We consider a quantitative trait y, for which the genetic component is underlain by random additive effects of MC causal variants. Without loss of generality, we assume causal variants to be shared between ancestries but allow their effect sizes to vary from one ancestry to another. Therefore, ancestry-specific causal variants are a special case with non-zero effect sizes in only one ancestry. We then assume that a GWAS of y has been performed in a discovery sample of a given ancestry, hereafter denoted by Population 1 and that a PGS, defined as the sum of minor allele counts weighted by their estimated effects from the discovery GWAS, is used to predict y in a target sample of another ancestry, hereafter denoted by Population 2. The study design is shown in Supplementary Fig. 1.
