Gene expression variation is a major contributor to phenotypic variation in human complex traits. Selection on complex traits may therefore be reflected in constraint on gene expression levels. Here, we explore the effects of stabilizing selection on cis- regulatory genetic variation in humans. We analyze patterns of expression variation at copy number variants and find evidence for selection against large increases in gene expression. Using allele-specific expression (ASE) data, we further show evidence of selection against smaller-effect variants. We estimate that, across all genes, singletons in a sample of 122 individuals have approximately 2.5 times greater effects on expression variance than common variants. Despite their increased effect sizes relative to common variants, we estimate that singletons in the sample studied explain, on average, only 5% of the heritability of gene expression from cis-regulatory variants. Finally, we show that genes depleted for loss-of-function variants are also depleted for cis-eQTLs and have low levels of allelic imbalance, confirming tighter constraint on the expression levels of these genes. We conclude that constraint on gene expression is present, but has relatively weak effects on most cis-regulatory variants, thus permitting high levels of gene-regulatory genetic variation.
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