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Hardy-Weinberg principle

The Hardy-Weinberg principle (HWP) (also Hardy-Weinberg equilibrium (HWE), Hardy-Weinberg law, also Chetverikov-Hardy-Weinberg principle) states that, under certain conditions, after one generation of random mating, the genotype frequencies at a single gene (or locus) will become fixed at a particular equilibrium value. It also specifies that those equilibrium frequencies can be represented as a simple function of the allele frequencies at that locus. In the simplest case of a single locus with two alleles A and a with allele frequencies of p and q, respectively, the HWP predicts that the genotypic frequencies for the AA homozygote to be p², the Aa heterozygote to be 2pq and the other aa homozygote to be q². The Hardy-Weinberg principle is an expression of the notion of a population in "genetic equilibrium" and is a basic principle of population genetics.

Table of contents

1 History 2 Explanation 2..1 Derivation of the Hardy-Weinberg principle 2..2 See also 3 References

History

Mendelian genetics was rediscovered in 1900. Yule (1902) attempted something akin to a selection model, and Castle (1903) showed that without selection, the genotype frequencies would remain stable. Pearson (1903) found one equilibrium position with values of p = q = 0.5. Later however Punnett introduced the problem to Hardy, with whom he played cricket. It was first formulated independently in 1908 by the British mathematician G. H. Hardy and the German physician Wilhelm Weinberg. For a historical note see Stern (1943). Hardy held applied mathematics in some contempt; and this comes across in his 1908 paper. Also, third apparently (according to Griffiths et al) independent discovery was made by the Russian Sergei Chetverikov (1926).

Explanation

The original assumptions for Hardy-Weinberg equilibrium (HWE) were the population under consideration is idealised, i.e.:

• infinite (or effectively so, so as to eliminate genetic drift)
• sexually reproducing
• randomly mating
• diploid

and experience:

• no selection
• no mutation
• no migration (gene flow)

Derivation of the Hardy-Weinberg principle

A more statistical description for the HWP, is that the alleles for the next generation for any given individual are chosen independently. Consider two alleles, A and a, with frequencies p and q, respectively, in the population then the different ways to form new genotypes can be derived using a Punnett square, where the size of each cell is proportional to the fraction of each genotypes in the next generation:

		Females
		A (p)	a (q)
Males	A (p)	AA (p2)	Aa (pq)
	a (q)	aA (qp)	aa (q2)

So the final three possible genotype frequencies, in the offspring, if the alleles are drawn independently become:

• p² (AA)
• 2pq (Aa)
• q² (aa)

The generalization of the HWP for more than two alleles, can be found by the multinomial formula. If the frequencies of the n alleles at a given locus A₁,..., A_n are given by p₁,...,p_n, then the frequency of the A_iA_j genotype is given by:

• 2p_ip_j if i≠j and;
• p_i² if i=j.

Testing deviation from the HWP is generally performed using Pearson's chi-square test, using the observed genotype frequencies obtained from the data and the expected genotype frequencies obtained using the HWP. For systems where there are large numbers of alleles, this may result in data with many empty possible genotypes and low genotype counts, because there are often not enough individuals present in the sample to adequately represent all genotype classes. If this is the case, then the asymptotic assumption of the chi-square distribution, will no longer hold, and it may be necessary to use a form of Fisher's "exact test" (see likelihood-ratio test).

See also

• Population genetics

References

• Castle W. E. (1903). The laws of Galton and Mendel and some laws governing race improvement by selection. Proc. Amer. Acad. Arts Sci. 35:233-242.
• Chetverikov S.S. (1926) On certain aspects of the evolutionary process from the standpoint of modern genetics. Translation by M. Barker and I. M. Lerner. 1961. Proc. Amer. Phil. Soc. 105:167-195.
• GH Hardy (1908). "Mendelian proportions in a mixed population". Science 28:49-50 available in Peters (1959) JSTOR stable url
• Pearson (1904). Mathematical contributions to the theory of evolution. XI. On the influence of natural selection on the variability and correlation of organs. Phil. Trans. Roy. Soc. Lond. A 200:1–66.
• Peters (1959). Classic Papers in Genetics. Prentice Hall, New Jersey.
• Stern C. (1943). "The Hardy-Weinberg law". Science 97:137-8 JSTOR stable url
• Weinberg W. (1908). "Über den Nachweis der Verebung beim Menschen". Jahresh. Verein f. Vaterl. Naturk in Wüttemberg 64:368-82.
• Yule G.U. 1902. Mendel’s laws and their probable relation to intra-racial heredity. New Phytol. 1:193–207, 222–238.

Topics in population genetics
Key concepts: Hardy-Weinberg law | Fisher's fundamental theorem | neutral theory
Selection: natural | sexual | artificial | ecological
Genetic drift: small population size | population bottleneck | founder effect
Founders: Ronald Fisher | J.B.S. Haldane | Sewall Wright
Related topics: evolution | microevolution | evolutionary game theory | fitness landscape
List of evolutionary biology topics

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