YehudahTzvi:
You are aware that the daughter of a giyores is perfectly kosher for a kohen to marry????
Halacha only require a kohen to marry someone born a Jew – it is irrelvant what the persons mother or grandmother is. That’s why the search for a “kohen” genetic pattern focuses on part of the the male chromosone unaffected by the female genetic materials.
When they distinguish genetics in a way that limits it to male and female ancestry, it turns out that their were probably a lot more female than male converts (logical for many reasons, conversion didn’t mean the same loss of legal status for women since women often had limited rights, mikva is less scary than a bris, when Jews migrated to a new area men were more likely to go than women, and in the case of Ashkenazim many if not most came to Europe as Roman prisoners – men were more likely to survive captivity). It’s also interesting that the evidence is that conversion was very rare after ancient times – which matches what our historians have claimed.