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.既往有关西诺-利普斯效应（Signor-Lipps effect）的研究大多聚焦于检验集群灭绝事件中的类群究竟是同步灭绝还是逐步消亡。然而，诸多学者提出了类群以独立脉冲式灭绝事件完成消亡的情景，但目前尚缺乏可用于量化此类脉冲式灭绝事件特征的方法学框架。本研究基于地层剖面中化石产出的层位，提出了一种用于估算集群灭绝事件中灭绝脉冲数量的方法。本研究并未采用传统的假设检验并默认同步灭绝为研究前提的思路，而是通过提问「何种数量的灭绝脉冲最能解释所观测到的化石记录」来重构研究问题。 本研究采用两步算法，不仅可估算灭绝脉冲的数量，还可得到每种可能脉冲数量对应的置信水平或后验概率。第一步，针对每种可能的脉冲数量，计算其最大似然估计值；第二步，为每种可能的脉冲数量计算赤池信息准则（Akaike Information Criterion，AIC）权重与贝叶斯信息准则（Bayesian Information Criterion，BIC）权重，并将k近邻分类器（k-Nearest Neighbor classifier）应用于上述权重，最终得到灭绝脉冲数量的置信水平向量。例如，我们可以有80%的置信度认为仅存在1次灭绝脉冲，15%的置信度认为存在2次脉冲，5%的置信度认为存在3次脉冲；换言之，我们可以断言有95%的置信度确定灭绝脉冲数量为1或2。通过模拟实验，本研究证明该方法在多种场景下均表现良好，但在化石保存潜力随时间下降的场景中存在局限性；且当脉冲数量较少时其效果最优，仅当样本量足够大时，才可适用于脉冲数量较多的情形。本研究最后以晚白垩世菊石数据集为例，对所提方法进行了演示验证。