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Tajima's D : ウィキペディア英語版
Tajima's D
Tajima's D is a statistical test created by and named after the Japanese researcher Fumio Tajima. The purpose of the test is to distinguish between a DNA sequence evolving randomly ("neutrally") and one evolving under a non-random process, including directional selection or balancing selection, demographic expansion or contraction, genetic hitchhiking, or introgression. A randomly evolving DNA sequence contains mutations with no effect on the fitness and survival of an organism. The randomly evolving mutations are called "neutral", while mutations under selection are "non-neutral". For example, you would expect to find that a mutation which causes prenatal death or severe disease to be under selection. When looking at the human population as a whole, we say that the population frequency of a neutral mutation fluctuates randomly (i.e. the percentage of people in the population with the mutation changes from one generation to the next, and this percentage is equally likely to go up or down) through genetic drift.
Tajima's D is computed as the difference between two measures of genetic diversity: the mean number of pairwise differences and the number of segregating sites, each scaled so that they are expected to be the same in a neutrally evolving population of constant size.
The strength of genetic drift depends on the population size. If a population is at a constant size with constant mutation rate, the population will reach an equilibrium of gene frequencies. This equilibrium has important properties, including the number of segregating sites S, and the number of nucleotide differences between pairs sampled (these are called pairwise differences). To standardize the pairwise differences, the mean or 'average' number of pairwise differences is used. This is simply the sum of the pairwise differences divided by the number of pairs, and is signified by \pi.
The purpose of Tajima's test is to identify sequences which do not fit the neutral theory model at equilibrium between mutation and genetic drift. In order to perform the test on a DNA sequence or gene, you need to sequence homologous DNA for at least 3 individuals. Tajima's statistic computes a standardized measure of the total number of segregating sites (these are DNA sites that are polymorphic) in the sampled DNA and the average number of mutations between pairs in the sample. The two quantities whose values are compared are both method of moments estimates of the population genetic parameter theta, and so are expected to equal the same value. If these two numbers only differ by as much as one could reasonably expect by chance, then the null hypothesis of neutrality cannot be rejected. Otherwise, the null hypothesis of neutrality is rejected.
==Scientific explanation==
Under the neutral theory model, for a population at constant size at equilibrium:
: E()=\theta=E\left(\frac}\right )=4N\mu
for diploid DNA, and
: E()=\theta=E\left(\frac}\right )=2N\mu
for haploid.
In the above formulas, ''S'' is the number of segregating sites, ''n'' is the number of samples, ''N'' is the effective population size,
\mu is the mutation rate at the examined genomic locus,
and ''i'' is the index of summation.
But selection, demographic fluctuations and other violations of the neutral model (including rate heterogeneity and introgression) will change the expected values of S and \pi, so that they are no longer expected to be equal. The difference in the expectations for these two variables (which can be positive or negative) is the crux of Tajima's ''D'' test statistic.
D\, is calculated by taking the difference between the two estimates of the population genetics parameter \theta\,. This difference is called d\,, and D is calculated by dividing d\, by the square root of its variance \sqrt (its standard deviation, by definition).
:
D=\frac
}

Fumio Tajima demonstrated by computer simulation that the D\, statistic described above could be modeled using a beta distribution. If the D\, value for a sample of sequences is outside the confidence interval then one can reject the null hypothesis of neutral mutation for the sequence in question.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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