F . Dove Hardy , Weinberg and Language Impediments

THE Hardy-Weinberg law is the cornerstone of dipalso, even more crucial, that Mendelism and Darwin’s loid population genetics. Yet it seems trivially obviidea of continuous evolution were compatible” (Proous, a routine application of the binomial theorem. And vine 1971, p. 85). Yule’s statement was a curious slip indeed it was so regarded by Hardy when he wrote his for a man who had introduced so much clarity into famous paper, a masterpiece of clarity: the rancorous debates between the mendelists and the biometricians. I suppose that even the greatest are entiTo the Editor of Science: I am reluctant to intrude in tled to one mental lapse. a discussion concerning matters of which I have no expert When I began teaching genetics, this principle was knowledge, and I should have expected the very simple point which I wish to make to have been familiar to called Hardy’s law. Later, Stern (1943) called attention biologists. However, some remarks of Mr. Udny Yule, to to an article of Weinberg (1908), who showed the same which Mr. R. C. Punnett has called my attention, suggest principle at the same time (for an English translation of that it may still be worth making.. . . Weinberg’s paper, see Boyer 1963, pp. 4–15). Weinberg Suppose that Aa is a pair of Mendelian characters, A being dominant, and that in any given generation the went farther. He showed that the principle would work number of pure dominants (AA), heterozygotes (Aa), for multiple alleles, which he postulated, not knowing and pure recessives (aa) are as p:2q:r. Finally, suppose that they had actually been discovered. He also pointed that the numbers are fairly large, so that mating may be out that the approach to a multilocus equilibrium was regarded as random, that the sexes are evenly distributed asymptotic rather than immediate. Not knowing of linkamong the three varieties, and that all are equally fertile. A little mathematics of the multiplication-table type is age, he assumed Mendelian independence. enough to show that in the next generation the numbers Since Stern’s article this has been called the Hardywill be as (p1q):2(p1q)(q1r):(q1r), or as p1:2q1:r1, say. Weinberg (HW) law. It was soon pointed out that both The interesting question is—in what circumstances will Pearson and Castle had still earlier used the HW princithis distribution be the same as that in the generation ple for special cases, but the cumbersome designation before? It is easy to see that the condition for this is q 5 pr. And since q1 5 p1r1, whatever the values of p, q, and “Castle-Pearson-Hardy-Weinberg law” soon fell under r may be, the distribution will in any case continue units own weight. Of course, a principle as simple as this changed after the second generation (Hardy 1908). must have occurred to many geneticists in the early days of the century. Sewall Wright once said that he had used Britain’s leading mathematician must have had a poor the idea in his own early calculations long before he impression of the quantitative skills of geneticists. The had heard of either Hardy or Weinberg. statement to which he took exception concerned the Why was Weinberg’s paper, published the same year dominant trait, brachydactyly. In discussing a paper by as Hardy’s, neglected for 35 years? The reason, I am Punnett, Yule said that eventually one would expect sure, is that he wrote in German. At the time, genetics three brachydactylous persons to one normal. was largely dominated by English speakers and, sadly, I have always found Yule’s statement surprising. It work in other languages was often ignored. We saw in was Yule who pointed out that Karl Pearson’s parentlast month’s Perspectives (Epperson 1999) that the offspring correlation of 1/3 applied only to a single great accomplishments of Gustav Malécot were unlocus with complete dominance and that without domiknown to such as Fisher and Wright, mainly because he nance it became 1/2, closer to the observed value. He wrote in French. Even those fluent in French were not also emphasized that environmental effects should be likely to read the often obscure journals in which he taken into account. Most important, as Provine has said: mainly published. There was, of course, another reason: “Yule was ahead of his time. In 1906 he was probably both Weinberg and Malécot wrote papers that were the only biometrician in England who recognized not only that Mendelism and biometry were compatible but difficult, even for native speakers. Malécot used a great