Mathematical bioeconomic modelling of the interaction between aquaculture and open sea fisheries

We analyze the problem of an integrated management of fisheries by using fish farming as a tool for restocking fish populations depleted by overfishing pressure. We first use a simple heuristic dynamic model, taken from a classical example of mathematical bioeconomics, in order to prove that fish restocking may be an efficient tool for sustainable fishery management in situations where excessive fishing effort is going to cause irreversible stock collapse. Then we propose a two-compartments bieconomic mathematical model, with age structure and age specific harvesting and restocking, to mimic a possible integrated interactions between aquaculture and open sea fisheries, where reared fish are used as substitutes for marine catches. The model proposed in this paper tries to fill a gap between the rich mathematical bioeconomic literature, mainly devoted to the description of open sea fisheries and/or marine protected areas, and the very poor literature on mathematical bioeconomic modelling of interactions between fish farming and fisheries.