Optimal harvesting of fish populations with nonlinear rates of predation and autocorrelated environmental variability

A common surplus production model incorporating a nonlinear rate of predation yields multiple, stable equilibria and, when forced with autocorrelated variability, has been invoked to qualitatively describe rapid ‘flips’ in marine fish abundances. In this paper, I used optimal control theory and stochastic dynamic programming to obtain optimal harvesting policies for populations described by this model. Multiple, locally optimal stock sizes may exist with a managment goal of sum of discounted yield, whereas a single optimum occurred with the goal of sum of discounted economic rent. The optimal policy for a population forced with autocorrelated variability and fluctuating between high and low equilibria required conservative (exploitative) behavior during poor (good) environmental conditions with high stocks and rebuilding of low stocks. Simulation of various harvest strategies applied to such a population revealed that, with a management goal of sum of discounted yield and a discount rate of 2.5%, the optimal policy provided more than twice the mean annual benefits as a constant fishing rate policy. The large differences in optimal policies for the management goals of sum of discounted yield and sum of discounted economic rent provide motivation to consider carefully what objectives should be sought from highly fluctuating fish stocks.