A Comparison of Methods to Estimate Additive–by–Additive–by–Additive of QTL×QTL×QTL Interaction Effects by Monte Carlo Simulation Studies

The goal of the breeding process is to obtain new genotypes with traits improved over the parental forms. Parameters related to the additive effect of genes as well as their interactions (such as epistasis of gene–by–gene interaction effect and additive–by–additive–by–additive of gene–by–gene–by–gene interaction effect) can influence decisions on the suitability of breeding material for this purpose. Understanding the genetic architecture of complex traits is a major challenge in the post-genomic era, especially for quantitative trait locus (QTL) effects, QTL–by–QTL interactions and QTL–by–QTL–by–QTL interactions. With regards to the comparing methods for estimating additive–by–additive–by–additive of QTL×QTL×QTL interaction effects by Monte Carlo simulation studies, there are no publications in the open literature. The parameter combinations assumed in the presented simulation studies represented 84 different experimental situations. The use of weighted regression may be the preferred method for estimating additive–by–additive–by–additive of QTL–QTL–QTL triples interaction effects, as it provides results closer to the true values of total additive–by–additive–by–additive interaction effects than using unweighted regression. This is also indicated by the obtained values of the determination coefficients of the proposed models.