Lanchester's attrition models and fights among social animals

Lanchester's models of attrition during warfare have served as the basis for several predictions about conflicts between groups of animals. These models and their extensions describe rates of mortality during battles as functions of the number and fighting abilities of individuals in each group, allowing analysis of the determinants of group strength and of the cumulative numbers of casualties. We propose modifications to Lanchester's models to improve their applicability to social animals. In particular, we suggest that the per-capita mortality rate of a group is a decreasing function of the fighting abilities of its members, that the mortality rate is an increasing function of the number of individuals in both groups, and that there will often be diminishing returns for increasing numerical advantage. Models incorporating these assumptions predict that the ability of social animals to win fights depends less on group size and more on individual prowess than under Lanchester's original models. We discuss how data on casualties can be used to distinguish among alternative attrition models.