Consistent waves of collective vigilance in groups using public information about predation risk

Consistent waves of collective vigilance in prey groups using public information about predation risk. Antipredator vigilance models have long assumed that individuals in groups monitor threats independently from one another. This assumption has been challenged recently, both theoretically and empirically. In particular, recent models predict that individuals should pay attention to the vigilance state of their neighbors and become increasingly vigilant when the proportion of vigilant neighbors is higher. Such copying can lead to temporal waves of collective vigilance in groups rather than random fluctuations. Here, we investigated the robustness of these predicted waves under varying ecological situations. Using an individual-based modeling approach, we show that such waves are predicted to occur in small and large groups, when copying only involves the nearest neighbor or the radius of copying is small or large or when the shape of the group is square or rectangular. However, when the influence of neighbors was restricted (e.g., by reducing the radius of influence, by only considering the nearest neighbor, or in more elongated groups), waves involved a smaller proportion of the group. In general, collective patterns were more organized when the copying tendency was strong and the frequency at which individuals can switch state was not too high. Our results show that collective waves of vigilance are a robust phenomenon emerging from the individual social behavior of group members, thus encouraging empirical scrutiny of the connection between individual and group vigilance.