Inclusive Fitness and Group Size with a Reconsideration of Group Sizes in Lions and Wolves

Here I present a simple model that expresses inclusive fitness as a function of group size when social groups contain relatives and individual fitness varies with group size. A general result of the model is that if individual fitness reaches a maximum at some group size, then inclusive fitness (of which individual fitness is a component; Hamilton 1964) will always peak at a larger group size (at which individual fitness is no longer maximized). On the premise that selection favors phenotypes that maximize inclusive fitness rather than individual fitness when the two differ with respect to the phenotypic variable of concern (Hamilton 1964; Wilson 1975), the model suggests we should expect many gregarious animals to live in groups that do not maximize individual foraging efficiency, minimize individual risks of predation, etc. The groups should be larger. An important implication of the model is that social grouping may evolve in spite of disadvantages to individuals because members of the group gain inclusive fitness by adding relatives that would not otherwise be present in the population. Caraco and Wolf (1975) and Nudds (1978) have examined the relationship of individual hunting efficiency to group sizes of lions and wolves, respectively. For both lions and wolves, the group size often exceeds a size optimal for individual hunting efficiency, and when the group size per individual hunter is considered, as is proper (Jarman 1974, Appendix 2), the deviation becomes more striking. Although other plausible explanations for the deviation of observed group sizes from those that maximize individual foraging efficiency have been advanced, the model I present here may account for the deviation for both lions and wolves in a general manner.