If I had to guess, I would propose that most extant Europeans will be discovered to be a 2-way West Asian/Ancestral European mix, just as most South Asians are a simple West Asian/Ancestral South Indian mix. In both cases, the indigenous component is no longer in existence and the South Asian/Atlantic_Baltic components that emerge in ADMIXTURE analyses represent a composite of the aboriginal component with the introduced West Asian one. And, like in India, some populations will be discovered to be "off-cline" by admixture with different elements: in Europe these will be Paleo-Mediterraneans like the Iceman, an element maximally preserved in modern Sardinians, as well as the East Eurasian-influenced populations at the North-Eastern side of the continent.
This does not seem to be totally implausible on the face of it. But it seems likely that any "West Asian" component is going to be much closer genetically to an "Ancestral European" mix than they were to "Ancestral South Indians," because the two former elements are probably part of a broader West Eurasian diversification which post-dates the separation of those groups from Southern and Eastern Eurasians. In other words, pulling out the distinct elements in Europeans is likely a more difficult task because the constituents of the mixture resemble each other quite a bit when compared to "Ancestral North Indians" vs. "Ancestral South Indians."
The bigger issue which this highlights though is that the reality that many of these clustering methods are temporally sensitive. Given enough time a "hybrid" population is no longer a hybrid, but rather a new distinctive population which itself can be a "parent." Recombination breaks apart the long range genetic physical associations which are the hallmarks of distinctive admixed ancestry on the genomic scale. That is why clustering methods easily generate a pure "South Asian" component. After at least ~3-4,000 years of continuous admixture the synthesis is now far less coarse, and the elements much more de facto miscible. And yet via other clustering techniques, such as principle components analysis, you get different results. The peculiar position of the "South Asian" individuals between Europeans and East Asians in direct proportion to their caste and regional origins becomes highly indicative of some sort of admixture event in different proportions as a function of geography and social context. The technique in Reconstructing Indian population history allowed for a resolution of this paradox by sifting through the variation and extracting out the ancestral components. The recent papers which came out on Australian Aboriginal genetics do something similar, in terms of making sense of somewhat puzzling results which are found
when generating inferences from aggregate genomic variation.
Imagine how much more difficult the task would have been if the ancestral components were much closer! I suspect that's what's going on in Europe. I'm not privy to any big secrets, but I have heard of whispers of research groups using Sardinians as a "pure" outgroup to model the changing demographics of Europe since the arrival of agriculture. What David Reich stated at the conference was not particularly surprising to me in light of that possibility. Sardinia regularly pops out as a weird outlier in many analyses. One simple possibility here is that that's simply a function of the fact that it's an island, and therefore has diverged from mainland populations due to isolation from conventional village-to-village mate exchange. Another possibility, mooted by Dienekes, is that it may be a repository of European genetic variation from earlier periods, relatively unaffected by later perturbations due to demographic changes. The main reason that I can give some credit to Dienekes' thesis has less to do with Sardinians than Basques. The French Basques in the HGDP are less atypical than the Sardinians, but in some runs they do lack a component which is most obviously classed as "West Asian," and which other French have. In Dienekes' own runs with a diverse array of Iberian populations this same distinction emerges. All of this reminds us that clustering methods give us great insights into how populations are related to each other, but they don't tell us about the details of how that relatedness came to be. It makes a great difference if an element is the outcome of relatively recent (<10,000 years) hybridization events, as opposed to having deeper roots. For example, admixture between Polynesians and Melanesians brings together two components, whatever their own prior origins, diverged on the order of 50,000 years before the present. And yet if the two groups mentioned earlier are correct than the Melanesian component itself must be decomposed into two fractions, one of which is much closer to the Polynesians than the other, our understanding of the past changes. As I implied earlier today I think the era of wild hypothesis generation in the area of the settling of Europe over the last 10,000 years is coming to the end. The combination of more powerful analytic techniques and the emergence of ancient DNA samples with which to calibrate, peg, and check, inferences from those techniques, will probably clarify our understanding of the past to a great extent.
Image credit: yomi955