Another advantage of large social groups is that they are attacked less often by predators.
that the main reason for the development of large groups of primates is the risk of ending up as prey. This risk of becoming a victim has even contributed directly to the selection of large brains, as it has been shown in many instances that predators attack members of species with small brains with a disproportionate frequency, relative to the frequency in their respective habitats. (p.250)
Dunbar compared the neocortex volume of monkeys and great apes with the sizes of the respective groups and determined the correlation discussed above. Applied to humans, Dunbar comes with a group size for humans of 150 individuals (the Dunbar Number).
He finds this number in many forms of human organisation: in the average size of hunting and gathering clans, in the size of European villages before the industrial revolution, in the size of personal networks, etc.
Obviously, the relationship between brain and social complexity in humans is similar to that of the great apes.
To summarise, with Dunbar: A comparatively large brain can be seen in mammals that are not primates, and in birds, where species live monogamously (with pair bonding) and where fathers often contribute to the care of the young.
In primates, brain size correlates with the size of the social group, which is related to the complexity of the social structure in primates.
The larger human brain and its greater social complexity fit seamlessly into the image offered by primates and in particular the great apes.