Hardy, Weinberg and Language Impediments

THE Hardy-Weinberg law is the cornerstone of diploid population genetics. Yet it seems trivially obvious, a routine application of the binomial theorem. And indeed it was so regarded by Hardy when he wrote his famous paper, a masterpiece of clarity: To the Editor of Science: I am reluctant to intrude in a discussion concerning matters of which I have no expert knowledge, and I should have expected the very simple point which I wish to make to have been familiar to biologists. However, some remarks of Mr. Udny Yule, to which Mr. R. C. Punnett has called my attention, suggest that it may still be worth making.... Suppose that Aa is a pair of Mendelian characters, A being dominant, and that in any given generation the number of pure dominants (AA), heterozygotes (Aa), and pure recessives (aa) are as p:2q:r. Finally, suppose that the numbers are fairly large, so that mating may be regarded as random, that the sexes are evenly distributed among the three varieties, and that all are equally fertile. A little mathematics of the multiplication-table type is enough to show that in the next generation the numbers will be as (p+q)2:2(p+q)(q+r):(q+r)2, or as p1:2q1:r1, say. The interesting question is–in what circumstances will this distribution be the same as that in the generation before? It is easy to see that the condition for this is q2 = pr. And since q 21 = p1r1, whatever the values of p, q, and r may be, the distribution will in any case continue unchanged after the second generation (Hardy 1908).