relative reproductive success estimates based on steelhead trout (Oncorhynchus mykiss) data: a Bayesian meta-analysis

The evaluation of the reproductive success (RS) of hatchery fish in the wild is one of the most important issues in hatchery supplementation, aquaculture, and conservation. Estimates of the relative reproductive success (RRS) have been used to evaluate RS. Because RRS may vary greatly depending on cross, years of release, and environmental conditions, we introduced a log-normal distribution to quantify the variation. The classical estimator of RRS based on multiple measurements is contrasted with the mean of this distribution. We derived the mean, variance, and relative bias and applied our Bayesian hierarchical model to 42 empirical RRS estimates of steelhead trout (Oncorhynchus mykiss) in the Hood River, Oregon, USA. The RRS estimate generally had an upward bias. Although the average level of RRS implied the reproductive decline of hatchery fish and wild-born hatchery descendants, we could not reject the null hypothesis that hatchery fish and their descendants have the same chance of having smaller RS than wild fish as they do of having larger RS than wild fish.