The paper by P. M. VanRaden discusses efficient methods for processing genomic data to enhance the reliability of estimated breeding values and to estimate thousands of marker effects simultaneously. The study developed algorithms and tested computer programs using simulated data for 2,967 bulls and 50,000 markers distributed across 30 chromosomes. The methods included linear and nonlinear systems of equations, with linear predictions assuming equal contribution of all markers to genetic variation and nonlinear predictions accounting for nonnormal prior distributions of marker or QTL effects. The reliability of predicted net merit for young bulls was significantly higher with genomic predictions (63%) compared to traditional methods (32%). Nonlinear predictions, which used iteration on data and nonlinear regression on marker deviations, further improved reliability to 66%. Computing times increased linearly with the number of genotypes, and the simulation provided a test for the programs, algorithms, time requirements, and prediction reliability. The study also explored different methods for estimating genomic relationships and inbreeding coefficients, finding that simple counts of homozygous loci and alleles shared were accurate and could be scaled to match pedigree inbreeding and relationships. The results suggest that genomic predictions can add information equivalent to about 20 additional daughters' records, and benefits are expected to increase over time as more relatives are genotyped. However, actual genomic reliabilities may be affected by linkage disequilibrium and subsequent selection, which were not simulated in this study.The paper by P. M. VanRaden discusses efficient methods for processing genomic data to enhance the reliability of estimated breeding values and to estimate thousands of marker effects simultaneously. The study developed algorithms and tested computer programs using simulated data for 2,967 bulls and 50,000 markers distributed across 30 chromosomes. The methods included linear and nonlinear systems of equations, with linear predictions assuming equal contribution of all markers to genetic variation and nonlinear predictions accounting for nonnormal prior distributions of marker or QTL effects. The reliability of predicted net merit for young bulls was significantly higher with genomic predictions (63%) compared to traditional methods (32%). Nonlinear predictions, which used iteration on data and nonlinear regression on marker deviations, further improved reliability to 66%. Computing times increased linearly with the number of genotypes, and the simulation provided a test for the programs, algorithms, time requirements, and prediction reliability. The study also explored different methods for estimating genomic relationships and inbreeding coefficients, finding that simple counts of homozygous loci and alleles shared were accurate and could be scaled to match pedigree inbreeding and relationships. The results suggest that genomic predictions can add information equivalent to about 20 additional daughters' records, and benefits are expected to increase over time as more relatives are genotyped. However, actual genomic reliabilities may be affected by linkage disequilibrium and subsequent selection, which were not simulated in this study.