Sustainability of a fishery under an ecosystemic constraint: A stochastic viable control model

In this paper, we examine the biological and economic sustainability of a fishery subject to an ecosystemic constraint. We consider an age-structured discrete time dynamic model of two species of the Bay of Biscay (ICES area VIIIa,b), with uncertainty in recruitment: the European Hake and the Nephrops. These two species are exploited by the Nephrops fishery, mainly composed by trawlers. These trawlers target Nephrops and get juvenile Hakes as a bycatch, inducing ecological, technical and economical interactions. We define sustainability using the viability framework of analysis. The viability objectives are represented by constraints and we examine what are the conditions on the bioeconomic states and exploitation decisions for the trajectories to respect that constraints. The viability of the fishery is depicted in terms of biological and economic constraints, and we define the probability that there are decisions ensuring the respect of the constraints despite the dynamic inertia and the uncertainties. The economic constraint is defined as a minimal gross return for the fleet to be economically viable. In order to take into account the ecological impact of that fishery on the ecosystem, we also consider an ecological constraint defined as a minimal target threshold for the recruitment of mature hakes. As the main part of juvenile hakes catches in that area are due to the Nephrops fishery, this constraint can be respected only by a limitation on the fleet's fishing effort. We adopt an ecosystem approach for the Nephrops fishery management via the inclusion of a contraint on bycatch of another fish stock, the European Hake, in the analysis of the probabilistic viability of the fishery. This approach allows us to take into account ecosystem complexity, and interactions between species and human activities, without increasing the complexity of studied dynamic systems (especially the number of states, and the number of dynamic equations representing the bioeconomic system and their interactions). Based on a stochastic analysis, we define the probability that both the economic and ecosystemic constraints are met, as a function of the level of these constraints. It means that we define the probability that a management policy allowing the dynamic exploitation system to respect both the economic and ecologial contraints exists. We compute this probability for any couple of economic and ecological constraint and show as a first result that the greater the sustainability objectives are, the lower the probability that there exist management decisions allowing to meet the constraint is. We then examine the relationship between the economic and ecological constraints, and emphasize the necessary conflict between environmental and economic objectives in this model for a given probability level. The analysis uses a dynamic programming approach, with computation in Scilab.