Ecological tradeoffs drive a power-law relationship between group size and population density in social foragers

Foraging animals have been documented forming groups in wide range of environments and taxa. Benefits of group foraging include reduced predation risk while costs include increased resource competition among group members. While the relative strengths of these factors are known to vary with density, it is unclear whether forager group sizes should also vary with density. Here, we model how the costs and benefits of group formation drive density dependence in group size when including the impacts of improved vigilance and increased intragroup competition. Our model predicts that forager group size will exhibit a one-third power-law relationship with their abundance when predator abundance is independent of prey abundance. We tested this prediction using empirical data of group-foraging birds and ungulates and found clear support for our theoretical predictions. Our results contribute to a growing body of work highlighting the importance of group formation in maintaining stability in predator and prey populations.