Analysis of compensatory Leslie matrix models for competing species

Analytic conditions determining the stability of equilibria to small perturbations are developed for general discrete time, multiple age-class models of two competing or mutualistic species. The conditions are simple to apply and can be stated ecologically as follows. Each of the interacting species must be stable in the absence of other species, and the strength of species self-interaction must be strong compared to the strength of interspecies interaction. These results can only be applied to models where intraspecific interactions occur within age classes. The stability conditions developed are applied to a particular two-species, two-age-class model useful in describing competing fish populations where the young-of-the-year suffer mortality due to predation by the other species. The applicability of the stability conditions to multispecies communities is also discussed.