Community Equilibria and Stability, and an Extension of the Competitive Exclusion Principle

It is shown in this paper that no stable equilibrium can be attained in an ecological community in which some r of the components are limited by less than r limiting factors. The limiting factors are thus put forward as those aspects of the niche crucial in the determination of whether species can coexist. For example, consider the following simple food web: Despite the similar positions occupied by the two prey species in this web, it is possible for them to coexist if each is limited by an independent combination of predation and resource limitation, since then two independent factors are serving to limit two species. On the other hand, if two species feed on distinct but superabundant food sources, but are limited by the same single predator, they cannot continue to coexist indefinitely. Thus these two species, although apparently filling distinct ecological niches, cannot survive together. In general, each species will increase if the predator becomes scarce, will decrease where it is abundant, and will have a characteristic threshold predator level at which it stabilizes. That species with the higher threshold level will be on the increase when the other is not, and will tend to replace the other in the community. If the two have comparable threshold values, which is certainly possible, any equilibrium reached between the two will be highly variable, and no stable equilibrium situation will result. This is not the same as dismissing this situation as "infinitely unlikely," which is not an acceptable argument in this case. Hutchinson's point of the preceding section vividly illustrates this. The results of this paper improve on existing results in three ways. First, they eliminate the restriction that all species are resource-limited, a restriction persistent in the literature. Second, the results relate in general to periodic equilibria rather than to constant equilibria. Third, the nature of the proof relates to the crucial question of the behavior of trajectories near the proposed equilibrium, and provides insight into the behavior of the system when there is an insufficient number of limiting factors.