Network scaling reveals consistent fractal pattern in hierarchical mammalian societies

Recent studies have demonstrated that human societies are hierarchically structured with a consistent scaling ratio across successive layers of the social network; each layer of the network is between three and four times the size of the preceding (smaller) grouping level. Here we show that similar relationships hold for four mammalian taxa living in multi-level social systems. For elephant (Loxodonta africana), gelada (Theropithecus gelada) and hamadryas (Papio hamadryas hamadryas) baboon, successive layers of social organization have a scaling ratio of almost exactly 3, indicating that such branching ratios may be a consistent feature of all hierarchically structured societies. Interestingly, the scaling ratio for orca (Orcinus orca) was 3.8, which might mean that aquatic environments place different constraints on the organization of social hierarchies. However, circumstantial evidence from a range of other species suggests that scaling ratios close to 3 may apply widely, even in species where hierarchical social structures have not traditionally been identified. These results identify the origin of the hierarchical, fractal-like organization of mammalian social systems as a fundamental question.