After hiking a mile through the cloud forest of southern Ecuador earlier this year, a group of other birders and I arrived at a bench beneath a trailside shelter. It faced a flat-topped, moss-covered rock at the edge of a thicket. Diego Velasques, our guide and a park guard at the Reserva Tapichalaca, removed a round plastic food carton from his bag, walked over to the rock, and scattered a few worms on its surface. He began to whistle, and then called urgently: “Venga! Venga! Venga!”— Come! Come! Come! He went on like this for a minute, then stopped and smiled at us. Soon, a water balloon of a bird, gray with a black cap and white cheeks, skittered up a log behind the rock, peeked up over it, then climbed on top to eat the worms. Standing before us was a Jocotoco Antpitta, one of Ecuador’s rarest birds, one not even described to science until 1999 and still known from only a few localities. Specifically, this bird was Panchito, who Velasques had named, trained, and...