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Complex traits arise from the combined effects of rare and common genetic variation, development and environment, but resolving their joint contributions has been limited by statistical power. Here, we meta-analyze effects of recurrent copy number variants (CNVs), polygenic scores, sex, age and medications on height and body mass index in 1,447,001 individuals across 6 biobanks and clinical cohorts. CNVs show largely mirror dose-dependent effects of deletions and duplications on both traits, but a subset of loci exhibit asymmetric dose-responses on adult height, consistent with buffering of one allele but not the other. Polygenic background and medications combine with CNVs in ways broadly consistent with additivity. However, detailed analyses of loci at 16p11.2 and 22q11.2 reveal context-dependent effects that vary across development, physiology and sex. At 22q11.2, the net effect of a CNV reflects opposing and reinforcing contributions of multiple genes, providing a potential mechanism for buffering of dosage effects. These results indicate that genetic effects follow additive patterns in aggregate, while context-dependent deviations are widespread for specific loci.