Forget those old tests. Have a look at this ADMIXTURE analysis from the study.
http://biorxiv.org/highwire/filestre...1/001552-2.pdf
It shows a cream colored component that peaks in the Caucasus and is found at decent levels in almost all Europeans, except Basques and Sardinians. MA-1 shows about a third of it in many of the higher K runs, but for him it switches to the Kalash-specific component in some of the runs.
Obviously, what we're seeing there is ANE admixture in Europe, West Asia and South Central Asia. But it's being expressed in a weird way as North Caucasian and Kalash components, similar to the old West Asian and Gedrosia components, and I'd say that's due to the isolation and drift in some of those isolated mountain communities.
That's why ADMIXTURE results are so difficult to use as signals of ancient population movements. You don't really know what you're looking at much of the time. It could be admixture from population A to population B, or in fact gene flow the opposite way, or maybe third party gene flow from population C.
But anyway, when we look at all of these results together, the thing that really sticks out is the high ANE in the North Caucasus. This is interesting, because Motala12 also had high ANE, and obviously MA-1 was purely ANE. So ANE obviously expanded into the Near East and South Central Asia from somewhere in the north, probably during the Bronze Age. What we don't know is whether this expansion was from Eastern Europe or Siberia, and only more ancient genomes can answer that question. Here's what the authors from this study say...
"A geographically parsimonious hypothesis would be that a major component of present-day European ancestry was formed in eastern Europe or western Siberia where western and eastern hunter-gatherer groups could plausibly have intermixed. Motala12 has an estimated WHG/(WHG+ANE) ratio of 81% (S12.7), higher than that estimated for the population contributing to modern Europeans (Fig. S12.14). Motala and Mal’ta are separated by 5,000km in space and about 17 thousand years in time, leaving ample room for a genetically intermediate population. The lack of WHG ancestry in the Near East (Extended Data Fig. 6, Fig. 1B) together with the presence of ANE ancestry there (Table S12.12) suggests that the population who contributed ANE ancestry there may have lacked substantial amounts of WHG ancestry, and thus have a much lower (or even zero) WHG/(WHG+ANE) ratio."