But, there are alternative theories, one of which purports that the Proto-Indo-Europeans were northern Europeoid pastoralists from the eastern European steppe. Since the North_European ancestral component is lacking in the Tyrolean Iceman and Gok4, the TRB Swede, it is conceivable that North_European bearing populations introduced this component during the Indo-European invasion.
Of course, there is absolutely no archaeological evidence for a massive migration out of the steppe into Europe, as even the main proponents of the steppe hypothesis accept, and as physical anthropology makes clear. And, we don't have to invoke an eastern European invasion to explain the North_European component, since it was present among pre-Indo-European hunter-gatherers from both Gotland and Iberia, as two ancient DNA studies have shown.
In any case, I took the HGDP and 1000Genomes European populations, together with the West_Asian and North_European Dodecad components, and calculated f3 statistics of the form:
f3(IE; Basque, Dodecad Component)
where Basque is either HGDP French_Basque or 1000 Genomes Pais_Vasco_1KG, and Dodecad Component is either West_Asian or North_European.
All the results can be found in the spreadsheet.
Again, there is evidence of West Asian+Basque admixture in all Indo-Europeans (|Z| less than -3) except the islanders from Canarias and Orkney, and the Russians; in the latter case, Basques are probably a poor stand-in for their pre-Indo-European ancestry. So, 32 of 38 comparisons are significant.
One would expect such negative f3 statistics to also apply in the North European+Basque case. After all, there are historically known migrations of Northern Europeoids into Western Europe (both Celts as well as Germanics) which did not affect Basques linguistically; moreover, Basques are southern Europeans, and many of the tested populations are northern Europeans, who are expected to turn up as mixtures of North European+Basque. However, a total of 16 of 38 comparisons are significant, involving, as expected mostly northern European populations.
It thus appears that geography and recent history is sufficient to explain the excess of North_European in some populations. Despite having a dataset with an excess of Iberian and North European populations, not many significant f3 statistics appear, and these are mostly as expected.
In conclusion, by comparing Basques vs. Indo-Europeans there appears no good evidence for the theory that Indo-European languages were brought into western Europe by a massive migration of northern Europeoids from eastern Europe. Basques do not appear distinctive in terms of the North_European component, but they do appear distinctive in terms of the West_Asian one.
This confirms previous ADMIXTURE analyses that Basques occupy an "intermediate" position along the north-south axis of variation in Europe, and an absolutely terminal one in terms of the West Asian component.
It is very interesting that ancient DNA research has provided clues about a very "uneven" landscape of prehistoric Europe, with Sardinian-like farmers in Sweden and Northern European-like hunter-gatherers in Iberia and very little in-betweens. But, these two elements eventually did mix, and, with the addition of a new group of people emanating from the highlands of West Asia, acquired their Indo-European speech, and went on to become the living nations of Europe.
Much remains to be discovered: the first ancient DNA traces of the constituent elements must be identified in space and time, and the history of their intermixture must be tracked.