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 aaagu effect ranged from - 14.74 to 15.61, while aaagw 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.

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.

Analytical and numerical comparisons of two methods of estimation of additive × additive × additive interaction of QTL effects.

This paper presents the analytical and numerical comparison of two methods of estimation of additive × additive × additive (aaa) interaction of QTL effects. The first method takes into account only the plant phenotype, while in the second we also included genotypic information from molecular marker observation. Analysis was made on 150 doubled haploid (DH) lines of barley derived from cross Steptoe × Morex and 145 DH lines from Harrington × TR306 cross. In total, 153 sets of observation was analyzed. In most cases, aaa interactions were found with an exert effect on QTL. Results also show that with molecular marker observations, obtained estimators had smaller absolute values than phenotypic estimators.