56 Sahotra Sarkar
It is possible that Haldane’s mathematical exploration of natural selection, start-
ing 1924, was also a response to Keith’s appeal. However, there is also a more
direct possible source for Haldane’s new-found interest in the mathematics of selec-
tion. Among his fellow residents at Trinity College at Cambridge (where Haldane
had become Reader in Biochemistry) was Norton. From the latter Haldane learnt
not only of Norton’s unpublished work, but also surmised that, the efforts of Jen-
nings, Robbins and Warren notwithstanding, the mathematical theory of natural
selection remained rudimentary. At this point, Haldane was unaware of either
Fisher’s or Wright’s work. Moreover, neither Fisher nor Wright had yet developed
detailed models of selection for specific circumstances that were potentially subject
to experimental test. At Cambridge, thanks to Punnett and Norton, that became
the focus of Haldane’s efforts.
In Haldane’s work, Punnett’s concern with the time taken by selection to estab-
lish a Mendelian variant translated into Haldane’s consistent preoccupation with
rates of change. Haldane does not start with an assumption of equilibrium and
then worry about deviations from it. His attitude even to the Hardy-Weinberg
rule was almost dismissive [1924a, 22]: it is merely a way for calculating genotypic
ratios in the absence of selection. Unlike Fisher, there was no commitment either
to the maintenance of variation in populations or to small selective differences.
Unlike what Wright would eventually emphasize, there was no commitment ei-
ther to a particular breeding or population structure. Initial conditions, whether
they be allele frequencies, selective differences, breeding structure, or mode of in-
heritance, that is, whether the organisms were haploid, diploid (that is, strictly
Mendelian) or polyploid, could all be arbitrary. From Haldane’s catholic point of
view, all options were up for exploration.
The framework for Haldane’s [1924a] theory of selection was clearly articulated
in the first part of a ten-paper series [1924, 19]:
Asatisfactorytheory of natural selection must be quantitative. In
order to establish the view that natural selection is capable of account-
ing for the known facts of evolution we must show not only that it can
cause a species to change, but that it can cause it to change at a rate
which will account for present and past transmutations. In any given
case we must specify:- The mode of inheritance of the character considered,
- The system of breeding in the group of organisms studied,
- The intensity of selection,
- Its incidence (e. g., on both sexes or only one), and
- The rate at which the proportion of organisms showing the char-
acter increases of diminishes.
It should then be possible to obtain an equation connecting (3) and
(5).