Harvesting and Dynamics in Some One-Dimensional Population Models

Abstract

We review some dynamical effects induced by constant effort harvesting in single-species discrete-time population models. We choose three different forms for the density-dependent recruitment function, which include the overcompensatory Ricker map for semelparous species; a modified Ricker model allowing for adult survivorship; and amodel with both strong Allee effect and overcompensation which results from incorporating mate limitation in the Ricker model. We show that these simple models exhibit some interesting (and sometimes unexpected) phenomena such as the hydra effect; bubbling; sudden collapses; and essential extinction. We underline the importance of two often underestimated issues that turn out to be crucial for management: census timing and intervention time. © Springer-Verlag Berlin Heidelberg 2014.