For decades, invaders ran amok on Maclellan Island, a 19-acre nature refuge in the middle of the Tennessee River, in the heart of Chattanooga. Last year Jim Stewart, the executive director of the Chattanooga Audubon Society, which owns the island, tried to fight the invasives with fire, specifically a prescribed burn. “He said ‘Jim, you really should get some goats out there,’” Mr. Stewart recalled. So that’s what Mr. Stewart did. Two months later, six rented goats, paid for by donations, set hoof on the island, along with their guardian dog, Beo, a Great Pyrenees.