Farming was first introduced to Europe in the mid-seventh millennium bc, and was associated with migrants from Anatolia who settled in the southeast before spreading throughout Europe. Here, to understand the dynamics of this process, we analysed genome-wide ancient DNA data from 225 individuals who lived in southeastern Europe and surrounding regions between 12000 and 500 bc. We document a west–east cline of ancestry in indigenous hunter-gatherers and, in eastern Europe, the early stages in the formation of Bronze Age steppe ancestry. We show that the first farmers of northern and western Europe dispersed through southeastern Europe with limited hunter-gatherer admixture, but that some early groups in the southeast mixed extensively with hunter-gatherers without the sex-biased admixture that prevailed later in the north and west. We also show that southeastern Europe continued to be a nexus between east and west after the arrival of farmers, with intermittent genetic contact with steppe populations occurring up to 2,000 years earlier than the migrations from the steppe that ultimately replaced much of the population of northern Europe.

Genetic predictions of height differ among human populations and these differences have been interpreted as evidence of polygenic adaptation. These differences were first detected using SNPs genome-wide significantly associated with height, and shown to grow stronger when large numbers of sub-significant SNPs were included, leading to excitement about the prospect of analyzing large fractions of the genome to detect polygenic adaptation for multiple traits. Previous studies of height have been based on SNP effect size measurements in the GIANT Consortium meta-analysis. Here we repeat the analyses in the UK Biobank, a much more homogeneously designed study. We show that polygenic adaptation signals based on large numbers of SNPs below genome-wide significance are extremely sensitive to biases due to uncorrected population stratification. More generally, our results imply that typical constructions of polygenic scores are sensitive to population stratification and that population-level differences should be interpreted with caution.Editorial note: This article has been through an editorial process in which the authors decide how to respond to the issues raised during peer review. The Reviewing Editor's assessment is that all the issues have been addressed (see decision letter).

Ancestry connects genetics and society in fundamental ways. For many people it has cultural, religious or even political significance, and can play a key role in shaping personal and public identities. People's desire to discover their own ancestry drives the multibillion-dollar genealogy industry, which has grown rapidly in the era of consumer genomics. Companies such as 23andMe and Ancestry now claim tens of millions of customers worldwide. In parallel, our scientific understanding of the human past is being transformed by studies of ancient and modern genetic data, which allow us to track changes in ancestry over space and time. Sophisticated methods have been developed to infer and visualise these relationships. Thus, it seems that both scientists and the wider public are learning more and more about ancestry, and there is an optimistic sense that genetic data provide an exhaustive repository of ancestral information. However, although frequently discussed, ancestry itself is rarely defined. We argue that this reflects widespread underlying confusion about what it means in different contexts and what genetic data can really tell us. This leads to miscommunication between researchers in different fields, and leaves customers open to spurious claims about consumer genomics products and overinterpretation of individual results. In wider usage, the terms ancestry and ancestors often indicate a general connection to people or things in the past. But in a genetic context they have a more specific meaning: your ancestors are the individuals from whom you are biologically descended and ancestry is information about them and their genetic relationship to you. Even here however, confusion arises from the way that ancestry is presented and discussed. Rather than emphasising its complex structure, results are often simplified in terms of discrete categories. While convenient and sometimes useful, ultimately this is misleading about the nature of ancestry. These labels can also impose contemporary political or cultural divisions which may be misrepresentative of ancestral relationships. Another source of confusion is that three distinct concepts-genealogical ancestry, genetic ancestry, and genetic similarity-are frequently conflated. We discuss them in turn, but note that only the first two are explicitly forms of ancestry, and that genetic data are surprisingly uninformative about either of them. Consequently, most statements about ancestry are really statements about genetic similarity, which has a complex relationship with ancestry, and can only be related to it by making assumptions about human demography whose validity is uncertain and difficult to test. Genealogical ancestry probably reflects the most common and intuitive understanding of the term ancestry. Consider your parents, grandparents, or even great-grandparents. You likely have a sense of these people as individuals, even if you have never met them. If one of them belonged to a particular group X, you might say that you have some "X" ancestry. You might even be able to claim ancestry in this way from more distant ancestors, based on

Variation at the FADS1/FADS2 gene cluster is functionally associated with differences in lipid metabolism and is often hypothesized to reflect adaptation to an agricultural diet. Here, we test the evidence for this relationship using both modern and ancient DNA data. We show that almost all the inhabitants of Europe carried the ancestral allele until the derived allele was introduced ∼8,500 years ago by Early Neolithic farming populations. However, we also show that it was not under strong selection in these populations. We find that this allele, and other proposed agricultural adaptations at LCT/MCM6 and SLC22A4, were not strongly selected until much later, perhaps as late as the Bronze Age. Similarly, increased copy number variation at the salivary amylase gene AMY1 is not linked to the development of agriculture although, in this case, the putative adaptation precedes the agricultural transition. Our analysis shows that selection at the FADS locus was not tightly linked to the initial introduction of agriculture and the Neolithic transition. Further, it suggests that the strongest signals of recent human adaptation in Europe did not coincide with the Neolithic transition but with more recent changes in environment, diet, or efficiency of selection due to increases in effective population size.

Population stratification continues to bias the results of genome-wide association studies (GWAS). When these results are used to construct polygenic scores, even subtle biases can cumulatively lead to large errors. To study the effect of residual stratification, we simulated GWAS under realistic models of demographic history. We show that when population structure is recent, it cannot be corrected using principal components of common variants because they are uninformative about recent history. Consequently, polygenic scores are biased in that they recapitulate environmental structure. Principal components calculated from rare variants or identity-by-descent segments can correct this stratification for some types of environmental effects. While family-based studies are immune to stratification, the hybrid approach of ascertaining variants in GWAS but reestimating effect sizes in siblings reduces but does not eliminate stratification. We show that the effect of population stratification depends not only on allele frequencies and environmental structure but also on demographic history.