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 and assuming simultaneous extinction as the default, we reframe the question by asking what number of pulses best explains the observed fossil record.

Using a two-step algorithm, we are able to estimate not just the number of extinction pulses, but also a confidence level or posterior probability for each possible number of pulses. In the first step, we find the maximum likelihood estimate of the extinction pulse locations for each possible number of pulses. In the second step, we calculate the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for each possible number of pulses, and then apply a k-Nearest Neighbor classifier to the set of AIC and BIC weights. This gives us a vector of confidence levels for the number of extinction pulses — for instance, we might be 80% confident that there was a single extinction pulse, 15% confident that there were two pulses, and 5% confidence that there were three pulses. Alternately, we can state that a 95% confidence interval for the number of extinction pulses is (1,2). We demonstrate the method using datasets on Late Cretaceous ammonites, for which a simultaneous extinction is strongly supported, and Cenomanian/Turonian foraminiferans, for which a gradual extinction with several pulses is supported.