Sustainability of fisheries through marine reserves: a robust modeling analysis.

Among the many factors that contribute to overexploitation of marine fisheries, the role played by uncertainty is important. This uncertainty includes both the scientific uncertainties related to the resource dynamics or assessments and the uncontrollability of catches. Some recent works advocate for the use of marine reserves as a central element of future stock management. In the present paper, we study the influence of protected areas upon fisheries sustainability through a simple dynamic model integrating non-stochastic harvesting uncertainty and a constraint of safe minimum biomass level. Using the mathematical concept of invariance kernel in a robust and worst-case context, we examine through a formal modeling analysis how marine reserves might guarantee viable fisheries. We also show how sustainability requirement is not necessarily conflicting with optimization of catches. Numerical simulations are provided to illustrate the main findings.