Feral cats have a taste for tiny, threatened marsupials like this bilby in Australia. Chang W. Lee/The New York Times

Feral cats take a heavy toll on wildlife. But they are especially a threat in Australia, which has no native feline species and is home to a menagerie of slow-to-reproduce, snack-size mammals. The solution? Smarter traps, sharpshooters and the “Felixer,” a machine that sprays toxic gel onto passing cats.