Regional Coexistence of Species and Competition between Rare Species

A model is developed for the coexistence and exclusion of species over a region of similar habitable patches. Since the balance of local extinction and colonization would leave some patches unoccupied even without competitors, species may coexist even when all the patches are the same. Regional competition coefficients are found when species affect the local extinction or migration rates of each other. Rare species can regulate each other and even exclude other species completely.