Data from: 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 or
gradually. However, many authors have proposed scenarios in which taxa go
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 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 for each possible number of pulses. In the second
step, we calculate the Akaike Information Criterion (AIC) and Bayesian
Information Criterion (BIC) weights for each possible number of pulses,
and then apply a k-Nearest Neighbor classifier to these 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. Equivalently, we can state that
we are 95% confidence that the number of extinction pulses is 1 or 2.
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 dataset of Late Cretaceous ammonites.