The G×E term will be biased in Model 2 when (a) the covariate is related to the genetic variable and the covariate-by-environment interaction coefficient is nonzero or (b) the covariate is related to environmental variable and the covariate-by-gene interaction coefficient is nonzero. Nevertheless, the decision of whether to include or drop covariates along with their interaction terms in a model should be based on theory, not on statistical significance. As demonstrated via simulation by Yzerbyt et al. (18), dropping non-significant covariate interaction terms can seriously inflate the type-I error rate of the G×E term. Terms that are non-significant can still share enough variance with the G×E term to change conclusions about its significance.
