Simple rules for establishment of effective marine protected areas in the age-structured metapopulation dynamics
The implementation of effective no-take marine reserves or marine protected areas (MPAs) is a central goal of modern fisheries science. Accordingly, a number of studies have been conducted to understand broad rules for the creation of MPAs and have tested the effects of marine reserves for specific regions of interest. However, there still exist many challenges for implementing effective MPAs. Deducing theoretical conditions guaranteeing that the introduction of MPAs will increase fishing yields in age-structured population dynamics is one such challenge. To derive such conditions, a simple mathematical model is developed that follows the metapopulation dynamics of a sedentary species. The obtained results suggest that moderate recruitment success of an individual's eggs is a necessary condition for an MPA plan to increase biomass yields. Furthermore, numerical simulations of the optimal fishing regime with MPAs aiming at maximizing the fishing yields suggest that biomass yields monotonically decrease with the fraction of the MPAs. The optimal fishing mortality rate suddenly jumps to a very high value, leading to a sudden decline in the population biomass, to a lower level than in a fishing regime with a constant fishing mortality rate. The decline in the population biomass is never observed in the fishing regime with a constant fishing mortality.