1 Weir & Cockerham, 1984
Weir BS, Cockerham CC (1984) Evolution 38:1358-1370
1.1 一对等位基因
\( \hat \theta = \frac{a}{a+b+c} \)
\( a = \frac{\bar n}{n_c} \left\{ s^2 - \frac{1}{\bar n - 1} \left[ \bar p (1 - \bar p) - \frac{r-1}{r} s^2 - \frac{1}{4} \bar h \right] \right\} \)
\( b = \frac{\bar n}{\bar n - 1} \left[ \bar p (1 - \bar p) - \frac{r-1}{r} s^2 - \frac{2 \bar n - 1}{4 \bar n} \bar h \right] \)
\( c = \frac{1}{2} \bar h \)
\( \bar n = \frac{\sum{n_i}}{r} \)
\( n_c = \frac{r \bar n - \sum{n_i^2} / r \bar n}{r-1} \)
\( \bar p = \frac{\sum{n_i \tilde p_i}}{r \bar n} \)
\( s^2 = \frac{\sum{n_i (\tilde p_i - \bar p)^2}}{(r-1) \bar n} \)
\( \bar h = \frac{\sum{n_i \tilde h_i}}{r \bar n} \)
1.2 复等位基因
\( \hat \theta = \frac{\sum \nolimits_u a_u }{\sum \nolimits_u \left(a_u + b_u + c_u \right)} \)
1.3 多个位点
\( \hat \theta = \frac{\sum\nolimits_l \sum\nolimits_u a_{lu}}{\sum\nolimits_l \sum\nolimits_u \left(a_{lu} + b_{lu} + c_{lu} \right)} \)
2 Weir & Hill, 2002
Weir BS, Hill WG (2002) Annu Rev Genet 36:721-750
\( \hat \theta _u = \frac{MSP_u - MSG_u}{MSP_u + (n_c - 1) MSG_u} \)
\( MSP_u = \frac{1}{r - 1} \sum\limits_{i=1}^r {n_i (\tilde p_{iu} - \bar p_u)^2} \)
\( MSG_u = \frac{1}{\sum\limits_{i=1}^r (n_i - 1)} \sum\limits_{i=1}^r n_i \tilde p_{iu} (1 - \tilde p_{iu}) \)
\( n_c = \frac{1}{r-1} \left( \sum\limits_{i=1}^r n_i - \frac{\sum\nolimits_{i=1}^r n_i^2}{\sum\nolimits_{i=1}^r n_i} \right) = \frac{1}{r-1} \sum\limits_{i=1}^r n_{ic} \)
\( n_{ic} = n_i - \frac{n_i^2}{\sum\nolimits_{i=1}^r n_i} \)
3 计算
Weir BS, Cockerham CC (1984) Evolution 38:1358-1370
Akey JM, et al. (2002) Genome Res 12:1805-1814
VCFtools
vcftools --vcf geno.vcf --weir-fst-pop pop1.txt --weir-fst-pop pop2.txt vcftools --vcf geno.vcf --weir-fst-pop pop1.txt --weir-fst-pop pop2.txt --fst-window-size 100000 --fst-window-step 25000
GCTA
gcta64 --bfile test --fst --sub-popu subpopu.txt --out test