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Ancient DNA studies have established that European Neolithic populations were descended from Anatolian migrants who received a limited amount of admixture from resident hunter-gatherers. Many open questions remain, however, about the spatial and temporal dynamics of population interactions and admixture during the Neolithic period. Using the highest-resolution genome-wide ancient DNA data set assembled to date --- a total of 177 samples, 127 newly reported here, from the Neolithic and Chalcolithic of Hungary (6000-2900 BCE, n = 98), Germany (5500-3000 BCE, n = 42), and Spain (5500-2200 BCE, n = 37) --- we investigate the population dynamics of Neolithization across Europe. We find that genetic diversity was shaped predominantly by local processes, with varied sources and proportions of hunter-gatherer ancestry among the three regions and through time. Admixture between groups with different ancestry profiles was pervasive and resulted in observable population transformation across almost all cultural transitions. Our results shed new light on the ways that gene flow reshaped European populations throughout the Neolithic period and demonstrate the potential of time-series-based sampling and modeling approaches to elucidate multiple dimensions of historical population interactions.

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