They are key players in the shape of modern Europe as the later paragraphs touch on:

Most European men alive today carry y chromosomes that were brought in by the Yamnaya migrants of the Bronze Age, a legacy of the privileged access the latter managed to obtain, by fair means or foul, to local women. Millions of men in Central and South Asia carry the same y chromosomes, since the Yamnaya expanded eastward too. In January Dr Willerslev’s group reported that a genetic predisposition to multiple sclerosis, an inflammatory disease of the central nervous system, arrived in Europe with the Yamnaya, and spread wherever their descendants did. It may have arisen as part of a package of immune changes that evolved in steppe herders, who lived close to their animals, to protect them against diseases of animal origin—including plague. In a modern context, it causes a different kind of disease.

What of the Indo-European languages? Language, like culture, does not require mass migration to spread, but as David Anthony, an archaeologist at Hartwick College in New York, explained, painstaking reconstructions of the vocabulary of early Indo-European languages, based on comparisons of their living descendants, indicate that their speakers knew wheeled transport, practised dairying and possibly rode horses. That constrains the place and time in which they could have lived, and Dr Anthony finds the Yamnaya to be the best fit. Many are now convinced that they spread these languages throughout the Old World.

Although linking physical remains, modern DNA and language can be tricky, it’s increasingly clear that the transition from the Neolithic to the Bronze Age wasn’t a simple evolution of culture in the existing populations. Instead there seems to be a discontinuity between those two groups caused by an influx of people from outside Europe.

It looks like the Yamnaya/Kurgans spread west from the Pontic Steppe into Europe, splitting into two branches. These are characterised by the Y chromosome R1a and R1b - roughly what would become the Germanic and Celtic people, respectively.

The debate is now largely about whether it was violent or more peaceful - that article is definitely leaning towards the latter and the former seems to largely arise from people struggling to grasp the scale of the timeline. If it had happened in decades it would likely have been messy but it took centuries at a time when people could move a long way in their lifetime (the Amesbury Archer was likely born in the Alps and was buried not far from Stonehenge).

However, this all needs a lot more work, especially ancient DNA analysis especially focused at that transition. They can provide useful results - there was one study done looking at the arrival of Anglo-Saxons into Britain and you can see the different groups mixing where this is, currently, less clear between the Neolithic people and the Celts.

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