DNA databases contain few, if any, samples from people of Native American descent who live in the United States, as tribal elders have discouraged members from participating in population genetics studies.

So how could researchers determine that Sen. Elizabeth Warren had a Native American ancestor?

They compared the Massachusetts Democrat's DNA with samples from people of indigenous descent who live elsewhere in the Americas — Mexico, Peru, Colombia, and Canada — as they share common ancestors who migrated from Asia thousands of years ago.

The result was announced this week on Warren's Senate campaign site: Warren has at least one Native American ancestor who lived approximately eight generations ago, give or take two generations, according to the analysis led by Stanford University scientist Carlos D. Bustamante.

"We are confident it is not an error," Bustamante told the Boston Globe.

Warren asked Bustamante to conduct the genetic analysis after President Trump and other Republicans mocked her claims of Native American ancestry, jokingly referring to her as "Pocahontas" and accusing her of using her heritage to advance her legal career.

Though her claims now have been validated by Bustamante's genetic study, a previous analysis by the Boston Globe found that any statements Warren made regarding her native ancestry did not play a role when she was hired for positions at the University of Pennsylvania and Harvard law schools. Documents and interviews with dozens of professors involved in hiring indicated that both schools viewed her as a white applicant, the Globe reported.

Warren's genome does appear to contain a small amount of Native American DNA. The analysis by the Stanford team, relying on indigenous DNA samples from outside the United States, is solid, said Theodore G. Schurr, a Penn anthropology professor who was not involved in the project.

People of indigenous origin who live in North, South, and Central America are descended from ancestors who migrated from Asia 16,000 years ago, Schurr said. The evidence comes from multiple sources, including genetics and 14,600-year-old campsites in what is now Chile, he said.

Anthropologists once thought these early migrants trekked to the Americas over a "land bridge" that has since become covered by water — the Bering Strait. But now, the consensus is that the voyagers pursued a route along the Pacific coast, since North America was covered by ice 16,000 years ago, Schurr said.

"If there were people 15,000 years ago down in South America, they had to find some means of getting there," the Penn professor said.

Using genetic samples from people who live in Peru, Mexico, and Colombia as reference points, the Stanford researchers identified five segments of DNA in Warren's genome with an indigenous origin, they said.

The team then performed an additional analysis on the longest of those segments — a stretch of 4.7 million DNA bases — located on Chromosome 10. Warren's sample lay halfway between similar segments collected from people of indigenous origin in Canada and Mexico, Bustamante and his colleagues calculated.

That fits with the narrative of early Asian settlers dispersing throughout the Americas, evolving slight genetic differences over thousands of years as they established separate populations.

"They're emerging out of a common gene pool," Schurr said. "It's a chromosomal segment that clearly shows ancestry in the Americas and not anywhere else."

The researchers compared Warren's DNA with reference samples at more than 600,000 sites in the genome. They did not analyze her complete genome, so they were not able to calculate what percentage of her genetic information was of indigenous origin.

In layperson's terms, people would say that if Warren had an indigenous ancestor eight generations ago, she was 1/256th Native American. But using fractions in that context is misleading, because going back in time, each additional generation contributes half of its DNA on average.

To understand why that is true, think of what happens going back just two generations. A person gets one copy of each gene from the mother, and one copy from the father — 50 percent from each. But in each case, that copy could have been passed down from either a grandfather or a grandmother. So on average, 25 percent of a person's genes come from each grandparent, but the share can be substantially higher or lower than that. The further back in time you go, the more it is misleading to speak of a certain fraction of one's ancestry.

The key point is that a fraction of Warren's DNA, however small, is consistent with evidence for a migration that changed the world, Schurr said.

"This happened at a singular moment in human history," he said.