Combined Multistage Linear Genomic Selection Indices To Predict the Net Genetic Merit in Plant Breeding

Abstract

A combined multistage linear genomic selection index (CMLGSI) is a linear combination of phenotypic and genomic estimated breeding values useful for predicting the individual net genetic merit, which in turn is a linear combination of the true unobservable breeding values of the traits weighted by their respective economic values. The CMLGSI is a cost-saving strategy for improving multiple traits because the breeder does not need to measure all traits at each stage. The optimum (OCMLGSI) and decorrelated (DCMLGSI) indices are the main CMLGSIs. Whereas the OCMLGSI takes into consideration the index correlation values among stages, the DCMLGSI imposes the restriction that the index correlation values among stages be zero. Using real and simulated datasets, we compared the efficiency of both indices in a two-stage context. The criteria we applied to compare the efficiency of both indices were that the total selection response of each index must be lower than or equal to the single-stage combined linear genomic selection index (CLGSI) response and that the correlation of each index with the net genetic merit should be maximum. Using four different total proportions for the real dataset, the estimated total OCMLGSI and DCMLGSI responses explained 97.5% and 90%, respectively, of the estimated single-stage CLGSI selection response. In addition, at stage two, the estimated correlations of the OCMLGSI and the DCMLGSI with the net genetic merit were 0.84 and 0.63, respectively. We found similar results for the simulated datasets. Thus, we recommend using the OCMLGSI when performing multistage selection.

Keywords: Genomic Prediction GenPred; Genomic estimated breeding value; Molecular marker effects; Multistage selection; Shared Data Resources; Total selection response.

Figure 1

Theoretical relationship between one truncation point ($u_1$) values, the total proportion retained ($q_1$) and the density values ($z(u_1)$) of the truncation point.

Figure 2

Theoretical relationship between two truncation point (u1 and u2) values and the density values [z(u1, u2)] of the truncation points.

Figure 3

Distribution of the total estimated OCMLGSI and DCMLGSI selection response values, under a two-stage breeding scheme, for a real dataset with $p=q_1{q}_2=$0.05 and 0.10.

Figure 4

Histograms of the estimated OCMLGSI and DCMLGSI values at stage 2, for a real dataset, when the number of genotypes was 67 (A) and 156 (B) for OCMLGSI, and 54 (C) and 136 (D) for DCMLGSI.

Figure 5

Quantile-quantile plot of the estimated OCMLGSI and DCMLGSI values at stage 2 for a real dataset when the number of genotypes was 67 (A) and 156 (B) for OCMLGSI, and 54 (C) and 136 (D) for DCMLGSI.