P.M. VanRaden

Efficient methods to compute genomic predictions.

Efficient methods for processing genomic data were developed to increase reliability of estimated breeding values and to estimate thousands of marker effects simultaneously. Algorithms were derived and computer programs tested with simulated data for 2,967 bulls and 50,000 markers distributed randomly across 30 chromosomes. Estimation of genomic inbreeding coefficients required accurate estimates of allele frequencies in the base population. Linear model predictions of breeding values were computed by 3 equivalent methods: 1) iteration for individual allele effects followed by summation across loci to obtain estimated breeding values, 2) selection index including a genomic relationship matrix, and 3) mixed model equations including the inverse of genomic relationships. A blend of first- and second-order Jacobi iteration using 2 separate relaxation factors converged well for allele frequencies and effects. Reliability of predicted net merit for young bulls was 63% compared with 32% using the traditional relationship matrix. Nonlinear predictions were also computed using iteration on data and nonlinear regression on marker deviations; an additional (about 3%) gain in reliability for young bulls increased average reliability to 66%. Computing times increased linearly with number of genotypes. Estimation of allele frequencies required 2 processor days, and genomic predictions required <1 d per trait, and traits were processed in parallel. Information from genotyping was equivalent to about 20 daughters with phenotypic records. Actual gains may differ because the simulation did not account for linkage disequilibrium in the base population or selection in subsequent generations.

Invited review: reliability of genomic predictions for North American Holstein bulls.

Genetic progress will increase when breeders examine genotypes in addition to pedigrees and phenotypes. Genotypes for 38,416 markers and August 2003 genetic evaluations for 3,576 Holstein bulls born before 1999 were used to predict January 2008 daughter deviations for 1,759 bulls born from 1999 through 2002. Genotypes were generated using the Illumina BovineSNP50 BeadChip and DNA from semen contributed by US and Canadian artificial-insemination organizations to the Cooperative Dairy DNA Repository. Genomic predictions for 5 yield traits, 5 fitness traits, 16 conformation traits, and net merit were computed using a linear model with an assumed normal distribution for marker effects and also using a nonlinear model with a heavier tailed prior distribution to account for major genes. The official parent average from 2003 and a 2003 parent average computed from only the subset of genotyped ancestors were combined with genomic predictions using a selection index. Combined predictions were more accurate than official parent averages for all 27 traits. The coefficients of determination (R(2)) were 0.05 to 0.38 greater with nonlinear genomic predictions included compared with those from parent average alone. Linear genomic predictions had R(2) values similar to those from nonlinear predictions but averaged just 0.01 lower. The greatest benefits of genomic prediction were for fat percentage because of a known gene with a large effect. The R(2) values were converted to realized reliabilities by dividing by mean reliability of 2008 daughter deviations and then adding the difference between published and observed reliabilities of 2003 parent averages. When averaged across all traits, combined genomic predictions had realized reliabilities that were 23% greater than reliabilities of parent averages (50 vs. 27%), and gains in information were equivalent to 11 additional daughter records. Reliability increased more by doubling the number of bulls genotyped than the number of markers genotyped. Genomic prediction improves reliability by tracing the inheritance of genes even with small effects.

Distribution and location of genetic effects for dairy traits

Genetic effects for many dairy traits and for total economic merit are evenly distributed across all chromosomes. A high-density scan using 38,416 single nucleotide polymorphism markers for 5,285 bulls confirmed 2 previously known major genes on Bos taurus autosomes (BTA) 6 and 14 but revealed few other large effects. Markers on BTA18 had the largest effects on calving ease, several conformation traits, longevity, and total merit. Prediction accuracy was highest using a heavy-tailed prior assuming that each marker had an effect on each trait, rather than assuming a normal distribution of effects as in a linear model, or that only some loci have nonzero effects. A prior model combining heavy tails with finite alleles produced results that were intermediate compared with the individual models. Differences between models were small (1 to 2%) for traits with no major genes and larger for heavy tails with traits having known quantitative trait loci (QTL; 6 to 8%). Analysis of bull recessive codes suggested that marker effects from genomic selection may be used to identify regions of chromosomes to search in detail for candidate genes, but individual single nucleotide polymorphisms were not tracking causative mutations with the exception of diacylglycerol O-acyltransferase 1. Additive genetic merits were constructed for each chromosome, and the distribution of BTA14-specific estimated breeding value (EBV) showed that selection primarily for milk yield has not changed the distribution of EBV for fat percentage even in the presence of a known QTL. Such chromosomal EBV also may be useful for identifying complementary mates in breeding programs. The QTL affecting dystocia, conformation, and economic merit on BTA18 appear to be related to calf size or birth weight and may be the result of longer gestation lengths. Results validate quantitative genetic assumptions that most traits are due to the contributions of a large number of genes of small additive effect, rather than support the finite locus model.

