1. ALL Turks are PREDOMINANTLY WESTERN EURASIAN and ALL Turks have high Ne. The "CENTRAL ASIAN" (which is largely Western Eurasian) CANNOT be emphasised above their WESTERN EURASIAN ANCESTRY. Where are the high FST values between Turks and "Europeans"? They don't exist? Of course they don't. Genetic distances between Italians (averaged) and Germans is ~0.004 and the same with Turks.
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Genetic distance DOES increase based on region because genetics are CLINAL (look it up), but if you think a 0.006 distance between Eastern Turks and Northern Italians is "very distant" oh boy, wait till you see the distances between Sardinians and Latvians.
2. The genetic distance between Germans and Northern Italians ranges from 0.003-0.004. Northern Italians are still largely a mix of "Western Mediterranean" and "Eastern Mediterranean" and are not glorified Germans.
3. This is where "European genetics" falls apart. German "Europeans"? FST values range from ~0.006-0.008. Northern Italian "Europeans"? FST values range from 0.002-0.005. Spanish "Europeans"? 0.003. Are Cypriots "European" or "Middle Eastern"? Either way, 0.000-0.003. What about Russian "Europeans"? 0.01-0.012. Turkish Jewish "European"? 0.001. You're gonna have to define "majorly European". There is NO world that allows Southern Italians and Poles and the EHG heavy Balts/East Slavs to be labelled as "genetically European". On the other hand, you'd BETTER have a DAMN good reason for meaningfully segregating Southern Italians and Azeris genetically.