THRESHOLD HARVESTING FOR SUSTAINABILITY OF FLUCTUATING RESOURCES

Abstract

Commercially important species often are overexploited, and many endan- gered mammals and birds are threatened by hunting and international trade. To sustain biological resources requires harvesting strategies that maximize yield while accounting for stochastic dynamics, uncertainty, and risk of resource collapse or extinction. For a large class of population dynamics, the optimal strategy is to harvest all individuals above a threshold population size, with no harvest below the threshold. Maximizing the expected cumulative harvest before extinction puts the optimal threshold at carrying capacity, re- gardless of the form of expected dynamics or the magnitude of stochasticity. Maximizing the mean annual yield lowers the optimal threshold, which then depends on the form of expected dynamics and the magnitude of stochasticity. Uncertainty in estimated population sizes increases the threshold, and with large uncertainty, the optimal strategy is proportional threshold harvesting, involving harvest of only a fraction of the excess in estimated pop- ulation above the threshold. The theoretical justification for the common strategy of a constant harvest rate is extremely weak in comparison to that for optimal threshold strat- egies. Thresholds are a necessary feature of any harvesting strategy with the objective of minimizing risks of resource depletion or extinction, while optimizing yields.