Social complexity and the fractal structure of group size in primate social evolution

Compared to most other mammals and birds, anthropoid primates have unusually complex societies characterised by bonded social groups. Among primates, this effect is encapsulated in the social brain hypothesis: the robust correlation between various indices of social complexity (social group size, grooming clique size, tactical behaviour, coalition formation) and brain size. Hitherto, this has always been interpreted as a simple, unitary relationship. Using data for five different indices of brain volume from four independent brain databases, we show that the distribution of group size plotted against brain size is best described as a set of four distinct, very narrowly defined grades which are unrelated to phylogeny. The allocation of genera to these grades is highly consistent across the different data sets and brain indices. We show that these grades correspond to the progressive evolution of bonded social groups. In addition, we show, for those species that live in multilevel social systems, that the typical sizes of the different grouping levels in each case coincide with different grades. This suggests that the grades correspond to demographic attractors that are especially stable. Using five different cognitive indices, we show that the grades correlate with increasing social cognitive skills, suggesting that the cognitive demands of managing group cohesion increase progressively across grades. We argue that the grades themselves represent glass ceilings on animals' capacity to maintain social and spatial coherence during foraging and that, in order to evolve more highly bonded groups, species have to be able to invest in costly forms of cognition.