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A gloved hand inserts a pipette of clear liquid into a test tube.

By now, millions of us have taken ancestry tests. We’ve spit into tubes and allowed our genetic information to be uploaded into databases. In return we’ve had our genomes assigned to different parts of the world. The fine print warns us not to rely on those results, despite their seeming precision: 0.1 percent Oceanian! It’s hard to resist telling friends and family that we’ve turned out to be partly sub-Saharan African or Middle Eastern or Scandinavian. But testing with a different company may yield different results, or we may log into our account one day and find that the allocations have changed. Often the tests create as many mysteries as they solve.

The explanations that testing companies give for these shifts tend to be passive and blandly opaque: Identifying “ancestry-informative markers” depends on “sufficient data” from “reference populations.” Errors are “noise.” In her smart, searching new book, “Futureface: A Family Mystery, an Epic Quest, and the Secret to Belonging,” the journalist and former MSNBC host Alex Wagner recounts being incorrectly assigned enough Scandinavian DNA that one of her grandparents could...