MPAs (Marine Protected Areas) are regions where fishing is restricted or prohibited. As a fisheries management tool, their purpose is to protect overharvested species and their habitats. This talk will introduce a collection of 2 patch models, where one patch represents the MPA and the other the Fishing Ground. In each patch a nonlinear ODE (or system of ODEs) specifies the fish dynamics, and these dynamics are coupled diffusively. The purpose of this talk is to use these models to start addressing the following basic scientific questions about the interplay of ecological parameters -in particular, the fish diffusivity- and measures of MPA effectiveness:
*Is diffusion always an equalizing force? That is, will the fish densities inside and outside the MPA tend to each other when diffusivity is increased?
*Simple models predict that fish density ratios inside versus outside the MPA decrease with fish mobility. But empirical data shows the opposite effect. How can this paradox be resolved?
*What is the effect of stage structure in the fish dynamics on the density ratios?
*What is the effect of a foodweb structure (such as predator-prey) on these ratios?
*What is the combined effect of stage and foodweb structure?
*In practice, usually only adult fish are harvested. Is this really an optimal