Fisher's fundamental theorem describes the change caused by natural selection as the change in gene frequencies multiplied by the partial regression coefficients for the average effects of genes on fitness. Fisher's result has generated extensive controversy in biology. I show that the theorem is a simple example of a general partition for change in regression predictions across altered contexts. By that rule, the total change in a mean response is the sum of two terms. The first ascribes change to the difference in predictor variables, holding constant the regression coefficients. The second ascribes change to altered context, captured by shifts in the regression coefficients. This general result follows immediately from the product rule for finite differences applied to a regression equation. Economics widely applies this same partition, the Oaxaca-Blinder decomposition, as a fundamental tool that can in proper situations be used for causal analysis. Recognizing the underlying mathematical generality clarifies Fisher's theorem, provides a useful tool for causal analysis, and reveals connections across disciplines.

翻译：费希尔基本定理将自然选择引起的演化描述为基因频率变化乘以基因对适应度平均效应的偏回归系数。费希尔的这一结论在生物学领域引发了广泛争议。本文证明该定理是回归预测在情境变化中分解的一般性规则的特例。根据该规则，平均响应的总变化可分解为两项之和：第一项将变化归因于预测变量的差异（保持回归系数恒定），第二项将变化归因于情境改变（体现为回归系数的偏移）。这一普遍结果可直接通过对回归方程应用有限差分乘积法则推导得出。经济学领域广泛应用的Oaxaca-Blinder分解法正是基于同一分解原理，该方法是特定情境下进行因果分析的基础工具。认识其底层数学普适性不仅能够澄清费希尔定理的本质，为因果分析提供实用工具，更能揭示跨学科之间的内在联系。