From this analysis by Dienekes, not much:
How Turkish are Anatolians? revisiting the question
In 2005, I estimated the Y-chromosome heritage of Turkic speakers on modern Anatolians at 11%.
In the same year, I estimated the Mongoloid admixture in Anatolian Turks at 6.2% on the basis of Y-chromosome and mtDNA. This is not inconsistent with the previous percentage, as the Turks, when they arrived in Anatolia were almost certainly of mixed Caucasoid-Mongoloid heritage.
Surprisingly, the maternal contribution from East Eurasia seems higher than the paternal one, on the basis of uniparental markers. But, that is not so surprising if one considers that the Turks who arrived to Anatolia were to a degree descended from Turkicized groups of Iranian steppe nomads bearing Caucasoid patrilineages. Already we have ancient DNA evidence of groups in Central Asia with Caucasoid patrlineages (R1a1) and mixed Caucasoid-Mongoloid mtDNA.
In 2007, some Turkish researchers estimated, using Alu polymorphisms, the Central Asian admixture in Turks at 13%, quite close to my own estimate, and, given the observation that there is more Mongoloid mtDNA than Mongoloid Y-chromosomes in modern Anatolians, the slight difference of 2% is probably taken care of.
In October, I estimated the Mongoloid admixture in Turks at 5.5%, quite close to the 6.2% arrived in 2005 using Y-chromosomes and mtDNA. Subsequently, my K=10 Dodecad analysis (spreadsheet) arrived at 6.7% sum of "East Asian" and "Northeast Asian" components. The slight increase is not surprising, as the K=10 analysis included a greater sampling of Mongoloid diversity.
In ISBA4, another group of Turkish researchers arrived at a 13% estimate for the nomadic Turkic element in modern Anatolian Turks.
Finally, my K=15 analysis has revealed 7.9% "eastern" components in Turks. Given that the "Central Siberian" component is equidistant from Caucasoids and Mongoloids, this translates into about 7.2% East Eurasian admixture. Again, the slightly larger result can be accounted by the sampling of even greater Mongoloid diversity, from the previously unsampled Siberia.
Y-chromosome, mtDNA, and autosomal DNA analysis by myself and by Turkish researchers all point to 6-7% of Turkish genetic heritage being specifically east Eurasian in origin, and about 1/7 of their genetic heritage coming from Central Asia.
I received an e-mail from a Turkish participant in the project, who wondered whether the K=15 analysis was supportive of much higher demographic influence of Central Asian Turks in the current Turkish population.
In particular, a back-of-the-envelope calculation of "eastern" components in Turks and Uzbeks led him to the conclusion that this was at least 20% and probably more.
Thus, I decided to perform direct ADMIXTURE analysis of Turks and Uzbeks to see what the estimate of Central Asian admixture in Turks actually is.
In the above figure, there are (left-to-right): 1 Dodecad Project 50% Turk-50% Laz showing no Central Asian admixture, 3 Dodecad Project Turks, 19 Turks from Behar et al. (2010), followed by Uzbeks (blue, with some seemingly admixed individuals), followed by 15 Dodecad Project Greeks and Armenians (red).
Behar et al. (2010) Turks have 15.4% Central Asian admixture; if we add the 3 Dodecad Project Turks to the sample, this becomes 14.4%. I'll be happy to tell the three Turks in the Project their individual proportions if they e-mail me.
In conclusion, this analysis too provides an estimate of the Central Asian component in Turks similar to all the ones listed in the beginning.
Estimating the precise genetic identity of nomadic Turks at their time of arrival in Anatolia is difficult to achieve. First of all, modern Anatolian Turks are a subset of recent Anatolians; second, there is the problem of how many Iranian-speakers were absorbed by the westward migrating Turks from Central Asia, and when; also, what was the impact of the Mongol expansion in Central Asia after Turks had already reached the west, and later what were the impacts of Chinese and Russian expansion in the Eurasian heartland.
It's all a big puzzle, but, for the time being 5-7% East Eurasian admixture in modern Anatolian Turks and about 1/7th of their heritage coming from Central Asia seems like a reasonable estimate.