The Signor-Lipps effect states that even a sudden mass extinction will invariably appear gradual in the fossil record, due to incomplete fossil preservation. Most previous work on the Signor-Lipps effect has focused on testing whether taxa in a mass extinction went extinct simultaneously or gradually. However, many authors have proposed scenarios in which taxa went extinct in distinct pulses. 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 amass 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 for each possible number of pulses. In the second step, we calculate the Akaike information criterion and Bayesian information criterion weights for each possible number of pulses, and then apply a k-nearest neighbor classifier to these weights. This method 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% confident that there were three pulses. Equivalently, we can state that we are 95% confident that the number of extinction pulses is one or two. Using simulation studies, we show that the method performs well in a variety of situations, although it has difficulty in the case of decreasing fossil recovery potential, and it is most effective for small numbers of pulses unless the sample size is large. We demonstrate the method using a data set of Late Cretaceous ammonites.