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. Because 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 false negatives. We incorporate proper prior information, including an estimated 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 point estimate of the extinction time, a standard deviation for the uncertainty in the estimate, and confidence intervals for the time of extinction. We apply our model to stratigraphic ranges of benthic foraminifera collected from the early Late Cretaceous (Cenomanian and Turonian) from Eastbourne, England.