title: The social brain: scale-invariant layering of Erdős-Rényi networks in small-scale human societies.
abstract: The cognitive ability to form social links that can bind individuals together into large cooperative groups for safety and resource sharing was a key development in human evolutionary and social history. The 'social brain hypothesis' argues that the size of these social groups is based on a neurologically constrained capacity for maintaining long-term stable relationships. No model to date has been able to combine a specific socio-cognitive mechanism with the discrete scale invariance observed in ethnographic studies. We show that these properties result in nested layers of self-organizing Erdős-Rényi networks formed by each individual's ability to maintain only a small number of social links. Each set of links plays a specific role in the formation of different social groups. The scale invariance in our model is distinct from previous 'scale-free networks' studied using much larger social groups; here, the scale invariance is in the relationship between group sizes, rather than in the link degree distribution. We also compare our model with a dominance-based hierarchy and conclude that humans were probably egalitarian in hunter-gatherer-like societies, maintaining an average maximum of four or five social links connecting all members in a largest social network of around 132 people.
authors.affiliation: Complex Systems Research Group, Faculty of Engineering and IT, The University of Sydney, Sydney, Australia michael.harre@sydney.edu.au.
authors.forename: Michael S
authors.identifier: 0000-0003-2199-2515
authors.initials: MS
authors.lastname: Harré
authors.affiliation: Complex Systems Research Group, Faculty of Engineering and IT, The University of Sydney, Sydney, Australia.
authors.forename: Mikhail
authors.initials: M
authors.lastname: Prokopenko
mesh_terms: D001921:Brain; D005260:Female; D006801:Humans; D008297:Male; D008962:Models, Theoretical; D012944:Social Support
keywords: Erdős–Rényi networks; discrete scale invariance; social brain hypothesis; social networks