Integrating batch marks and radio tags to estimate the size of a closed population with a movement model

Movement models require individually identifiable marks to estimate the movement rates among strata. But they are relatively expensive to apply and monitor. Batch marks can be readily applied, but individual animal movements cannot be identified. We describe a method to estimate population size in a stratified population when movement takes place among strata and animals are marked with a combination of batch and individually identifiable tags. A hierarchical model with Bayesian inference is developed that pools information across segments on the detection efficiency based on radio-tagged fish and also uses the movement of the radio-tagged fish to impute the movement of the batch-marked fish to provide estimates of the population size on a segment and river level. The batch marks provide important information to help estimate the movement rates, but contribute little to the overall estimate of the population size. In this case, the approximate equal catchability among strata in either sample obviates the need for stratification.