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Hardy-Weinberg principle
The Hardy-Weinberg principle (HWP) (also Hardy-Weinberg equilibrium (HWE), Hardy-Weinberg law, 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 p^{2}, the Aa heterozygote to be 2pq and the other aa homozygote to be q^{2}. The Hardy-Weinberg principle is an expression of the notion of a population in "genetic equilibrium" and is a basic principle of population genetics.
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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. Karl Pearson (1903) found one equilibrium position with values of p = q = 0.5. Later however Punnett introduced the problem to G. H. Hardy, a British mathematician, with whom he played cricket. It was first formulated independently in 1908 by Hardy and the German physician Wilhelm Weinberg . For a historical note see Stern (1943). Hardy held applied mathematics in some contempt; his view of biologists use of mathematics comes across in his 1908 paper where he describes this as "very simple". Also, third apparently (according to Griffiths et al) independent discovery was made by the Russian Sergei Chetverikov (1926).
Assumptions
The original assumptions for Hardy-Weinberg equilibrium (HWE) were the population under consideration is idealised, that is:
- infinite (or effectively so, so as to eliminate genetic drift)
- Censored page
- randomly mating
- diploid
and experience:
Mathematics
Hardy-Weinberg equations
In a population for which the above assumptions are true that has two possible alleles, A and a, at a given locus, with frequencies p and q respectively, the following equations hold true:
- p + q = 1
- p^{2} + 2pq + q^{2} = 1
Derivation
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 (p^{2}) | Aa (pq) |
a (q) | aA (qp) | aa (q^{2}) |
So the final three possible genotype frequencies, in the offspring, if the alleles are drawn independently become:
- p^{2} (AA)
- 2pq (Aa)
- q^{2} (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 A_{1},..., A_{n} are given by p_{1},...,p_{n}, then the frequency of the A_{i}A_{j} genotype is given by:
- 2p_{i}p_{j} if i≠j and;
- p_{i}^{2} 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 also
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 ESP copy http://www.esp.org/foundations/genetics/classical/hardy.pdf
- 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 http://links.jstor.org/sici?sici=0036-8075%2819430205%293%3A97%3A2510%3C137%3ATH
L%3E2.0.CO%3B2-8 - 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 |
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Key concepts: Hardy-Weinberg law | Fisher's fundamental theorem | neutral theory |
Selection: natural | Censored page | 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 |