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Gray and Atkinson analysed 87 languages from Irish to Afghan.
The conclusion will be controversial, as there is no consensus on where Indo-European languages came from.
Some linguists believe that Kurgan horsemen carried them out of central Asia 6,000 years ago.
Words are better understood than grammar as a guide to language history; the same sentence structure can arise independently in different tongues.
The resulting tree matches many existing ideas about language development.
The work was funded by the Howard Hughes Medical Institute. A family tree of Indo-European languages suggests they began to spread and split about 9,000 years ago.