Dynamics of two-species contest competition models subject to Allee effects

In this article, we propose a general two species contest competition model subject to Allee effects and study its population dynamics to obtain insights on how the interplay of Allee effects and contest competitions affect the persistence and the extinction of two competing species. By using the monotone dynamical theory and the properties of critical curves for non-invertible maps, our analysis indicates that our model has relatively simple dynamics, i.e., every trajectory converges to an equilibrium, under conditions that either the product of two species’ relative competition degree (i.e., the ratio of the nonlinearity of intra-specific competition coefficient to its inter-specific competition coefficient) is greater than 1 or this product is less than 1 but the maximum intrinsic growth rate of one species is not too large. We provide an approximation of the basins of attractions for the boundary attractors (i.e., the extinction of one or both species) which suggests that contest competitions make species more prone to extinction than scramble competitions do. In addition, by comparing to dynamics of two species scramble competition models subject to Allee effects, our study suggest that (i) Both contest and scramble competition models can have three boundary attractors or four attractor among which three are boundary attractors and one is an interior attractor, however, scramble competition model may have the extinction of both species as its only attractor, i.e., the essential extinction of two species due to strong Allee effects; (ii) Scramble competition model may have much more complicated dynamical structure of interior attractors than contest one may have; and (iii) Scramble competition may be more likely to promote the coexistence of two species at low and high densities. Our results have potential to be useful for conservation biology.