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European agriculture originated in the Near East about 9,000 years ago. The Neolithic reached almost all areas suitable for agriculture by 5,000 yr BP (before present). The routes and times of the spread of agriculture through Europe are relatively well established, but not its manner of spreading. This could have been by cultural diffusion with few genetic consequences. By contrast, Ammerman and Cavalli-Sforza proposed that the spread of farming increased local population densities, causing demic expansion into new territory and diffusive gene flow between the neolithic farmers and mesolithic groups. We have now tested observed genetic patterns against expectations derived from the demic expansion hypothesis. We found significant partial correlations of genetic distances with a distance matrix especially designed to represent the spread of agriculture on that continent, when geographic distances are held constant. These findings support the hypothesis of Ammerman and Cavalli-Sforza and invite further investigation into Renfrew's hypothesis on the origin of the Indo-European languages.