Am Nat. 2020 Feb;195(2):145-165. doi: 10.1086/706339. Epub 2019 Dec 17.
Gaussian processes, such as Brownian motion and the Ornstein-Uhlenbeck process, have been popular models for the evolution of quantitative traits and are widely used in phylogenetic comparative methods. However, they have drawbacks that limit their utility. Here we describe new, non-Gaussian stochastic differential equation (diffusion) models of quantitative trait evolution. We present general methods for deriving new diffusion models and develop new software for fitting non-Gaussian evolutionary models to trait data. The theory of stochastic processes provides a mathematical framework for understanding the properties of current and future phylogenetic comparative methods. Attention to the mathematical details of models of trait evolution and diversification may help avoid some pitfalls when using stochastic processes to model macroevolution.
高斯过程，如布朗运动和奥恩斯坦-乌伦贝克过程，已成为定量性状进化的流行模型，并广泛应用于系统发育比较方法中。然而，它们存在一些限制其应用的缺点。在这里，我们描述了新的、非高斯随机微分方程（扩散）的定量性状进化模型。我们提出了从新的扩散模型中推导出一般方法，并开发了新的软件，用于将非高斯进化模型拟合到性状数据中。随机过程的理论为理解当前和未来系统发育比较方法的性质提供了数学框架。关注性状进化和多样化的模型的数学细节，可能有助于避免在使用随机过程来模拟宏观进化时出现一些陷阱。
