It all started when Sigrid E. Johnson was 62. She got a call from an old friend, asking her to participate in a study about DNA ancestry tests and ethnic identity. She agreed. Ms. Johnson thought she knew what the outcome would be. When she was 16, her mother told her that she had been adopted as an infant. Her biological mother was an Italian woman from South Philadelphia, and her father was a Black man. The results, however, told a different story. Today on The Sunday Read, what the growth in DNA testing, with its surprises and imperfections, means for people’s sense of identity.