Abstract
We consider the effect of a top predator on the stability of a system of competing prey species. In the first instance, this is done in detail for two prey species where the predators either behave in a completely random way, interfere with each other or switch to the more abundant prey at any time. The analysis is then extended to the case of n similar prey species, either competing equally or competing with their two nearest neighbours in exploiting a one-dimensional resource spectrum. It is found that predator switching can produce local stability when the prey species overlap completely and even when the competition coefficients are greater than one. This, however, is more difficult to attain for nearest neighbour competition. In either case switching is advantageous to the predators, since it allows them to coexist successfully with their prey over a wider range of conditions.
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