CONFIDENCE INTERVALS FOR THE DURATION OF A MASS EXTINCTION

The Signor-Lipps effect holds that a truly simultaneous extinction of a group of taxa may appear gradual in the fossil record due to incomplete fossil preservation. To account for this effect, much work in the last two decades has been devoted to devising statistical tests for a simultaneous extinction of all taxa in a stratigraphic section. But rather than being limited to rejecting or failing to reject this single scenario, ideally we should estimate the range of extinction scenarios that is consistent with the fossil record. In other words, rather than testing the oversimplified distinction of “simultaneous or gradual?”, we should be asking “how gradual?”

To answer this question, what is needed is a confidence interval for the duration of a mass extinction, either in terms of the time or stratigraphic thickness between the first and last taxon to go extinct. For example, we would like to be able to say, with 95% confidence, that the extinction took place over a duration of 100,000 to 150,000 years, or over 4 to 7 meters of stratigraphic thickness. This does not deny the possibility of a truly simultaneous extinction; rather, in this framework, a simultaneous extinction is one in which the confidence interval contains a possible duration of zero meters.

We propose a method for calculating such confidence intervals based on the positions of fossil occurrences. There is no simple formula for such a confidence interval; instead, the interval is defined implicitly using the relationship between intervals and hypothesis tests. We describe a brute-force method that conceptually demonstrates how the method works. We are currently developing a fast implementation of the method, which is described elsewhere at this meeting. As an illustrative example, we apply our confidence interval to data from the end-Permian mass extinction