Bell Beaker pottery spread across western and central Europe beginning around 2750 BCE before disappearing between 2200–1800 BCE. The forces propelling its expansion are a matter of long-standing debate, with support for both cultural diffusion and migration. We present new genome-wide data from 400 Neolithic, Copper Age and Bronze Age Europeans, including 226 Beaker-associated individuals. We detected limited genetic affinity between Iberian and central European Beaker-associated individuals, and thus exclude migration as a significant mechanism of spread between these two regions. However, migration played a key role in the further dissemination of the Beaker Complex, a phenomenon we document most clearly in Britain, where the spread of the Beaker Complex introduced high levels of Steppe-related ancestry and was associated with a replacement of ~90% of Britain’s gene pool within a few hundred years, continuing the east-to-west expansion that had brought Steppe-related ancestry into central and northern Europe 400 years earlier.

Edge adjacency relationships in molecular graphs have been used to define a new topographic index. The novel index is calculated considering molecules as weighted graphs, where the elements of edges set are substituted by the bond orders between connected atoms in the molecule. Good linear correlations were found between molar refractivity of alkanes and the proposed (F) index. The applicability of the novel index in QSAR studies was evaluated by using a data of pharmacokinetic properties for a series of amphetamine derivatives. The results obtained were statistical and pharmacologically significant. Special interest is dedicated to discrimination of isomers, including heteroatom's differentiation and conformational isomerism.

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This corrects the article DOI: 10.1038/nature25738.