Here’s a conundrum: What do you do about an animal that is wreaking havoc abroad but is endangered at home?

Take that cute European rabbit pictured above. In Australia, its population has reached plague proportions, helping to push some marsupials to the brink of extinction. But in the rabbit’s native France, Spain, and northern Africa, its numbers have dropped so precipitously because of disease, hunting, and habitat loss that the International Union for the Conservation of Nature lists it as “near threatened.”

In fact, 15 percent of mammals and 10 percent of birds considered nonnative in one part of the world are listed by the IUCN as threatened, according to Dov Sax, a conservation biologist at Brown University, and Heinke Jager of the Charles Darwin Foundation. The researchers presented their findings at the Society for Conservation Biology’s North America Congress for Conservation Biology in Missoula, Mont., this week.

Such numbers are prompting a rethink among biologists, with some scientists saying that if we are to preserve global biodiversity, we may have to embrace the nonnative species among us.

“We still have a pretty one-dimensional view on nonnative species—that they’re undesirable,” said Sax. “But that is cracking a bit.”

That’s because the rate of species extinction is accelerating.

Related How the California Island Fox Outfoxed Extinction

As of January 2013, the United States Fish and Wildlife Service had listed 1,436 species found in the U.S. as endangered or threatened. “By 2100 we can expect a much higher fraction of our native species to be endangered,” said Sax.

Stuart Pimm, a biologist at Duke University, is among the scientists who believe the planet is on the verge of a sixth great extinction. For every 1 million species, 100 to 1,000 go extinct each year, mostly because of human-caused habitat destruction and climate change, according to a study Pimm published in May.

“Species can be both good and bad,” said Edwin Grosholz, a conservation ecologist at the University of California, Davis. “We need to think about the circumstances. We can’t simply label them as one or the other.”

For instance, the California clapper rail, a long-legged, hen-like bird once abundant around San Francisco Bay, is now endangered and has become dependent on an invasive salt marsh cordgrass for its nesting habitat. So the eradication of an invasive species could compromise the recovery of a native endangered one.

Then there’s the wattle-necked softshell turtle. It is now endangered in its native China and Vietnam, as it is hunted for the food trade. But the turtle is flourishing on the Hawaiian islands of Kauai and Oahu, where Chinese immigrants introduced the reptile in the 1850s.

Instead of harming native wildlife, the turtle is helping it by preying on other nonnative species, including largemouth bass, Asian catfish, and Tahitian prawns.

“If you want to preserve species, then a lot of these nonnative species around the world can do that in the long run,” said Sax.