A fast re-sampling method for using reliability ratings of sightings with extinction-date estimators

The pattern of sightings of a species that is rare, and then no longer observed, can be used to estimate its extinction date. However, other than physical captures or specimens, the veracity of any sighting is ambiguous, and should be treated probabilistically when used to infer extinction dates. We present a simple yet powerful computational approach for incorporating observational reliability into extinction date estimators (EDE). Our method (1) combines repeated within-year sightings probabilistically, (2) samples observations using reliability as an inclusion probability, (3) infers a probability distribution and summary statistics of extinction dates with any EDE, and (4) computes the frequency distribution of the extinction date. We applied this method to eight exemplar sighting records covering a range of lengths, sighting rates and uncertainties, using a variety of statistical EDEs, and compared these results with a threshold approach for selecting sightings. We also demonstrated a robust coverage of "true" extinction dates based on selected real-world examples of rediscovered species and confirmed extinctions, and simulated sighting records. Our approach represents a powerful generalization of past work because it is not predicated on any specific method for inferring extinction dates, and yet is simple to implement (with R script provided).