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Large radiocarbon datasets have been analysed statistically to identify, on the one hand, the dynamics and tempo of dispersal processes and, on the other, demographic change. This is particularly true for the spread of farming practices in Neolithic Europe. Here we combine the two approaches and apply them to a new, extensive dataset of 14,535 radiocarbon dates for the Mesolithic and Neolithic periods across the Near East and Europe. The results indicate three distinct demographic regimes: one observed in or around the centre of farming innovation and involving a boost in carrying capacity; a second appearing in regions where Mesolithic populations were well established; and a third corresponding to large-scale migrations into previously essentially unoccupied territories, where the travelling front is readily identified. This spatio-temporal patterning linking demographic change with dispersal dynamics, as displayed in the amplitude of the travelling front, correlates and predicts levels of genetic admixture among European early farmers.

Amplitude of travelling front as inferred from 14C predicts levels of genetic admixture among European early farmers