Mid-term bio-economic optimization of multi-species fisheries

•We analyze the dynamics of a multi-species fisheries system in the presence of harvesting.•We propose a rather general model for studying multi-species interactions which covers previous ones.•We solve a new problem: finding the optimal strategy for a mid-term horizon with a fixed final stock of each species.•The proposed method is not gravely influenced by the dimensionality of the problem or by the complexity of the model. In this paper, we analyze the dynamics of a multi-species fisheries system in the presence of harvesting. We solve the problem of finding the optimal harvesting strategy for a mid-term horizon with a fixed final stock of each species, while maximizing the expected present value of total revenues. The problem is formulated as an optimal control problem. For its solution, we combine techniques derived from Pontryagin’s Maximum Principle, cyclic coordinate descent and the shooting method. The algorithm we develop can solve problems both with inter-species competition and with predator–prey behaviors. Several numerical examples are presented to illustrate the different possibilities of the method and a study of the dependence of the behavior on some parameters is performed.