ESTIMATING THE DURATION OF A MASS EXTINCTION

Several hypothesis tests have been developed to test whether a set of fossil finds is consistent with a simultaneous or gradual extinction. Most previous work has taken the null hypothesis to be simultaneous extinction. Failing to reject such a null hypothesis indicates that the extinction could have been simultaneous, even though it may appear gradual (the Signor-Lipps effect). However, such a conclusion does not exclude the possibility of a truly gradual extinction. In fact, the same set of fossil finds can be consistent both with simultaneous extinction and a range of gradual extinction scenarios.

Thus, instead of asking “Was the extinction gradual?”, perhaps a better question to ask is “How gradual could the extinction have been?”. While much work has been done previously on testing for simultaneous extinctions, there are fewer methods for testing gradual extinctions. Previous work in our lab aimed to answer this question by investigating the special case of two-pulse extinctions and estimating the time or stratigraphic distance separating the two extinction pulses.

We propose a new method that extends our previous work to estimating the time or stratigraphic distance separating the first and last extinctions of any number of extinction pulses, a quantity we refer to as delta. Our method gives a confidence interval for delta, thereby estimating the duration of the extinction event. For example, we might find that the fossil record in a stratigraphic section is consistent with a gradual extinction over 5 to 30 meters. In this framework, a possibly simultaneous extinction is one whose confidence interval contains zero. We apply our method to datasets from the end-Permian and end-Cretaceous extinctions.