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.
