Quasi-linkage equilibrium (QLE) is a mathematical approximation used in solving population genetics problems. Motoo Kimura introduced the notion to simplify a model of Fisher's fundamental theorem. QLE greatly simplifies population genetic equations whilst making the assumption of weak selection and weak epistasis.[1] Selection under these conditions rapidly changes allele frequencies to a state where they evolve as if in linkage equilibrium. Kimura originally provided the sufficient conditions for QLE in two-locus systems, but recently several researchers have shown how QLE occurs in general multilocus systems.[2] QLE allows theorists to approximate linkage disequilibria by simple expressions, often simple functions of allele or genotype frequencies, thereby providing solutions to highly complex problems involving selection on multiple loci or polygenic traits.[3] QLE also plays an important role in justifying approximations in the derivation of quantitative genetic equations from mendelian principles.
Simple Modeledit
Let , , and represent the frequencies of the four possible genotypes in a haploid two-locus-two-allele model. Kimura's original model[1] showed that
approaches a stable state rapidly if epistatic effects are small relative to recombination. Deviations from will be reduced by the recombination fraction every generation.
Referencesedit
^ abKimura, Motoo (1965). "Attainment of quasi linkage equilibrium when gene frequencies are changing by natural selection". Genetics. 52 (5): 875–890. doi:10.1093/genetics/52.5.875. PMC1210959. PMID 17248281.
^Nagylaki, Thomas; Hofbauer, Joseph; Brunovsky, Pavel (1999). "Convergence of multilocus systems under weak epistasis or weak selection". Journal of Mathematical Biology. 38 (2): 103–133. doi:10.1007/s002850050143. PMID 10085555. S2CID 1220489.
^Kirkpatrick, Mark; Johnson, Toby; Barton, Nicholas (2002). "General Models of Multilocus Evolution". Genetics. 161 (4): 1727–1750. doi:10.1093/genetics/161.4.1727. PMC1462196. PMID 12196414.
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quasi, linkage, equilibrium, mathematical, approximation, used, solving, population, genetics, problems, motoo, kimura, introduced, notion, simplify, model, fisher, fundamental, theorem, greatly, simplifies, population, genetic, equations, whilst, making, assu. Quasi linkage equilibrium QLE is a mathematical approximation used in solving population genetics problems Motoo Kimura introduced the notion to simplify a model of Fisher s fundamental theorem QLE greatly simplifies population genetic equations whilst making the assumption of weak selection and weak epistasis 1 Selection under these conditions rapidly changes allele frequencies to a state where they evolve as if in linkage equilibrium Kimura originally provided the sufficient conditions for QLE in two locus systems but recently several researchers have shown how QLE occurs in general multilocus systems 2 QLE allows theorists to approximate linkage disequilibria by simple expressions often simple functions of allele or genotype frequencies thereby providing solutions to highly complex problems involving selection on multiple loci or polygenic traits 3 QLE also plays an important role in justifying approximations in the derivation of quantitative genetic equations from mendelian principles Simple Model editLet X displaystyle X nbsp Y displaystyle Y nbsp Z displaystyle Z nbsp and U displaystyle U nbsp represent the frequencies of the four possible genotypes in a haploid two locus two allele model Kimura s original model 1 showed thatR X U Y Z displaystyle R frac XU YZ nbsp approaches a stable state R displaystyle hat R nbsp rapidly if epistatic effects are small relative to recombination Deviations from R displaystyle hat R nbsp will be reduced by the recombination fraction every generation References edit a b Kimura Motoo 1965 Attainment of quasi linkage equilibrium when gene frequencies are changing by natural selection Genetics 52 5 875 890 doi 10 1093 genetics 52 5 875 PMC 1210959 PMID 17248281 Nagylaki Thomas Hofbauer Joseph Brunovsky Pavel 1999 Convergence of multilocus systems under weak epistasis or weak selection Journal of Mathematical Biology 38 2 103 133 doi 10 1007 s002850050143 PMID 10085555 S2CID 1220489 Kirkpatrick Mark Johnson Toby Barton Nicholas 2002 General Models of Multilocus Evolution Genetics 161 4 1727 1750 doi 10 1093 genetics 161 4 1727 PMC 1462196 PMID 12196414 nbsp This evolution related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Quasi linkage equilibrium amp oldid 1090694553, wikipedia, wiki, book, books, library,
