No sign marks the start of the trail to one of the last unspoiled habitats in all of Africa. I wouldn’t see it anyway. I’m crammed into an 11-passenger van carrying 13 people and a heap of backpacks as it navigates to that unmarked spot in a scientific reserve that sprawls across the southern end of Bioko, a mountainous tropical island 20 miles off the west coast of central Africa. A sweaty forearm is smashed against my sweaty shoulder. Three knees dig into my back through the thin seat. I’m not complaining—the porters behind me will lug our expedition’s gear for two days over 18 rugged miles into the Gran Caldera de Luba, a rainforest-blanketed volcanic crater whose 7,400-foot-high walls create a natural sanctuary for a dazzling array of wildlife. The few dozen people who make the arduous journey each year come mostly to survey monkeys. Our group is venturing into this primeval realm to document its far-lesser-known inhabitants, especially birds. If we’re really...