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Sociality is primarily a coordination problem. However, the social (or communication) complexity hypothesis suggests that the kinds of information that can be acquired and processed may limit the size and/or complexity of social groups that a species can maintain. We use an agent-based model to test the hypothesis that the complexity of information processed influences the computational demands involved. We show that successive increases in the kinds of information processed allow organisms to break through the glass ceilings that otherwise limit the size of social groups: larger groups can only be achieved at the cost of more sophisticated kinds of information processing that are disadvantageous when optimal group size is small. These results simultaneously support both the social brain and the social complexity hypotheses.

In this paper we present a new approach to modelling group coordination, based on dyadic synchronisation in a non-panmictic, structured network (a problem that applies widely to all species that live in medium to large groups). Using this approach, we present three models with three new theoretical results. (1) Multi-layered networks are optimal for groups that face costs associated with maintaining relationships among the members, combined with costs associated with information flows. (2) The presence of a social hierarchy can be an adaptive feature of the community: the steeper the optimal social hierarchy is, the fewer relationships group members need to have. (3) Falling communication costs lead to a less steep optimal social hierarchy in communities in which socially useful information is evenly distributed, but to an even steeper social hierarchy in groups in which socially useful information is uneven. Thus we show how, when communication is costly, cooperation can give rise to communities that are socially highly structured.