The Probable Datum Method (PDM): a technique for estimating the age of origination or extinction of nannoplankton

Abstract

Accurate interpretation of origination and extinction of fossil species is crucial to answering a variety of questions in paleontology. Fossil datums, the observed age of first or last occurrences, are subject to sampling error as a result of preservation and low abundances near range endpoints. This sampling error can cause local range offset, an age difference between the observed first or last occurrence of a species and its true origination or extinction. Here, we develop and test a new technique, the Probable Datum Method (PDM), that can be used to assess the extent of local range offset for nannofossil species. The PDM estimates the original abundance of a taxon and its probable true age of first or last occurrence. The PDM uses a model in which original abundance is related to count abundance through preservation and the counting process. This model is empirically parameterized, including an experimental determination of false positive and error rates of a nannofossil count. The model is simulated then inverted to estimate likely original abundance and true datum age from count abundance data. We first test the PDM in a positive control experiment with known parameter values. This experiment shows that the PDM is robust and returns known values accurately. Next we apply the method to the origination of nannoplankton after the Cretaceous/Paleogene boundary to test whether first occurrences were synchronous between widely spaced locations. The PDM results suggest that observed diachrony of K/Pg originations cannot be explained by the effects of local range offset; rather, in some cases they indicate truly diachronous first occurrences between localities. Although the technique was developed to analyze nannoplankton ranges, the statistical nature of the PDM, its experimentally derived parameters, and its parsimonious nature should make it applicable to many micropaleontological studies that interpret patterns of origination and extinction.