But as real ecosystems take on exotic species, they do not show any sign of being saturated, Dr. Sax said. In their paper, Dr. Sax and Dr. Gaines analyze the rise of exotic species on six islands and island chains. Invasive plants have become naturalized at a steady pace over the last two centuries, with no sign of slowing down. In fact, the total diversity of these islands has doubled.

Image A MIX California poppy and ryegrass, invasive New Zealand plants. Right, native vine and invasive Pride of Madeira. Credit... Dov Sax

Fish also show this pattern, said James Brown of the University of New Mexico. He said that whenever he visits a river where exotic fish have been introduced, “I ask, ‘Have you seen any extinctions of the natives?’ ” “The first response you get is, ‘Not yet,’ as if the extinction of the natives is an inevitable consequence. There’s this article of faith that the net effect is negative.”

Dr. Brown does not think that faith is warranted. In Hawaii, for example, 40 new species of freshwater fish have become established, and the 5 native species are still present. Dr. Brown and his colleagues acknowledge that invasive species can push native species out of much of their original habitat. But they argue that native species are not becoming extinct, because they compete better than the invasive species in certain refuges.

These scientists also point out that exotics can actually spur the evolution of new diversity. A North American plant called saltmarsh cordgrass was introduced into England in the 19th century, where it interbred with the native small cordgrass. Their hybrid offspring could not reproduce with either original species, producing a new species called common cordgrass.

Long before humans moved plants around, many plants hybridized into new species by this process. “Something like a third of the plant species you see around you formed that way,” Dr. Sax said.

Biological invasions also set off bursts of natural selection. House sparrows, for example, have moved to North America from Europe and have spread across the whole continent. “Natural selection will start to change them,” Dr. Sax said. “If you give that process enough time, they will become new species.”

“The natives themselves are also likely to adapt,” Dr. Sax added. Some of the fastest rates of evolution ever documented have taken place in native species adapting to exotics. Some populations of soapberry bugs in Florida, for example, have shifted from feeding on a native plant, the balloon vine, to the goldenrain tree, introduced from Asia by landscapers in the 1950s. In five decades, the smaller goldenrain seeds have driven the evolution of smaller mouthparts in the bugs, along with a host of other changes.