Impact of blending the genomic relationship matrix with different levels of pedigree relationships or the identity matrix on genetic evaluations

Evaluations using single-step genomic BLUP require blending the genomic relationship matrix (G) with a positive definite matrix to ensure nonsingularity for solving the mixed model equations. Many organizations blend G with a proportion of the numerator relationship matrix for genotyped animals (A22) to improve stability and possibly add a residual polygenic effect. However, when nearly all the polygenic variance is explained by G, blending with A22 may cause inflation and add excess computing time; thus, blending with an identity matrix (I) multiplied by a small value may be a better solution. The objective of this study was to evaluate changes in reliability and inflation of genomic estimated breeding values, convergence rate, elapsed wall-clock time for blending G with different levels of A22 or I, and develop a more time-efficient blending method. A US Holstein cattle data set was used with 9.7 million animals in the pedigree, 569,404 animals with genotypes, and 10.1 million stature phenotypes. Blending G by adding a small value to the diagonal elements had comparable performance to A22 with fewer rounds to convergence required to solve the system of equations. Reliability and inflation of genomic estimated breeding values ranged from 0.63 to 0.68 and 0.86 to 0.89 for all blending scenarios tested. The current blending default in the BLUPF90 software is to replace G with (1 – β)G + βA22, where β equals 0.05. In this study, β values of 0.30, 0.20, 0.05, 0.01, 0.005, and 0.001 were evaluated with A22 and I. Negligible differences in elapsed computing time between the blending types and levels were observed. Subsequently, the current blending algorithm used in the BLUPF90 family of programs was optimized, reducing the blending time from approximately 2 h to 5 min for A22 and less than 1 s for I. The new time difference between blending with A22 or I is negligible and not computationally critical. The results indicate that blending G with A22 does not have clear advantages over blending with a small proportion of I.