Deviations from genetic additivity driven by rare variants at biobank scale.

Additive genetic models are the default for genome-wide association studies, but deviations from additivity are crucial for understanding disease mechanisms and therapeutic responses. Yet existing methods for testing nonadditivity are computationally infeasible for large-scale analysis or rely on Hardy-Weinberg assumptions, making them unsuitable for rare variants in large biobanks. We use an orthogonal allelic recoding framework that enables scalable testing of nonadditive genetic effects without Hardy-Weinberg assumptions while integrating seamlessly with existing linear mixed models. Analyzing up to 399,943 UK Biobank individuals across 2906 plasma proteins and 55 quantitative traits, we demonstrate that approximately one-third of cognate gene-protein relationships exhibit nonlinear dose responses. We identify recessive effects, including FUT10 variants associated with reduced lung function, and validate these findings in the All of Us cohort. We show that many complex traits show partial recessivity, reconciling conflicting inheritance patterns in the literature, and that joint two-degree-of-freedom models substantially improve statistical power when the underlying trait is partially recessive. Our framework efficiently partitions additive and nonadditive heritability components at biobank scale, providing a quantitative map of gene dose-response relationships with direct implications for therapeutic target identification and precision medicine.