“We are not separate tribes of Latinos and whites and blacks in America,” Mr. Ball said. “We’ve all mingled, and we have done so for generations.”

The outlines of Mrs. Obama’s family history unfolded from 19th century probate records, yellowing marriage licenses, fading photographs and the recollections of elderly women who remember the family. Ms. Smolenyak, who has traced the ancestry of many prominent figures, began studying the first lady’s roots in earnest after conducting some preliminary research into Mrs. Obama’s ancestry for an article published in The New York Times earlier this year.

Of the dozens of relatives she identified, Ms. Smolenyak said, it was the slave girl who seemed to call out most clearly.

“Out of all Michelle’s roots, it’s Melvinia who is screaming to be found,” she said.

When her owner, David Patterson, died in 1852, Melvinia soon found herself on a 200-acre farm with new masters, Mr. Patterson’s daughter and son-in law, Christianne and Henry Shields. It was a strange and unfamiliar world.

In South Carolina, she had lived on an estate with 21 slaves. In Georgia, she was one of only three slaves on property that is now part of a neat subdivision in Rex, near Atlanta.

Whether Melvinia labored in the house or in the fields, there was no shortage of work: wheat, corn, sweet potatoes and cotton to plant and harvest, and 3 horses, 5 cows, 17 pigs and 20 sheep to care for, according to an 1860 agricultural survey.

It is difficult to say who might have impregnated Melvinia, who gave birth to Dolphus around 1859, when she was perhaps as young as 15. At the time, Henry Shields was in his late 40s and had four sons ages 19 to 24, but other men may have spent time on the farm.