The power of experiments for estimating relative reproductive success of hatchery-born spawners

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Abstract
An a priori power analysis was conducted to aid the design of experiments aimed at estimating the reproductive success of hatchery-born spawners relative to wild-born spawners using parentage assignment. Power was defined as the probability of rejecting the null hypothesis of equal reproductive contributions of hatchery- and wild-born spawners. A maximum likelihood estimator of relative reproductive success and its variance were derived. The estimator allowed multiple brood years of data, which was an extension of current approaches. Power increased with stock productivity, initial spawner abundance, fraction of recruits and spawners sampled, and the number of brood years examined. Power decreased with error variance used in the production function. Assuming a fixed total number of spawners, power was a concave-down function of the fraction of hatchery-born spawners. Using nominal values of productivity, error variance, and fraction of hatchery-born spawners, an experiment could achieve 0.8 power if it was run for at least 5 years or if it was applied to a stock with high initial female spawners (>200) and run for at least 2 years.

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