Genomic evaluations with many more genotypes

BackgroundGenomic evaluations in Holstein dairy cattle have quickly become more reliable over the last two years in many countries as more animals have been genotyped for 50,000 markers. Evaluations can also include animals genotyped with more or fewer markers using new tools such as the 777,000 or 2,900 marker chips recently introduced for cattle. Gains from more markers can be predicted using simulation, whereas strategies to use fewer markers have been compared using subsets of actual genotypes. The overall cost of selection is reduced by genotyping most animals at less than the highest density and imputing their missing genotypes using haplotypes. Algorithms to combine different densities need to be efficient because numbers of genotyped animals and markers may continue to grow quickly.MethodsGenotypes for 500,000 markers were simulated for the 33,414 Holsteins that had 50,000 marker genotypes in the North American database. Another 86,465 non-genotyped ancestors were included in the pedigree file, and linkage disequilibrium was generated directly in the base population. Mixed density datasets were created by keeping 50,000 (every tenth) of the markers for most animals. Missing genotypes were imputed using a combination of population haplotyping and pedigree haplotyping. Reliabilities of genomic evaluations using linear and nonlinear methods were compared.ResultsDiffering marker sets for a large population were combined with just a few hours of computation. About 95% of paternal alleles were determined correctly, and > 95% of missing genotypes were called correctly. Reliability of breeding values was already high (84.4%) with 50,000 simulated markers. The gain in reliability from increasing the number of markers to 500,000 was only 1.6%, but more than half of that gain resulted from genotyping just 1,406 young bulls at higher density. Linear genomic evaluations had reliabilities 1.5% lower than the nonlinear evaluations with 50,000 markers and 1.6% lower with 500,000 markers.ConclusionsMethods to impute genotypes and compute genomic evaluations were affordable with many more markers. Reliabilities for individual animals can be modified to reflect success of imputation. Breeders can improve reliability at lower cost by combining marker densities to increase both the numbers of markers and animals included in genomic evaluation. Larger gains are expected from increasing the number of animals than the number of markers.

The genomic evaluation system in the United States: Past, present, future

Implementation of genomic evaluation has caused profound changes in dairy cattle breeding. All young bulls bought by major artificial insemination organizations now are selected based on such evaluation. Evaluation reliability can reach approximately 75% for yield traits, which is adequate for marketing semen of 2-yr-old bulls. Shortened generation interval from using genomic evaluations is the most important factor in increasing the rate of genetic improvement. Genomic evaluations are based on 42,503 single nucleotide polymorphisms (SNP) genotyped with technology that became available in 2007. The first unofficial USDA genomic evaluations were released in 2008 and became official for Holsteins, Jerseys, and Brown Swiss in 2009. Evaluation accuracy has increased steadily from including additional bulls with genotypes and traditional evaluations (predictor animals). Some of that increase occurs automatically as young genotyped bulls receive a progeny test evaluation at 5 yr of age. Cow contribution to evaluation accuracy is increased by decreasing mean and variance of their evaluations so that they are similar to bull evaluations. Integration of US and Canadian genotype databases was critical to achieving acceptable initial accuracy and continues to benefit both countries. Genotype exchange with other countries added predictor bulls for Brown Swiss. In 2010, a low-density chip with 2,900 SNP and a high-density chip with 777,962 SNP were released. The low-density chip has increased greatly the number of animals genotyped and is expected to replace microsatellites in parentage verification. The high-density chip can increase evaluation accuracy by better tracking of loci responsible for genetic differences. To integrate information from chips of various densities, a method to impute missing genotypes was developed based on splitting each genotype into its maternal and paternal haplotypes and tracing their inheritance through the pedigree. The same method is used to impute genotypes of nongenotyped dams based on genotyped progeny and mates. Reliability of resulting evaluations is discounted to reflect errors inherent in the process. Further increases in evaluation accuracy are expected because of added predictor animals and more SNP. The large population of existing genotypes can be used to evaluate new traits; however, phenotypic observations must be obtained for enough animals to allow estimation of SNP effects with sufficient accuracy for application to the general population.

