Gene-environment interaction (GxE) is a well-known source of non-additive inheritance. GxE can be important in applications ranging from basic functional genomics to precision medical treatment. Further, GxE effects elude inherently-linear LMMs and may explain missing heritability. We propose a simple, unifying mixed model for polygenic interactions (GxEMM) to capture the aggregate effect of small GxE effects spread across the genome. GxEMM extends existing LMMs for GxE in two important ways. First, it extends to arbitrary environmental variables, not just categorical groups. Second, GxEMM can estimate and test for environment-specific heritability. In simulations where the assumptions of existing methods do not hold, we show that GxEMM improves estimates of ordinary and GxE heritability and increases power to test for polygenic GxE. We then use GxEMM to prove that the heritability of major depression (MD) is reduced by stress, which we previously conjectured but could not prove with prior methods, and that a tail of polygenic GxE effects remains unexplained by MD GWAS.

GxEMM: Extending linear mixed models to general gene-environment interactions