Short communication: Calculating analytical reliabilities for single-step predictions

It has been shown that single-step genomic BLUP (ssGBLUP) can be reformulated, resulting in an equivalent SNP model that includes the explicit imputation of gene contents of all ungenotyped animals in the pedigree. This reformulation reveals the underlying mechanism enabling ungenotyped animals to contribute information to genotyped animals via estimates of marker effects and consequently to the reliability of genomic predictions, a key feature generally associated with the single-step approach. Irrespective of which BLUP formulation is used for genomic prediction, with increasing numbers of genotyped animals, the marker-oriented model is recommended when calculating the reliabilities of genomic predictions. This approach has the advantage of a manageable and stable size of the model matrix that needs to be inverted to calculate analytical prediction error variances of marker effects, an advantage that also holds for prediction with the single-step model. However, when including imputed genotypes in the design matrix of marker effects, an additional imputation residual term has to be considered to account for the prediction error of imputation. We summarize some of the theoretical aspects associated with the calculation of analytical reliabilities of single-step predictions. Derivations are based on the equivalent reformulation of ssGBLUP as a marker-oriented model and the calculation of prediction error variances of marker effects. We propose 2 approximations that allow for a substantial reduction of the complexity of the matrix operations involved, while retaining most of the relevant information required for reliability calculations. We additionally provide a general framework for an implementation of single-step reliability approximation using standard animal model reliabilities as a starting point. Finally, we demonstrate the effectiveness of the proposed approach using a small example extracted from data of the routine evaluation on dual-purpose Fleckvieh (Simmental) cattle.     

National single-step genomic method that integrates multi-national genomic information

The aim of this paper was to develop a national single-step genomic BLUP that integrates multi-national genomic estimated breeding values (EBV) and associated reliabilities without double counting dependent data contributions from the different evaluations. Simultaneous use of all data, including phenotypes, pedigree, and genotypes, is a condition to obtain unbiased EBV. However, this condition is not always fully met, mainly due to unavailability of foreign raw data for imported animals. In dairy cattle genetic evaluations, this issue is traditionally tackled through the multiple across-country evaluation (MACE) of sires, performed by Interbull Centre (Uppsala, Sweden). Multiple across-country evaluation regresses all the available national information onto a joint pedigree to obtain country-specific rankings of all sires without sharing the raw data. In the context of genomic selection, the issue is handled by exchanging sire genotypes and by using MACE information (i.e., MACE EBV and reliabilities), as a valuable source of “phenotypic” data. Although all the available data are considered, these “multi-national” genomic evaluations use multi-step methods assuming independence of various sources of information, which is not met in all situations. We developed a method that handles this by single-step genomic evaluation that jointly (1) uses national phenotypic, genomic, and pedigree data; (2) uses multi-national genomic information; and (3) avoids double counting dependent data contributions from an animal’s own records and relatives’ records. The method was demonstrated by integrating multi-national genomic EBV and reliabilities of Brown Swiss sires, included in the InterGenomics consortium at Interbull Centre, into the national evaluation in Slovenia. The results showed that the method could (1) increase reliability of a national (genomic) evaluation; (2) provide consistent ranking of all animals: bulls, cows, and young animals; and (3) increase the size of a genomic training population. These features provide more efficient and transparent selection throughout a breeding program.     

Use of a single-step approach for integrating foreign information into national genomic evaluation in Holstein cattle

