Data from: A nonstationary Markov model detects directional evolution in hymenopteran morphology

Directional evolution has played an important role in shaping the morphological, ecological, and molecular diversity of life. However, standard substitution models assume stationarity of the evolutionary process over the time scale examined, thus impeding the study of directionality. Here we explore a simple, nonstationary model of evolution for discrete data, which assumes that the state frequencies at the root differ from the equilibrium frequencies of the homogeneous evolutionary process along the rest of the tree (i.e., the process is nonstationary, nonreversible, but homogeneous). Within this framework, we develop a Bayesian approach for testing directional versus stationary evolution using a reversible-jump algorithm. Simulations show that when only data from extant taxa are available, the success in inferring directionality is strongly dependent on the evolutionary rate, the shape of the tree, the relative branch lengths, and the number of taxa. Given suitable evolutionary rates (0.1–0.5 expected substitutions between root and tips), accounting for directionality improves tree inference and often allows correct rooting of the tree without the use of an outgroup. As an empirical test, we apply our method to study directional evolution in hymenopteran morphology. We focus on three character systems: wing veins, muscles, and sclerites. We find strong support for a trend toward loss of wing veins and muscles, while stationarity cannot be ruled out for sclerites. Adding fossil and time information in a total-evidence dating approach, we show that accounting for directionality results in more precise estimates not only of the ancestral state at the root of the tree, but also of the divergence times. Our model relaxes the assumption of stationarity and reversibility by adding a minimum of additional parameters, and is thus well suited to studying the nature of the evolutionary process in data sets of limited size, such as morphology and ecology.

定向演化（directional evolution）在塑造生命的形态、生态与分子多样性方面发挥了关键作用。然而，标准替换模型（substitution models）假设在所考察的时间尺度内，演化过程（evolutionary process）具有平稳性（stationarity），这极大阻碍了定向演化相关研究的推进。我们针对离散数据提出了一种简单的非平稳演化模型（nonstationary model），该模型设定根节点处的状态频率（state frequencies），与系统发育树其余分支上齐次演化过程（homogeneous evolutionary process）的平衡频率（equilibrium frequencies）并不一致——即该过程为非平稳、不可逆但齐次的。在此框架下，我们开发了一种基于贝叶斯方法（Bayesian approach）的检验策略，通过可逆跳跃算法（reversible-jump algorithm）来区分定向演化与平稳演化两种模式。模拟实验结果显示，当仅能获取现存类群（extant taxa）的数据时，定向演化的推断成功率强烈依赖于演化速率（evolutionary rate）、系统发育树的拓扑结构、相对分支长度以及类群总数。当演化速率处于适宜区间（根节点至末端类群（tips）的期望替换数为0.1~0.5）时，纳入定向演化的考量可提升系统发育树推断的准确性，且通常无需借助外类群（outgroup）即可正确确定系统发育树的根位置。作为实证检验，我们将该方法应用于膜翅目（Hymenoptera）形态学的定向演化研究。我们聚焦于三类性状系统（character systems）：翅脉、肌肉与骨片（sclerites）。研究结果强烈支持翅脉与肌肉趋向于丢失的演化趋势，而骨片的演化则无法排除平稳性假设。在总证据定年方法（total-evidence dating approach）中加入化石与时间信息后，我们发现考虑定向演化不仅能更精准地估计系统发育树根节点的祖先状态，还能优化分歧时间（divergence times）的估计结果。我们的模型仅通过增加极少量额外参数，便放宽了平稳性与可逆性的假设，因此非常适用于探究形态学、生态学等有限规模数据集的演化过程本质。