# McDonald–Kreitman test

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In statistical genetics, the McDonald–Kreitman test looks for ancient selection over long periods, as opposed to the steady accumulation of mutations that confer no selective advantage predicted by the neutral theory. It was first devised by John H. McDonald and Martin Kreitman in 1991, based on an investigation of differences in amino acid sequence of the alcohol dehydrogenase gene in Drosophila.[1] Nucleotide differences between the coding regions of homologous genes of related species are enumerated and sorted into four categories, as shown below:

FixedPolymorphic
SynonymousDsPs
NonsynonymousDnPn

Sites are classed as polymorphic if they show any variation within species, while they are classed as fixed if they differ between species but not within them. If the ratio of fixed differences to polymorphisms is much higher for nonsynonymous changes (i.e. Dn/PnDs/Ps), this indicates that genetic changes have been subject to positive selection.

The McDonald–Kreitman test itself consists of the G-test performed on the numbers in the table above, which would indicate whether the two ratios are significantly different. As an extension of this, Smith and Eyre-Walker proposed estimating the proportion of base substitutions fixed by natural selection, α,[2] using a simple formula:

$\alpha = 1 - \frac{D_sP_n}{D_nP_s}$

Using this formula, the authors estimated that 45% of amino acid differences between Drosophila simulans and D. yakuba are estimated to have been fixed by selection, while 35% of amino acid differences between primates are estimated to be fixed by selection.

Note that Dn and Ds are count estimates and therefore different from KA and KS (or dN and dS) which are rate estimates. The Ka/Ks ratio (or ω, dN/dS ratio) is the ratio of the number of non-synonymous substitutions per non-synonymous site (Ka) to the number of synonymous substitutions per synonymous site (Ks).

## References

1. ^ John H. McDonald & Martin Kreitman (1991). "Adaptive protein evolution at the Adh locus in Drosophila" (PDF). Nature 351 (6328): 652–654. Bibcode 1991Natur.351..652M. doi:10.1038/351652a0. PMID 1904993.
2. ^ Nick G. C. Smith & Adam Eyre-Walker (2002). "Adaptive protein evolution in Drosophila" (PDF). Nature 415 (6875): 1022–1024. Bibcode 2002Natur.415.1022S. doi:10.1038/4151022a. PMID 11875568.