The spatial distribution of small- and large-scale fisheries in a marine protected area

In this paper we analyze the problem of designing the access of small- and large-scale fishermen to a fishing reproductive area. The problem is studied from the point of view of a regulator in charge of deciding whether or not to give access to large-scale fishermen to a reproductive zone historically assigned to artisanal fishermen. In case of granting access, the regulator need to fix the percent of this area opened to each of the agents. This problem is motivated by a study case in Chile in which an artisanal reserve exist in the coastal reproductive area. Industrial fishermen periodically request access to this area arguing that artisanal fishermen does not have enough capacity to capture the biological surplus in the area. The model is introduced stepwise and takes into account both the different kind of activities involved and the oceanographic properties including different rates of growth and biomass transfer between patches. We end up with an optimal control problem that find social relevant solutions. The resulting control problem is treated using a calculus of variation approach and conditions ensuring the existence of interior solutions are proposed. Finally, we conduct a numerical example in order to analyze the feasibility of the proposed conditions.