Complex dynamics of survival and extinction in simple population models with harvesting

We study the effects of constant harvesting in a discrete population model that includes density-independent survivorship of adults in a population with overcompensating density dependence. The interaction between the survival parameter and other parameters of the model (harvesting rate, natural growth rate) reveal new phenomena of survival and extinction. The main differences with the dynamics of survival and extinction reported for semelparous populations with overcompensatory density dependence are that there can be multiple windows of extinction and conditional persistence as harvesting increases or the intrinsic growth rate is increased, and that, in case of bistability, the basin of attraction of the nontrivial attractor may consist of an arbitrary number of disjoint connected components.