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I think we'd better wait for the paper on this one as the abstract is very poorly worded.
This is what they actually say:
" Our results indicate that Central Anatolian Neolithic individuals genetically resembled the first migrant Neolithic populations found in Europe, rather than modern-day Anatolians. At the same time, Central Anatolian Neolithic individuals appear to cluster together, to the exclusion of other Neolithic populations. Using simulations, we evaluate demographic models that could explain these patterns. Our results suggest that the migration processes that eventually reached Southwestern Europe around 8,000 BP had their demographic roots directly within the Near East, but possibly not in Central Anatolia, in line with the cultural diffusion hypothesis. We discuss our results in the context of material cultural exchange patterns of the Neolithic period."
Isn't the plain sense meaning of this that there is a difference, even if a very slight one, between this group and the other Neolithic populations? Now, I would want to see not only Admixture but formal stats to support that, of course. Even then, who says that the difference would be varying levels of "WHG like" admixture? That slight difference might be slightly more CHG for all we know.
As to their statements about the demographic source of the flow into Europe all that might mean is that as Paschou et al proposed, the jumping off point for Europe was southeastern Anatolia/northern Levant, and that the flow was not, as has been long suggested, directly from northwestern Anatolia.
Their last comment about all of this being "in line with the cultural diffusion process" makes no sense to me. Unless we find that the people living in southern Greece, the Aegean, and perhaps other parts of far southern Europe were already EEF like long before the first discoveries of agriculture, then I don't see how agriculture could have only culturally diffused into Europe. Even if that proves to be true, that there were repeated Neolithic flows is also pretty clear, given the J2 and E-V13 that only shows up later.
Non si fa il proprio dovere perchè qualcuno ci dica grazie, lo si fa per principio, per se stessi, per la propria dignità. Oriana Fallaci