In order to illustrate why this method is more appropriate for modeling G × E with three category genotypic variables we used R software to plot graphs showing properties of regression lines with an interaction term modeled using Eq. (1) [the four parameter model] and Eq. (3) [the six parameter model]. The R script is presented in Appendix B. For n = 10,000 individuals we assigned random values for a prototypical environmental variable (E) taking values between 0 and 10 with the same probability, and G variables having three levels: 0, 1 and 2. The G variable satisfies Hardy–Weinberg equilibrium conditions with minor allele frequency p = 0.5, so the numbers of individuals for G = 0, 1 and 2 levels are np(1 − p) = 2,500, 2np(1 − p) = 5,000 and n(1 − p)(1 − p) = 2,500, respectively. Then for each G level we assumed that the Phenotypes were linearly dependent on the environmental variable with the error having a normal distribution with mean = 0 and SD = 0.1. Figure 2 presents simulated data and observed
