A research team, lead by Wieland Huttner, found that genes for brain size were found only in humans. Quote:
"Through isolating subpopulations of human brain, they noticed the gene ARHGAP11B: it is only found in humans and in our closest relatives, the Neanderthals and Denisova-Humans, but not in chimpanzees...This gene manages to trigger brain stem cells to form a bigger pool of stem cell... We noticed that the gene ARHGAP11B is especially active in basal brain stem cells. These cells are really important for the expansion of the neocortex during evolution."
This is an intriguing discover, especially when considering that chimpanzees share approximately 99% of the genes humans have, and yet humans have this ARHGAP11B, and three times the brain size.
Further intrigue is found in the fact that the gene also works in mice, despite mice not naturally producing it.
As for the implications of differing brain sizes, that would require a different thread...