OPTIMAL HARVESTING OF FISH POPULATIONS WITH NONLINEAR RATES OF PREDATION AND AUTOCORRELATED ENVIRONMENTAL VARIABILITY

A common surplus production model incorporating a nonlinear rate of pr edation yields multiple, stable equilibria and, when forced with autoc orrelated variability, has been invoked to qualitatively describe rapi d ''flips'' in marine fish abundances. In this paper, I used optimal c ontrol theory and stochastic dynamic programming to obtain optimal har vesting policies for populations described by this model. Multiple, lo cally optimal stock sizes may exist with a management goal of sum of d iscounted yield, whereas a single optimum occurred with the goal of su m of discounted economic rent. The optimal policy for a population for ced with autocorrelated variability and fluctuating between high and l ow equilibria required conservative (exploitative) behavior during poo r (good) environmental conditions with high stocks and rebuilding of l ow 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 th an twice the mean annual benefits as a constant fishing rate policy. T he large differences in optimal policies for the management goals of s um of discounted yield and sum of discounted economic rent provide mot ivation to consider carefully what objectives should be sought from hi ghly fluctuating fish stocks.