Trade-off between fertility and predation risk drives a geometric sequence in the pattern of group sizes in baboons

Group-living offers both benefits (protection against predators, access to resources) and costs (increased ecological competition, the impact of group size on fertility). Here, we use cluster analysis to detect natural patternings in a comprehensive sample of baboon groups, and identify a geometric sequence with peaks at approximately 20, 40, 80 and 160. We suggest (i) that these form a set of demographic oscillators that set habitat-specific limits to group size and (ii) that the oscillator arises from a trade-off between female fertility and predation risk.