Frank Steven A
Department of Ecology and Evolutionary Biology, University of California, Irvine, California, 92697-2525.
Evolution. 1997 Dec;51(6):1712-1729. doi: 10.1111/j.1558-5646.1997.tb05096.x.
A general framework is presented to unify diverse models of natural selection. This framework is based on the Price Equation, with two additional steps. First, characters are described by their multiple regression on a set of predictor variables. The most common predictors in genetics are alleles and their interactions, but any predictor may be used. The second step is to describe fitness by multiple regression on characters. Once again, characters may be chosen arbitrarily. This expanded Price Equation provides an exact description of total evolutionary change under all conditions, and for all systems of inheritance and selection. The model is first used for a new proof of Fisher's fundamental theorem of natural selection. The relations are then made clear among Fisher's theorem, Robertson's covariance theorem for quantitative genetics, the Lande-Arnold model for the causal analysis of natural selection, and Hamilton's rule for kin selection. Each of these models is a partial analysis of total evolutionary change. The Price Equation extends each model to an exact, total analysis of evolutionary change for any system of inheritance and selection. This exact analysis is used to develop an expanded Hamilton's rule for total change. The expanded rule clarifies the distinction between two types of kin selection coefficients. The first measures components of selection caused by correlated phenotypes of social partners. The second measures components of heritability via transmission by direct and indirect components of fitness.
本文提出了一个通用框架，以统一各种自然选择模型。该框架基于普莱斯方程，并增加了两个步骤。首先，通过对一组预测变量的多元回归来描述性状。遗传学中最常见的预测变量是等位基因及其相互作用，但也可以使用任何预测变量。第二步是通过对性状的多元回归来描述适合度。同样，性状可以任意选择。这个扩展的普莱斯方程对所有条件下以及所有遗传和选择系统的总进化变化提供了精确描述。该模型首先用于对费希尔自然选择基本定理的新证明。然后明确了费希尔定理、定量遗传学中的罗伯逊协方差定理、自然选择因果分析的兰德 - 阿诺德模型以及亲缘选择的汉密尔顿规则之间的关系。这些模型中的每一个都是对总进化变化的部分分析。普莱斯方程将每个模型扩展为对任何遗传和选择系统的进化变化进行精确的总体分析。这种精确分析用于推导扩展的汉密尔顿总变化规则。扩展后的规则明确了两种亲缘选择系数之间的区别。第一种衡量由社会伙伴的相关表型引起的选择成分。第二种衡量通过适合度的直接和间接成分传递的遗传力成分。
