Aggregation and the competitive exclusion principle

A mathematical model for aggregation in a single animal population is set up. It relies on two premises. First, there is an advantage to individuals in the population in grouping together, for example for social purposes or to reduce the risk of predation. Second, the intra-specific competition at a point depends not simply on the population density at that point but on the average population density near the point, since the animals may move to find resources. The model is then extended to competing populations, and inter-specific competition is also assumed to depend on an average population density. It is shown that the resulting aggregation may lead to the co-existence of populations one of which would otherwise be excluded by the other. This finding is discussed with regard to the Competitive Exclusion Principle.