By DNA there is rarely any non-mixed population of ethnic groups. That applies both to maternal(unless interbreeding is a preference) and paternal lineages, as people are quite mixed, but borders of cultures and beliefs(in various myths - including about their ancestry) is what is holding societies together.

By appearance admixture is the one that defines looks and that includes racial look and it is question of mere 3 generations for descendants to look like anyone else around them, as that is where admixture differences are washed out. USA has a lot of issues in this matter, like with "one blood drop rule" that is still used in definitions of races and also cultural war issue, which is affecting rest of the world in these matters not to mention taboo subject of races.