Low genetic variation can pose a serious threat to survival. When a new threat appears — a new disease, for instance — some individuals may have the genes to resist it and others lack them. In a population with low genetic variation, none of the animals may have the right genes to survive.

Inbred populations also often share mutations that are bad for health, shortening life spans or reducing the number of offspring. Dr. Wayne and his colleagues found that island foxes have many more harmful mutations than gray foxes on the mainland.

On the face of it, the island foxes should have vanished long ago. “But that hasn’t happened to them in thousands of years,” Dr. Wayne said. “They’re an exception to the paradigm.”

Dr. Wayne speculated that island foxes might enjoy some sort of special protection. It’s possible, for example, that as top predators on a small island, they didn’t have to face the challenges that other inbred animals do. Or perhaps the people who lived on the islands helped them survive.

Or, while the genes of island foxes may be almost entirely identical, maybe they are activated in the animals in varying patterns. Experiences early in life can program genes to switch on and off, a phenomenon called epigenetics.

“It might also be some combination of all of the above,” Dr. Wayne said.

Other researchers suggest that island foxes have been protected in more familiar ways. Newly arrived foxes could have rejuvenated the Channel Island gene pool with some fresh variation.

“Their study has not ruled out occasional immigrants reaching the islands,” said Richard Frankham, a geneticist at Macquarie University in Australia.