Compensatory and overcompensatory dynamics in prey–predator systems exposed to harvest

Density dependent prey–predator systems under the impact of harvest are considered. The recruitment functions for both the prey and predator belong to the Deriso–Schnute family which allow us to study how the dynamical behaviour of both populations changes when compensatory density dependence turns overcompensatory. Depending on the degree of overcompensation, we show in the case of no harvest that an increase of the fecundity of the prey always acts in a destabilizing fashion. If the degree of overcompensation becomes sufficiently large, such an increase can lead to large amplitude chaotic oscillations of the prey, which actually may drive the predator population to extinction. The impact of harvest also depends on the degree of overcompensatory density dependence. If only the prey is the target population, increased harvest in general seems to stabilize the dynamics. On the other hand, harvesting only the predator may in some cases tend to stabilize dynamics, but there are also parameter regions where this turns out to be a strong destabilizing effect.