When you’ve found two of everything else.
That’s the conclusion of a fascinating, if disappointing, paper about the ivory-billed woodpecker in the latest issue of Conservation Biology. Most experts believe the “Lord God” bird was driven to extinction in the middle of the twentieth century. Occasional reports of sightings, however, have kept some hope alive. A report from Arkansas in 2004, for example, inspired detailed censuses of several areas with promising habitat. Sadly, no unambiguous evidence of IBWPs appeared.
Which raises an important question: when should you stop looking? Nicholas, J. Gotelli, Anne Chao, Robert K. Colwell, Wen-Han Hwang, and Gary R. Graves used statistics and cost-benefit analysis to derive a simple stopping rule:
We evaluated whether the census efforts at these localities were sufficient to discover an Ivory-billed Woodpecker if it had been present and derived a practical stopping rule for deciding when to abandon the search in a particular site. An efficient stopping rule that incorporates rewards of discovery and costs of additional sampling should be triggered at the smallest sample size q satisfying f1/q < c/R, where f1 is the number of singletons (species observed exactly once during a census), c is the cost of making a single observation, and R is the reward for detecting each previously undetected species (Rasmussen & Starr 1979). Because R for an Ivory-billed Woodpecker is extremely large relative to c, c/R is close to zero. Thus, a simple, empirical stopping rule is to stop searching when each observed species is represented by at least 2 individuals in the sample (f1= 0). The same stopping rule can be derived independently from theorems originally developed by Turing and Good for cryptographic analyses (Good 1953, 2000). Both derivations imply that when f1= 0, the probability of detecting a new species approaches zero. We applied this stopping rule to the census data for the set of species that regularly winter in bottomland forest, such as the Ivory-billed Woodpecker, which was sedentary and occupied year-round territories.
According to that stopping rule, the search should be called off at one location (Congaree River, South Carolina) and is close to hopeless in the other three (Choctawhatchee River, Florida; Pearl River, Louisiana and Mississippi; and Pascagoula River, Mississippi).
Based on these and other data, the authors conclude that the probability that ivory-billed woodpeckers still inhabit the southeastern United States are less than 1 in 10,000.