The result, they announced in Thursday’s issue of the journal Science, is that “we found decisive support for an Anatolian origin over a steppe origin.” Both the timing and the root of the tree of Indo-European languages “fit with an agricultural expansion from Anatolia beginning 8,000 to 9,500 years ago,” they report.

But despite its advanced statistical methods, their study may not convince everyone.

The researchers started with a menu of vocabulary items that are known to be resistant to linguistic change, like pronouns, parts of the body and family relations, and compared them with the inferred ancestral word in proto-Indo-European. Words that have a clear line of descent from the same ancestral word are known as cognates. Thus “mother,” “mutter” (German), “mat’ ” (Russian), “madar” (Persian), “matka” (Polish) and “mater” (Latin) are all cognates derived from the proto-Indo-European word “mehter.”

Dr. Atkinson and his colleagues then scored each set of words on the vocabulary menu for the 103 languages. In languages where the word was a cognate, the researchers assigned it a score of 1; in those where the cognate had been replaced with an unrelated word, it was scored 0. Each language could thus be represented by a string of 1’s and 0’s, and the researchers could compute the most likely family tree showing the relationships among the 103 languages.

A computer was then supplied with known dates of language splits. Romanian and other Romance languages, for instance, started to diverge from Latin after A.D. 270, when Roman troops pulled back from the Roman province of Dacia. Applying those dates to a few branches in its tree, the computer was able to estimate dates for all the rest.

The computer was also given geographical information about the present range of each language and told to work out the likeliest pathways of distribution from an origin, given the probable family tree of descent. The calculation pointed to Anatolia, particularly a lozenge-shaped area in what is now southern Turkey, as the most plausible origin — a region that had also been proposed as the origin of Indo-European by the archaeologist Colin Renfrew, in 1987, because it was the source from which agriculture spread to Europe.