Limiting similarity of competitive species and demographic stochasticity

The limiting similarity of competitive species and its relationship with the competitive exclusion principle is still one of the most important concepts in ecology. In the 1970s, May [R. M. May, Stability and Complexity in Model Ecosystems (Princeton University, Princeton, NJ, 1973)] developed a concise theoretical framework to investigate the limiting similarity of competitive species. His theoretical results show that no limiting similarity threshold of competitive species can be identified in the deterministic model system whereby species more similar than this threshold never coexist. Theoretically, for competitive species coexisting in an unvarying environment, deterministic interspecific interactions and demographic stochasticity can be considered two sides of a coin. To investigate how the "tension" between these two forces affects the coexistence of competing species, a simple two-species competitive system based only on May's model system is transformed into an equivalent replicator equation. The effect of demographic stochasticity on the system stability is measured by the expected drift of the Lyapunov function. Our main results show that the limiting similarity of competitive species should not be considered to be an absolute measure. Specifically, very similar competitive species should be able to coexist in an environment with a high productivity level but big differences between competitive species should be necessary in an ecosystem with a low productivity level.