Allee effect in a prey–predator system

We construct a model of a specialist predator and its prey species for the case of non-overlapping generations and we assume that the prey obeys to the Allee effect. We observe that, for small values of the minimal viable population of the prey, there are stable dynamical configurations corresponding either to stable fixed points or to a stable limit cycle which supports quasiperiodic orbits. In this last case we observe the paradox of enrichment, where an initial increase of the population of the prey may lead to cycles of very fast increase and subsequent decrease of the predator population. This behavior increases the probability of extinction due to unpredictable external factors. We consider also non-zero dispersal probability of the prey to neighboring sites and observe that predation causes the disappearance of a rescue effect, even when the Allee threshold is small.