Mid-term bio-economic optimization of multi-species fisheries
L. Bayon, P. Fortuny Ayuso, P. J. Garcia-Nieto, J. A. Otero, P. M. Suarez, C. Tasis
TL;DR
The paper tackles mid-term, finite-horizon optimization of a multi-species fishery with fixed end stocks $x_i(T)$, seeking to maximize discounted revenues under nonlinear biological and economic dynamics. It introduces a scalable solution framework that fuses Pontryagin's Maximum Principle, cyclic coordinate descent, and a shooting-based coordination parameter $K$ to solve the problem as a sequence of unidimensional optimal control problems, ensuring feasibility and convergence. Numerical experiments on a three-species system show rapid convergence (a few CCD passes) and reveal harvesting patterns that peak mid-interval and taper toward the terminal time while achieving the prescribed final stocks, demonstrating practical policy implications for mid-term planning. The approach is flexible enough to accommodate pure competition, predator–prey interactions, and higher-order couplings, providing a robust tool for deterministic, multi-species bioeconomic management with fixed-terminal constraints and scalable complexity control.
Abstract
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.