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.

过往针对西诺-利普斯效应（Signor-Lipps effect）的相关研究，大多聚焦于检验大灭绝事件中各分类群的灭绝模式究竟为同步发生还是渐进式演化。然而，诸多学者提出了分类群以独立脉冲式事件发生灭绝的假说场景，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。本研究提出一种基于地层剖面中化石产出位置数据，估算大灭绝事件脉冲次数的方法；与传统假设检验以同步灭绝作为默认前提的思路不同，本研究将研究问题重构为：何种脉冲次数的灭绝模式最能契合观测得到的化石记录。本研究采用两步法算法，不仅可估算灭绝脉冲的次数，还能为每种可能的脉冲次数计算置信水平或后验概率。第一步中，我们针对每一种可能的脉冲次数计算其最大似然估计值；第二步中，我们为每种可能的脉冲次数计算赤池信息准则（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, k-NN）分类器应用于这些权重数据。由此可得到灭绝脉冲次数的置信水平向量：例如，我们可以得到80%的置信度支持仅存在1次灭绝脉冲，15%的置信度支持存在2次脉冲，5%的置信度支持存在3次脉冲。等价而言，我们可以说明：有95%的置信度认为灭绝脉冲次数为1次或2次。通过模拟实验验证，本方法在多种场景下均表现良好，但在化石产出潜力逐渐降低的场景中存在局限；且除非样本量足够大，否则该方法在脉冲次数较少时的效果最优。最后，我们通过晚白垩世菊石数据集对本方法进行了实例演示。