Genotype-by-environment interaction (GxE) occurs when the size of a genetic effect varies systematically across levels of the environment and when the size of an environmental effect varies systematically across levels of the genotype. However, total variance in the phenotype may shift as a function of the moderator irrespective of its etiology such that the proportional effect of the predictor is constant. We expand the traditional GxE regression model to directly account for heteroscedasticity associated with both the genotype and the measured environment. We then derive a test statistic, ξ, for inferring whether GxE can be attributed to an effect of the moderator on the dispersion of the phenotype. We apply this method to identify genotype-by-birth year interactions for Body Mass Index (BMI) that are distinguishable from general secular increases in the variance of BMI or associations of the genetic predictors (both PGS and individual loci) with BMI variance. We provide software for analyzing such models.

中文翻译：

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基因-环境相互作用分析中相互作用与分散效应的区别

当遗传效应的大小在整个环境水平上系统地变化时，并且当环境效应的大小在基因型水平上系统地变化时，就会发生按环境分型的基因相互作用。但是，表型的总方差可能会根据主持人的病因而变化，而与主持人的病因无关，因此预测器的比例效应是恒定的。我们扩展了传统的GxE回归模型，以直接考虑与基因型和测量环境相关的异方差。然后，我们得出检验统计量ξ，以推断GxE是否可归因于调节剂对表型分散的影响。我们应用这种方法来识别体重指数（BMI）的按出生年份的基因型交互作用，该交互作用可与BMI变异的一般长期增长或遗传预测因子（PGS和单个基因座）与BMI变异的关联相区别。我们提供用于分析此类模型的软件。