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 have developed a method for estimating the true stratigraphic range of a taxon that works well for both uniform and variable recovery potential. The method is able 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 (2006–2007) grant year, I worked out some of the statistical background necessary for attacking the problem and tested some preliminary models. David J. Chudzicki '07 worked in the lab during summer 2007, and we achieved some preliminary but encouraging results. In addition, we solved a related problem that is a special case of the proposed research — deriving the optimal estimator of the true stratigraphic range when fossil recovery potential is uniform. Our manuscript describing these findings is currently in revision for Paleobiology.
In 2007–2008, the second year of the grant period, we made substantial progress on the project. Working with me were Phil Everson, a faculty colleague at Swarthmore, and Dasol Park '10, a Swarthmore mathematics major who joined the lab in summer 2008. We have derived a confidence interval for the true endpoint of a stratigraphic range that does not assume uniform recovery potential and does not require a priori knowledge of the fossil recovery function. Using extensive simulations, we show that our confidence interval method achieves correct coverage probabilities under a variety of fossil recovery functions (e.g., 95% confidence intervals are correct 95% of the time), which existing methods are not able to do successfully.
We have thus essentially solved the problem originally proposed. We are continuing to develop point estimates for the true time of extinction, a problem related to the originally proposed project of deriving confidence intervals. 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.
In February 2008, I gave a talk presenting our initial results at the University of Pennsylvania Geobiology Symposium. In October 2008, I gave a talk presenting more complete results at the Geological Society of America Annual Meeting in Houston. At the same meeting, Mr. Park gave a poster describing our methodology. In the coming year, we will disseminate our results by writing a paper for submission to Paleobiology.
Career impact: During spring 2008, I was promoted to Associate Professor with tenure. The research experience supported by the PRF was a valuable addition to my credentials.
Mr. Chudzicki started PhD program in mathematics at the University of Chicago in fall 2007. Mr. Park is currently completing his junior year at Swarthmore and is considering attending graduate school in math or computer science. For both students, the mathematical, programming, and research skills they developed while working on the project should prove beneficial as they continue their education.
