Inferring extinction risks from sighting records

Estimating the probability that a species is extinct based on historical sighting records is important when deciding how much effort and money to invest in conservation policies. The framework we offer is more general than others in the literature to date. Our formulation allows for definite and uncertain observations, and thus better accommodates the realities of sighting record quality. Typically, the probability of observing a species given it is extant/extinct is challenging to define, especially when the possibility of a false observation is included. As such, we assume that observation probabilities derive from a representative probability density function. We incorporate this randomness in two different ways ("quenched" versus "annealed") using a framework that is equivalent to a Bayes formulation. The two methods can lead to significantly different estimates for extinction. In the case of definite sightings only, we provide an explicit deterministic calculation (in which observation probabilities are point estimates). Furthermore, our formulation replicates previous work in certain limiting cases. In the case of uncertain sightings, we allow for the possibility of several independent observational types (specimen, photographs, etc.). The method is applied to the Caribbean monk seal, Monachus tropicalis (which has only definite sightings), and synthetic data, with uncertain sightings.