Spatial heterogeneity and interspecific competition

A model of two competing species is presented in which each species is able to disperse over a single spatial axis. The spatial axis is composed of two intervals with different carrying capacities. We ask the question: If species one is alone and at population dynamic equilibrium, then when can species two successfully invade when rare? We say that an interval is “suitable” if the interval can be invaded by species two in the absence of dispersal by both species, and we say an interval is “unsuitable” if the interval cannot be invaded by species two in the absence of dispersal by both species. We offer three findings: (I) If one interval is suitable and the other is unsuitable, then the success of invasion depends upon the length of the suitable interval. Invasion succeeds if the suitable interval is larger than a threshold minimum and fails otherwise. (II) It is possible for species two to invade even though both intervals are unsuitable. (III) It is possible for species two to fail to invade even though both intervals are suitable.