Let me make something explicit: I believe that the model outlined in First Farmers is too simple, and that extant patters of linguistic and genetic variation need to accept the likelihood of multiple population reorganizations across vast swaths of Eurasia within the last 10,000 years. The classic case in point are the Turks. Because of their exotic character vis-a-vis the populations which they displaced and assimilated we can peg rather easily their expansion. Between 0 and 1000 AD they began to make themselves felt across a broad expanse of Eurasia from the eastern fringes of Europe to the western fringes of China, and south toward the world of Islam. Between 1000 and 1800 the Turkic peoples took over much of Eurasia for various periods of time (e.g., the Ottomans, Safavids, and Mughals, were Turkic, while the Golden Horde which imposed the Tatar Yoke were mostly Turkic, not Mongol). It is notable to me that Turkic peoples contributed ~10 percent to the genetic ancestry of modern Anatolians. This is a significant achievement, because Anatolia has been a densely populated seat of agricultural civilization for almost the whole history of agriculture! In Central Asia Turks genetically admixed significantly, to the point of preponderance, with the Iranian substrate.
Why does this matter? Because if it hadn’t happened, and it hadn’t happened in the light of history, I doubt we’d believe it! The Turks were obscure tribes in Central Eurasia 2,000 years ago. There was no anticipating that somehow they would overturn what had been the Iranian world of western Inner Asia, and, that they would break through into the civilized societies of the periphery, to the point of taking them over from above, and assimilating them from below. I do not think the Turks are exceptional in this. It must have happened many times in the past. We just need to open our minds to the possibilities.