The use of weighted multiple linear regression to estimate QTL × QTL × QTL interaction effects of winter wheat (Triticum aestivum L.) doubled-haploid lines

Knowledge of the magnitude of gene effects and their interactions, their nature, and contribution to determining quantitative traits is very important in conducting an effective breeding program. In traditional breeding, information on the parameter related to additive gene effect and additive-additive interaction (epistasis) and higher-order additive interactions would be useful. Although commonly overlooked in studies, higher-order interactions have a significant impact on phenotypic traits. Failure to account for the effect of triplet interactions in quantitative genetics can significantly underestimate additive QTL effects. Understanding the genetic architecture of quantitative traits is a major challenge in the post-genomic era, especially for quantitative trait locus (QTL) effects, QTL–QTL interactions, and QTL–QTL–QTL interactions. This paper proposes using weighted multiple linear regression to estimate the effects of triple interaction (additive–additive–additive) quantitative trait loci (QTL–QTL–QTL). The material for the study consisted of 126 doubled haploid lines of winter wheat (Mandub × Begra cross). The lines were analyzed for 18 traits, including percentage of necrosis leaf area, percentage of leaf area covered by pycnidia, heading data, and height. The number of genes (the number of effective factors) was lower than the number of QTLs for nine traits, higher for four traits and equal for five traits. The number of triples for unweighted regression ranged from 0 to 9, while for weighted regression, it ranged from 0 to 13. The total aaa(gu) effect ranged from − 14.74 to 15.61, while aaa(gw) ranged from − 23.39 to 21.65. The number of detected threes using weighted regression was higher for two traits and lower for four traits. Forty-nine statistically significant threes of the additive-by-additive-by-additive interaction effects were observed. The QTL most frequently occurring in threes was 4407404 (9 times). The use of weighted regression improved (in absolute value) the assessment of QTL–QTL–QTL interaction effects compared to the assessment based on unweighted regression. The coefficients of determination for the weighted regression model were higher, ranging from 0.8 to 15.5%, than for the unweighted regression. Based on the results, it can be concluded that the QTL–QTL–QTL triple interaction had a significant effect on the expression of quantitative traits. The use of weighted multiple linear regression proved to be a useful statistical tool for estimating additive-additive-additive (aaa) interaction effects. The weighted regression also provided results closer to phenotypic evaluations than estimator values obtained using unweighted regression, which is closer to the true values.