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.

此前针对希诺-利普斯效应（Signor-Lipps effect）的相关研究，多聚焦于检验集群灭绝事件中的分类单元究竟是同步灭绝还是逐步灭绝。然而诸多学者提出了分类单元以独立脉冲形式灭绝的情景模型，但目前针对这类脉冲式灭绝事件的特征量化方法仍较为匮乏。本研究基于地层剖面中的化石产出位置，提出一种可估算集群灭绝事件中灭绝脉冲数量的方法。与过往以假设检验为基础、默认分类单元同步灭绝的研究范式不同，本研究将问题重构为：多少个灭绝脉冲能够最优地解释观测到的化石记录。我们采用两步算法，不仅可估算灭绝脉冲的数量，还能为每种可能的脉冲数量计算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，求解其最大似然估计值。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）与贝叶斯信息准则（Bayesian Information Criterion, BIC）权重，随后将k近邻（k-Nearest Neighbor）分类器应用于这些权重。由此可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，5%的置信度认为存在3次。换言之，我们可以说明，我们有95%的置信度认为灭绝脉冲的数量为1或2。通过模拟实验，我们验证了该方法在多种场景下均表现良好，但在化石产出潜力随时间衰减的场景中效果欠佳；且除非样本量足够大，否则该方法在脉冲数量较少时的表现最为出色。我们通过晚白垩世菊石数据集对该方法进行了实例演示。