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The farmers themselves may have moved, or natives may have adopted words along with agricultural technology.
The conclusion will be controversial, as there is no consensus on where Indo-European languages came from.
Lahn offers an analogy: Medieval monks would copy manuscripts and each copy would inevitably contain errors — accidental mutations.
Years later, a ruler declares one of those copies the definitive manuscript, and a rush is on to make many copies of that version — so whatever changes from the original are in this presumed important copy become widely disseminated.
The differences between words, or DNA sequences, are a measure of how closely languages, or species, are related.
Gray and Atkinson analysed 87 languages from Irish to Afghan.
Scientists attempt to date genetic changes by tracing back to such spread, using a statistical model that assumes genes have a certain mutation rate over time.
For the microcephalin gene, the variation arose about 37,000 years ago, about the time period when art, music and tool-making were emerging, Lahn said.
"The genetic evolution of humans in the very recent past might in some ways be linked to the cultural evolution," he said.
Francis Collins, director of the National Human Genome Research Institute.
Aside from not knowing what the gene variants actually do, no one knows how precise the model Lahn used to date them is, Collins added.
That the defining feature of humans — our large brains — continued to evolve as recently as 5,800 years ago, and may be doing so today, promises to surprise the average person, if not biologists.
"We, including scientists, have considered ourselves as sort of the pinnacle of evolution," noted lead researcher Bruce Lahn, a University of Chicago geneticist whose studies appear in Friday's edition of the journal Science.