Antipredatory vigilance usually decreases in groups. The generally accepted "collective detection" explanation implies that because there are more eyes to scan the surroundings for predators, individuals in a group can lower their personal investment in vigilance without increasing their predation risk. The role of other factors, such as numerical risk dilution caused by the mere presence of companions, has been neglected. In a model, we explore a dilution game when foragers in groups have access to protective cover. We show that foragers can take advantage of risk dilution and that this leads to changes in vigilance with group size without the need to invoke collective detection. We identify a cost to maintaining high levels of vigilance as less vigilant foragers gather food faster and so depart the group sooner (to reach cover) leaving more vulnerable stragglers behind. In groups, there is a scramble to reach safe sites that can induce a reduction in vigilance levels. Such a mechanism operates less forcefully in large groups because individuals in these groups are less vulnerable to the departure of an individual. We also demonstrate that individuals should adopt lower levels of vigilance, to reach safe sites sooner, when predator evasion is compromised or when the rate of food intake is high. The model provides new insights into the mechanisms underlying changes in vigilance with group size in animals.
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