The causal meaning of Fisher's average effect

TL;DR

This paper clarifies Fisher's original concept of the average effect as a causal, rather than purely statistical, measure of gene influence, emphasizing its importance in evolutionary theory and gene-trait mapping.

Contribution

It reconciles the statistical and causal interpretations of Fisher's average effect, highlighting the causal perspective's advantages and implications for evolutionary biology.

Findings

Fisher's average effect is best understood as a causal, weighted average of phenotypic change.

The causal and statistical views can be aligned under certain genetic frequency conditions.

Fisher's causal interpretation has foundational importance for evolutionary theory and gene-trait studies.

Abstract

In order to formulate the Fundamental Theorem of Natural Selection, Fisher defined the average excess and average effect of a gene substitution. Finding these notions to be somewhat opaque, some authors have recommended reformulating Fisher's ideas in terms of covariance and regression, which are classical concepts of statistics. We argue that Fisher intended his two averages to express a distinction between correlation and causation. On this view the average effect is a specific weighted average of the actual phenotypic changes that result from physically changing the allelic states of homologous genes. We show that the statistical and causal conceptions of the average effect, perceived as inconsistent by Falconer, can be reconciled if certain relationships between the genotype frequencies and non-additive residuals are conserved. There are certain theory-internal considerations favoring Fisher's original formulation in terms of causality; for example, the frequency-weighted mean of the average effects equaling zero at each locus becomes a derivable consequence rather than an arbitrary constraint. More broadly, Fisher's distinction between correlation and causation is of critical importance to gene-trait mapping studies and the foundations of evolutionary biology.