Persistence and global stability in a selection-mutation size-structured model

Abstract

We analyse a selection-mutation size-structured model with n ecotypes competing for common resources. Uniform persistence and robust uniform persistence are established, when the selection-mutation matrix r is irreducible, i.e. individuals of one ecotype may contribute directly or indirectly to individuals of other ecotypes. Similar results are also presented for a particular reducible form of T. In the case of pure selection in which the offspring of one ecotype belong to the same ecotype, i.e. Γ = I, the identity matrix, we prove that the boundary equilibrium that describes competitive exclusion, with the fittest being the winner ecotype, is globally asymptotically stable. We show that small perturbations of the pure selection matrix lead to the existence of globally asymptotically stable interior equilibria. For the case when the selection-mutation matrix is reducible, we present and discuss the outcome of a series of numerical simulations. © 2011 Taylor & Francis.