Studies of DNA from ancient samples provide a valuable opportunity to gain insight into past evolutionary and demographic processes. Bayesian phylogenetic methods can estimate evolutionary rates and timescales from ancient DNA sequences, with the ages of the samples acting as calibrations for the molecular clock. Sample ages are often estimated using radiocarbon dating, but the associated measurement error is rarely taken into account. In addition, the total uncertainty quantified by converting radiocarbon dates to calendar dates is typically ignored. Here, we present a tool for incorporating both of these sources of uncertainty into Bayesian phylogenetic analyses of ancient DNA. This empirical calibrated radiocarbon sampler (ECRS) integrates the age uncertainty for each ancient sequence over the calibrated probability density function estimated for its radiocarbon date and associated error. We use the ECRS to analyse three ancient DNA data sets. Accounting for radiocarbon-dating and calibration error appeared to have little impact on estimates of evolutionary rates and related parameters for these data sets. However, analyses of other data sets, particularly those with few or only very old radiocarbon dates, might be more sensitive to using artificially precise sample ages and should benefit from use of the ECRS.

The maritime expansion of Scandinavian populations during the Viking Age (about AD 750-1050) was a far-flung transformation in world history^1,2. Here we sequenced the genomes of 442 humans from archaeological sites across Europe and Greenland (to a median depth of about 1×) to understand the global influence of this expansion. We find the Viking period involved gene flow into Scandinavia from the south and east. We observe genetic structure within Scandinavia, with diversity hotspots in the south and restricted gene flow within Scandinavia. We find evidence for a major influx of Danish ancestry into England; a Swedish influx into the Baltic; and Norwegian influx into Ireland, Iceland and Greenland. Additionally, we see substantial ancestry from elsewhere in Europe entering Scandinavia during the Viking Age. Our ancient DNA analysis also revealed that a Viking expedition included close family members. By comparing with modern populations, we find that pigmentation-associated loci have undergone strong population differentiation during the past millennium, and trace positively selected loci-including the lactase-persistence allele of LCT and alleles of ANKA that are associated with the immune response-in detail. We conclude that the Viking diaspora was characterized by substantial transregional engagement: distinct populations influenced the genomic makeup of different regions of Europe, and Scandinavia experienced increased contact with the rest of the continent.