Bayesian mark–recapture estimation with an application to a salmonid smolt population

Abstract

We developed a Bayesian probability model for mark–recapture data. Three alternative versions of the model were applied to two sets of data on the abundance of migrating Atlantic salmon (Salmo salar) smolt populations, and the results were then compared with those of two widely used maximum likelihood models (Petersen method and a model using stratified data). Our model follows the basic principles of stochastic models presented for stratified data. In contrast to the earlier models, our model can deal with sparse data. Moreover, even weak dependencies between the studied parameters and the possible factors affecting them can be used to improve the plausibility of the estimates. The assumptions behind our approach are more realistic than those of earlier models, taking into account such factors as overdispersion, which is expected to be present in the mark–recapture data of salmon smolts because of their schooling behavior. Our examples also show that assumptions about the model structure can have a substantial impact on the resulting inferences on the size of the smolt run, especially in terms of the precision of the estimate.