The larger the brain, more precisely: the neocortex (historically the youngest part of the cerebral cortex) in a primate species,

the larger the group in which this primate species can live. That implies that the size of the brain depends on the number of social contacts that individuals of this species manage. Dunbar continues:

Furthermore, additional analyses have shown that a number of behavioural patterns that are particularly associated with the social complexity of primates are also correlated with the relative size of the neocortex.

These include the size of the grooming clique (grooming: mutual body and fur care), the use of alternative mating strategies in males, the use of coalitions and alliances, manoeuvring for tactical deception, and the quality of social play. (pp. 247s)