An empirical test of Lanchester's square law: mortality during battles of the fire ant Solenopsis invicta.

Lanchester's models of attrition describe casualty rates during battles between groups as functions of the numbers of individuals and their fighting abilities. Originally developed to describe human warfare, Lanchester's square law has been hypothesized to apply broadly to social animals as well, with important consequences for their aggressive behaviour and social structure. According to the square law, the fighting ability of a group is proportional to the square of the number of individuals, but rises only linearly with fighting ability of individuals within the group. By analyzing mortality rates of fire ants (Solenopsis invicta) fighting in different numerical ratios, we provide the first quantitative test of Lanchester's model for a non-human animal. Casualty rates of fire ants were not consistent with the square law; instead, group fighting ability was an approximately linear function of group size. This implies that the relative numbers of casualties incurred by two fighting groups are not strongly affected by relative group sizes and that battles do not disproportionately favour group size over individual prowess.