The analysis below, courtesy of DNA Tribes, is based on autosomal STRs, which are primarily designed for forensic work rather than studying ancient admixtures. Nevertheless, it looks like a very solid effort, and seems to correlate well with ancient DNA results from Europe published to date, including preliminary finds from Greece by the BEAN project (see here). I think the concept of a hybrid Mesolithic/Neolithic "buffer" zone near the Balkans as a source of most of the extant European gene pool makes a lot of sense. It can explain things that, say, a steppe hypothesis based on a late Indo-European invasion of Europe cannot, like the current dominance of R1b in Western Europe. The only point I'd argue with is the suggestion that the Indo-European (IE) migrations took place during the Neolithic. I think they were a phenomenon of the metal ages, and sprang from the "Mixed buffer populations" of what is today known as East Central Europe.
Europe’s links in the larger context of world civilizations began long ago during the Neolithic period, when Eurasian related hunting-fishing cultures came in contact with new agricultural (farming and animal herding) societies from the Fertile Crescent. This Neolithic transition brought Europe into a network of trade and technology based primarily in the Middle East, but eventually reaching distant parts of Asia and Africa. This process linked cultures and laid the earliest foundations for the global communications and trade of the modern period.
The population changes involved in this transformation are just beginning to be understood. However, populations involved probably included: (1) Neolithic traders and settlers (probably related to Fertile Crescent populations); (2) Archaic hunting-fishing cultures (probably related to earlier Middle Eastern migrants as well as indigenous Siberian populations); and (3) Mixed buffer populations generated by the interactions between (1) and (2) (see Figure 1).
These mixed buffer populations would have bridged two very different worlds during this period of transition. Frontier settlements would have attracted individuals from European hunting-fishing cultures who were interested in peaceful interactions with incoming Neolithic populations. This would have created a fertile setting for new technologies and social forms to emerge (possibly including the early Indo-European languages). To provide a modern analogy, this dynamic process of cultural mixing in Neolithic Europe might have been similar to the formation of Spanish speaking Mestizo cultures throughout Latin America in the past 500 years.
These mixed cultures might have been among the first predecessors of most extant European populations, descended from both archaic hunting-fishing populations and Neolithic populations of the Fertile Crescent. These buffer cultures would have first emerged near the Balkan Peninsula, and later expanded and/or migrated outside of Southeastern Europe.
DNA Tribes®, Evidence for Early Migrations to Europe from West Asia and Siberia (STR), DNA Tribes® Digest January 2, 2013