YehudahTzvi: Genetic studies have shown that all Jews share common distinctive ancestry, so the majority of present-day Jewish genes are not from converts. However, it is clear that some conversion has occurred over time, to the extent that nearly all Jews must have at least some ancestors who are converts (and not just Avraham Avinu and the Imahos…) One genetic study estimated that 4% of the Ashkenazic population per generation were converts (that seems too high to me, even though I’ve read about some stories of entire gentile villages converting in the 19th century and earlier.) The paper “Multiple Origins of Ashkenazi Levites: Y Chromosome Evidence for Both Near Eastern and European Ancestries” claims to show that over half of Ashkenazic Levites have Eastern European Y-Chromosome (R1a1a) (which is much different than the case of the Kohanim, who clearly have a common Middle Eastern origin). Interestingly, the paper notes that the Gemara discusses the possibility of someone whose father is not Jewish becoming a Levite. (I wish they had cited the source.)
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