Disentangling phenotype scale, amplification, and effect heterogeneity underlying polygenic GxE architecture of complex traits

While polygenic gene-by-environment (GxE) signals are increasingly detected in biobank data, it is often unclear whether they reflect the phenotype's measurement scale or one of two biologically distinct mechanisms: heterogeneous genetic effects across environmental strata (effect heterogeneity) or systematically larger but correlated effects in one stratum (amplification). We introduce REGENA (Robust Estimator of Gene-ENvironment Architectures), a variance-component method that disentangles these contributions at biobank scale by learning a phenotype transformation that minimizes scale-induced GxE, thereby assessing scale-dependence while jointly estimating the cross-environment genetic correlation and environment-specific genetic variances. In simulations, REGENA is well-calibrated and powerful while recovering the transformation underlying scale-dependent GxE. Applied to 43 quantitative traits and seven environmental exposures in 291,273 UK Biobank individuals, REGENA finds that roughly half of trait-environment pairs with significant GxE are scale-dependent. Among the remaining scale-independent trait-environment pairs, GxE heritability accounted for an average of 15% of additive heritability and was driven primarily by effect heterogeneity (accounting for 71% of GxE heritability on average) although there was substantial variation in its relative contribution across trait-environment pairs. Environment-specific effects tend to make a larger contribution at lower allele frequencies, accounting for 6% of genetic variance in low-frequency variants versus 3.9% at common variants (signed test p = 1.7e-24). Modeling these distinctions improves environment-specific polygenic prediction (14% on average), with the largest gains for pairs whose genetic effects are least correlated across environments (p = 4.0e-3; 3.8-fold for testosterone stratified by sex and 2.32-fold for waist-hip ratio stratified by alcohol consumption). Further, environment-stratified GWAS detects 174 loci missed by pooled GWAS with 67 having opposite-signed effects across strata.