Aquaculture, pollution and fishery - dynamics of marine industrial interactions

Abstract

We model bioeconomic interrelations between a commercial fishery and an aquaculture industry by using a dynamical systems theory approach. The biomass follows a logistic growth where the pollution emerging from aquaculture is accounted for by means of a retardation term. We investigate the existence and stability of the equilibrium states of this model as a function of the growth-retardation parameter and find that a necessary (but not sufficient) condition for stability is low and moderate values of the emission-remediation ratio. Three intervals of the growth-retardation parameter are identified in this regime of the emission-remediation ratio. The regime of low and negligible influence of the pollution on the biomass evolution gives rise to the existence of an asymptotically stable equilibrium state characterized by a finite biomass and a finite effort in the fishery. In the same regime we identify two unstable equilibrium states of which the former one is characterized by no effort in the fishery, whereas the latter one is characterized by no biomass and no effort. When the growth retardation parameter exceeds a certain threshold, the fishery becomes unprofitable and the equilibrium state characterized by no effort in the fishery becomes asymptotically stable. By a further increase in this parameter above a higher threshold value, also the biomass is wiped out and the equilibrium state characterized by no biomass and no effort becomes asymptotically stable.