The use of multi-trait across-country evaluation (MACE) and the exchange of genomic information among countries allows national breeding programs to combine foreign and national data to increase the size of the training populations and potentially increase accuracy of genomic prediction of breeding values. By including genotyped and nongenotyped animals simultaneously in the evaluation, the single-step genomic BLUP (GBLUP) approach has the potential to deliver more accurate and less biased genomic evaluations. A single-step genomic BLUP approach, which enables integration of data from MACE evaluations, can be used to obtain genomic predictions while avoiding double-counting of information. The objectives of this study were to apply a single-step approach that simultaneously includes domestic and MACE information for genomic evaluation of workability traits in Canadian Holstein cattle, and compare the results obtained with this methodology with those obtained using a multi-step approach (msGBLUP). By including MACE bulls in the training population, msGBLUP led to an increase in reliability of genomic predictions of 4.8 and 15.4% for milking temperament and milking speed, respectively, compared with a traditional evaluation using only pedigree and phenotypic information. Integration of MACE data through a single-step approach (ssGBLUP_IM) yielded the highest reliabilities compared with other considered methods. Integration of MACE data also helped reduce bias of genomic predictions. When using ssGBLUP_IM, the bias of genomic predictions decreased by half compared with msGBLUP using domestic and MACE information. Therefore, the reliability and bias of genomic predictions for both traits improved substantially when a single-step approach was used for evaluation compared with a multi-step approach. The use of a single-step approach with integration of MACE information provides an alternative to the current method used in Canadian genomic evaluations.     

Autoregressive single-step test-day model for genomic evaluations of Portuguese Holstein cattle

The multiple-lactation autoregressive test-day (AR) model is the adopted model for the national genetic evaluation of dairy cattle in Portugal. Under this model, animals' permanent environment effects are assumed to follow a first-order autoregressive process over the long (auto-correlations between parities) and short (auto-correlations between test-days within lactation) terms. Given the relevance of genomic prediction in dairy cattle, it is essential to include marker information in national genetic evaluations. In this context, we aimed to evaluate the feasibility of applying the single-step genomic (G)BLUP to analyze milk yield using the AR model in Portuguese Holstein cattle. In total, 11,434,294 test-day records from the first 3 lactations collected between 1994 and 2017 and 1,071 genotyped bulls were used in this study. Rank correlations and differences in reliability among bulls were used to compare the performance of the traditional (A-AR) and single-step (H-AR) models. These 2 modeling approaches were also applied to reduced data sets with records truncated after 2012 (deleting daughters of tested bulls) to evaluate the predictive ability of the H-AR. Validation scenarios were proposed, taking into account young and proven bulls. Average EBV reliabilities, empirical reliabilities, and genetic trends predicted from the complete and reduced data sets were used to validate the genomic evaluation. Average EBV reliabilities for H-AR (A-AR) using the complete data set were 0.52 (0.16) and 0.72 (0.62) for genotyped bulls with no daughters and bulls with 1 to 9 daughters, respectively. These results showed an increase in EBV reliabilities of 0.10 to 0.36 when genomic information was included, corresponding to a reduction of up to 43% in prediction error variance. Considering the 3 validation scenarios, the inclusion of genomic information improved the average EBV reliability in the reduced data set, which ranged, on average, from 0.16 to 0.26, indicating an increase in the predictive ability. Similarly, empirical reliability increased by up to 0.08 between validation tests. The H-AR outperformed A-AR in terms of genetic trends when unproven genotyped bulls were included. The results suggest that the single-step GBLUP AR model is feasible and may be applied to national Portuguese genetic evaluations for milk yield.     