Design of a bovine low-density SNP array optimized for imputation

The Illumina BovineLD BeadChip was designed to support imputation to higher density genotypes in dairy and beef breeds by including single-nucleotide polymorphisms (SNPs) that had a high minor allele frequency as well as uniform spacing across the genome except at the ends of the chromosome where densities were increased. The chip also includes SNPs on the Y chromosome and mitochondrial DNA loci that are useful for determining subspecies classification and certain paternal and maternal breed lineages. The total number of SNPs was 6,909. Accuracy of imputation to Illumina BovineSNP50 genotypes using the BovineLD chip was over 97% for most dairy and beef populations. The BovineLD imputations were about 3 percentage points more accurate than those from the Illumina GoldenGate Bovine3K BeadChip across multiple populations. The improvement was greatest when neither parent was genotyped. The minor allele frequencies were similar across taurine beef and dairy breeds as was the proportion of SNPs that were polymorphic. The new BovineLD chip should facilitate low-cost genomic selection in taurine beef and dairy cattle.

Genomic imputation and evaluation using high-density Holstein genotypes

Genomic evaluations for 161,341 Holsteins were computed by using 311,725 of 777,962 markers on the Illumina BovineHD Genotyping BeadChip (HD). Initial edits with 1,741 HD genotypes from 5 breeds revealed that 636,967 markers were usable but that half were redundant. Holstein genotypes were from 1,510 animals with HD markers, 82,358 animals with 45,187 (50K) markers, 1,797 animals with 8,031 (8K) markers, 20,177 animals with 6,836 (6K) markers, 52,270 animals with 2,683 (3K) markers, and 3,229 nongenotyped dams (0K) with >90% of haplotypes imputable because they had 4 or more genotyped progeny. The Holstein HD genotypes were from 1,142 US, Canadian, British, and Italian sires, 196 other sires, 138 cows in a US Department of Agriculture research herd (Beltsville, MD), and 34 other females. Percentages of correctly imputed genotypes were tested by applying the programs findhap and FImpute to a simulated chromosome for an earlier population that had only 1,112 animals with HD genotypes and none with 8K genotypes. For each chip, 1% of the genotypes were missing and 0.02% were incorrect initially. After imputation of missing markers with findhap, percentages of genotypes correct were 99.9% from HD, 99.0% from 50K, 94.6% from 6K, 90.5% from 3K, and 93.5% from 0K. With FImpute, 99.96% were correct from HD, 99.3% from 50K, 94.7% from 6K, 91.1% from 3K, and 95.1% from 0K genotypes. Accuracy for the 3K and 6K genotypes further improved by approximately 2 percentage points if imputed first to 50K and then to HD instead of imputing all genotypes directly to HD. Evaluations were tested by using imputed actual genotypes and August 2008 phenotypes to predict deregressed evaluations of US bulls proven after August 2008. For 28 traits tested, the estimated genomic reliability averaged 61.1% when using 311,725 markers vs. 60.7% when using 45,187 markers vs. 29.6% from the traditional parent average. Squared correlations with future data were slightly greater for 16 traits and slightly less for 12 with HD than with 50K evaluations. The observed 0.4 percentage point average increase in reliability was less favorable than the 0.9 expected from simulation but was similar to actual gains from other HD studies. The largest HD and 50K marker effects were often located at very similar positions. The single-breed evaluation tested here and previous single-breed or multibreed evaluations have not produced large gains. Increasing the number of HD genotypes used for imputation above 1,074 did not improve the reliability of Holstein genomic evaluations.

