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. The same partition also arises in demography and thermodynamics. 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变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。费希尔的这一结果在生物学界引发了广泛争议。本文证明，该定理是回归预测在变化情境中变动的普遍分解法则的一个简单示例。根据该法则，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（保持回归系数不变）；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的乘积法则推导得出。经济学领域广泛应用的Oaxaca-Blinder分解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。同样的分解形式也出现在人口统计学和热力学中。认识其底层数学普遍性不仅有助于澄清费希尔定理，为因果分析提供实用工具，同时揭示了跨学科之间的内在联系。