Quantitative analyses of tuna movement have been slower to develop, with treatment often confined to drawing arrows on maps to represent the long-range movement of a few tagged individuals. In fact, several general classes of models can be applied to the quantitative analysis of fish movement. Bulk transfer models, where exchange rates between large regions are characterized by transfer coefficients, were first developed in the 1950s. In some cases, these models have closed form solutions, are easily implemented in computer code, and have parameters that can be estimated statistically from tagging data. Although bulk transfer models can predict changes in population size in arbitrary regions, they cannot be used to predict the changes in population density at an arbitrary point within a region because they are not continuous in space.
Models based on diffusion concepts are continuous in both space and time.
These models have a long history in animal ecology and their potential application to fisheries population modeling also dates back to 1950s. Although the diffusion concept suggests that the population moves at random, it does not require that individual fish move randomly. Because purely diffusive movement will ultimately produce a uniform distribution of the population at equilibrium, other factors such as directional movement or spatial variability in recruitment, mortality, or population growth rate are required to maintain persistent gradients in population density. Directional movements are easily incorporated into a diffusion model by introducing advective terms. The application of advection-diffusion models to fish population dynamics has grown recently.