The good people from the Estonian Biocentre have just put out a preprint at bioRxiv focusing on the genetic origins of Turkic-speaking nomads. It's a solid effort based on a wide range of samples and several standard analyses, including a massive fastIBD run. The authors' conclusions are very sensible and probably correct:
Most of the Turkic peoples studied, except those in Central Asia, genetically resembled their geographic neighbors, in agreement with the elite dominance model of language expansion. However, western Turkic peoples sampled across West Eurasia shared an excess of long chromosomal tracts that are identical by descent (IBD) with populations from present-day South Siberia and Mongolia (SSM), an area where historians center a series of early Turkic and non-Turkic steppe polities. The observed excess of long chromosomal tracts IBD (> 1cM) between populations from SSM and Turkic peoples across West Eurasia was statistically significant. Finally, we used the ALDER method and inferred admixture dates (~9th–17th centuries) that overlap with the Turkic migrations of the 5th–16th centuries. Thus, our results indicate historical admixture among Turkic peoples, and the recent shared ancestry with modern populations in SSM supports one of the hypothesized homelands for their nomadic Turkic and related Mongolic ancestors.
However, even tough the paper includes a lot of detail, I still find it somewhat underwhelming. The blame lies with Lazaridis et al. 2013/2014, which really raised the bar for papers of this sort, using several ancient genomes and very sophisticated techniques to try and unravel the deep ancestry of Europeans (see here and here). It's probably unreasonable of me to expect most population genetics papers to be so thorough, but it's still disappointing when they're not.
Also, thanks to Lazaridis et al. as well as a few other recent ancient DNA studies, we now know that the prehistory of Eurasia was probably more complex than anyone had imagined only a few years ago. Once upon a time is was OK to blame any sort of seemingly eastern genetic signals on Genghis Khan or Attila the Hun. These days you'd look like a bit of an idiot trying that sort of thing.
So yes, in this case the authors probably got it right, and they probably did pick up signals of Turkic migrations from south Siberia and surrounds. But let's wait and see what a good number of ancient genomes reveal about the origins, direction and time frames of population movements across the Eurasian steppe and Taiga belt.
Bayazit Yunusbayev, Mait Metspalu, Ene Metspalu, et al., The Genetic Legacy of the Expansion of Turkic-Speaking Nomads Across Eurasia, bioRxiv posted online July 30, 2014