Abstract:The Hardy-Weinberg law has been used widely for about one hundred years with little question as to the foundations laid down by its originators. The basic assumption of random mating, that is choice of mates by a process akin to that of a lottery, was shown to produce genotypic proportions following the "binomial-square" rule, the so-called Hardy-Weinberg proportions (HWP). It has been assumed by many that random mating was the only way of pairing genes capable of producing HWP. However it has been shown that … Show more
“…However, he was in the vanguard of efforts to exploit Mendelism to advance human and medical genetics. For example Weinberg (1908) was a notable contribution to the genetics of twinning in man (Stark 2006). A few writers, such as the late James Crow, did appreciate his work (Crow 1999).…”
Section: Resultsmentioning
confidence: 99%
“…At about that time he started to produce an impressive list of publications, since his activities and contacts as a medical practitioner gave him access to medical data and provided a stimulus to develop genetic and statistical concepts. His "Hardy-Weinberg law" article, Weinberg (1908), was a study of the genetics of twinning in humans (Stark 2006). Edwards (2008) begins with tribute to Weinberg's comprehensive formulation of the Hardy-Weinberg law.…”
Wilhelm Weinberg (1862-1937) is a largely forgotten pioneer of human and medical genetics. His name is linked with that of the English mathematician G. H. Hardy in the Hardy-Weinberg law, pervasive in textbooks on population genetics since it expresses stability over generations of zygote frequencies AA, Aa, aa under random mating. One of Weinberg's signal contributions, in an article whose centenary we celebrate, was to verify that Mendel's segregation law still held in the setting of human heredity, contrary to the then-prevailing view of William Bateson (1861Bateson ( -1926, the leading Mendelian geneticist of the time. Specifically, Weinberg verified that the proportion of recessive offspring genotypes aa in human parental crossings Aa · Aa (that is, the segregation ratio for such a setting) was indeed p ¼ 1 4 . We focus in a nontechnical way on his procedure, called the simple sib method, and on the heated controversy with Felix Bernstein in the 1920s and 1930s over work stimulated by Weinberg's article.
“…However, he was in the vanguard of efforts to exploit Mendelism to advance human and medical genetics. For example Weinberg (1908) was a notable contribution to the genetics of twinning in man (Stark 2006). A few writers, such as the late James Crow, did appreciate his work (Crow 1999).…”
Section: Resultsmentioning
confidence: 99%
“…At about that time he started to produce an impressive list of publications, since his activities and contacts as a medical practitioner gave him access to medical data and provided a stimulus to develop genetic and statistical concepts. His "Hardy-Weinberg law" article, Weinberg (1908), was a study of the genetics of twinning in humans (Stark 2006). Edwards (2008) begins with tribute to Weinberg's comprehensive formulation of the Hardy-Weinberg law.…”
Wilhelm Weinberg (1862-1937) is a largely forgotten pioneer of human and medical genetics. His name is linked with that of the English mathematician G. H. Hardy in the Hardy-Weinberg law, pervasive in textbooks on population genetics since it expresses stability over generations of zygote frequencies AA, Aa, aa under random mating. One of Weinberg's signal contributions, in an article whose centenary we celebrate, was to verify that Mendel's segregation law still held in the setting of human heredity, contrary to the then-prevailing view of William Bateson (1861Bateson ( -1926, the leading Mendelian geneticist of the time. Specifically, Weinberg verified that the proportion of recessive offspring genotypes aa in human parental crossings Aa · Aa (that is, the segregation ratio for such a setting) was indeed p ¼ 1 4 . We focus in a nontechnical way on his procedure, called the simple sib method, and on the heated controversy with Felix Bernstein in the 1920s and 1930s over work stimulated by Weinberg's article.
“…Surely something as déclassé as 3:1 ratios was not to be preferred to GALTON's sophisticated and seductive mathematics. (p. 1333) But we leave the last word to Mayo (2008): Li (1988), followed and elaborated by Stark (2006aStark ( , 2006b, showed that panmixia is not the only breeding structure that can yield HW proportions, so that panmixia is a sufficient but not a necessary condition for HWE. However, no natural population is known to manifest the other possible breeding structures so that it appears unlikely that they need to be considered in data collection and analysis.…”
Section: Closing Remarksmentioning
confidence: 99%
“…In the interests of completing the 'story' , we explain how this is so. As discussed below, Weinberg used the property of stability to explore the question of a possible genetic basis for the occurrence of twins in humans (Stark, 2006a).…”
) 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 , 2 pq, 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.
“…Weinberg (1908) used the HW distribution to analyze the inheritance of twinning in man. Stark (2006b) noted that Weinberg's analysis may need to be modified in the light of Li's paper. Stark and Seneta (2012) show that a paper of a Russian mathematician S. N. Bernstein was a fundamental, though largely unrecognized, contribution to genetic analysis by reason of its connection with the HW law.…”
The Hardy-Weinberg (HW) principle explains how random mating (RM) can produce and maintain a population in equilibrium, that is, with constant genotypic proportions. When proportions diverge from HW form, it is of interest to estimate the fixation index F, which reflects the degree of divergence. Starting from a sample of genotypic counts, a mixed procedure gives first the orthodox estimate of gene frequency q and then a Bayesian estimate of F, based on a credible prior distribution of F, which is described here.
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