328 Margaret Morrison
variance in fitness is in fact the variation resulting from the additive effects of
genes. But the very notion of fitness itself was also reconceptualized by Fisher. In
his presentation he designated a number of quantities as representing particular
aspects of a population. m is the Malthusian parameter referring to the growth
rate of the population, M is the mean of this parameter and measures the fitness
of the population; W is the genetic variation in fitness, also described as the rate
of increase in fitness due to natural selection. C is a constant representing the
relation between fitness and population increase and D specifies the rate of loss
due to deterioration of the environment. Fisher described the relation among these
quantities as follows:
dM/dt + M/C = W-D.While this doesn’t actually state the fundamental theorem, the relationship is
important for understanding what the theorem actually says. Fisher explicitly
claims that the rate of increase of overall fitness at any given moment dM/dt is
the result of a balance between the additive genetic variance in fitness W and
the totality of effects contributed by the environment. His goal was to isolate
within an evolving populationtheparticular feature of it that could be identified
solely with the operation of natural selection. In order to do this he made use
of the methodology developed in 1918 and 1922 that allowed him to analyse the
variance of a character into the additive effects of genes, dominance, epistasis
and environmental effects. What the theorem states then is an equality between
something that is constantly being maximized (the fitness due to selection only)
and a variance.
As Price [1972] has pointed out, it has long been a mystery what exactly Fisher
meant by his fundamental theorem and how he derived it. Adding to the problem
is the fact that most of the discussion and statement of the theorem is done in non-
mathematical language; hence one has to rely on the precision of the definitions he
uses. As Price points out, part of the confusion results from two different accounts
of the theorem. One refers to the rate of increase in fitness due to all changes
in gene ratio and the other to the rate of increase in the average value of the
Malthusian parameter ascribable to natural selection. In the former case we must
include the effects of dominance, epistasis etc. while in the latter we have only
the process of selection which involves the distribution of gene frequencies alone
(the additive effects of genes) and not the interaction between genes. In Fisher’s
eyes the theorem identified that which was maximised by natural selection, the
genetic variance in fitness. The statistical distribution of genes was for him the
fundamental language in which all evolutionary processes should be expressed and
understood. To summarise then, the rate of increase in fitness due to changes in
the gene ratio was equal to the genetic variance of the fitness W that the population
exhibited. If fitness was a measure of the ability of a gene to survive and reproduce,
then natural selection acted to increase the fitness of the population.
Once again Fisher appealed to a physical model, namely, gas theory, as a way of
grounding the regularity with which W could be expected to vary. He claimed that