I may well be wrong, but there’s no point in waiting until they dig up and sequence every last body in Eurasia. Time to stick my neck out.
Here’s my current best guess concerning the Indo-European expansion:
It all started pretty far to the East. There, some crazy locals first tamed the horse. I’m thinking that they were something like the Botai culture, riding and hunting horses, but not farmers. They may well have milked those horses – by the way, horse milk is much richer in lactose than human or cow milk.
These early horsemen were genetically similar to the Ancient North Eurasians, or as those who know have dubbed them, Sibermen.
Having horses made them natural raiders, let them expand. Lactose tolerance might have helped.
A fraction of them conquered some farmers (a mixture of Middle Eastern types and others similar to western hunter-gatherers) in the eastern Ukraine, imposed their language, and roared into northern Europe. This accounts for the Centum languages: they have probably some additions from whatever language those Ukie farmers were speaking. Some people from this group (Tocharians) must have made a wrong turn and eventually ended up in Western China. Even today some Uighurs show the mark of those red-headed strangers.
But that centum expansion didn’t come first. Other, earlier kinds of Indo-Europeans had already destroyed the old EEF culture in the Balkans – and although they seem to have had some ANE ancestry, they apparently had very little WHG ancestry. You see mixtures of EEF and ANE in Greece and Albania, but almost no WHG. This has to be the result of a separate, early Indo-European expansion. Looks as if this might have gone on into Anatolia – the Hitties, Luwian, Palaic.
Nor was it the last. There must have been some peoples in the real Indo-European homeland (farther to the east than the Yamna culture) who had not yet conquered a bunch of motley farmers and had remained mostly ANE. Considerably later, now charioteers, some of them moved south, conquered some more Armenian-like farmers (the Bactria-Margiana culture, BMAC, located in the southern part of what used to be Soviet Central Asia, now Trashcanistan) (but no WHG types) and then went on to conquer India and Iran. Some ended up in odd corners like Nuristan and the Chitral Valley: here’s a young Kalash boy.
Both the European Centum expansion and the later Indo-Aryan expansion carried the same lactose-tolerance mutation., which has never been found in aDNA from the EEF farmers. Of course it could have been around in Old Europe, just still rare, but the simplest explanation for finding the same common mutation in Europe and north India is that it was spread by the Indo-Europeans themselves.
The WHG hunters had blue eyes, the same mutation as today, while the early European farmers had SLC24A5, but as of yet I’ve not seen any ancient examples of the alleles that give varied hair color in Europeans. Blondes and redheads are rare in Basques and Sardinians – I’m wondering if the ANE are the source.