Cannibalism in clumped populations

A simple model for the introduction of a cannibalistic mutant into a noncannibalistic population (or vice versa) is developed for the case where the offspring of an adult are clumped. It is assumed that there is no difference between the cannibals and noncannibals except for eating habits. Conditions on the parameters specifying the population are derived such that noncannibalism is favored over cannibalism when these conditions are satisfied. Specifically, it is shown that noncannibalism is favored in a diffuse, highly clumped population if the probability of encountering one cannibal after another is greater than twice the probability of encountering a cannibal after encountering a noncannibal.