Global dynamics in a stage-structured discrete-time population model with harvesting.

The purpose of this paper is to analyze the effect of constant effort harvesting upon global dynamics of a discrete-time population model with juvenile and adult stages. We consider different scenarios, including adult-only mortality, juvenile-only mortality, and equal mortality of juveniles and adults. In addition to analytical study of equilibria of the system, we analyze global dynamics by means of an automated set-oriented rigorous numerical method. We obtain a comprehensive overview of the dynamics as the harvest rate and survival probability change. In particular, we determine the range of parameters for which the population abundance gets larger in spite of an increase in the harvest rate (so-called hydra effect), and for which subsequent increases in harvesting effort can magnify fluctuations in population abundance (destabilize it) and then stabilize it again (so-called bubble effect).