Interpreting SNP heritability in admixed populations.

SNP heritability is defined as the proportion of phenotypic variance explained by genotyped SNPs and is believed to be a lower bound of heritability ( h 2 ), being equal to it if all causal variants are known. Despite the simple intuition behind , its interpretation and equivalence to h 2 is unclear, particularly in the presence of population structure and assortative mating. It is well known that population structure can lead to inflation in estimates. Here we use analytical theory and simulations to demonstrate that estimates of are not guaranteed to be equal to h 2 in admixed populations, even in the absence of confounding and even if the causal variants are known. We interpret this discrepancy arising not because the estimate is biased, but because the estimand itself as defined under the random effects model may not be equal to h 2 . The model assumes that SNP effects are uncorrelated which may not be true, even for unlinked loci in admixed and structured populations, leading to over- or under-estimates of relative to h 2 . For the same reason, local ancestry heritability may also not be equal to the variance explained by local ancestry in admixed populations. We describe the quantitative behavior of and as a function of admixture history and the genetic architecture of the trait and discuss its implications for genome-wide association and polygenic prediction.