78 Sahotra Sarkar
this was what he had predicted in 1924 when it was not taken seriously. “If
biologists had a little more respect for algebra and arithmetic”, Haldane (p.
40) noted, “they would have accepted the existence of such intense selection
thirty years before they actually did so”;(iv) his own methods had first provided a technique for quantifying the type of
evolutionary morphological change that Mayr found important.The list goes on, each example detailing how, without mathematical analysis,
verbal claims about evolutionary processes could not ever be directly appraised.
These examples were intended to pave the way for the fundamental point: “In
the consideration of evolution, a mathematical theory may be regarded as a kind
of scaffolding within which a reasonably secure theory expressible in words may
be built up. I have given examples to show that without such a scaffolding ver-
bal arguments are insecure” (p. 42). Moreover, mathematical analysis allows the
exploration of different possible explanations of the same observed phenomenon.
In the case of polymorphism, for instance, Fisher [1922] had shown how heterosis
could maintain polymorphism, and this came to be generally accepted. But Hal-
dane and Jayakar [1963] had shown that selection in fluctuating directions also
sufficed to explain polymorphism. Though he did not believe that this mechanism
was more frequent than Fisher’s, he suggested that, had it been offered first, it
might very well have commanded the greater allegiance. “The best way to avoid
such contingencies”, he argued, “is to investigate mathematically the consequences
following from a number of hypotheses which may seem rather farfetched and, if
they would lead to observed results, looking in nature or the laboratory for their
truth or falsehood” (p. 44).
Finally, Haldane went on a counter-attack. He accepted that Mayr had made
sympatric speciation far less probable than before. But he showed that Mayr’s ver-
bal arguments lacked precision and were sometimes so apparently contradictory
that they could not even be formalized by those who favored precise reasoning.
He accused Mayr of “a considerable ignorance of the earlier literature of beanbag
genetics” (p. 48). For instance, Mayr had claimed that “the classical theory of
genetics took it for granted that superior mutations would be incorporated into the
genotype of the species while the inferior ones would be eliminated” [1963, 215].
Haldane pointed out that Fisher had shown the exact contrary, that heterosis
could preserve polymorphism, in 1922 and that he, Haldane, had extended that
result in 1926. He pointed out that Fisher [1918] had considered epistasis sys-
tematically and wondered why Mayr thought that the mathematical geneticists
ignored such interactions. Lastly, he went on to provide a scathing assessment of
Mayr’s alternative framework:
Mayr devotes a good deal of space to such notions as ‘genetic cohesion’,
‘the coadapted harmony of the gene pool,’ and so on. These apparently
became explicable ‘once the genetics of integrated gene complexes had
replaced the old beanbag genetics’. So far as I can see, Mayr attempts