Inferring bounded evolution in phenotypic characters from phylogenetic comparative data

Our understanding of phenotypic evolution over macroevolutionary timescales largely relies on the use of stochastic models for the evolution of continuous traits over phylogenies. The two most widely used models, Brownian motion and the Ornstein–Uhlenbeck (OU) process, differ in that the latter includes constraints on the variance that a trait can attain in a clade. The OU model explicitly models adaptive evolution toward a trait optimum and has thus been widely used to demonstrate the existence of stabilizing selection on a trait. Here we introduce a new model for the evolution of continuous characters on phylogenies: Brownian motion between two reflective bounds, or Bounded Brownian Motion (BBM). This process also models evolutionary constraints, but of a very different kind. We provide analytical expressions for the likelihood of BBM and present a method to calculate the likelihood numerically, as well as the associated R code. Numerical simulations show that BBM achieves good perfor...我们对宏演化尺度下的表型演化认知，在很大程度上依赖于针对系统发育（phylogeny）上连续性状演化的随机模型。目前应用最为广泛的两类模型为布朗运动（Brownian motion）与奥恩斯坦-乌伦贝克（Ornstein–Uhlenbeck，OU）过程，二者的核心差异在于后者纳入了性状在支系（clade）内所能达到的方差约束。OU模型可显式模拟朝向性状最优值的适应性演化，因此被广泛用于验证性状上稳定选择的存在性。本研究提出一种针对系统发育上连续性状演化的全新模型：双反射界下的布朗运动，即有界布朗运动（Bounded Brownian Motion，BBM）。该过程同样可用于模拟演化约束，但约束类型与OU模型截然不同。我们推导了BBM似然的解析表达式，并提供了一种数值计算似然的方法，同时附上了对应的R代码。数值模拟结果表明，BBM可取得良好的性能（原文此处截断为“perfor...”，未完整收尾）。