Harvest in a fluctuating environment and conservative harvest for the Fox surplus production model

Relations between optimal yield and abundance in a fluctuating environment and conditions for a conservative level of harvest were obtained for the Fox surplus production model and compared with those for the logistic surplus production model. Environmental variation was included in the optimization of harvest with the Fox surplus production model to obtain a relation in which the maximum sustainable yield (MSY) and biomass at the MSY varied as the environment varied. The relation can be applied for management of fisheries at the optimum levels in a fluctuating environment. For both models there is only one maximum sustainable yield under equilibrium conditions, but in a variable environment the maximum sustainable yield and optimum biomass and effort vary as the environment varies. The results were applied to the blue crab (Callinectes sapidus) fishery of the Chesapeake Bay. Although several numerical results for the logistic and Fox models were similar, the parameter estimates were different and the Fox model predicted a much larger decrease in population abundance at the MSY. Harvesting at a conservative level with either the Fox model or the logistic model could increase blue crab abundance substantially with little decrease in harvest. At a conservative level of harvest, there is a 20% increase in biomass with a 6% decrease in yield for the logistic model and a 37% increase in biomass with a 9% decrease in yield for the Fox model. Both the Fox and the logistic surplus production models indicate that the blue crab fishery has been consistently over harvested.