Multifactorial methods integrating haplotype and epistasis effects for genomic estimation and prediction of quantitative traits.

The rapid growth in genomic selection data provides unprecedented opportunities to discover and utilize complex genetic effects for improving phenotypes, but the methodology is lacking. Epistasis effects are interaction effects, and haplotype effects may contain local high-order epistasis effects. Multifactorial methods with SNP, haplotype, and epistasis effects up to the third-order are developed to investigate the contributions of global low-order and local high-order epistasis effects to the phenotypic variance and the accuracy of genomic prediction of quantitative traits. These methods include genomic best linear unbiased prediction (GBLUP) with associated reliability for individuals with and without phenotypic observations, including a computationally efficient GBLUP method for large validation populations, and genomic restricted maximum estimation (GREML) of the variance and associated heritability using a combination of EM-REML and AI-REML iterative algorithms. These methods were developed for two models, Model-I with 10 effect types and Model-II with 13 effect types, including intra- and inter-chromosome pairwise epistasis effects that replace the pairwise epistasis effects of Model-I. GREML heritability estimate and GBLUP effect estimate for each effect of an effect type are derived, except for third-order epistasis effects. The multifactorial models evaluate each effect type based on the phenotypic values adjusted for the remaining effect types and can use more effect types than separate models of SNP, haplotype, and epistasis effects, providing a methodology capability to evaluate the contributions of complex genetic effects to the phenotypic variance and prediction accuracy and to discover and utilize complex genetic effects for improving the phenotypes of quantitative traits.