Brown had a chance to revive the dispute this week, when, acting as a surrogate for Donald Trump, he defended the presumptive Republican nominee's use of the name "Pocahontas" to describe Warren. (Warren had appeared at a rally with Hillary Clinton, whom she supports.)

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"As you know, she's not Native American," Brown said on a conference call, according to our Dave Weigel. But he did offer some ways that Warren might prove him wrong: "Harvard can release the records, she can authorize the release of those records, or she can take a DNA test."

To which my response was: Can she? Would a DNA test actually answer that question?

No.

Nanibaa' Garrison is a bioethicist and assistant professor of pediatrics at Seattle Children's Hospital. A Native American, she earned a PhD in the Department of Genetics at Stanford, with a dissertation focused on ancestry. In a phone call Tuesday afternoon, she explained why Brown's suggestion -- and the Republican National Committee insisted on Tuesday that it was only that, a suggestion -- wouldn't do any good.

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"It's really difficult to say that a DNA test would be able to identify how much Native American ancestry a person has," Garrison said.

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That's because determinations of ancestry are based on "ancestry-informative markers" -- genetic flags that offer probabilities of the likelihood of certain ancestries. Most of those markers, AIMs, are "based on global populations that are outside of the U.S.," she said, "primarily people of European descent, people of Asian descent and people of African descent.

Those three populations are not enough to determine how much Native American ancestry a person has." There are some companies that are obtaining DNA from Native Americans to fill that gap -- but that's almost certainly not enough information to make that identification.

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Warren's understanding of her heritage was that she was part Cherokee, perhaps as little as 1/32nd based on outside sleuthing. (Brown dismissed that claim specifically on this week's call.) The odds of identifying a particular tribal identity are essentially zero, according to Garrison, but such a small percentage of Native American blood would also make identification much harder, even if the necessary AIMs existed.

Remember how genetics works. You are a mix of your mother's genes and your father's -- some from each. They are themselves a mix of their parents, who are a mix of their parents. That 1/32nd takes us back five generations -- to, literally, one person's genes in a potential pool of 32 pairs. Even a test that was fine-tuned to pick out Native American identity might not find any on Warren's genes, because the requisite markers simply may not have made the cut over multiple generations.

"It would be impossible to go back that far," Garrison said. "One-32nd is low enough that, even if she does have Native American ancestry, just by chance the genes that show up on these AIM panels might not necessarily be passed down, even if she might have other genetic variants that are highly prevalent among Native Americans. It's all just by chance, what you inherit from your parents."

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It gets worse for Brown's plan. Even if there were AIMs for Native Americans and even if Warren's gene pool were more heavily Native American than she believed, we're still only talking about probabilities. "There's a confidence interval that's associated with [the results]," Garrison said. "That confidence interval can be very wide, especially when you're talking about such low ancestral contribution." So maybe Warren gets the results back and it says that she's Native American -- but that it can only be determined with 20 percent confidence. Scott Brown might not be convinced.

Since I had her, I asked Garrison whether DNA tests might become a part of the presidential vetting process, the way that a doctor's letter is de rigeur for candidates these days. Could we someday see demands -- er, suggestions -- like Brown's be an actual part of the process to reveal any potential health problems down the road?

Not any time soon. Huntington disease, for example, can be spotted in DNA -- but the test wouldn't tell you when the disease might develop, which doesn't do you much good if you're worried about a four-year window. "There are so many different environmental factors or dietary factors and other health behaviors that would feed into whether or not a disease might develop and what time in their life it would develop," Garrison said, making that sort of prediction impossible. (For now, at least.)

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Brown's point, of course, wasn't to encourage detailed exploration of the extent to which analysis of human DNA could prove or disprove a particular lineage. His point was to raise questions about Warren more broadly, by focusing on an area in which she made an unprovable claim.

Incidentally, a DNA test might end up showing that Brown has Native American heritage.

"I know of some people who identify as white who are not aware of any Native American history and who know that their family originates from Europe," Garrison said, "but just by chance they also might have a small signature of African or Asian ancestry that just happens to show up because it's all based on statistics."