Stark Alan E, Seneta Eugene
School of Mathematics and Statistics FO7, University of Sydney, Sydney, NSW, Australia.
Twin Res Hum Genet. 2013 Aug;16(4):782-9. doi: 10.1017/thg.2013.40. Epub 2013 Jun 17.
G. H. Hardy (1877-1947) and Wilhelm Weinberg (1862-1937) had very different lives, but in the minds of geneticists, the two are inextricably linked through the ownership of an apparently simple law called the Hardy-Weinberg law. We demonstrate that the simplicity is more apparent than real. Hardy derived the well-known trio of frequencies {q 2, 2pq, p 2} with a concise demonstration, whereas for Weinberg it was the prelude to an ingenious examination of the inheritance of twinning in man. Hardy's recourse to an identity relating to the distribution of types among offspring following random mating, rather than an identity relating to the mating matrix, may be the reason why he did not realize that Hardy-Weinberg equilibrium can be reached and sustained with non-random mating. The phrase 'random mating' always comes up in reference to the law. The elusive nature of this phrase is part of the reason for the misunderstandings that occur but also because, as we explain, mathematicians are able to use it in a different way from the man-in-the-street. We question the unthinking appeal to random mating as a model and explanation of the distribution of genotypes even when they are close to Hardy-Weinberg proportions. Such sustained proportions are possible under non-random mating.
G. H. 哈代（1877 - 1947）和威廉·温伯格（1862 - 1937）有着截然不同的人生，但在遗传学家的心目中，两人通过一条看似简单的定律——哈代 - 温伯格定律紧密相连。我们证明这种简单性更多是表面而非实质的。哈代通过简洁的论证得出了著名的频率三元组{q², 2pq, p²}，而对温伯格来说，这是对人类双胞胎遗传进行巧妙研究的前奏。哈代诉诸的是与随机交配后后代类型分布相关的恒等式，而非与交配矩阵相关的恒等式，这可能就是他没有意识到非随机交配也能达到并维持哈代 - 温伯格平衡的原因。“随机交配”这个词总是与该定律联系在一起。这个词难以捉摸的性质是产生误解的部分原因，但也因为，正如我们所解释的，数学家使用它的方式与普通人不同。我们质疑不假思索地将随机交配作为基因型分布的模型和解释，即使它们接近哈代 - 温伯格比例。在非随机交配情况下也可能出现这种持续的比例。
