Competitive overlap and coexistence

The possibility of equilibrium is studied for model assemblages of competing species and their resources. The “assemblage niche” is defined as the set of resource productivities which yields an equilibrium population exceeding zero for all species. A radius of this set, which is a measure of the ability of the assemblage to have equilibrium states, is defined and estimated. This radius decreases as resource utilization overlap increases; the behavior is compared with known results concerning response to rapid resource fluctuations. A system of ordinary differential equations having such an equilibrium is studied. It is shown that a global asymptotic stability property holds in regions with boundaries defined by a certain scalar function, if the specific productivity satisfies a monotonicity condition. This generalizes known results, which have been obtained for antisymmetric Lotka-Volterra systems.