Data from: Phylogenetic analysis using Lévy processes: finding jumps in the evolution of continuous traits

Gaussian processes, a class of stochastic processes including Brownian motion and the Ornstein–Uhlenbeck process, are widely used to model continuous trait evolution in statistical phylogenetics. Under such processes, observations at the tips of a phylogenetic tree have a multivariate Gaussian distribution, which may lead to suboptimal model specification under certain evolutionary conditions, as supposed in models of punctuated equilibrium or adaptive radiation. To consider non-normally distributed continuous trait evolution, we introduce a method to compute posterior probabilities when modeling continuous trait evolution as a Lévy process. Through data simulation and model testing, we establish that single-rate Brownian motion (BM) and Lévy processes with jumps generate distinct patterns in comparative data. We then analyzed body mass and endocranial volume measurements for 126 primates. We rejected single-rate BM in favor of a Lévy process with jumps for each trait, with the lineage leading to most recent common ancestor of great apes showing particularly strong evidence against single-rate BM.高斯过程（Gaussian processes）是一类涵盖布朗运动（Brownian motion）与奥恩斯坦-乌伦贝克过程（Ornstein–Uhlenbeck process）的随机过程，在统计系统发育学领域被广泛应用于连续性状演化的建模工作。在此类过程的框架下，系统发育树末端的观测值服从多元高斯分布，但在间断平衡（punctuated equilibrium）或适应辐射（adaptive radiation）模型所假设的部分演化条件下，该模型设定可能并非最优。为实现非正态分布的连续性状演化建模，我们提出了一种将连续性状演化建模为莱维过程（Lévy process）时的后验概率计算方法。通过数据模拟与模型检验，我们证实单速率布朗运动（single-rate Brownian motion, BM）与带跳跃的莱维过程会在比较数据中生成显著不同的分布模式。随后我们对126种灵长类的体重与颅内容积测量数据展开分析，结果拒绝单速率布朗运动模型，转而支持各性状对应的带跳跃莱维过程；其中指向类人猿最近共同祖先的演化支，展现出尤为强烈的拒绝单速率布朗运动的统计学证据。