ACS PRF | ACS
All e-Annual Reports
44152-GB8
Estimating True Ranges of Fossil Taxa from Stratigraphic Data When Recovery Potential is Not Uniform
Summary of project: Most existing methods for estimating the true stratigraphic range of a fossil taxon require the assumption of uniform fossil recovery potential — that fossils are equally likely to be found at any point within the taxon's true range. This assumption is unrealistic, because factors such as the taxon's abundance and the amount of fossiliferous rock outcrop affect recovery potential. Other methods do not make this unrealistic assumption, but they instead require a priori quantitative knowledge of recovery potential that is often difficult to obtain. In my project, I am developing a method for estimating the true stratigraphic range of a taxon that works well for both uniform and variable recovery potential. I propose to estimate fossil recovery potential from the data itself, so that a priori knowledge of recovery potential is not required.
Research progress: During the first year of the grant period substantial progress was made. During the 2006–2007 academic year, I worked out some of the statistical background necessary for attacking the problem and refined the preliminary models that I had previously developed. I continued work during summer 2007, during which I worked with David J. Chudzicki, a Swarthmore undergraduate who had graduated in May 2007. He began by exploring the literature on estimating stratigraphic ranges and by learning advanced concepts of mathematical statistics, including profile likelihood, density estimation, and Bayesian modeling. We then worked together to develop and test new methodology, which required David to learn programming in Mathematica and R (a statistical programming environment). We have arrived at encouraging preliminary results. I am continuing to refine the models we developed, and we anticipate writing a paper for submission to Paleobiology in the coming year.
While working on the proposed problem, we also solved a related problem that is a special case of the proposed research — that of estimating true stratigraphic ranges when fossil recovery potential is uniform. We derived the optimal estimators of the true range and proved that these estimators are the best estimators possible (e.g., the confidence interval having the shortest average length). Using simulations, we showed that these optimal estimators substantially outperform existing methods. We have submitted a manuscript presenting these findings, which is currently in review at Paleobiology. We anticipate that these findings will have substantial impact on paleontologists, stratigraphers, and others for whom precise estimation of stratigraphic ranges plays an important role in their research.
Career impact: During fall 2007, I am being considered for promotion and tenure. The research experience supported by the PRF and the submitted manuscript will be valuable additions to my credentials.
Mr. Chudzicki will be starting a PhD program in mathematics at the University of Chicago in fall 2007, and the mathematical, programming, and research skills he developed while working on the project should prove beneficial as he continues his education.
