An advection–diffusion–reaction model for the estimation of fish movement parameters from tagging data, with application to skipjack tuna (Katsuwonus pelamis)

Abstract

The mobility of fish populations is often ignored in population dynamics models. However, in many cases (with tunas being a prime example), movement and spatial heterogeneity may be striking features of the fish populations and their exploitation. We describe a general quantitative framework to estimate movement and mortality of fish populations from tagging data. Movement is represented by an advection-diffusion process, which is the population equivalent of individual movement based on a biased random walk. Finite difference approximations for solving the partial differential equation are provided. The model is parameterized by assuming that movement parameters are homogeneous within specified geographical regions and seasons, that fishing mortality is proportional to fishing effort, and that natural mortality is constant over area and time. All model parameters are estimated simultaneously by maximum likelihood. The method is illustrated by application to skipjack tuna (Katsuwonus pelamis) in the western Pacific Ocean. Skipjack movement is shown to be highly variable at both seasonal and interannual time scales. Comparison with the results of a spatially aggregated analysis of the same data reveals that the spatial model provides a much better fit to the data and, unlike the spatially aggregated model, enables estimation of the natural mortality rate free of the effects of movement within the model domain.