Finding rare species and estimating the probability that all occupied sites have been found

Detecting occupied sites of rare species, and estimating the probability that all occupied sites are known within a given area, are desired outcomes for many ecological or conservation projects. Examples include managing all occupied sites of a threatened species or eradicating an emerging invader. Occupied sites may remain undetected because (1) sites where the species potentially occurs had not been searched, and (2) the species could have been overlooked in the searched sites. For rare species, available data are typically scant, making it difficult to predict sites where the species probably occurs or to estimate detection probability in the searched sites. Using the critically endangered Rose's mountain toadlet (Capensibufo rosei), known from only two localities, we outline an iterative process aimed at estimating the probability that any unknown occupied sites remain and maximizing the chance of finding them. This includes fitting a species distribution model to guide sampling effort, testing model accuracy and sampling efficacy using the occurrence of more common proxy species, and estimating detection probability using sites of known presence. The final estimate of the probability that all occupied sites were found incorporates the uncertainties of uneven distribution, relative area searched, and detection probability. Our results show that very few occupied sites of C. rosei are likely to remain undetected. We also show that the probability of an undetected occupied site remaining will always be high for large unsearched areas of potential occurrence, but can be low for smaller areas intended for targeted management interventions. Our approach is especially useful for assessing uncertainty in species occurrences, planning the required search effort needed to reduce probability of unknown occurrence to desired levels, and identifying priority areas for further searches or management interventions.