But the only theory that explains why animals in general have particular brain sizes is the one that maps brain size onto social group size. Robin Dunbar19 has demonstrated that within a given group of vertebrate species—primates, carnivores, ungulates, birds, reptiles, or fish—the logarithm of the brain size is almost perfectly proportional to the logarithm of the social group size. In other words, all over the animal kingdom, brains grow to manage larger and larger groups. Social animals are smart animals.