Ecological Interactions Drive a Power-Law Relationship Between Group Size and Population Density in Social Foragers

Past work has shown that group formation in foraging animals aids in resource acquisition and reduces the number of interactions with predators. However, group formation can also increase competition for resources among group members. Here, we model how the individual costs and benefits of group formation drive group size. Our model predicts that when competition for resources occurs within and between groups, forager group size will exhibit a one-third power-law relationship with population abundance. However, if groups form due to intragroup competition and predation, we predict either a one-half power-law relationship with population abundance or a constant group size depending on the coupling between predator and prey. Using empirical data on group foraging birds and ungulates, we found a scaling relationship consistent with the one-third power-law, suggesting that hierarchical competition drives the average group size. Our results support work highlighting the importance of density-dependent group formation in maintaining population stability.