Testing the predictions of Lanchester's laws of combat with a continously polymorphic ant species

Lanchester’s laws of combat (linear and square law) have become popular for predicting attrition rates in interactions between groups of social organisms. The linear law assumes individuals engage in a series of one on one duels and rate of attrition of combatants is determined by an individual’s fighting ability, such as body size. The square law assumes larger groups of individuals can concentrate attacks on members of the smaller group and predicts the larger a group becomes relative to its enemy, the fewer the casualties it will sustain, and thus more likely it is to “win" the contest. To test these predictions, we used a combination of lab and field experiments with the red imported fire ant, Solenopsis invicta. From the lab experiments we staged competitive interactions between colonies with equal biomass but differnent body sizes in open arenas and confined (tubing/tunnel) foraging arenas. Colonies with more, small workers show no significant effect of arena type or size of competitor on worker mortality. However, in colonies with fewer, large workers there was a significant effect of arena type, competitor, and their interaction on attrition. Larger bodied ants suffered greater losses in open arenas where smaller bodied ants attacked simultaneously (supporting the square law). In the field, we used above and below ground traps to examine the body size distribution of S. invicta foragers in open and closed (tunnel) environments. We found no difference in the number of foragers above versus below-ground. However, we did find more, larger workers below-ground (supporting the linear law). The results of both experiments support predictions of Lanchester’s laws and suggest the predictions of each law are context dependent.