That said for the sake of an argument, it's definitely possible to have had a native american ancestor and their genes just migrate naturally out their ancestors over time. Should take more than a few generations but if you think about it, first ancestor is 50% and it halves each generation until it's basically nothing. If we're talking recent though like five generations back then no way, should still be like 3%.
It's still very unlikely due to crossover.
Like...26 chromosomes, but even within one chromosome they will cross in random places:
Hmm...assuming she was born in 1950... grandparent 1925 g grandparent 1900 gg grandparent 1875 ggg grandparent 1850 gggg grandparent 1825 ggggg grandparent 1800 gggggg grandparent 1775 ggggggg grandparent 1750 gggggggg grandparent 1725 ggggggggg grandparent 1700 gggggggggg grandparent 1675 ggggggggggg grandparent 1650 gggggggggggg grandparent 1625
(And realistically that's about as far back as you can go, cause that would require like...one of the first settlers from Jamestown Virginia.)
That said, going back that far would actually produce a 0.006% on average DNA relationship. Given that these DNA tests don't seem to get more accurate than 0.1%, and the process of gene swapping is random anyway so it could be LESS than 0.006%...yes, she could be 1/16384 Native American and it wouldn't show up on the test.
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The mitochondrial test, however, doesn't show shit. Mitochondrial DNA is only passed down from your mother, meaning your mother has basically the same Mitochondrial DNA as you, and basically the same Mitochondrial DNA as her mother, and her grandmother, and her great grandmother and so on. If it's showing 99% European, then that just means that one side of her family (her unbroken matriarchal line) was definitely European, no questions asked.
But then how does the Mito DNA say part Native American? ---
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