Inbreeding systems: Classification by a canonical form

Stark, Alan E.

doi:10.1007/bf00276989

Cited by 12 publications

(16 citation statements)

References 2 publications

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“…A compact formula giving a range of nonrandom mating tables that reproduce HWP is given by Stark (2005). This was adapted from a more general formula that was used by Stark (1980) to classify systems of partial inbreeding. Other relevant sources are Stark (1977) and A. E. Stark (unpublished results).…”

Section: Li's Modelmentioning

confidence: 99%

A Clarification of the Hardy–Weinberg Law

Stark¹

2006

Genetics

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C. C. Li showed that Hardy-Weinberg proportions (HWP) can be maintained in a large population by nonrandom mating as well as random mating. In particular he gave the mating matrix for the symmetric case in the most general form possible. Thus Li showed that, once HWP are attained, the same proportions can be maintained by what he called pseudorandom mating. This article shows that, starting from any genotypic distribution at a single locus with two alleles, the same in each sex, HWP can be reached in one round of nonrandom mating with no change in allele frequency. In the model that demonstrates this fact, random mating is represented by a single point in a continuum of nonrandom possibilities.

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Section: Li's Modelmentioning

confidence: 99%

A Clarification of the Hardy–Weinberg Law

Stark¹

2006

Genetics

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“…This is idealistic in that the original formulation and current usage was and is based on the assumption of random mating. It has been shown by Stark (1980, 2005, 2006a,b, 2007) and Li (1988) that random mating with Mendelian coefficients is a sufficient, but not a necessary, condition for Hardy-Weinberg equilibrium. Failure to appreciate this non-necessity is widespread in the genetics literature.…”

Section: Discussionmentioning

confidence: 99%

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

Stark

Seneta

2012

Genet. Mol. Biol.

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Around 1923 the soon-to-be famous Soviet mathematician and probabilist Sergei N. Bernstein started to construct an axiomatic foundation of a theory of heredity. He began from the premise of stationarity (constancy of type proportions) from the first generation of offspring. This led him to derive the Mendelian coefficients of heredity. It appears that he had no direct influence on the subsequent development of population genetics. A basic assumption of Bernstein was that parents coupled randomly to produce offspring. This paper shows that a simple model of non-random mating, which nevertheless embodies a feature of the Hardy-Weinberg Law, can produce Mendelian coefficients of heredity while maintaining the population distribution. How W. Johannsen’s monograph influenced Bernstein is discussed.

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“…The same possibility is implicit in a formula of Stark (1980). Stark (2006a) showed that it is possible to reach HW form with one round of NRM. It is still possible to find statements that RM is a necessary condition for HW proportions -for example, on page 664 of Russell (2006), though this is by no means rare.…”

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confidence: 86%

Estimation of Divergence from Hardy–Weinberg Form

Stark

2015

Twin Res Hum Genet

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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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Inbreeding systems: Classification by a canonical form

Cited by 12 publications

References 2 publications

A Clarification of the Hardy–Weinberg Law

A Clarification of the Hardy–Weinberg Law

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

Estimation of Divergence from Hardy–Weinberg Form

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