Inferring Population Structure and Admixture Proportions in Low-Depth NGS Data

. 2018 Aug 21;210(2):719–731. doi: 10.1534/genetics.118.301336

Algorithm 1: SVD method for estimating individual allele frequencies.

1. The centered genotype dosages are constructed as

E_{i}^{(C)} = E_{i} - 2 \hat{p}

for

i = 1, \dots, n .

2. Perform SVD on the centered genotype dosages,

E^{(C)} = W Δ U^{T},

where

W

will represent population structure similarly to

V .

3. Define

{\hat{E}}_{D}^{(C)}

to be the prediction of the centered genotype dosages using only the top D principal components,

{\hat{E}}_{D}^{(C)} = W_{1 : D} Δ_{1 : D} U_{1 : D}^{T} .

4. Estimate

\hat{Π}

by adding

2 \hat{p}

{\hat{E}}_{D}^{(C)}

row-wise and scaling by

1 / 2,

based on

{\hat{π}}_{i s} \approx 1 / 2 E [G_{i s}] .