Dynamics of a generalized Beverton-Holt competition model subject to Allee effects

In this article, we propose a generalized Beverton-Holt competition model subject to Allee effects and study its population dynamics to obtain insights on how the interplay of Allee effects and contest competition affects the persistence and the extinction of two competing species. By using the theory of monotone dynamics and the properties of critical curves for non-invertible maps, our analysis indicates that the proposed model has relatively simple dynamics, i.e., almost every trajectory converges to a locally asymptotically stable equilibrium if the intensity of intra-specific competition intensity exceeds that of inter-specific competition. This equilibrium dynamics is also possible when the intensity of intraspecific competition intensity is less than that of inter-specific competition but under conditions that the maximum intrinsic growth rate of one species is not too large. The coexistence of two competing species occurs only if the system has four interior equilibria. We provide an approximation to the basin attractions of the boundary attractors (i.e., the extinction of one or both species) which suggests that contest species are prone to extinction at low densities. Our study suggests the following points of our generalized Beverton-Holt competition model: (i) The model can have only three boundary attractors without coexistence or four attractors among which only one is a persistent attractor; (ii) The model has only equilibrium dynamics; and (iii) The synergy between Allee effects and contest competition make two competing species prone to extinct.