Data from: 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
quantitative traits evolve and, more importantly, we detail how it can be
fitted to empirical data. Using simulations, we show that the model has
good behavior both in terms of discrimination from alternative models and
in terms of parameter inference. We provide R code to fit the model to
empirical data using either maximum-likelihood or Bayesian estimation, and
illustrate the use of this code with two empirical examples of body mass
evolution in mammals. FPK should greatly expand the set of
macroevolutionary scenarios that can be studied since it opens the way to
estimating macroevolutionary landscapes of any conceivable shape.

长期尺度下的数量性状演化，通常借助随机扩散模型开展研究。不过当前宏观演化研究者可用的研究工具集仅局限于两类核心模型：布朗运动（Brownian motion）与奥恩斯坦-乌伦贝克（Ornstein-Uhlenbeck）过程，及其部分扩展形式。本研究提出一种极具普适性的模型，用于推断同时受随机扩散与任意形式、任意强度确定性力作用的数量性状演化动力学，可适配定向趋势、分裂选择（disruptive selection）、多峰宏观演化景观等多种典型演化场景。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（Fokker-Planck）方程，其在群体遗传学中亦被称为科尔莫戈罗夫向前（Kolmogorov forward）方程。因此我们将此模型命名为FPK，即福克-普朗克-科尔莫戈罗夫（Fokker-Planck-Kolmogorov）模型。我们首先阐释该模型如何用于刻画数量性状所处的宏观演化景观，更重要的是，详细说明了如何将其适配至经验数据集。通过模拟实验验证，本模型在与备选模型的区分度以及参数推断两方面均表现优异。我们提供基于R语言的代码，可通过最大似然（maximum-likelihood）估计或贝叶斯（Bayesian）估计将模型适配至经验数据，并以两个哺乳动物体质量演化的经验案例演示了该代码的使用方法。由于FPK模型为估算任意形式的宏观演化景观提供了可能，其将极大拓展可研究的宏观演化场景范围。