SNP heritability: What are we estimating?

The SNP heritability [Formula] has become a central concept in the study of complex traits. Estimation of [Formula] based on genomic variance components in a linear mixed model using restricted maximum likelihood has been widely adopted as the method of choice were individual level data are available. Empirical results have suggested that this approach is not robust if the population of interest departs from the assumed statistical model. Prolonged debate of the appropriate model choice has yielded a number of approaches to account for frequency- and linkage disequilibrium dependent genetic architectures. Here we analytically resolve the question of how these estimates relate to [Formula] of the population from which samples are drawn. In particular, we show that the correct model for the purpose of inference about [Formula] does not require knowledge of the true genetic architecture of a trait. More generally, our results provide a complete perspective of these class of estimators of [Formula], highlighting practical shortcomings of current practise. We illustrate our theoretical results using simulations and data from UK Biobank.