The uncertainty in the true end point of a fossil's stratigraphic range when stratigraphic sections are sampled discretely

Stratigraphic sections are often sampled at well-defined discrete points. B ecause of the incompleteness of the fossil record, a particular species may not be observed even when it is extant at a sampling point. We introduce a model and Bayesian analysis for estimating the true time of disappearance of a lineage from a section in the face of the possibility that failure to find the species beyond its observed stratigraphic range may represent fals e negatives. We incorporate proper prior information, including ail estimat ed longevity of the species and the probability that it will be observed if extant. Our analysis produces a posterior density for the true extinction time of the species. Summaries of this probability distribution provide a p oint estimate of the extinction time, a standard deviation for the uncertai nty in the estimate, and confidence intervals for the time of extinction. W e apply our model to stratigraphic ranges of benthic foraminifera collected from the early Late Cretaceous (Cenomanian and Turonian)from Eastbourne, E ngland.