340 A. W. F. Edwards
work to influence the overall mean fitness of a population, which must always be
roughly constant for a population to remain at about the same size. It is as though
Fisher’s theorem has been interpreted as a kind of ‘big-bang’ theory of evolution
whereas it is in fact more descriptive of a ‘steady-state’ evolutionary universe.
Secondly, even taking the naive interpretation of the theorem as exactly true
for the simplest case of a single genetic locus with additive fitnesses, it still does
not follow that gene-frequency change will be such as to maximise the increase in
fitness. The mathematics simply does not imply this as a consequence. (We look
at what can in fact be said in the next section.)
Unfortunately, two powerful strains of misunderstanding corrupted the interpre-
tation of the theorem. The first is quickly disposed of. It is easy to find examples
of populations modelled mathematically in which it is not true that the overall
mean fitness increases; ironically, the first was put forward by Fisher himself [1941]
in a failed attempt to rescue his theorem from misinterpretation. In consequence
many commentators, mainly American, have wrongly maintained that the theorem
had been disproved by counter-example and could therefore be only approximately
true at best.
The second misunderstanding was Sewall Wright’s conception of an ‘adaptive
landscape’ of fitness up which populations would move, like hill-walkers ascending
a peak by the steepest route. It lent itself to the extension, important in Wright’s
view of evolution, that this landscape was complex and multi-peaked and that
an important element of change was the ability of populations to make stochastic
jumps from one place to another, thus enabling valleys to be crossed and higher
peaks of fitness attained. Wright eventually admitted that his supposition that
progress would be by the steepest route could not be justified mathematically
(at least, not in the normal gene-frequency space — see the next section), but
the whole development, which became the dominant paradigm in evolutionary
genetics, derived originally from his reading of The Genetical Theoryand the
Fundamental Theorem.
Wright had called the mean fitness of a population ‘W’, and Fisher’s last sally
against it was scathing:
I have never indeed written aboutW and its relationships, and now
that the alleged relationship has been brought to my attention, I must
point out that the existence of such a “potential function” as that
which Wright designates byW, is not a general property of natural
populations, but arises only from the special and restricted cases which
Wright has chosen to consider. Selective tendencies are not, in general,
analogous to what mechanicians describe as a conservative system of
forces. To assume this property is one of the gravest faults of Wright’s
formulation.(For the source of this quotation, and all historical points, see [Edwards, 1994];
for a critique of Wright’s ‘shifting balance’ theory of evolution and its stochastic
component, see [Coyneet al., 1997].)