Maximisation Principles in Evolutionary Biology 339the variance is to a larger extent ascribable to environmental variations’ [Fisher
and Ford, 1926] (repeated in [Fisher and Ford, 1928]).
Calling the relative genetic contributions of individuals their fitnesses, inThe
Genetical Theory of Natural SelectionFisher sought a relationship between the
variance in fitness in the population and the fitness of the whole population (as
measured by the mean of the individual fitnesses). What he found (in modern
terminology;cf. [Edwards, 1994]) was that
The rate of increase in the mean fitness of a population ascribable to
natural selection acting through changes in gene frequencies is equal
to its additive genetic variance in fitness.InThe correlation between relativesFisher had already shown how the total
genotypic variance at a single locus in a population, that is, the variance con-
tributed by the variability of genotypes in an environment assumed uniform, could
be considered as the sum of two components. The first component, now called the
additive genetic variance, is due to the additive effects of the genes (‘an addi-
tive part which reflects the genetic nature without distortion’), whilst the second,
residual component, the dominance variance, is due to the non-additive effects
of the genes. The basic idea comes from linear regression: regress the genotypic
values on the number (0, 1 or 2) of genes of a particular allelic type and the resul-
tant analysis of variance separates the linear (‘additive genetic’) and the residual
(‘dominance’) effects. (For more information consult, for example, the books by
Falconer [1989], or Edwards, [2000].)
The Fundamental Theorem can be viewed as an adaptation of the growth-
rate theorem to the particular needs of population genetics (though it is in fact
anachronistic to do so). It tells us how the changes in gene frequencies brought
about by natural selection affect the mean fitness.
4 EVOLUTION AS FITNESS-MAXIMISATION. (2) MISINTERPRETING
THE FUNDAMENTAL THEOREMIt may seem, and has seemed to many, that a theorem which gives the rate at
which the mean fitness of a population increases must imply that the course of
evolution can be charted by elucidating the route that would increase the fitness
as rapidly as possible, a triumphant mathematization of the ‘invisible hand’. In
the genetical context this is not the case, for two reasons.
In the first place, this is not the theorem Fisher proved. The unravelling of
the Fundamental Theorem took many years (see [Edwards, 1994; 2002b], for the
history) but it is now entirely clear that it refers only to the change in that compo-
nent of the overall fitness that can be ascribed directly to gene-frequency change.
Moreover, Fisher embedded his theorem in a discussion inThe Genetical Theory
that emphasizes that this change is only one part of the change in fitness, and that
other factors such as mutation and changes in the environment are continuously at