Dr. Gibson returned to the same 12 islands in 2012 and repeated the survey. He started on a 25-acre island. The first survey had found seven species of mammals. Dr. Gibson spent a week checking traps on the island and found only a single species: the Malayan field rat.

This was a startling find for two reasons. One was the drastic crash in diversity. The other was that the Malayan field rat wasn’t on the islands when they first formed. Malayan field rats thrive around villages and farms and other disturbed habitats. The rats Dr. Gibson trapped must have come from the surrounding rain forests, where they still remain scarce. When they swam to the islands, they found fragmented forests that they could dominate.

“I thought, ‘Wow, what if this trend holds?'” said Dr. Gibson. “And it did.”

On most of the islands, all the native species were gone, replaced by the rats. Only on a few islands did some species still cling to existence. Dr. Gibson surveyed an additional four islands and found they also had just one or two species, suggesting that all the islands were suffering massive extinctions in about 20 years.

“No one expected to see such rapid extinctions,” said Dr. Gibson.

Dr. Gibson suspects that the small size of the island forests makes them particularly vulnerable to invasion by the rats. The diversity of mammals he trapped in the mainland forests was the same as in the first surveys in the 1990s.

“This study confirms for mammals what we’ve long known for birds,” said Stuart L. Pimm, the president of Saving Species and a professor at Duke. In 2003, Dr. Pimm and his colleagues studied records of birds from forest fragments in the Amazon and found species going extinct at a comparable rate.

Dr. Pimm and Dr. Gibson agreed that the fast pace of extinction in forest fragments gives an urgency to conserving the large swaths of tropical forest that still remain. “Our study shows we may need to do that very quickly,” said Dr. Gibson.