Long AbstractCopy number variants (CNVs) have large effects on complex traits, but they are rare and remain challenging to study. As a result, our understanding of biological functions linking gene dosage to complex traits remains limited, and whether these functions sensitive to gene dosage are similar to those underlying the effects of rare single nucleotide variants (SNVs) and common variants remains unknown.MethodsWe developed FunBurd, a functional burden analysis, to test the association of CNVs aggregated within functional gene sets. We applied this approach in 500,000 individuals from the UK Biobank to associate 43 complex traits with CNVs disrupting 172 gene sets across tissues and cell types. We compared CNV findings with those from common variants and LoF (Loss of Function) SNVs in the same cohort using the same functional gene sets.ResultsAll 43 traits showed FDR significant associations with CNVs. Brain tissue and neuronal cell-types showed the highest levels of pleiotropy. Most of the functional gene set associations could, in part, be explained by genetic constraint, except for brain related processes. Shared genetic contributions between pairs of traits were concordant across types of variants, but on average 2-fold higher, for rare CNVs and SNVs compared to common variants.Functional enrichment across traits found limited overlap between CNVs and common variants. Moreover, the effects of deletions and duplications were negatively correlated for most traits.In conclusion, we present new methods to separate the contributions of genetic constraint and gene function to the associations of CNVs with complex traits. Overall, the functional convergence between different types of variants -even between deletions and duplications- remains limited.Short AbstractCopy number variants (CNVs) have large effects on complex traits, but they are rare and remain challenging to study. As a result, our understanding of biological functions linking gene dosage to complex traits remains limited.FunBurd (functional burden analysis) was applied in 500,000 individuals from the UKBiobank to associate 43 complex traits with CNVs disrupting 172 tissues/cell type gene sets.All 43 traits showed associations with CNVs. Brain tissue and neuronal cell types showed the highest levels of pleiotropy. Most of the functional gene set associations could, in part, be explained by genetic constraint, except for brain-related processes. Shared genetic contributions between pairs of traits were 2-fold higher for rare compared to common variants. The functional convergence between different types of variants -even between deletions and duplications- was limited. Our findings provide insights to separate the contributions of genetic constraint and gene function to the associations of CNVs with complex traits.