Rice Sean H
Department of Biological Sciences, Texas Tech University, Lubbock, TX 79409, USA.
BMC Evol Biol. 2008 Sep 25;8:262. doi: 10.1186/1471-2148-8-262.
Evolution involves both deterministic and random processes, both of which are known to contribute to directional evolutionary change. A number of studies have shown that when fitness is treated as a random variable, meaning that each individual has a distribution of possible fitness values, then both the mean and variance of individual fitness distributions contribute to directional evolution. Unfortunately the most general mathematical description of evolution that we have, the Price equation, is derived under the assumption that both fitness and offspring phenotype are fixed values that are known exactly. The Price equation is thus poorly equipped to study an important class of evolutionary processes.
I present a general equation for directional evolutionary change that incorporates both deterministic and stochastic processes and applies to any evolving system. This is essentially a stochastic version of the Price equation, but it is derived independently and contains terms with no analog in Price's formulation. This equation shows that the effects of selection are actually amplified by random variation in fitness. It also generalizes the known tendency of populations to be pulled towards phenotypes with minimum variance in fitness, and shows that this is matched by a tendency to be pulled towards phenotypes with maximum positive asymmetry in fitness. This equation also contains a term, having no analog in the Price equation, that captures cases in which the fitness of parents has a direct effect on the phenotype of their offspring.
Directional evolution is influenced by the entire distribution of individual fitness, not just the mean and variance. Though all moments of individuals' fitness distributions contribute to evolutionary change, the ways that they do so follow some general rules. These rules are invisible to the Price equation because it describes evolution retrospectively. An equally general prospective evolution equation compliments the Price equation and shows that the influence of stochastic processes on directional evolution is more diverse than has generally been recognized.
进化涉及确定性和随机过程，已知这两者都会促成定向进化改变。许多研究表明，当适应性被视为一个随机变量，即每个个体都有一系列可能的适应度值分布时，个体适应度分布的均值和方差都会促成定向进化。不幸的是，我们现有的最通用的进化数学描述——普赖斯方程，是在适应性和后代表型都是确切已知的固定值这一假设下推导出来的。因此，普赖斯方程在研究一类重要的进化过程时能力有限。
我提出了一个用于定向进化改变的通用方程，它结合了确定性和随机过程，适用于任何进化系统。这本质上是普赖斯方程的一个随机版本，但它是独立推导出来的，并且包含一些在普赖斯公式中没有类似项的项。这个方程表明，选择的效应实际上会因适应性的随机变化而放大。它还推广了种群被拉向适应度方差最小的表型这一已知趋势，并表明这与被拉向适应度正不对称性最大的表型的趋势相匹配。这个方程还包含一个在普赖斯方程中没有类似项的项，它涵盖了亲本的适应性对其后代表型有直接影响的情况。
定向进化受到个体适应度的整个分布的影响，而不仅仅是均值和方差。尽管个体适应度分布的所有矩都对进化改变有贡献，但它们这样做的方式遵循一些一般规则。这些规则对于普赖斯方程是不可见的，因为它是回顾性地描述进化。一个同样通用的前瞻性进化方程补充了普赖斯方程，并表明随机过程对定向进化的影响比通常所认识到的更加多样。
