Fisheries Management Under Cyclical Population Dynamics

Cycles in environmental conditions (e.g., sea-surface temperature) directly impact fish growth. This paper extends the classical Gordon-Schaefer fishery model by replacing the constant growth rate with a cyclical growth rate. The optimal harvest rate is shown to fluctuate, but the cycle of the harvest rate lags the cycle of the biological growth function with the highest harvest rate occurring after biological conditions start to decline. Simulations contrast various fishing policies and illustrate the proclivity to crash a fishery if it is wrongfully managed as if there is a constant growth rate with i.i.d. environmental shocks. Finally, we show that small cyclical fluctuations in one species can result in large fluctuations in the optimal harvest rate of another species if the fish species are interlinked through predator-prey relationships.