Polygenic localization aims to identify a minimal set of SNPs causally explaining a given proportion of common SNP heritability. To define polygenic localization, we first define Mp*, as the smallest integer k such that ∑i∈{s1,…,sk}βi2/∑i=1mβi2≥p, where βi are standardized SNP effect sizes, sj denotes a ranking of βi2 such that βs12≥βs22≥…≥βsm2, and m is the number of common SNPs. Unfortunately, βi2 is unknown in practice. Polygenic localization therefore estimates an upper-bound of Mp*, denoted as Mp. We define Mp as the smallest integer k′ such that ∑i∈{s′1,…,s′k′}βi2/∑i=1mβi2≥p, where s′ is a possibly non-optimal ranking of SNPs. We note that Mp≥Mp* by construction. We provide a full derivation of Polygenic localization in the Supplementary Note.
