80 Sahotra Sarkar
Intentional or not, it was a remarkable exercise in self-service.
How credible is Waddington and Mayr’s critique of theoretical population ge-
netics? The evidence, on the whole, is decisively against them. Waddington made
three independent claims: (i) that the mathematical work of Fisher, Haldane,
Wright, and others had contributed “very few qualitatively new ideas”; (ii) that
this work had not led to the discovery of any new theorems or conceptual rela-
tionships; and (iii) that it had not led to “any noteworthy quantitative statements
about evolution”. Mayr implicitly endorsed all of these claims. Explicitly, he em-
phasized the third one and added two new criticisms: (i) that the definition of
fitness in these models ignored factors such as variable dominance, epistasis, tem-
poral dependence of selection processes,etc.; and (ii) that the dynamics described
by these models made a variety of unjustified simplifying assumptions.
Haldane’s remarks from 1953 already provide ample response to Waddington’s
first claim. In particular, without Fisher’s and Wright’s pioneering mathematical
analyses, it is hard to see how the idea of drift could have entered evolutionary
theory. His second claim fares even worse. There is at least one conceptual re-
lationship in evolutionary theory which has been regarded as interesting enough
to have a cottage industry built around it [Crow, 1990a]. This is Fisher’s so-
called “Fundamental Theorem of Natural Selection”. Though neither Wright nor
Haldane brought it up in their responses to Mayr and Waddington, Fisher un-
doubtedly would have. But this theorem is not the only conceptual relationship
to emerge from the mathematical work. The Hardy-Weinberg rule, the simplest
and perhaps the most fundamental relation of population genetics has its origin in
mathematics. Though Punnett suspected that, without selection (in a one-locus
two-allele model with random mating and discrete generations), dominants would
not gradually replace recessives (as was then commonly believed), he was unable
to prove it without the mathematical help of Hardy [Punnett, 1950]. As Hal-
dane noted in 1964, all such intuitions require mathematical exploration for their
correctness to be judged.
Waddington’s third claim was unjustified even in the early 1950s, as Section 3 of
this paper amply documents. Quantitative work by Norton, starting around 1910
had shown how rapidly even small selective differences could establish a dominant
trait, and how ineffective selection is for a recessive trait. Haldane’s “Mathemat-
ical Theory” extended this work to more complicated models and systematically
connected the models to field data. Haldane’s examples in his defense of beanbag
genetics underscores this point. What is less understandable is Mayr’s emphasis
on this criticism. Mayr’s first new criticism, about the definition of fitness, was
simply an error, as Wright pointed out. His second, about the simplifying assump-
tions made in the mathematical population geneticists’ models, is correct. But,
as is evident form Haldane’s list of achievements, what is striking about mathe-
matical population genetics is the extent to which it could provide useful results
in spite of these assumptions.
However, Mayr’s positive thesis about the achievements of the naturalists has
more merit. There should be little doubt that the field and experimental work