Sen. Elizabeth Warren (D-Mass.) rejected a call this week by a Massachusetts newspaper to take a DNA test to prove her Native American heritage, saying it is a cherished piece of family lore and noting that she has never used it to get ahead.

She might also add that such a test may not prove anything — or at least it couldn’t establish the absence of Native American ancestry her critics might be hoping to find.

If Warren were to take one of the widely available commercial “spit tests” and DNA related to a Native American tribe showed up, she would have positive proof that her family stories are true.

But if no such DNA were evident, that would not mean she didn’t have Native American ancestry.

The large DNA testing company 23&me analyzes DNA inherited from recent ancestors on both sides of a person’s family and figures out the proportion of the person’s DNA that comes from each of 31 worldwide populations.

A person inherits on average 50 percent of his or her DNA from a parent, 25 percent from a grandparent, 12.5 percent from a great-grandparent, and so on. Along the way, much material gets left out. The further down the line the generations go, the more likely it is that a genetic line will not show up — meaning that a bona fide Native American ancestor could well be absent from Warren’s results.

The senator’s stories of Cherokee and Delaware Indian heritage have drawn flak — including taunts from President Trump, who has frequently has called her “Pocahontas,” repeating the slur at a rally on Saturday night. Last week, the Berkshire Eagle, a newspaper in Pittsfield, Mass., urged her to take a test to settle the matter, and the topic has since reverberated across other media.

Warren doubled down on her account of her family ancestry in an interview Sunday with NBC’s “Meet the Press.” “It’s a part of me and nobody’s going to take that part of me away,” she told host Chuck Todd.

Although the presence of Native American ancestry in a DNA test would be informative, its absence would not rule it out, said Ann Turner, a genetic genealogist and the co-author of “Trace Your Roots with DNA.”

“If the Native American ancestry is more than a few generations back, it might not be detectable,” she said. “Also, many people who self-identified as Native American a few generations back were already admixed, making it even less likely to be detected.”

Even for those with a known Native American in the family tree, a DNA test might not reveal it because of recombination, the random shuffling of genes that occurs each time DNA is passed down to the next generation.

A 47-part tweetorial by Kim TallBear, a Native studies professor at the University of Alberta, underscores the point, as does an article on 23&me’s website:

“In the case of Native American ancestry, you may have inherited little or no DNA directly from your Native American ancestors. The farther back in your history you look, the less likely you are to have inherited DNA directly from every single one of your ancestors. This means that you can be directly descended from a Native American without having any DNA evidence of that Native American ancestry.”

As DNA tests become more ubiquitous, politicians may be increasingly called upon to submit to them as proof of identity with one group or another. That may be entertaining, considering the many surprises that can show up in the results. But it won’t prove a negative.