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.

以往针对希诺-利普斯效应（Signor-Lipps effect）的相关研究，大多聚焦于检验集群灭绝事件中的各类分类群究竟是同步灭绝还是逐步消亡。然而诸多学者已提出分类群以离散脉冲形式灭绝的情景模型，但目前针对此类脉冲式灭绝事件的特征量化方法仍十分有限。本研究提出一种基于地层剖面中化石产出位置的集群灭绝脉冲数量估算方法。不同于传统假设检验以同步灭绝作为默认前提的研究思路，我们将研究问题重构为：何种数量的灭绝脉冲能够最优解释观测到的化石记录。
我们采用两步算法，不仅可估算集群灭绝的脉冲数量，还能针对每种可能的脉冲数量计算其置信水平或后验概率（posterior probability）。第一步，我们为每种可能的脉冲数量求解最大似然估计值；第二步，我们针对每种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，并将k近邻分类器（k-Nearest Neighbor classifier）应用于上述权重。由此可得到灭绝脉冲数量的置信水平向量：例如，我们有80%的置信度认为仅存在一次灭绝脉冲，15%的置信度对应两次脉冲的情形，剩余5%的置信度指向三次脉冲的情况。换言之，我们可以认定有95%的置信度表明灭绝脉冲数量为1或2。通过模拟实验我们证明，该方法在多种场景下均表现良好，但在化石恢复潜力逐渐降低的情形下效果欠佳；且除非样本量足够庞大，否则该方法在脉冲数量较少时的表现最优。我们采用晚白垩世菊石数据集对该方法进行了实例演示。