Haldane and the Emergence of Modern Evolutionary Theory 77that some genes which seriously lower human fitness are only kept in
being by mutation.... Another idea which seems to me qualitatively
new is that, because a selective advantage of the heterozygote over
both homozygotes will preserve both of a pair of [alleles] indefinitely,
we may expect most of the genetic variation in an outbred popula-
tion to be due to genes with this peculiar property. Such ideas as
these pass rapidly from being mathematical theorems to being com-
mon sense. Other ideas with a superficial appeal to common sense, for
example that dominants must oust recessives, appear to require mathe-
matical disproof to prevent their spread. Mathematical biologists have
also suggested what other biologists should measure. (pp. ix–x)Haldane went on to discuss examples. With a display of striking intellectual
irresponsibility, Waddington ignored these remarks when he republished his criti-
cism verbatim in 1957.
But Waddington was peripheral to the development of evolutionary theory, and
his criticism (by itself) would have probably had little influence without their en-
dorsement by Mayr who, along with Dobzhansky, Simpson, and a few others, was
at the forefront of evolutionary theory in the 1950s and 1960s. In 1964, Haldane
took up Mayr’s challenge and provided a defense of mathematical population ge-
netics. The result is a methodological classic, an ultimate defense of reductionism
in evolutionary biology. Haldane started with the passage fromAnimal Species
and Evolutionthat was quoted above, and Mayr’s “provocative question” from
- He admitted that the models of mathematical population genetics made
simplifying assumptions. Then he proceeded, by explicitly listing achievements,
to argue for the importance of even single locus models, basically the only ones to
which the epithet “beanbag genetics” could be attributed with justice:^36
(i) Wright and he had shown around 1930 that, if a species had a population of
over a hundred thousand, the mutation rate does not determine the rate of
evolution, even if selection is weak;(ii) using the same basic model, Haldane had been able to provide the first
estimate of a human mutation rate when there is an equilibrium between
mutation and selection. How soon such an equilibrium is reached in different
genetic contexts could only be known from a mathematical analysis;(iii) Mayr [1963, 191] had mis-stated the situation even with respect to some de-
velopments whose importance he admitted. Mayr had claimed that Haldane
[1932] had assumed only small selective differences in his work; that, to the
contrary, in the case of industrial melanism in the peppered moth,Biston
betularia, a selective difference of 30 -50% had been observed; and that Hal-
dane had only reached that conclusion in 1957. Haldane pointed out that(^36) The qualification “basically” is only necessary because additive multiple locus models (that
is, those with no epistasis) with complete linkage are also “beanbag” models in Mayr’s sense.
Formally, these are the same as single locus models with a higher number of alleles.