The effectiveness of marine protected areas for predator and prey with varying mobility

Marine protected areas (MPAs) are regions in the ocean where fishing is restricted or prohibited. Although several measures for MPA performance exist, here we focus on a specific one, namely the ratio of the steady state fish densities inside and outside the MPA. Several 2 patch models are proposed and analyzed mathematically. One patch represents the MPA, whereas the second patch represents the fishing ground. Fish move freely between both regions in a diffusive manner. Our main objective is to understand how fish mobility affects MPA performance. We show that MPA effectiveness decreases with fish mobility for single species models with logistic growth, and that densities inside and outside the MPA tend to equalize. This suggests that MPA performance is highest for the least mobile species. We then consider a 2 patch Lotka-Volterra predator-prey system. When one of the species moves, and the other does not, the ratio of the moving species first remains constant, and ultimately decreases with increased fish mobility, again with a tendency of equalization of the density in both regions. This suggests that MPA performance is not only highest for slow, but also for moderately mobile species. The discrepancy in MPA performance for single species models and for predator-prey models, confirms that MPA design requires an integrated, ecosystem-based approach. The mathematical approaches advocated here complement and enhance the numerical and theoretical approaches that are commonly applied to more complex models in the context of MPA design.