In genetic studies, especially of the data from the Human Genome Diversity Project, Russians appear to have at least 10% East Eurasian, often rising to as high as 15% in many individuals (and then some isolated cases even higher).
East Eurasian primarily describes the admixture seen at near 95+% in Han Chinese and Japanese (EDIT: And Malaysia), and present to high degrees in Mongolians, Siberians and other North Asians, and around half or slightly more than half of Native Americans.
West Eurasian, by contrast, describes admixture seen commonly in Europe and West Asia (Caucasus, Middle East) today.
The labels refer to, I suppose, the ancestor branch from whom modern branches sprang from.
Russians having this much East Eurasian admixture fits the gradient seen today, with other people within Russia (Tatars, Udmurt, Chuvash, etc) having 20% or more. And of course we see it in high proportions across Central Asia, nearing half or more in some communities in places like Kazakhstan, Kyrgyzstan, etc. Though it bears mentioning that it's highly variant and you can find people in these countries who have 20% or less, living right alongside their neighbors who have 50% or more.
Ancient genomes from Central Asia and Russia show much less East Eurasian. If we stick to the Bronze Age period, there's almost none. If you go back earlier enough (I refer to the genomes of hunter gatherers from Karelia and Samara), you get a few %, but typically 5% or less. So through the Bronze Age, those genomes are almost entirely derived from West Eurasian genetic branches.
This is, again, not entirely a surprise because we know Central Asia was initially populated by West Eurasian, Caucasian-type people for quite a while through the Bronze Age.
And we know that people from eastern Asia, carrying East Eurasian genetic admixture, swept westwards across the Asian Steppe. Turkic-Mongolic tribes especially. But this happened very recently in history (within the last two millennia).
So, is that indeed where modern Russians got their East Eurasian admixture from? From the various Turkic and Mongolic tribes that came via the Steppe? Did it mostly happen before or after the Mongol Empire? It's hard to imagine it permeating the entire people like that in so recent a timeframe.
HGDP Russian samples are exclusively from Kargopol, which is quite an exotic location in terms of Russian genetic variation. They represent only the fringe North Russian population which comprises about 5% of Russians. These north Russians living on the North-Eastern rim of European Russia have considerable Finnic/Uralic admixture due to assimilation of indigenous peoples in the wake of Russian colonization. According to S.Kozlov’s autosomal research they are 50/50 Balto-Slavic and Finnic, in Perm they are 2/3 Finnic 1/3 Slavic, small remote locations like Mezen and Pinega seem to have 75-100% Finnic ancestry. As for the rest 95% of Russians there are no signs of substantial East-Asian admix except for population in the Urals with slightly elevated share of Uralic component. There is no detectable genetic impact of Mongols/Turkic tribes. If you look closely at the published research papers you will see that East-Asian admix for most Russians except north populations is on par with Italians, Germans et c. It is crystal clear in K2 chart.
