The genetic differences between the ancestral (post-Bell Beaker) Celtic population of Great Britain, the people of the Atlantic Coast of Europe, and the people of Denmark and Southwestern Scandinavia are subtle. So, it takes reasonable large, and reasonably high quality samples of modern and ancient DNA to distinguish them in the course of piecing together with genetic, historical, archaeological, and linguistic evidence to form a coherent narrative of the waves of migration that gave rise to the modern British people.
The linguistic evidence supported by historical accounts long ago made clear that the English language arrived in England as a result of Anglo-Saxon migration to and conquest of Great Britain, especially in Eastern England in the early Middle Ages. This account was supported by a major study with a very large sample of moderately high quality modern DNA evidence from Britain published in 2015.
But, due to the subtly of the regional differences in population genetics between the relevant regions and a paucity of ancient DNA from the thirty or more generations earlier when it happened, it was hard to determine with confidence from that data that the Anglo-Saxon migration to England shifted more than a modestly small percentage of population genetics of Eastern England.
In this case, the language shift from a Celtic substrate to Old English in England would have been largely a case of elite dominance driven language shift, not unlike what happened in Hungary, half a millennium later.
But a new study with more ancient DNA from the relevant time period corroborated by anthropological analysis of the grave contexts of ancient DNA specimen source remains with differing levels of DNA from different regional sources, allowing scholars to distinguish between the subtly different genetic populations with more confidence have shifted that narrative considerably.
Now, it appears that in parts of Eastern England as much as three-quarters of the population's genetic ancestry (including a very similar peak 75% of Y-DNA suggesting a gender balanced migration rather than a male dominated conquest of local populations) was Anglo-Saxon, rather than being derived from the Celtic substrate in the region. This supports a different narrative of language shift due to large scale population replacement in the region. The paper states:
The history of the British Isles and Ireland is characterized by multiple periods of major cultural change, including the influential transformation after the end of Roman rule, which precipitated shifts in language, settlement patterns and material culture…The extent to which migration from continental Europe mediated these transitions is a matter of long-standing debate…
Here we study genome-wide ancient DNA from 460 medieval northwestern Europeans—including 278 individuals from England—alongside archaeological data, to infer contemporary population dynamics.
We identify a substantial increase of continental northern European ancestry in early medieval England, which is closely related to the early medieval and present-day inhabitants of Germany and Denmark, implying large-scale substantial migration across the North Sea into Britain during the Early Middle Ages.
As a result, the individuals who we analysed from eastern England derived up to 76% of their ancestry from the continental North Sea zone, albeit with substantial regional variation and heterogeneity within sites. We show that women with immigrant ancestry were more often furnished with grave goods than women with local ancestry, whereas men with weapons were as likely not to be of immigrant ancestry.
A comparison with present-day Britain indicates that subsequent demographic events reduced the fraction of continental northern European ancestry while introducing further ancestry components into the English gene pool, including substantial southwestern European ancestry most closely related to that seen in Iron Age France.
The new study also picks up a significant, but more slow and steady migration of people from across the English channel in France, in the centuries following the Anglo-Saxon migration (possibly related to the Norman Conquest).
UPDATED September 26, 2022:
The post-Roman transformation of Britain was particularly significant with a profound change in material culture, architecture, agricultural practices and language. The archaeological finds point to a source located on the coasts of the North Sea, notably in Northern Germany (Schleswig-Holstein and Lower Saxony), the Netherlands (Friesland) and Denmark (Jutland). According to historical writings (see in particular those of Bede the Venerable), it seems that the Britto-Roman population was replaced by migrants from the continent and speaking a Germanic language. However, the extent of this replacement is subject to much debate. . . .
early individuals from the Middle Ages of England are distributed along the gradient that connects the Bronze Age populations of the British Isles (WBI) to those of the Middle Ages of the Netherlands, from Germany and Denmark (CNE), and the majority of them overlap with the latter.
These results indicate that medieval populations in England have different proportions of CNE and WBI ancestry. In the ancient populations of the British Isles, the proportion of CNE ancestry is almost nil in the Bronze Age and the Iron Age. It increases to about 15% during the Roman period, to reach 76% during the early medieval period.
. . .
Analysis of Y-chromosome haplogroups shows that while ancient individuals from the British Isles of the Bronze Age and Iron Age are overwhelmingly haplogroup R1b-L21, ancient individuals from the early Middle Age have more varied haplogroups with the appearance of R1b-U106, R1a-M420, I2a1-L460 and I1-M253 found mainly in Northern or Central Europe.
Finally, the comparison of the X and Y chromosomes shows that there are no significant differences between men and women in their participation in Anglo-Saxon migration.
