Hardy & Weinberg

The Hardy Weinberg Equilibrium (HWE) is such a fundamental 'law' in Mendellian genetics. Wikipedia has done a fairly good job summarizing so I am just going to shamelessly copy-paste from there. :) Essentially the principle is based on the random pairing of genetic material during mating. In a system where there is true randomness, at 'steady state' the genotypic frequencies are in 'equilibrium' and will remain relatively stable year after year. In pharmacogenetics, when we are looking at population frequencies of genetic variants, it is always useful to establish if the observed frequencies are consistent with the HWE.

From Wikipedia:
In the simplest case of a single locus with two alleles: the dominant allele is denoted A and the recessive a and their frequencies are denoted by p and q; freq(A) = p; freq(a) = q; p + q = 1. If the population is in equilibrium, then we will have freq(AA) = p² for the AA homozygotes in the population, freq(aa) = q² for the aa homozygotes, and freq(Aa) = 2pq for the heterozygotes.


The HWE is named after G. H. Hardy and Wilhelm Weinberg.

From Wikipedia:

Mendelian genetics were rediscovered in 1900. However, it remained somewhat controversial for several years as it was not then known how it could cause continuous characteristics. Udny Yule (1902) argued against Mendelism because he thought that dominant alleles would increase in the population. The American William E. Castle (1903) showed that without selection, the genotype frequencies would remain stable. Karl Pearson (1903) found one equilibrium position with values of p = q = 0.5. Reginald Punnett, unable to counter Yule's point, introduced the problem to G. H. Hardy, a British mathematician, with whom he played cricket. Hardy was a pure mathematician and held applied mathematics in some contempt; his view of biologists' use of mathematics comes across in his 1908 paper where he describes this as "very simple".

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 q₁² = p₁r₁, whatever the values of p, q, and r may be, the distribution will in any case continue unchanged after the second generation

The principle was thus known as Hardy's law in the English-speaking world until Curt Stern (1943) pointed out that it had first been formulated independently in 1908 by the German physician Wilhelm Weinberg (see Crow 1999). Others have tried to associate Castle's name with the Law because of his work in 1903, but it is only rarely seen as the Hardy–Weinberg–Castle Law.