A comparison of alternative random regression and reaction norm models for whole genome predictions1

Whole genome prediction (WGP) based on high density SNP marker panels is known to improve the accuracy of breeding value (BV) prediction in livestock. However, these accuracies can be compromised when genotype by environment interaction (G×E) exists but is not accounted for. Reaction norm (RN) and random regression (RR) models have proven to be useful in accounting for G×E in pre-WGP evaluations by modeling BV as linear or higher order functions of environmental or temporal covariates. We extend these RR/RN models based on several alternative specifications for SNP-specific intercepts and linear slopes on environmental covariates. One specification is based on bivariate normality (BVN) of SNP-specific intercepts and slopes, whereas 2 others, IW-BayesA and based on inverted Wishart (IW) extensions IW-BayesB, are, respectively, bivariate Student t extensions of currently popular models without (BayesA) or with (BayesB) variable selection. We highlight alternative specifications based on the square root free Cholesky decomposition (CD) of SNP-specific variance-covariance (VCV) matrices in an attempt to better differentially model environmentally sensitive from environmentally robust QTL. Two CD specifications were considered with (CD-BayesB) or without (CD-BayesA) any variable selection on intercept and slope effects. We compared each of the 5 models based on an RN simulation study. Six scenarios were considered based on differences in overall genetic correlations between SNP-specific intercept and slope effects as well as on heritabilities and numbers of environmentally robust versus sensitive QTL. In most scenarios, IW-BayesA had the greatest accuracy, whereas CD-BayesB exhibited the greatest accuracy in low complexity architectures (i.e., low number of QTL). In an RR application of a Duroc × Pietrain resource population at Michigan State University, 5,271 SNP markers and 928 F2 animals with known pedigree were analyzed for backfat thickness at wk 10, 13, 16, 19, and 22. SNP-based RR methods had a 2.5% greater (P < 0.0001) cross-validation accuracy for predicting phenotypes than the SNP-based conventional BayesA/BayesB and/or pedigree based RR BLUP; however, none of the proposed RR models had performances that were different from each other.