Correlation among traits is a fundamental feature of biological systems. From morphological characters, to transcriptional or metabolic networks, the correlations we routinely observe between traits reflect a shared regulation that remains poorly understood and difficult to study. To address this problem, we developed a new and flexible approach that allows us to identify factors associated with variation in correlation between individuals. Here, we use data from three large human cohorts to study the effects of genetic variation and environmental perturbation on correlations among mRNA transcripts and among NMR metabolites. We first show that environmental exposures (namely, infection and disease) lead to a systematic loss of correlation, which we define as 'decoherence'. Using longitudinal data, we show that decoherent metabolites are better predictors of whether someone will develop metabolic syndrome than metabolites commonly used as biomarkers of this disease. Finally, we show that correlation itself is a trait under genetic control: specifically, we mapped and replicated hundreds of 'correlation QTLs', which often involve transcription factors or their known target genes. Together, this work furthers our understanding of how and why coordinated biological processes break down, and highlights the role of decoherence in disease emergence.