群体分化指数 FST

Posted 2020-11-30 hjbreg

1  Weir & Cockerham, 1984

Weir BS, Cockerham CC (1984) Evolution 38:1358-1370

1.1  一对等位基因

$$ hat heta  = frac{a}{a+b+c} $$

$$ a = frac{ar n}{n_c} left{ s^2 - frac{1}{ar n - 1} left[ ar p (1 - ar p) - frac{r-1}{r} s^2 - frac{1}{4} ar h ight] ight} $$

$$ b = frac{ar n}{ar n - 1} left[ ar p (1 - ar p) - frac{r-1}{r} s^2 - frac{2 ar n - 1}{4 ar n} ar h ight] $$

$$ c = frac{1}{2} ar h $$

$$ ar n = frac{sum{n_i}}{r} $$

$$ n_c = frac{r ar n - sum{n_i^2} / r ar n}{r-1} $$

$$ ar p = frac{sum{n_i ilde p_i}}{r ar n} $$

$$ s^2 = frac{sum{n_i ( ilde p_i - ar p)^2}}{(r-1) ar n} $$

$$ ar h = frac{sum{n_i ilde h_i}}{r ar n} $$

1.2  复等位基因

$$ hat heta  = frac{sum olimits_u a_u }{sum olimits_u left(a_u + b_u + c_u ight)} $$

1.3  多个位点

$$ hat heta  = frac{sum olimits_l sum olimits_u a_{lu}}{sum olimits_l sum olimits_u left(a_{lu} + b_{lu} + c_{lu} ight)} $$

2  Weir & Hill, 2002

Weir BS, Hill WG (2002) Annu Rev Genet 36:721-750

$$ hat heta _u = frac{MSP_u - MSG_u}{MSP_u + (n_c - 1) MSG_u} $$

$$ MSP_u = frac{1}{r - 1} sumlimits_{i=1}^r {n_i ( ilde p_{iu} - ar p_u)^2} $$

$$ MSG_u = frac{1}{sumlimits_{i=1}^r (n_i - 1)} sumlimits_{i=1}^r n_i ilde p_{iu} (1 - ilde p_{iu}) $$

$$ n_c = frac{1}{r-1} left( sumlimits_{i=1}^r n_i - frac{sum olimits_{i=1}^r n_i^2}{sum olimits_{i=1}^r n_i} ight) = frac{1}{r-1} sumlimits_{i=1}^r n_{ic} $$

$$ n_{ic} = n_i - frac{n_i^2}{sum olimits_{i=1}^r n_i} $$

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