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Condoleezza Rice, former US Secretary of State and national security adviser, ought to be a tough woman to surprise. Yet when Henry Louis Gates Jr, host of a US television series called Finding Your Roots, revealed that nearly half of her genetic ancestry could be traced to Europe, Rice, an African American, told Gates, “I’m stunned.”

Although it is no secret that many African Americans have some European ancestry — a legacy of the transatlantic slave trade — advances in DNA analysis are beginning to provide more detailed insight for individuals. Commercial ancestry testing, once the province of limited information of dubious accuracy, is taking advantage of whole-genome scans, sophisticated analyses and ever-deeper databases of human genetic diversity to help people to answer a simple question: where am I from?

Until a few years ago, most ancestry tests for individuals relied on short stretches of DNA in cell-powering organelles called mitochondria, which are inherited through the mother, or on the Y chromosome, which a father passes down to his sons. As humans fanned out from Africa some 40,000 to...