Do Lanchester's laws of combat describe competition in ants?

Lanchester's laws are mathematical models, originally designed to model military combat, that describe battle outcomes based on the sizes of armies and the potencies of individual fighting units. The "square law" describes a scenario in which small-sized competitors may use a numerical advantage to overcome large-sized competitors in simultaneous combat. The "linear law" describes how a competitor with large-sized fighting units may use one-on-one combat to favor victory when outnumbered. Lanchester's laws have been suggested as an important regulator of interspecific competition in social insects, but without experimental support. In this study, experimental platforms were designed to invoke the conditions of both Lanchester's laws in a community of ants in lowland tropical wet forest in Costa Rica. I measured behavioral dominance at the food platforms in two separate manners: an ordinal ranking of the number of workers present, and the monopoly of the food platforms. At the platform invoking simultaneous combat, satisfying the square law, small-sized ants were more behaviorally dominant by numerical superiority. At the platform invoking one-on-one combat, satisfying the linear law, larger ants were more behaviorally dominant by monopoly. These results suggest that Lanchester's laws explain, in part, the outcome of interspecific competition in ants.