The butterfly that goes from Canada to Mexico and partway back lives six to nine months, but when it mates and lays eggs, it may have gotten only as far as Texas, and breeding butterflies live only about six weeks. So a daughter born on a Texas prairie goes on to lay an egg on a South Dakota highway divider that becomes a granddaughter. That leads to a great-granddaughter born in a Winnipeg backyard. Come autumn, how does she find her way back to the same grove in Mexico that sheltered her great-grandmother?

To test their ability to reorient themselves, Dr. Taylor has moved butterflies from Kansas to Washington, D.C. If he releases them right away, he said, they take off due south, as they would have where they were. But if he keeps them for a few days in mesh cages so they can see the sun rise and set, “they reset their compass heading,” he said. “The question is: How?”