Intelligence is a complex trait that involves many different genes interacting with each other and with the environment. If one gene changes, the immediate effect may be beneficial, but there will be side effects at other genes, and most of those side effects will likely be harmful. The bigger the effect at any one gene, the greater the likelihood of negative side effects elsewhere.
So evolution has proceeded through tinkering. A small effect here, a small effect there, but nothing that will rock the boat.
We must therefore pool data from many genes to understand the evolution of complex traits like intelligence. This is what Davide Piffer (2013) has done in a recent study. He began with seven genes (SNPs) whose different alleles are associated with differences in intellectual capacity, as measured by PISA or IQ tests. Then, for fifty human populations, he looked up the prevalences of the alleles that seem to increase intellectual capacity. Finally, for each population, he calculated their average prevalence at all seven genes.
The average prevalence was 39% among East Asians, 36% among Europeans, 32% among Amerindians, 24% among Melanesians and Papuan-New Guineans, and 16% among sub-Saharan Africans. The lowest scores were among San Bushmen (6%) and Mbuti Pygmies (5%).