Although most early medieval individuals from England can be modeled as genetically mixing between the two sources CNE and WBI, some individuals require consideration of a third source from southern Europe. or west, similar to the genomes of ancient Iron Age individuals from France. This ancestry is mainly found in south-east England, notably at the archaeological sites of Apple Down, Eastry, Dover Buckland and Rookery Hill. This third source is also essential to be able to model the current population of England . . . ancestry from the Iron Age of France appears to arrive as early as the early Middle Ages at some sites in south-east England. Elsewhere it seems to arrive later.
The arrival of Anglo-Saxons in England, which this genetic data corroborates was a gender balanced mass migration that rapidly reached three-quarters of the gene pool, explains the language shift from Celtic and residual Roman English Latin with Old English.
The next wave of migration from France is presumably mostly associated with the Norman Conquest (which is traditionally associated with the year 1066 CE) although there was some French migration before the Norman Conquest. In this period, Old English became French influenced Middle English, and "Law French" penetrated English courts. But, the French migration wave had less of a linguistic impact than the Anglo-Saxon one, transforming Old English but not replacing it entirely with French. The transition to Middle English also seems to have been most strongest among Norman elites and in urban areas.
The body text of the paper says:
We estimate that the ancestry of the present-day English ranges between 25% and 47% England EMA CNE-like, 11% and 57% England LIA-like and 14% and 43% France IA-like. There are substantial genetic differences between English regions, with less ancient continental ancestry (England EMA CNE or France IA related) evident in southwestern and northwestern England as well as along the Welsh borders. By contrast, we saw peaks in CNE-like ancestry of up to 47% for southeastern, eastern and central England, especially Sussex, the East Midlands and East Anglia. We found substantial France IA ancestry only in England, but not in Wales, Scotland or Ireland, following an east-to-west cline in Britain (Pearson’s |r| > 0.86), accounting for as much as 43% of the ancestry in East Anglia. Very similar results were produced using LowerSaxony EMA as a source for CNE ancestry.
One potential caveat in this analysis is our relatively sparse Roman sample from England, where we particularly lack samples from the south, which might have pre-existing France IA-related ancestry. We, therefore, turned to one of our early medieval sites, the post-Roman cemetery of Worth Matravers at the southern coast of Dorset, whose individuals have nearly no CNE ancestry (less than 6% on average), and thus may serve as a more temporally close proxy for post-Roman Britain before the arrival of CNEs. When used as a source in our model, we found that the estimates of France IA-related ancestry in present-day England changed by less than 3% on average across the regions, suggesting that France IA-related ancestry entered England to a substantial amount after the Roman period. . . .
Our three-way population model for present-day England supports a view of post-Roman English genetic history as punctuated by gene flow processes from at least two major sources: first, the attested arrival of CNE ancestry during the Early Middle Ages from northern Germany, the Netherlands and Denmark, and second, the arrival of ancestry related to France IA. Although we cannot precisely date the order of those arrivals, at least substantial amounts of France IA-related ancestry seem to be absent in northern and eastern England during the Early Middle Ages and therefore must have arrived there subsequently. In other parts of England, however, it may have entered together with CNE ancestry or even earlier. Notably in southern England, namely, Eastry, Apple Down and Rookery Hill, several early medieval individuals already exhibit France IA-related ancestry, which probably results, at least in part, from localized mobility between the south of England and the Frankish areas of Europe during the Early Middle Ages. Indeed, Frankish material culture is evident in these regions, particularly in Kent and Sussex. Admixture from this second source is, therefore, unlikely to have resulted from a single discrete wave. More plausibly, it resulted from pulses of immigration or continuous gene flow between eastern England and its neighbouring regions.
The modern proportions are shown below:
To only slightly oversimplify, the people of modern ethnically Celtic regions of Ireland, Scotland and Wales never had and still do not have very much Anglo-Saxon or French ancestry (and didn't receive much of an earlier Roman demic contribution either).
In contrast, England received and continues to have a substantial amount of both Anglo-Saxon and French ancestry, on top of the Roman contribution to its pre-Roman, genetically Bell Beaker-like Celtic substrate (which in some areas of England accounts for only 20% or so of the current population genetic mix). But, Anglo-Saxon ancestry penetrated somewhat further than French ancestry did.
Modern English emerged from Middle English in roughly the Elizabethan period also know for Shakespeare's works, starting about five centuries ago, or perhaps a bit earlier. That transition is outside the date range considered in this study.
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Also, people in the Northern Isles of Scotland, such as Shetland and Orkney, appear from their genetics to have inbreeding a levels similar to that of Ashkenazi Jews, resulting in high levels of certain genetic diseases caused by recessive genes.