I've just spotted a few interesting extras in the final draft of Lazaridis et al. that appeared in Nature last month, including this quote from page 126 of the freely available supp info:
The finding of high ANE ancestry in the North Caucasus might suggest that the Caucasus is a potential source of this type of ancestry in Europe. However, when we try to fit present-day Europeans as a 3-way mixture of a North Caucasian population+EEF+WHG in the structure of Fig. S14.20 this model is successful for only 5 populations (Bergamo, Bulgarian, Italian_South, Spanish_North, Tuscan using Lezgins as a sister group to the admixing population). Admixture from the Caucasus would need to be substantial to account for observed ANE levels in Europe (e.g., for a European population with ~15% ANE ancestry, almost half of its ancestry must come from a Lezgin-like population with ~29% ANE ancestry; this would account for the ANE ancestry but would greatly dilute its WHG-related ancestry, and yet present-day Europeans have increased affinity to WHG in Extended Data Fig. 4 relative to Stuttgart).
This was rather obvious anyway, but I know that there are a lot of people online who cherish the notion that Europe was invaded in a big way by groups from the Caucasus and/or Anatolia during the Bronze Age, and I'm guessing this paragraph was a response to the comments that the authors received from these people during the public review process.
Indeed, the updated supp info also has a couple of new Principal Component Analyses (PCA) of West Eurasian populations, with which Lazaridis et al. underline the point that most Europeans and Near Easterners form "two discontinuous clines" in such analyses (pages 76-80). I could be wrong, but the impression I get is that they're again communicating how very improbable it is for most Europeans to harbor any Near Eastern and Caucasian admixture that post dates the Neolithic transition.
This of course leaves pre-Turkic far Eastern Europe, Western Siberia and/or Central Asia as the source(s) of the ANE-rich population movements that apparently had such a profound impact on most of the European gene pool after the final Neolithic.
Lazaridis et al., Ancient human genomes suggest three ancestral populations for present-day Europeans, Nature, 513, 409–413 (18 September 2014), doi:10.1038/nature13673
Coming soon: genome-wide data from more than forty 3-9K year-old humans from the ancient Russian steppe
Corded Ware Culture linked to the spread of ANE across Europe