Competitive exclusion and coexistence in a nonlinear refuge-mediated selection model

Abstract

A selection model with n traits is considered. It is assumed that the mortality function is density dependent and that individuals with "weak" traits are able to disperse to a safe refuge patch and avoid competition with individuals carrying the strongest trait. It is shown that if any subpopulation with a "weak" trait does not have a safe refuge then it will become extinct. Therefore, for survival of n traits n - 1 safe refuge patches are needed. When n - 1 refuge patches are available global stability of the interior equilibrium is proved provided that the fittest trait is sufficiently better than the other traits. Finally, two special cases with linear and Beverton-Holt density dependent mortality functions are studied in detail.