Mr. Hutchinson also learned that his mother was not an only child, but had a brother. A genealogist helped him track down some first cousins in Alabama, who said they had been told never to contact Mr. Hutchinson or his family.

The cousins were delighted to hear from him. He plans to visit next year at Mardi Gras.

Mr. Hutchinson’s results were enlightening, but in other contexts ethnicity has posed a particularly knotty problem for DNA testing firms. The very definitions of “race” and “ethnicity” are fuzzy, said Joseph Pickrell, a computational geneticist at the New York Genome Center laboratory, affiliated with Columbia University.

“Different people mean different things when they say ‘race,’” he said. In the United States, for example, a person with almost any African ancestry often is identified as black.

“That’s not necessarily the case in other parts of the world,” Dr. Pickrell said.

Researchers at 23andMe acknowledged the difficulty in a recent paper, writing, “It is important to note that ancestry, ethnicity, identity and race are complex labels that result both from visible traits, such as skin color, and from cultural, economic, geographical and social factors.”

In a recent study, the researchers decided to use Census Bureau definitions — black, white, Hispanic — to ask how often people who identify as one race actually have genetic markers indicating a mixed heritage.

After examining data from 160,000 customers who agreed to participate, the geneticists learned that 3.5 percent of those who said they were white actually had DNA that was 1 percent or more African in origin.