POPULATION EXTINCTION AND OPTIMAL RESOURCE-MANAGEMENT

The optimal exploitation of a population is considered for three stoch astic population models; these allow both demographic and environmenta l variability and the possibility of extinction. The dynamics are line ar in the harvest rate; the optimal policy then recommends harvesting at the maximal rate above a critical level (the 'threshold') and at ze ro rate below. However, in all cases the optimal threshold differs rad ically according as to whether one maximizes the total return before e xtinction or the rate of return per unit time over the period before e xtinction. In the former case the optimal threshold is at the determin istic equilibrium level of the unexploited population, in the latter c ase it is approximately at the level of maximal sustainable production . Part of the explanation is that maximization of total yield turns ou t to be almost equivalent to maximization of time to extinction. Both average yield rate and the expected time to extinction vary with the p olicy, but the second much more powerfully. Both the criteria above ar e extreme: one obtains a balanced criterion (and an intermediate thres hold) if one maximizes rate of return (before extinction) subject to t he conservation requirement of a lower bound on the expected time to e xtinction. In the case when extinction is excluded because of a potent ial 'rescue effect' one comes to the same view by taking account of th e relative time needed to restart an obliterated population. The pract ical implication is that more attention should be paid to extinction a nd restart times. For vulnerable populations it is likely that maximal utilization before an inevitable extinction will be achieved at low h arvest rates. For large populations or metapopulations, with large tim es to extinction or quick recovery from a temporary extinction, classi cal resource models are appropriate.