Coordination costs may counteract the positive effects of a larger group size in determining the winner of...

Collective defense of territories and resources is a key benefit of group living and is often modeled as a public goods game. Although larger animal groups have the potential to mobilize greater fighting power in between-group competition, this advantage may be constrained by coordination. Our review of quantitative studies shows that, independent of a population's average group size, larger groups usually win, with few exceptions. We examined one such case in vervet monkeys. As expected, group size was positively correlated with group spatial spread, and more dispersed groups were less likely to win encounters, implicating coordination problems. We then developed a mathematical model showing that, as coordination costs rise with group size due to spatial spread, they can cancel the usual "strength in numbers" advantage of larger groups in between-group conflicts. Our work highlights how between-group competition provides a natural setting for integrating ecological constraints into models of N-player cooperation.