Application of a canonical transformation to detection of quantitative trait loci with the aid of genetic markers in a multi-trait experiment

Effects of individual quantitative trait loci (QTLs) can be isolated with the aid of linked genetic markers. Most studies have analyzed each marker or pair of linked markers separately for each trait included in the analysis. Thus, the number of contrasts tested can be quite large. The experimentwise type-I error can be readily derived from the nominal type-I error if all contrasts are statistically independent, but different traits are generally correlated. A new set of uncorrelated traits can be derived by application of a canonical transformation. The total number of effective traits will generally be less than the original set. An example is presented for DNA microsatellite D21S4, which is used as a marker for milk production traits of Israeli dairy cattle. This locus had significant effects on milk and protein production but not on fat. It had a significant effect on only one of the canonical variables that was highly correlated with both milk and protein, and this variable explained 82% of the total variance. Thus, it can be concluded that a single QTL is affecting both traits. The effects on the original traits could be derived by a reverse transformation of the effects on the canonical variable.

Selection of single-nucleotide polymorphisms and quality of genotypes used in genomic evaluation of dairy cattle in the United States and Canada

Nearly 57,000 single-nucleotide polymorphisms (SNP) genotyped with the Illumina BovineSNP50 BeadChip (Illumina Inc., San Diego, CA) were investigated to determine usefulness of the associated SNP for genomic prediction. Genotypes were obtained for 12,591 bulls and cows, and SNP were selected based on 5,503 bulls with genotypes from a larger set of SNP. The following SNP were deleted: 6,572 that were monomorphic, 3,213 with scoring problems (primarily because of poor definition of clusters and excess number of clusters), and 3,649 with a minor allele frequency of <2%. Number of SNP for each minor allele frequency class (> or =2%) was fairly uniform (777 to 1,004). For 5 contiguous SNP assigned to chromosome 7, no bulls were heterozygous, which indicated that those SNP are actually on the nonpseudoautosomal portion of the X chromosome. Another 178 SNP that were not assigned to a chromosome but that had many fewer heterozygotes than expected were also assigned to the X chromosome. Existence of Hardy-Weinberg equilibrium was investigated by comparing observed with expected heterozygosity. For 11 SNP, the observed percentage of heterozygous individuals differed from the expected by >15%; therefore, those SNP were deleted. For 2,628 SNP, the genotype at another SNP was highly correlated (i.e., genotypes were identical for >99.5% of bulls), and those were deleted. After edits, 40,874 SNP remained. A parent-progeny conflict was declared when the genotypes were alternate homozygotes. Mean number of conflicts was 2.3 when pedigree was correct and 2,411 when it was incorrect. The sire was genotyped for >93% of animals. Maternal grandsire genotype was similarly checked; however, because alternate homozygotes could be valid, a conflict threshold of 16% was used to indicate a need for further investigation. Genotyping consistency was investigated for 21 bulls genotyped twice with differences primarily from SNP that were not scored in one of the genotypes. Concordance for readable SNP was extremely high (99.96-100%). Thousands of SNP that were polymorphic in Holsteins were monomorphic in Jerseys or Brown Swiss, which indicated that breed-specific SNP sets are required or that all breeds need to be considered in the SNP selection process. Genotypes from the Illumina BovineSNP50 BeadChip are of high accuracy and provide the basis for genomic evaluations in the United States and Canada.

International genomic evaluation methods for dairy cattle

BackgroundGenomic evaluations are rapidly replacing traditional evaluation systems used for dairy cattle selection. Higher reliabilities from larger genotype files promote cooperation across country borders. Genomic information can be exchanged across countries using simple conversion equations, by modifying multi-trait across-country evaluation (MACE) to account for correlated residuals originating from the use of foreign evaluations, or by multi-trait analysis of genotypes for countries that use the same reference animals.MethodsTraditional MACE assumes independent residuals because each daughter is measured in only one country. Genomic MACE could account for residual correlations using daughter equivalents from genomic data as a fraction of the total in each country and proportions of bulls shared. MACE methods developed to combine separate within-country genomic evaluations were compared to direct, multi-country analysis of combined genotypes using simulated genomic and phenotypic data for 8,193 bulls in nine countries.ResultsReliabilities for young bulls were much higher for across-country than within-country genomic evaluations as measured by squared correlations of estimated with true breeding values. Gains in reliability from genomic MACE were similar to those of multi-trait evaluation of genotypes but required less computation. Sharing of reference genotypes among countries created large residual correlations, especially for young bulls, that are accounted for in genomic MACE.ConclusionsInternational genomic evaluations can be computed either by modifying MACE to account for residual correlations across countries or by multi-trait evaluation of combined genotype files. The gains in reliability justify the increased computation but require more cooperation than in previous breeding programs.