Competition can rescue endangered species subject to strong Allee effects

In this article, we study population dynamics of a general two-species discrete-time competition model where each species suffers from strong Allee effects and scramble intra-competition. We focus on how combination of intra-specific and inter-specific competition affect the extinction and coexistence of these two competing species that are subject to strong Allee effects. We derive sufficient conditions on the extinction, essential-like extinction and coexistence for such models. One of most interesting findings is that competition can promote coexistence of these two species. This is supported by the outcome of singe species models with strong Allee effects. In addition, we apply theoretical results to a symmetric competition model with strong Allee effects induced by predator saturation where we give a completed study of its possible equilibria and attractors. Numerical simulations are performed to support our results.