The causes of biological gigantism have received much attention, but only f
or individual organisms. What selection pressures might favour the evolutio
n of gigantic societies? Here we consider the largest single-queen insect s
ocieties, those of the Old World army ant Dorylus, single colonies of which
can have 20 million workers. We propose that colony gigantism in Dorylus a
rises as a result of an arms race and test this prediction by developing a
size-structured mathematical model. We use this model for exploring and pot
entially explaining differences in colony size, colony aggression and colon
y propagation strategies in populations of New World army ants Eciton and O
ld World army ants Dorylus. The model shows that, by determining evolutiona
rily stable strategies (ESSs), differences in the trophic levels at which t
hese army ants live feed forwards into differences in their densities and c
ollision rates and. hence, into different strategies of growth, aggression
and propagation. The model predicts large colony size and the occurrence, p
ropagation strategy of battles and a colony-propagation strategy involving
highly asymmetrical divisions in Dorylus and that Eciton colonies should be
smaller, non-combative and exhibit equitable binary fission. These ESSs ar
e in excellent agreement with field observations and demonstrate that garga
ntuan societies can arise through arms races.