Academic journal article Genetics

G. H. Hardy (1908) and Hardy-Weinberg Equilibrium

Academic journal article Genetics

G. H. Hardy (1908) and Hardy-Weinberg Equilibrium

Article excerpt

More attention to the History of Science is needed, as much by scientists as by historians, and especially by biologists, and this should mean a deliberate attempt to understand the thoughts of the great masters of the past, to see in what circumstances or intellectual milieu their ideas were formed, where they took the wrong turning or stopped short on the right track.

Fisher 1959, pp. 16-17

On closer examination, however, the hope of finding a "first" comes to grief because of the historically dynamic character of ideas. If we describe a result with sufficient vagueness, there seems to be an endless sequence of those who had something within the vague specifications. Even plagiarists usually introduce innovations! If we specify the idea or result precisely, it turns out that exact duplications seldom occur, so that every mathematical event is a "first", and the priority question becomes trivial.

May 1975, pp. 315-317

ALTHOUGH this is an account of G. H. Hardy's role in establishing the existence of what is now known as "Hardy-Weinberg equilbrium," we start withWeinberg's description of the problem and its solution, which cannot be bettered. To do so is also to recognize that his solution in fact preceded Hardy's (which was obtained independently).

On January 13, 1908, Wilhelm Weinberg read to an evening meeting in Stuttgart, Germany, a paper in which he "derived the general equilibrium principle for a single locus with two alleles" (Weinberg 1908; Provine 1971; English translations in Boyer 1963; Jameson 1977). Mendel (1866) had already initiated population genetics by considering the consequences of continued selfing starting with the cross Aa × Aa, obtaining 1 AA: 2 Aa: 1 aa in the first generation and

2^sup n^ - 1 AA: 2 Aa : 2^sup n^ - 1 aa

in the nth (assuming for simplicity that each plant produced four seeds). With A dominant to a as usual this gives phenotypic proportions 2^sup n^ + 1 "A": 2^sup n^ - 1 "a" as noted by Weinberg [although Mendel's nth generation was his (n - 1)th]. He did not explicitly refer to Mendel, but he was surely familiar with Mendel's paper. He went on, "This situation appears much different when Mendelian inheritance is viewed under the influence of panmixia"(Weinberg1908) and, startingwith arbitrary proportions m and n (not the same n as before; m+n=1) of each of the two homozygotes AA and aa, he obtained "by application of the symbolism of the binomial theorem" the daughter generation

m^sup 2^AA+2mnAa +n^sup 2^aa:

Another generation of random mating led by direct calculation to the same proportions among the offspring and "We thus obtain the same distribution of pure types and hybrids for each generation under panmixia" (Weinberg 1908). Weinberg then uses his result to work out the numbers of the two phenotypes to be expected among the relatives of an individual of known phenotype, but this does not now concern us. Rather, he has established the "Hardy-Weinberg law" in the most obvious and direct manner.

Meanwhile in England, between the rediscovery of Mendel's paper in 1900 and the publication by themathematician G. H. Hardy of the same result as Weinberg's in July 1908 in the American weekly Science (Hardy 1908), confusion reigned. The animosity between Karl Pearson's "biometricians" and William Bateson's "Mendelians" had so clouded the atmosphere that not until Bateson's lieutenant R. C. Punnett appealed to his mathematical friend G. H. Hardy wasWeinberg's simple law independently derived.

The story of how Britain's foremost mathematician became involved in a simple problem genetics has been told many times, often with embellishments. Many years later Punnett gave his own account in a lecture (Punnett 1950). Provine (1971) has given an account of the surrounding events leading up to Hardy's Science letter, and Bulmer (2003) a slightly fuller one. Yet there is still more to be said, in particular how the lack of understanding between the biometricians and the Mendelians delayed the solution to a problem that, if both parties had paid more attention to Mendel's paper itself, should never have arisen. …

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