Human stature in the Near East and Europe ca. 10,000–1000 BC: its spatiotemporal development in a Bayesian errors-in-variables model

We generated genome-wide data from 69 Europeans who lived between 8,000-3,000 years ago by enriching ancient DNA libraries for a target set of almost 400,000 polymorphisms. Enrichment of these positions decreases the sequencing required for genome-wide ancient DNA analysis by a median of around 250-fold, allowing us to study an order of magnitude more individuals than previous studies and to obtain new insights about the past. We show that the populations of Western and Far Eastern Europe followed opposite trajectories between 8,000-5,000 years ago. At the beginning of the Neolithic period in Europe, ∼8,000-7,000 years ago, closely related groups of early farmers appeared in Germany, Hungary and Spain, different from indigenous hunter-gatherers, whereas Russia was inhabited by a distinctive population of hunter-gatherers with high affinity to a ∼24,000-year-old Siberian. By ∼6,000-5,000 years ago, farmers throughout much of Europe had more hunter-gatherer ancestry than their predecessors, but in Russia, the Yamnaya steppe herders of this time were descended not only from the preceding eastern European hunter-gatherers, but also from a population of Near Eastern ancestry. Western and Eastern Europe came into contact ∼4,500 years ago, as the Late Neolithic Corded Ware people from Germany traced ∼75% of their ancestry to the Yamnaya, documenting a massive migration into the heartland of Europe from its eastern periphery. This steppe ancestry persisted in all sampled central Europeans until at least ∼3,000 years ago, and is ubiquitous in present-day Europeans. These results provide support for a steppe origin of at least some of the Indo-European languages of Europe. Show more

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. Show more

Many investigators use the reduced major axis (RMA) instead of ordinary least squares (OLS) to define a line of best fit for a bivariate relationship when the variable represented on the X-axis is measured with error. OLS frequently is described as requiring the assumption that X is measured without error while RMA incorporates an assumption that there is error in X. Although an RMA fit actually involves a very specific pattern of error variance, investigators have prioritized the presence versus the absence of error rather than the pattern of error in selecting between the two methods. Another difference between RMA and OLS is that RMA is symmetric, meaning that a single line defines the bivariate relationship, regardless of which variable is X and which is Y, while OLS is asymmetric, so that the slope and resulting interpretation of the data are changed when the variables assigned to X and Y are reversed. The concept of error is reviewed and expanded from previous discussions, and it is argued that the symmetry-asymmetry issue should be the criterion by which investigators choose between RMA and OLS. This is a biological question about the relationship between variables. It is determined by the investigator, not dictated by the pattern of error in the data. If X is measured with error but OLS should be used because the biological question is asymmetric, there are several methods available for adjusting the OLS slope to reflect the bias due to error. RMA is being used in many analyses for which OLS would be more appropriate. Show more