Genetic evidence suggests that the reptiles somehow managed millions of years ago to make an ocean crossing from North America to Fiji.

For decades, the native iguanas of Fiji and Tonga have presented an evolutionary mystery. Every other living iguana species dwells in the Americas, from the Southwestern United States to the Caribbean and parts of South America. So how could a handful of reptilian transplants have ended up on two islands in the South Pacific, over 4,970 miles away?

“The question has definitely captured the imagination of scientists and the public alike,” said Simon G. Scarpetta, an evolutionary biologist at the University of San Francisco.

In research published Monday in the Proceedings of the National Academy of Sciences, Dr. Scarpetta and his colleagues make the case that the ancestors of Fiji’s iguanas crossed on mats of floating vegetation. Such a voyage across nearly 5,000 miles of open ocean would be the longest known by a nonhuman vertebrate.

Rafting — the term scientists use for hitching a ride across oceans on uprooted trees or tangles of plants — has long been recognized as a way for small creatures on land to reach islands, said Hamish G. Spencer, an evolutionary geneticist at the University of Otago in New Zealand who was not involved in the study. Usually those are invertebrates, whose small size means they can survive a long way in an uprooted tree trunk. While examples from nonflying vertebrates are relatively rare, he added, lizards and snakes seem to be able to raft farther than mammals, perhaps because their slower metabolism allows them to fast for a long time.

Iguana species have proved adept at making shorter crossings. In 1995, Dr. Scarpetta said, scientists observed at least 15 green iguanas rafting nearly 200 miles on hurricane debris from one Caribbean island to another. And researchers have long agreed that the ancestors of the iguanas of the Galápagos Islands made the nearly 600-mile trip from South America on bobbing vegetation.

A crossing to Fiji, however, represents an almost unimaginable challenge. While some researchers suggested that the Fiji iguana’s ancestors had rafted there as well, Dr. Spencer said, others pointed to the vast distances as a reason for skepticism. They countered that the iguanas were the remnant of an extinct group, one that had possibly crossed over land from the Americas to Asia or Australia, and then made the relatively easier crossing to Fiji and Tonga.

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