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Background  The spread of agriculture into Europe and the ancestry of the first European farmers have been subjects of debate and controversy among geneticists, archaeologists, linguists and anthropologists. Debates have centred on the extent to which the transition was associated with the active migration of people as opposed to the diffusion of cultural practices. Recent studies have shown that patterns of human cranial shape variation can be employed as a reliable proxy for the neutral genetic relationships of human populations.    Methodology/Principal Findings  Here, we employ measurements of Mesolithic (hunter-gatherers) and Neolithic (farmers) crania from Southwest Asia and Europe to test several alternative population dispersal and hunter-farmer gene-flow models. We base our alternative hypothetical models on a null evolutionary model of isolation-by-geographic and temporal distance. Partial Mantel tests were used to assess the congruence between craniometric distance and each of the geographic model matrices, while controlling for temporal distance. Our results demonstrate that the craniometric data fit a model of continuous dispersal of people (and their genes) from Southwest Asia to Europe significantly better than a null model of cultural diffusion.    Conclusions/Significance  Therefore, this study does not support the assertion that farming in Europe solely involved the adoption of technologies and ideas from Southwest Asia by indigenous Mesolithic hunter-gatherers. Moreover, the results highlight the utility of craniometric data for assessing patterns of past population dispersal and gene flow.

Craniometric Data Supports Demic Diffusion Model for the Spread of Agriculture into Europe