Data from: A non-stationary 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 hampering the study of directionality. Here we explore a simple, non-stationary 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 non-stationary, non-reversible, 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 is 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 to 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 towards 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 datasets of limited size, such as morphology.

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，标准置换模型（substitution models）假设在所考察的时间尺度内，进化过程保持平稳性（stationarity），这一前提阻碍了定向演化相关研究的开展。在此，我们针对离散数据构建了一款简洁的非平稳进化模型，该模型假定序列根部的状态频率与谱系其余部分上齐次进化过程（homogeneous evolutionary process）的平衡频率（equilibrium frequencies）存在差异，即该过程为非平稳、不可逆但齐次的。基于此框架，我们开发了一种贝叶斯方法，借助可逆跳变（reversible-jump）算法来检验定向演化与平稳演化的差异。模拟实验表明，若仅能获取现存类群（extant taxa）的数据，定向性推断的成功率强烈依赖于进化速率、谱系树形态、分支长度相对比例以及类群数量。当进化速率处于合理范围（根节点至末梢的期望置换数为0.1至0.5）时，考虑定向性可提升谱系树推断的准确性，且通常无需借助外类群（outgroup）即可正确确定树的根节点位置。作为实证检验，我们将该方法应用于膜翅目（hymenopteran）形态特征的定向演化研究。我们聚焦于三类性状系统：翅脉、肌肉与骨片。研究结果强烈支持翅脉与肌肉呈现退化趋势，而骨片的演化则无法排除平稳性假设。在总证据定年（total-evidence dating）框架中纳入化石与时间信息后，我们发现考虑定向性不仅能更精准地估算树根部的祖先状态，还可优化分化时间的估计结果。我们的模型仅通过新增极少量参数，就放宽了平稳性与可逆性的假设，因此十分适用于探究形态学这类规模有限的数据集的进化过程本质。