A FAST ALGORITHM FOR ESTIMATING THE DURATION OF A MASS EXTINCTION

In the past few decades, there has been much interest in determining whether mass extinction events were simultaneous or gradual. This task, however, is complicated by the incompleteness of the fossil record. Using statistical methods, a number of authors have accounted for such Signor-Lipps effects in testing whether a pattern of fossil occurrences is consistent with a simultaneous extinction. In such tests, the null hypothesis is typically that the extinction was simultaneous, with the alternative hypothesis being that the extinction was gradual. If the record of fossil occurrences does not strongly contradict the null hypothesis, we conclude the extinction could have been simultaneous.

However, even if the null hypothesis is not rejected, it is incorrect to infer that the null hypothesis must therefore be true. In fact, any set of fossil occurrences that is consistent with a simultaneous extinction is also consistent with a variety of gradual extinction scenarios. The important question, then, is not “Was the extinction simultaneous or gradual?”, but rather “How gradual was it?”

To answer this question, we propose a method for calculating a confidence interval on the duration of a mass extinction event, defined as the time or stratigraphic distance—possibly zero in the case of a truly simultaneous extinction—between the first and the last taxa to go extinct. To calculate the confidence interval, we take advantage of the relationship between confidence intervals and hypothesis tests: that is, a confidence interval is the set of values that would not be rejected by a hypothesis test. A conceptually straightforward but slow algorithm for carrying out the calculations is described elsewhere at this meeting. Here we describe an efficient algorithm to carry out these calculations. The algorithm exploits redundancies in the hypothesis tests to speed up running time by orders of magnitude. As an illustrative example, we apply the method to estimating the tempo of the end-Permian mass extinction.