Harvesting strategies for fluctuating populations based on uncertain population estimates

This paper deals with models for optimal annual harvesting of populations in a fluctuating environment. By adopting threshold harvesting and assuming known population size, the optimal threshold that maximizes the expected cumulative yield before extinction is derived. The optimal threshold is practically independent of the form of density regulation, is smaller than the carrying capacity, and decreases with the environmental variance. We also analyse the effect of uncertainty in the population estimates, defined by a parameter theta(0), which is the coefficient of variation in the population estimate when the population is at the carrying capacity. By adopting threshold harvesting based on the estimated population size, the optimal threshold increases with theta(0). For large uncertainty in the estimates we propose a new harvesting strategy called proportional threshold harvesting for which only a given fraction, q, of the difference between the population estimate and the threshold is harvested if the population estimate is larger than the threshold. Numerical calculations show that this method is preferable to pure threshold harvesting when the uncertainty in the estimate exceeds some value depending on the environmental variance. A formula for the optimal threshold for a given q and a small theta(0) is derived. This formula is also independent of the form of density regulation. We also give examples of numerical calculations of the expected time to extinction, mean annual yield and the mean fraction of years the population can be harvested. Finally, we present some simulations demonstrating population fluctuations and harvesting based on uncertain population estimates. (C) 1997 Academic Press Limited.