Commenter Nehemiah writes:

It is implausible that the Bushmen populations (which once occupied a much larger range than today) lived in total isolation from non-Bushmen populations. Presumably the mutation or mutations that facilitated the emergence of grammar appeared or came together in one population first. This development was so valuable that the relevant genes had a high chance of being preserved and spreading to fixation if even a small amount of interbreeding occurred with a neighboring population. Thus, even if Bushmen (and Pygmies, BTW) split off between 200kya and 300kya, that would not have prevented the spread of an especially valuable mutation from any one human population to all the rest. I argue that a limited vocabulary already existed in all sapiens populations (and probably some non-Sapiens populations as well), but the appearance of the “grammar gene(s)” made vocabulary immensely more useful so that it was now worthwhile to coin many more words, and the more intelligent band members could master the use and comprehension of this expanding vocabulary much better than the less intelligent. The grammar mutation should have spread relatively rapidly from any human population to all the rest. If we backcrossed with Neanderthals and Denisovans, I cannot imagine that there was not also gene flow to (and from) Bushmen (and Pygmies) as well. Further, I know of no reason to presume that grammar did not first emerge in Bushmen and spread to non-Bushmen rather than vice versa. We simply do not know.

Neanderthals possessed our FOXP2 gene and a hyoid bone that facilitate speech, but the larynx was still in a more anterior position, as in an infant of our species, which restricted the number of vowel sounds that could be formed, and therefore the number of words that could be created. I argue that if Neanderthal has possessed grammatical language at an earlier date, there would have been evolutionary selection for a larynx positioned so that a larger number of words could be formed. Thus, I also argue that grammar evolved sometime after Neanderthals split from the lineage that led to sapiens, and our sudden and rapid colonization of the world in the last 70ky suggests that the grammatically structured use of vocabular evolved shortly before we exploded suddenly over the world’s surface, since the appearance of grammatical language is the most likely advantage that allowed us to expand rapidly and to quickly displace our rivals who were longer established and better adapted to the local environment.

The notion that a small number of genetic mutation(s) gave rise to behavioral modernity and the upper Paleothic revolution is associated with paleontologist Richard Klein:

But geneticist David Reich is having none of it:

Expanding our analysis to the whole genome, we could not find any location–apart from mitochondrial DNA and the Y chromosome, where all people living today share a common ancestor less than 320,000 years ago. This is a far longer time scale than the one required by Klein’s hypothesis. If Klein was right, it would be expected that there would be places in the genome, beyond mitochondrial DNA and the Y chromosome, where almost everyone shares a common ancestor within the last hundred thousand years. But these do not in fact seem to exist.

Our results do not completely rule out the hypothesis of a single critical genetic change. There is a small fraction of the genome that contains complicated sequences that are difficult to study and that was not included in our survey. But the key change, if it exists, is running out of places to hide….

From Who are we and how we got here by David Reich, pg 18

But while Reich largely rejects the idea of a single (or small number) of genetic mutations giving rise to behavior modernity, he seems open to the possibility that “…coordinated natural selection on combinations of many mutations simultaneously–did enable new cognitive capacities…”

See also: The importance of brain shape