Department of Biological Sciences, Texas Tech University, Lubbock, TX 79409, USA.
Philos Trans R Soc Lond B Biol Sci. 2020 Apr 27;375(1797):20190353. doi: 10.1098/rstb.2019.0353. Epub 2020 Mar 9.
The Price equation shows that evolutionary change can be written in terms of two fundamental variables: the fitness of parents (or ancestors) and the phenotypes of their offspring (descendants). Its power lies in the fact that it requires no simplifying assumptions other than a closed population, but realizing the full potential of Price's result requires that we flesh out the mathematical representation of both fitness and offspring phenotype. Specifically, both need to be treated as stochastic variables that are themselves functions of parental phenotype. Here, I show how new mathematical tools allow us to do this without introducing any simplifying assumptions. Combining this representation of fitness and phenotype with the stochastic Price equation reveals fundamental rules underlying multivariate evolution and the evolution of inheritance. Finally, I show how the change in the entire phenotype distribution of a population, not simply the mean phenotype, can be written as a single compact equation from which the Price equation and related results can be derived as special cases. This article is part of the theme issue 'Fifty years of the Price equation'.
价格方程表明，进化变化可以用两个基本变量来表示：父母（或祖先）的适应性和它们后代（后代）的表型。它的强大之处在于，它除了封闭群体之外不需要任何简化假设，但要充分发挥普赖斯结果的潜力，我们需要充实适应性和后代表型的数学表示。具体来说，两者都需要被视为随机变量，而这些随机变量本身就是亲本表型的函数。在这里，我展示了新的数学工具如何在不引入任何简化假设的情况下实现这一点。将适应性和表型的这种表示与随机价格方程相结合，揭示了多变量进化和遗传进化的基本规律。最后，我展示了如何将种群整个表型分布的变化（不仅仅是平均表型）写成一个单一的紧凑方程，从该方程中可以推导出价格方程和相关结果作为特例。本文是主题为“价格方程五十年”的一部分。
