Abstract
We consider a two-species hierarchical competition model with a strong Allee effect. The Allee effect is assumed to be caused by predator saturation. Moreover, we assume that there is a silverback' species x that gets first choice of the resources and where growth is limited by its own intraspecific competition, while the second inferior' species y gets whatever is left. Both species x and y are assumed to have the property of strong Allee effect. In this paper we determine the impact of the presence of the Allee effect on the global dynamics of both species.