Inferring about the extinction of a species using certain and uncertain sightings

The sighting record of threatened species is often used to infer the possibility of extinction. Most of these sightings have uncertain validity. Solow and Beet(2014) developed two models using a Bayesian approach which allowed for uncertainty in the sighting record by formally incorporating both certain and uncertain sightings, but in different ways. Interestingly, the two methods give completely different conclusions concerning the extinction of the Ivory-billed Woodpecker. We further examined these two methods to provide a mathematical explanation, and to explore in more depth, as to why the results differed from one another. It was found that the first model was more sensitive to the last uncertain sighting, while the second was more sensitive to the last certain sighting. The difficulties in choosing the appropriate model are discussed.