Predator-prey Dynamics with Intraspecific Competition and an Allee Effect in the Predator Population

Abstract

The study of the Allee effect on the stability of equilibria of predator-prey systems is of recent interest to mathematicians, ecologists, and conservationists. Many theoretical models that include the Allee effect result in an unstable coexistence equilibrium. However, empirical evidence suggests that predator-prey systems exhibiting density-dependent growth at small population densities still can achieve coexistence in the long term. We review an often cited model that incorporates an Allee effect in the predator population resulting in an unstable coexistence equilibrium, and then present a novel extension to this model which includes a term modeling intraspecific competition within the predator population. The additional term penalizes predator population growth for large predator to prey density ratios. We use equilibrium analysis to define the regions in the parameter space where the coexistence equilibrium is stable, and show that there exist biologically reasonable parameter sets which produce a stable coexistence equilibrium for our model.