An Application of Optimal Control to the Sustainable Harvesting Strategies of Ghana’s Sardinella Fishery

Abstract

The main objective of this study was to apply optimal control techniques to determine the optimal harvesting strategies that would ensure the sustainability of the Sardinella aurita for future generations. In this vein, the Gordon-Schaefer bioeconomic model was employed to aid in the analyses. The model was initially analysed using three different rates of harvest: constant, proportional and periodic. Also reviewed were the Craven model, the Goh model, the optimal yield model and the model with effective utilisation factor. The models were subjected to bifurcation analyses to determine the stability properties; and the static reference points, maximum sustainable yield (MSY), maximum economic yield (MEY) and open access yield (OAY), computed. Also determined was the dynamic reference point, optimum sustainable yield (OSY). An original model incorporating the total allowable catch (TAC) showed that, for the binding constraints, the resource should be harvested if and only if the marginal net revenue of harvest as a result of applying the maximum effort exceeds the difference of the shadow price of fish stock and the shadow price of the TAC. The model developed to simulate the effects of illegal fishing practices on fish stocks revealed that the increased catchability induced by the illegal methods severely depletes the stocks, to as low less than half of the carrying capacity in finite time. Employing a dynamic effort, predator-prey model with reserve area and critical biomass level, the optimal fishing strategy indicates that the critical biomass level must be set at the MSY level in order to attain sustainability of the resource. In general, all the models indicate that the optimal fishing effort must be set at the OSY level: estimated at 351;328 trips annually at a discount rate of 15%, provided the initial fish stock size is at least 554;654 tonnes. Recommendations are offered to the Fisheries Commission.