ESTIMATING THE NUMBER OF PULSES IN A MASS EXTINCTION

Most previous work on the Signor-Lipps effect has focused on testing whether taxa in a mass extinction went extinct simultaneously as opposed to gradually. Many authors, however, have proposed scenarios in which taxa go extinct in distinct pulses or stages. Little methodology has been developed for quantifying characteristics of such pulsed extinction events. Here we introduce a method for estimating the number of pulses in a mass extinction, based on the positions of fossil occurrences in a stratigraphic section. Rather than using a hypothesis test, which assumes simultaneous extinction as a default, we reframe the question by asking what number of pulses best explains the observed fossil record.

For each possible number of pulses (from 1 to the total number of taxa) we calculate the likelihood for each possible extinction scenario with that number of pulses. From this we are able to determine the scenario having the maximum likelihood for each number of pulses. We then use Akaike Information Criterion (AIC), which quantifies the fit of a model to the data while accounting for the model’s complexity, to compare these likelihoods and find the optimal number of pulses.

Our framework has several advantages compared to classical hypothesis testing. First, we are able to determine relative weights for each number of pulses, rather than just a binary reject/do not reject decision. Second, in a hypothesis testing framework, the null hypothesis is privileged in the sense that it is the default, and is not rejected unless it is disproved beyond a reasonable doubt. While this asymmetry may be beneficial in some situations (e.g., a clinical trial for testing a new drug), it is not clear in our situation that simultaneous extinction should be favored as the null hypothesis. Third, a hypothesis test asks whether the observed data are consistent with the null hypothesis. However, even if the data are consistent with the null hypothesis (i.e., simultaneous extinction), they may be more consistent with other hypotheses (i.e., pulsed extinction).

We demonstrate the method by applying it to datasets from the end-Cretaceous and end-Permian extinctions.