Estimating Incursion of Hatchery Fish into a Wild Population: a Bayesian Approach

There is strong and growing interest in estimating the proportion of hatchery fish that are in a natural population (the incursion rate). In a sample of fish from the relevant population, some of them are observed to be marked, indicating their origin as hatchery fish. The observed proportion of marked fish is affected by the proportion originally marked (often known only to a close approximation), differential survival (usually lower) of marked fish relative to unmarked hatchery fish, and rates of mark retention, and mark detection. Bayesian methods can work well in a setting such as this, wherein there is a relative paucity of relevant data, but for which there may be considerable expert opinion regarding these values.  We propose and study Bayesian estimation of the incursion rate of hatchery fish in a wild population using Monte Carlo Markov Chain (MCMC) methods, and offer a freely available interactive Excel tool with which to implement the algorithm.