Simple rules for establishment of effective marine protected areas in an age-structured metapopulation.

The implementation of effective protected areas is one of the central goals of modern conservation biology. In the context of fisheries management and marine ecosystem conservation, marine reserves often play a significant role to achieve sustainable fisheries management. Consequently, a substantial number of studies have been conducted to establish broad rules for the creation of MPAs, or to test the effects of MPAs in specific regions. However, there still exist many challenges for implementing MPAs that are effective at meeting their goals. Deducing theoretical conditions guaranteeing that the introduction of marine reserves will increase fisheries yields in age-structured population dynamics is one such challenge. To derive such conditions, a simple mathematical model is developed that follows an age-structured metapopulation dynamics of a sedentary species. The obtained results suggest that a sufficiently high fishing mortality rate and moderate recruitment success of an individual's eggs is a necessary for marine reserves to increase fisheries yields. The numerical calculations were conducted with the parameters of red abalone (Haliotis rufescens) to visualize and to check validity of the analytical results. They show good agreement with the analytical results, as well as the results obtained in the previous works.