CONFIDENCE INTERVALS FOR THE DURATION OF A MASS EXTINCTION

There are several statistical methods for distinguishing whether a mass extinction is sudden or gradual, based on the stratigraphic positions of fossil taxa. This distinction, however, is in some sense a false dichotomy. A “gradual” mass extinction can encompass a wide range of scenarios, from nearly simultaneous to very protracted. Moreover, a dataset of stratigraphic positions can be consistent with both sudden and gradual scenarios. Here, instead of asking whether an extinction event was sudden or gradual, we reframe the question as “how gradual was it?” To do so, we calculate a confidence interval for the duration of the extinction, defined as the difference between the ages or stratigraphic positions of the first and last taxa to go extinct. In this framework, an interval that includes zero indicates that the data are consistent with a simultaneous extinction (although they may also be consistent with a range of gradual scenarios). Our approach follows that of Wang et al 2012 (Paleobiology). However, their approach assumes uniform recovery and preservation of fossils, a strong and typically unrealistic assumption. Here, we relax this assumption by incorporating the approach of Wang et al 2016 (Paleobiology), which used the Reflected Beta distribution to model fossil recovery potential. We describe a Monte Carlo (simulation-based) methodology to compute confidence intervals, which relies on inverting a series of hypothesis tests, and demonstrate the method on an illustrative dataset.