Quasi-linkage equilibrium (QLE) is a mathematical approximation used in solving population genetics problems.
Motoo Kimura
(November 13, 1924 – November 13, 1994) was a Japanese biologist best known for introducing the neutral theory of molecular evolution in 1968. He became one of the most influential theoretical population geneticists. He is remembered in genet ...
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.
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.
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.
QLE also plays an important role in justifying approximations in the derivation of
quantitative genetic equations from
mendelian
Mendelian inheritance (also known as Mendelism) is a type of biological inheritance following the principles originally proposed by Gregor Mendel in 1865 and 1866, re-discovered in 1900 by Hugo de Vries and Carl Correns, and later popularize ...
principles.
Simple Model
Let
,
,
and
represent the frequencies of the four possible
genotypes
The genotype of an organism is its complete set of genetic material. Genotype can also be used to refer to the alleles or variants an individual carries in a particular gene or genetic location. The number of alleles an individual can have in a ...
in a haploid two-locus-two-allele model. Kimura's original model
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.
References
Evolutionary biology
Population genetics
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