Phenotypic distribution and selection response for linear-product gene-environment interaction in quantitative traits

Gene-environment interaction is often described by linear phenotypic plasticity but has recently also been expressed as function of the product of genotype and environmental variables. While this model can be fitted in a multiple regression scenario, little has been written on the distribution of the product of breeding values and environment, GE , its expected moments, and the theoretical impact on phenotypic selection. Here we will explore these topics introducing the distribution for GE , its mean and variance, and its expected impact of lowering realized heritability due to is increasing the phenotypic variance.