Quantifying the Uncertainty in Times of Appearance and Disappearance in the Fossil Record: A Bayesian Approach

Harvard University, Cambridge MA

Investigators

Abstract

0000385 Marshall The most powerful methods for quantifying the incompleteness of the fossil record in local sections are based on Strauss and Sadler's (1989) confidence interval approach. This family of methods (including the distribution-free and generalized methods of Marshall [1994, 1997]) assume that the section has been continuously sampled, and that fossils may be found essentially anywhere in the section. However, in most sections these assumptions are violated, either because only parts of the section have been (e.g., for core data), or can be, sampled, or because fossils are restricted to specific bedding planes, or narrow stratigraphic intervals. As an alternative, Weiss and Marshall (1999) developed a Bayesian approach for estimating the uncertainty in stratigraphic end points of taxa in local sections that have been sampled discretely. However, the method is based on some overly simple assumptions: that collecting intensity is equal at all sampled horizons; that species remain at the same relative abundance at all times; and, that the beds sampled have no vertical thickness. Further, our approach (like all others) does not make use of abundance data in the fossil record. Here we propose to develop the method presented in Weiss and Marshall (1999) into a series of more sophisticated methods that can accommodate the inhomogeneities typically seen in the fossil record, as well as take advantage of abundance data when it is recorded. Our ultimate goal is to provide a statistical "tool-kit" that can be broadly applied to a wide range of problems.