Disturbances allow coexistence of competing species
We give the first mathematically rigorous proof that disturbances allow competing species to coexist. This work provides a mathematical framework to explain the existence of fugitive species and the role played by disturbances in increasing or decreasing the biodiversity of ecosystems. We study modifications of the metapopulation model for patchy environments proposed by Caswell and Cohen (1990, 1991). For the one- and two-species models we give necessary and sufficient conditions on the parameters for the existence of a non-trivial equilibrium solution, which is shown to be always globally stable.