A general model for estimating macroevolutionary landscapes

The evolution of quantitative characters over long timescales is often studied using stochastic diffusion models. The current toolbox available to students of macroevolution is however limited to two main models: Brownian motion and the Ornstein-Uhlenbeck process, plus some of their extensions. Here we present a very general model for inferring the dynamics of quantitative characters evolving under both random diffusion and deterministic forces of any possible shape and strength, which can accommodate interesting evolutionary scenarios like directional trends, disruptive selection, or macroevolutionary landscapes with multiple peaks. This model is based on a general partial differential equation widely used in statistical mechanics: the Fokker-Planck equation, also known in population genetics as the Kolmogorov forward equation. We thus call the model FPK, for Fokker-Planck-Kolmogorov. We first explain how this model can be used to describe macroevolutionary landscapes over which quanti...

长时间尺度下数量性状的演化通常采用随机扩散模型进行研究。然而，宏观进化研究者现有的工具集仅限于两种主要模型：布朗运动（Brownian motion）和奥恩斯坦-乌伦贝克过程（Ornstein-Uhlenbeck process），以及它们的部分扩展形式。本文提出一种极具通用性的模型，用于推断数量性状在任意形式和强度的随机扩散与确定性力共同作用下的演化动态，该模型可适配多种有趣的进化场景，如定向趋势、分裂选择或具有多峰值的宏观进化景观。该模型基于统计力学中广泛应用的通用偏微分方程——福克-普朗克方程（Fokker-Planck equation），其在群体遗传学中亦被称为柯尔莫哥洛夫前向方程（Kolmogorov forward equation）。因此，我们将该模型命名为FPK，即福克-普朗克-柯尔莫哥洛夫（Fokker-Planck-Kolmogorov）的缩写。我们首先阐述该模型如何用于描述宏观进化景观，其中数量性状...