Haldane and the Emergence of Modern Evolutionary Theory 51the well-known British mathematician, G. H. Hardy.^3 Suppose that a trait is
controlled by one gene (or “locus”) which takes one of two forms or “alleles”,Aor
a. Then each diploid organism has eitherAA,Aaoraaas its genotype. Suppose
pandqare the relative frequencies ofAanda, respectively, in the population in
some generation (p+q= 1). Assuming that the population is large (in principle,
infinite), that it mates at random with respect to this trait, and that there is no
selection, the Hardy-Weinberg rule stated that the genotypesAA,Aaandaahave
frequenciesp^2 ,2pqandq^2 , respectively, in the next and all subsequent generations.
The effect of selection, non-random mating, and other such factors would be to
drive a populationaway from the Hardy-Weinberg ratios.^4 Weinberg [1909a,b;
1910] continued the mathematical exploration of Mendelism and went on to argue
— as had Yule before him — that Pearson’s negative assessment was unjustified.
Pearson [1910] remained unimpressed, accusing Weinberg of giving a “curiously
ignorant account of the biometric treatment of heredity” [p. 381n].
Meanwhile, in 1910, Hardy’s example immediately led a young mathematician
at Cambridge, H. T. J. Norton, to write the first thesis in mathematical genetics.
Persistent ill health prevented him from immediately publishing most of his results.
However, he calculated a “selection table” for R. C. Punnett’s [1915]Mimicry in
Butterflies. This table showed that even mild selection could be quite effective in
promoting the rapid spread of an allele in a population. For those who worried
about whether there had been enough time for natural selection to have created
the observed patterns of evolutionary change, Norton’s table provided reassurance,
though only in the very restricted context of what he had modeled.
Meanwhile, in the United States, the mathematical exploration of consequences
of Mendelian inheritance began around 1912 with the work of H. S. Jennings [1912]
who first calculated the results of self-fertilization, rather than random mating, on
the genetic composition of a population, and then generalized this treatment to
study inbreeding [Jennings, 1914]. Pearl [1913; 1914a,b] and Fish [1914] continued
to explore these models.^5 In 1916, going beyond inbreeding and autosomal factors,
Jennings considered the effects of “assortative” or preferential mating between like
phenotypes and sex-linked factors [Jennings, 1916]. Wentworth and Remick [1916]
extended some of these results.
Jennings [1917] extended his arguments to a pioneering discussion of two locus
models. LetA,aandB,bpairs of alleles at two loci. He found out that, if the
system of mating was known, it was possible to calculate the frequencies of the
(^3) Pearson [1904] had already proved a special case of the same result (when both alleles have
the same frequency), but Weinberg [1908] and Hardy [1908] deserve credit for recognizing and
stating it in its full generality.
(^4) However, as Hardy [1908], noted the ratios were “stable” in the sense that, not only did they
remain the same generation after generation in the absence of interfering factors, if there was a
deviation in some generation, the distribution would simply shift to another set of frequencies
(say,p′^2 ,2p′q′,q′^2 ) which would also persist ever afterwards.
(^5) Pearl [1913] incorrectly suggested that inbreeding other than self-fertilization did not nec-
essarily increase the frequency of homozygotes but subsequently corrected this error and gave
formulae for the effects of brother-sister mating [Pearl, 1914a,b]. H. D. Fish, who was the first
to notice Pearl’s error, went on to explore mating between parent and offspring [Fish, 1914].