Proportional threshold harvesting in discrete-time population models

Threshold-based harvesting strategies tend to give high yields while protecting the exploited population. A significant drawback, however, is the possibility of harvesting moratoria with their socio-economic consequences, if the population size falls below the threshold and harvesting is not allowed anymore. Proportional threshold harvesting (PTH) is a strategy, where only a fraction of the population surplus above the threshold is harvested. It has been suggested to overcome the drawbacks of threshold-based strategies. Here, we use discrete-time single-species models and rigorously analyze the impact of PTH on population dynamics and stability. We find that the population response to PTH can be markedly different depending on the specific population model. Reducing the threshold and allowing more harvest can be destabilizing (for the Ricker and Hassell map), stabilizing (for the quadratic map), or both (for the generalized Beverton-Holt map). Similarly, management actions in the form of increasing the threshold do not always improve population stability-this can also be due to bistability. Our results therefore emphasize the importance of a rigorous analysis in investigating the impact of PTH on population stability.