Genomic Prediction Accuracies Using Regularized Quantile Regression (RQR) Methodology

The objective of this work was to evaluate the use of regularized quantile regression (RQR) for genomic prediction analyses in traits with or without skewness, and with different proportions of epistatic variance. Data were simulated for 2,500 individuals. The genome included 5K markers and 50 QTL for a lowly heritable trait (heritability=0.1) simulated for six scenarios: combinations of trait distributions (symmetric normal or positive skewed) and percentage of epistatic and additive genetic variances (100% epistatic, 50% epistatic and 50% additive, 100% additive). Only additive-by-additive effects were simulated for epistasis. Three replicates were generated per scenario. Estimation of marker effects was performed using 2,000 individuals (training). The remaining 500 individuals were used for validation. Accuracy was calculated as the correlation between genomic estimated breeding values and true breeding values. Analyses were performed using Bayesian LASSO (BLASSO) and RQR considering three quantiles (0.15 [RQR_0.15], 0.50[RQR_0.50], 0.85[RQR_0.85]) in R. Results are shown in Table 1. Overall, accuracies of genomic prediction for the normal symmetric trait were variable. There was no relationship between RQR quantiles and accuracies of genomic prediction. In general, accuracies of genomic prediction decreased as the proportion of epistatic variance increased. The highest accuracies of genomic prediction were 0.15 (BLASSO), 0.17 (BLASSO), and 0.20 (RQR_0.15), for the proportions of epistatic variance of 100%, 50%, and 0%, respectively. For the positively skewed trait, the greatest accuracies were obtained for RQR_0.15, with 0.16, 0.26, and 0.27, followed by RQR_0.50, with 0.12, 0.18, and 0.21, for the proportions of epistatic variance of 100%, 50%, and 0%, respectively. Accuracies for RQR_0.15 were 77%, 53%, and 50% greater than those obtained using BLASSO. For RQR, accuracies decreased as quantiles increased. Within each method, accuracies were similar for proportions of epistatic variances of 50% and 0%. In conclusion, for the symmetric normal trait, BLASSO had, overall, slightly greater accuracies than for RQR. In contrast, RQR presented greater accuracies of genomic prediction compared to BLASSO when quantiles 0.15 and 0.50 were used for the trait with positive skewness. These results suggest that improved accuracy of genomic prediction for skewed traits can be obtained using RQR.

Table1. Accuracies of genomic prediction

Trait distribution		Percentage of epistatic/additive genetic variance
	Methodology		100%/0%	50%/50%	0%/100%
Symmetric Normal	Blasso		0.15	0.17	0.19
	RQR0.15		0.10	0.16	0.13
	RQR0.50		0.14	0.13	0.20
	RQR0.85		0.11	0.16	0.16
Positive Skewness	BLASSO		0.09	0.17	0.18
	RQR0.15		0.16	0.26	0.27
	RQR0.50		0.12	0.18	0.21
	RQR0.85		0.05	0.12	0.12