Competitive exclusion and coexistence in an n-species Ricker model

We analyse a discrete-time Ricker competition model with n competing species and give sufficient conditions, which depend on the competition coefficients only, for one species to survive (not necessarily at an equilibrium) and to drive all the other species to extinction. Our results complement and extend similar existing results from the literature. For the model reduced to three species ([Formula: see text]), we also investigate various scenarios under which all species coexist, in the sense that each species is robustly uniformly persistent. We provide a few numerical simulations to illustrate that coexistence does not necessarily mean convergence to the interior equilibrium, and that the interior dynamics can be quite complex.