An adaptive dynamic model of a vigilance game among group foragers

In group foraging animals, vigilance tends to decrease as group size increases. A forager in a group receives a vigilance benefit not only when it is being vigilant itself but also when a group mate is being vigilant. The many eyes hypothesis supposes that individuals exhibit lower vigilance in larger groups because of this. However, changes in safety resulting from the vigilance benefit conferred by group mates can change the decision to join or leave a group so as vigilance changes because of changes in group size, group size may also change in response to changes in vigilance. Additionally, individuals may have poor information about the vigilance strategies of their neighbors. We present a game theoretical model of vigilance that incorporates dynamic group sizes and does not require behavioral monitoring of the vigilance strategies of others. For systems at equilibrium, maximum vigilance decreases with increased group size. Furthermore, by varying intraspecific competition we show an inverse relationship between group size and vigilance. Thus, we provide a mechanism in support of the many eyes hypothesis from an evolutionary game theory perspective and conclude that variation in intraspecific competition and its effect on group size may be responsible for the relationship.