  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.
