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Tajima's D 中性进化检验

时间:2019-11-09 22:00:49      阅读:571      评论:0      收藏:0      [点我收藏+]

标签:limit   bsp   stat   between   ima   number   phi   tab   reg   

Tajima F (1989) Genetics 123:585-595

1  Average number of pairwise nucleotide differences

$$ \hat k = \frac{\sum\sum_{i<j} k_{ij}}{\binom{n}{2}} $$

\( k_{ij} \), the number of nucleotide differences between the $i$-th and $j$-th DNA sequences

2  D statistic

$$ D = \frac{\hat k - \frac{S}{a_1}}{\sqrt{e_1 S + e_2 S (S-1)}} $$

$$ a_1 = \sum \limits_{i=1}^{n-1} \frac{1}{i} $$

$$ a_2 = \sum \limits_{i=1}^{n-1} \frac{1}{i^2} $$

$$ b_1 = \frac{n+1}{3(n-1)} $$

$$ b_2 = \frac{2(n^2+n+3)}{9n(n-1)} $$

$$ c_1 = b_1 - \frac{1}{a_1} $$

$$ c_2 = b_2 - \frac{n+2}{a_1 n} + \frac{a_2}{a_1^2} $$

$$ e_1 = \frac{c_1}{a_1} $$

$$ e_2 = \frac{c_2}{a_1^2 + a_2} $$

\( S \), the number of segregating (or polymorphic) sites in the sample

3  计算

Tajima F (1989) Genetics 123:585-595

Carlson CS, et al. (2005) Genome Res 15:1553-1565

vcftools --vcf geno.cvf --TajimaD 100000

4  示例

一个 SNP 标记,5 个个体

A A C C C

两两个体间基因型差异

i j d
1 2 0
1 3 1
1 4 1
1 5 1
2 3 1
2 4 1
2 5 1
3 4 0
3 5 0
4 5 0

\( pi = n1*n2 / (n*(n-1)/2) = 2*n1*n2 / (n*(n-1)) = 2*2*3/(4*5) = 0.6 \)

Tajima's D 中性进化检验

标签:limit   bsp   stat   between   ima   number   phi   tab   reg   

原文地址:https://www.cnblogs.com/hjbreg/p/11827788.html

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