Measuring linkage disequilibrium and improvement of pruning and clumping in structured populations.

Standard measures of linkage disequilibrium (LD) are affected by admixture and population structure, such that loci that are not in LD within each ancestral population appear linked when considered jointly across the populations. The influence of population structure on LD can cause problems for downstream analysis methods, in particular those that rely on LD pruning or clumping. To address this issue, we propose a measure of LD that accommodates population structure using the top inferred principal components. We estimate LD from the correlation of genotype residuals and prove that this LD measure remains unaffected by population structure when analyzing multiple populations jointly, even with admixed individuals. Based on this adjusted measure of LD, we can perform LD pruning to remove the correlation between markers for downstream analysis. Traditional LD pruning is more likely to remove markers with high differences in allele frequencies between populations, which biases measures for genetic differentiation and removes markers that are not in LD in the ancestral populations. Using data from moderately differentiated human populations and highly differentiated giraffe populations we show that traditional LD pruning biases FST and principal component analysis (PCA), which can be alleviated with the adjusted LD measure. In addition, we show that the adjusted LD leads to better PCA when pruning and that LD clumping retains more sites with the retained sites having stronger associations.