Stability, bifurcations and hydra effects in a stage-structured population model with threshold harvesting

Abstract

In this paper, we investigate the dynamics of a discrete-time stage-structured population model where juveniles and adults may be subject to threshold harvesting. This management policy allows the harvesting of the target population only if its size exceeds a predetermined threshold. It is commonly used for maintaining biomass, obtaining a higher yield, and preventing population collapse. We focus on the response of the structured populations to harvesting and study how they can be affected by considering different thresholds for each age class. We find all possible equilibria of the system and analyze their stability; we show that harvesting does not destabilize globally stable equilibria. We discuss when hydra effects may occur, more specifically, we determine when the adult population size can increase at equilibrium in response to an increase in its per-capita mortality rate as a consequence of threshold harvesting. A rigorous 2-parameter bifurcation diagram is given for semelparous populations, which helps to understand the general case when adult survivorship rates are low. Numerical results complement the bifurcation analysis in the general case.