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

Abstract

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 nonhuman 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.

Why do not all workers work? Colony size and workload during emigrations in the ant Temnothorax albipennis

“…Workers in smaller colonies have sometimes been predicted to work harder (Houston et al 1988;Franks and Partridge 1993), whereas another study predicts higher workload in larger colonies (Schmid-Hempel 1990). Empirical support seems equivocal, with some support for higher individual effort in smaller (Fewell et al 1991;London and Jeanne 2003) or larger colonies (Schmid-Hempel 1990;Herbers and Choiniere 1996;Plowes and Adams 2005), and some studies finding no clear effect (Wolf and Schmid-Hempel 1990;Beekman 2004). What is the effect of colony size on individual workload, and are larger colonies likely to have a more skewed workload distribution, creating some highly active and many inactive workers?…”

Fight tactics in wood ants: individuals in smaller groups fight harder but die faster

“…[3,21]). By contrast, in the field group size can vary during the course of an agonistic encounter, owing to the process of recruitment (e.g.…”

“…After 24 h had elapsed since the start of the contests, the number of dead and surviving individuals in each group was counted [21]. Groups as a whole were then weighed to the nearest 0.0001 g. The mean body mass of individuals in each group was then calculated as a measure of average individual RHP, a measure that has previously been found to influence group contest outcome in F. rufa [3].…”

Fight the power: Lanchester's laws of combat in human evolution

“…These "laws" are mathematical equations that model the dynamics of conflict and its outcomes, and were originally developed with modern human warfare in mind. Although they have long been used in military operational research (for reviews, see MacKay, 2006;Wrigge, Fransen, & Wigg, 1995), they have only recently been applied to explain variation in the patterns of conflict in animals such as ants, birds, lions, and chimpanzees (Franks & Partridge, 1993;Mosser & Packer, 2009;Plowes & Adams, 2005;Shelley, Tanaka, Ratnathicam, & Blumstein, 2004;Whitehouse & Jaffe, 1996), including manipulation experiments showing variation in fighting behavior as parameters were changed (McGlynn, 2000;Wilson, Britton, & Franks, 2002).…”