Fox–Wright function: Difference between revisions

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'''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 while making the assumption of weak [[natural selection|selection]] and weak [[epistasis]].<ref  name="kimura">{{cite journal|last=Kimura|first=Motoo|title=Attainment of quasi linkage equilibrium when gene frequencies are changing by natural selection|journal=Genetics|year=1965|volume=52|pages=875–890}}</ref> 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.<ref name=nagylaki>{{cite journal|last=Nagylaki|first=Thomas|coauthors=Hofbauer, Joseph; Brunovsky, Pavel|title=Convergence of multilocus systems under weak epistasis or weak selection|journal=Journal of Mathematical Biology|year=1999|volume=38|pages=103–133}}</ref> 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.<ref name=kjb>{{cite journal|last=Kirkpatrick|first=Mark|coauthors=Johnson, Toby; Barton, Nicholas|title=General Models of Multilocus Evolution|journal=Genetics|year=2002|volume=161|pages=1727–1750}}</ref> QLE also plays an important role in justifying approximations in the derivation of [[quantitative genetics|quantitative genetic]] equations from [[mendelian]] principles.
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Let <math>X</math>, <math>Y</math>, <math>Z</math> and <math>U</math> represent the frequencies of the four possible [[genotypes]] in a haploid two-locus-two-allele model. Kimura's original model<ref name="kimura"/> showed that
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<math>
R = \frac{XU}{YZ}
</math>
 
approaches a stable state <math>\hat{R}</math> rapidly if epistatic effects are small relative to recombination.  Deviations from <math>\hat{R}</math> will be reduced by the [[recombination (biology)|recombination]] fraction every generation.
 
== References ==
{{Reflist}}
 
<!--- Categories --->
 
[[Category:Evolutionary biology]]
[[Category:Population genetics]]
 
 
{{evolution-stub}}

Latest revision as of 16:40, 17 February 2014

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