On S.N. Bernstein's derivation of Mendel's Law and 'rediscovery' of the Hardy-Weinberg distribution

Stark, Alan E.; Seneta, E.

doi:10.1590/s1415-47572012005000025

Cited by 7 publications

(9 citation statements)

References 33 publications

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“…He says that, comparably, Gustave Malécot did not receive adequate recognition because most of his research was published in French. Stark and Seneta (2012) find that Sergei N. Bernstein's articles on Mendel's first law, published in French and Russian, remained largely unknown. Similarly, Stark and Seneta (2011) find that a report, published in Russian, detailing repetition of some of Mendel's experiments attracted no interest outside Russia, even though it was contested there during the Lysenko era, and by no less than the great mathematician Andrei Kolmogorov.…”

Section: Reads In Translationmentioning

confidence: 96%

Wilhelm Weinberg’s Early Contribution to Segregation Analysis

Stark

Seneta

2013

Genetics

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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.

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Section: Reads In Translationmentioning

confidence: 96%

Wilhelm Weinberg’s Early Contribution to Segregation Analysis

Stark

Seneta

2013

Genetics

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“…The notation used here is a modified version of that given in Stark & Seneta [7,9]. Identity (7) allows for non-random mating (NRM) as well as random mating (RM).…”

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confidence: 99%

“…Stark & Seneta [7] put Bernstein's result in a more general context, and gave a more transparent derivation, by modifying the mating system. The population is still assumed to be maintained in equilibrium, which thus becomes foundational, but is not necessarily in the form of (1).…”

Section: Introductionmentioning

confidence: 99%

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Hardy-Weinberg Equilibrium as Foundational

Stark¹,

Seneta²

2014

Int. J. Stats. Med. Res.

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The Hardy-Weinberg Principle explains how random mating can produce and maintain a population in equilibrium, that is: with constant genotypic proportions. The Hardy-Weinberg formula is in constant use as a basis for developing population genetics theory. Here we give a complete description of a model which can sustain equilibrium but with a general mating system, thereby giving a much broader basis on which to develop population genetics. It was S. N. Bernstein who first showed how Mendel's first law could be justified simply on the basis of observations of populations in equilibrium. We show how the model can be applied to exploring the change in incidence of a genetic disorder.

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“…This can be streamlined with the use of some basic matrix algebra (Stark & Seneta, 2012). We feel that it is useful in clarifying key elements of the HW law, although we recognize that the approach will not please all tastes.…”

Section: Deriving Hwp and Properties Of The Stationary Statementioning

confidence: 99%

A Reality Check on Hardy–Weinberg

Stark

Seneta

2013

Twin Res Hum Genet

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) 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.

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On S.N. Bernstein's derivation of Mendel's Law and 'rediscovery' of the Hardy-Weinberg distribution

Cited by 7 publications

References 33 publications

Wilhelm Weinberg’s Early Contribution to Segregation Analysis

Wilhelm Weinberg’s Early Contribution to Segregation Analysis

Hardy-Weinberg Equilibrium as Foundational

A Reality Check on Hardy–Weinberg

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