According to an article I came across today on the BBC, a study by researchers in New Zealand suggests that Indo-European languages originated in Anatolia about 8-9,500 years ago, and not in the Central Asian steppes about 5-6,000 years ago, as many believe.
The researchers used methods developed to study virus epidemics to work out the relationships between Indo-European languages and where they came from, and they concluded that the spread of the languages coincided with the expansion of farming 8-9,500 years ago. There aren’t many details of their method in the article, but it does mention that they compared vocabulary across 100 modern and ancient languages using phylogenetic analysis.
More details are available in Science (if you have access).
