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

Electronic supplementary material is available online at https://dx.doi.org/10.6084/m9.figshare.c.4015705.Mammal social group size represents a trade-off between the costs and benefits of sociality [1] subject to a limit set by habitat productivity [2]. For most birds and mammals, one of the major benefits of living in groups is protection from predators [3–7], with the benefits typically increasing with group size. The costs arise from a combination of competition for access to food [2,8] and the social stresses created by living in close proximity [9–13]. These costs are invariably reflected in female fertility, such that fertility correlates negatively with group size across mammals [9,14] (see the electronic supplementary material). The difficulty for those mammalian taxa that live in bonded social groups [15] (as opposed to more casual aggregations) is that there are structural constraints on a group’s ability to shed members when the group becomes too large; instead, the group has to continue growing until it is large enough to fission. Rather than maintaining a steady state through ‘trickle emigration’ (individual animals emigrating on their own), groups will oscillate in size across a range set by the minimum acceptable group size [2]. We here explore how fertility and predation risk intersect to determine group size across habitats in an intensely social primate, baboons (genus Papio). We first use cluster analysis to ask whether the distribution of group sizes is unimodal or multi-modal. A unimodal distribution would suggest that groups are randomly distributed around a taxon-typical mean, whereas a multi-modal distribution, especially if those modes are fractally related, would suggest a regular pattern of fission. We then ask whether female fertility varies systematically with group size and, if so, whether this might explain the distribution of group sizes.European Research Council Advanced Investigator grant (no. 295663) to R.I.M.D