Haldane and the Emergence of Modern Evolutionary Theory 63The final part of the “Mathematical Theory” consisted of a collection of theorems
about artificial selection, more important for breeders than for an understand-
ing of evolution in nature [Haldane, 1934]. With its publication ended the most
sustained research program of Haldane’s career. It had begun in 1922 and had
dominated his work for over a decade. The “Mathematical Theory” was Haldane’s
most important contribution population genetics.^24
To a first approximation, at least, it is clear what the “Mathematical Theory”
had achieved. In 1922, when Haldane had embarked on his project, as Wright
[1968, 3], has aptly observed, “the precise effect of selection on the composition
of a Mendelian population had been presented in only the simplest cases”. The
“Mathematical Theory” was the first comprehensive examination of that effect.
In 1922, it could still be doubted that natural selectionalone, acting on blind
variation produced by mutations, could account for all of evolutionary change
and, in particular, for the observed rates of evolutionary change. Alternatives
such as orthogenesis were still viable candidates as mechanisms of evolutionary
change. The “Mathematical Theory”, along with the work of Fisher and Wright,
and the work emerging from Chetverikov’s group in the Soviet Union, removed
these alternatives and put the discussion of the power of a natural selection on an
entirely new level of rigor: from now on, verbal intuitions had to be supplemented
by quantitative reasoning. There would later be worries about the power of natural
selection. Wright would initiate these worries in 1932, as he began to emphasize
the role of drift in evolution. Haldane, himself, had realized that natural selection,
unless very strong, could also prove to be ineffective in some circumstances, for
instance, in the spread of recessive alleles in a random mating population. Later,
there was an even stronger challenge to the basic thrust of the “Mathematical
Theory”, when Mayr would suggest that quantitative reasoning is of little use
in evolutionary theory. But these later disputes would occur in a permanently
transformed conceptual space. This was what the “Mathematical Theory”, and
the ongoing work of Fisher and Wright in the 1920’s, had achieved.
Nevertheless, unlike the work of Fisher and Wright, there is no central theme
to the “Mathematical Theory”, no grand hypothesis ofthepreferred mode of evo-
lutionary change. Fisher insisted on the importance of natural selection acting
mainly upon single genes in large panmictic populations. Wright would eventually
emphasize drift, isolation and population structure though he did not deny the
importance of selection. Fisher put his faith in what he called the “fundamental
theorem of natural selection”, that the increase in fitness of a population through
selection would be equal to its additive genetic (genic) variance in fitness. Wright
(^24) Fifteen years after the completion of the series, in 1949, when the mathematician, J. Neyman
began composing a short treatise on probability and statistics, with a chapter devoted to genetics,
he asked Haldane for his most important papers (J. Neyman to Haldane, November 14, 1949,
Box 19, UCL). Haldane’s response was unequivocal: “I think my most important work is in the
Transactions of the Cambridge Philosophical Society from 1924 to 1936” (Haldane to J. Neyman,
November 22, 1949, Box 19, UCL). The details of the statement are inaccurate — only Part I of
the “Mathematical Theory” had appeared in theTransactions; the next eight appeared in the
Proceedings.