Testing the moderation of quantitative gene by environment interactions in unrelated individuals

Abstract

The environment can moderate the effect of genes – a phenomenon called gene-environment (GxE) interaction. There are two broad types of GxE modeled in human behavior – qualitative GxE, where the effects of individual genetic variants differ depending on some environmental moderator, and quantitative GxE, where the additive genetic variance changes as a function of an environmental moderator. Tests of both qualitative and quantitative GxE have traditionally relied on comparing the covariances between twins and close relatives, but recently there has been interest in testing such models on unrelated individuals measured on genomewide data. However, to date, there has been no ability to test quantitative GxE effects in unrelated individuals using genomewide data because standard software cannot solve nonlinear constraints. Here, we introduce a maximum likelihood approach with parallel constrained optimization to fit such models. We use simulation to estimate the accuracy, power, and type I error rates of our method and to gauge its computational performance, and then apply this method to IQ data measured on 40,172 individuals with whole-genome SNP data from the UK Biobank. We found that the additive genetic variation of IQ tagged by SNPs increases as socioeconomic status (SES) decreases, opposite the direction found by several twin studies conducted in the U.S. on adolescents, but consistent with several studies from Europe and Australia on adults.