Assets of imputation to ultra-high density for productive and functional traits

The aim of this study was to evaluate different-density genotyping panels for genotype imputation and genomic prediction. Genotypes from customized Golden Gate Bovine3K BeadChip [LD3K; low-density (LD) 3,000-marker (3K); Illumina Inc., San Diego, CA] and BovineLD BeadChip [LD6K; 6,000-marker (6K); Illumina Inc.] panels were imputed to the BovineSNP50v2 BeadChip [50K; 50,000-marker; Illumina Inc.]. In addition, LD3K, LD6K, and 50K genotypes were imputed to a BovineHD BeadChip [HD; high-density 800,000-marker (800K) panel], and with predictive ability evaluated and compared subsequently. Comparisons of prediction accuracy were carried out using Random boosting and genomic BLUP. Four traits under selection in the Spanish Holstein population were used: milk yield, fat percentage (FP), somatic cell count, and days open (DO). Training sets at 50K density for imputation and prediction included 1,632 genotypes. Testing sets for imputation from LD to 50K contained 834 genotypes and testing sets for genomic evaluation included 383 bulls. The reference population genotyped at HD included 192 bulls. Imputation using BEAGLE software (http://faculty.washington.edu/browning/beagle/beagle.html) was effective for reconstruction of dense 50K and HD genotypes, even when a small reference population was used, with 98.3% of SNP correctly imputed. Random boosting outperformed genomic BLUP in terms of prediction reliability, mean squared error, and selection effectiveness of top animals in the case of FP. For other traits, however, no clear differences existed between methods. No differences were found between imputed LD and 50K genotypes, whereas evaluation of genotypes imputed to HD was on average across data set, method, and trait, 4% more accurate than 50K prediction, and showed smaller (2%) mean squared error of predictions. Similar bias in regression coefficients was found across data sets but regressions were 0.32 units closer to unity for DO when genotypes were imputed to HD density. Imputation to HD genotypes might produce higher stability in the genomic proofs of young candidates. Regarding selection effectiveness of top animals, more (2%) top bulls were classified correctly with imputed LD6K genotypes than with LD3K. When the original 50K genotypes were used, correct classification of top bulls increased by 1%, and when those genotypes were imputed to HD, 3% more top bulls were detected. Selection effectiveness could be slightly enhanced for certain traits such as FP, somatic cell count, or DO when genotypes are imputed to HD. Genetic evaluation units may consider a trait-dependent strategy in terms of method and genotype density for use in the genome-enhanced evaluations.     

Comparison of genomic predictions for lowly heritable traits using multi-step and single-step genomic best linear unbiased predictor in Holstein cattle

The success and sustainability of a breeding program incorporating genomic information is largely dependent on the accuracy of predictions. For low heritability traits, large training populations are required to achieve high accuracies of genomic estimated breeding values (GEBV). By including genotyped and nongenotyped animals simultaneously in the evaluation, the single-step genomic BLUP (ssGBLUP) approach has the potential to deliver more accurate and less biased genomic evaluations. The aim of this study was to compare the accuracy and bias of genomic predictions for various traits in Canadian Holstein cattle using ssGBLUP and multi-step genomic BLUP (msGBLUP) under different strategies, such as (1) adding genomic information of cows in the analysis, (2) testing different adjustments of the genomic relationship matrix, and (3) using a blending approach to obtain GEBV from msGBLUP. The following genomic predictions were evaluated regarding accuracy and bias: (1) GEBV estimated by ssGBLUP; (2) direct genomic value estimated by msGBLUP with polygenic effects of 5 and 20%; and (3) GEBV calculated by a blending approach of direct genomic value with estimated breeding values using polygenic effects of 5 and 20%. The effect of adding genomic information of cows in the evaluation was also assessed for each approach. When genomic information was included in the analyses, the average improvement in observed reliability of predictions was observed to be 7 and 13 percentage points for reproductive and workability traits, respectively, compared with traditional BLUP. Absolute deviation from 1 of the regression coefficient of the linear regression of de-regressed estimated breeding values on genomic predictions went from 0.19 when using traditional BLUP to 0.22 when using the msGBLUP method, and to 0.14 when using the ssGBLUP method. The use of polygenic weight of 20% in the msGBLUP slightly improved the reliability of predictions, while reducing the bias. A similar trend was observed when a blending approach was used. Adding genomic information of cows increased reliabilities, while decreasing bias of genomic predictions when using the ssGBLUP method. Differences between using a training population with cows and bulls or with only bulls for the msGBLUP method were small, likely due to the small number of cows included in the analysis. Predictions for lowly heritable traits benefit greatly from genomic information, especially when all phenotypes, pedigrees, and genotypes are used in a single-step approach.     

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 (R²) were 0.05 to 0.38 greater with nonlinear genomic predictions included compared with those from parent average alone. Linear genomic predictions had R² 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 R² 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.     

Technical note: Methods for interim prediction of single-step breeding values for young animals

Single-step genomic evaluations have the advantage of simultaneously combining all pedigree, phenotypic, and genotypic information available. However, systems with a large number of genotyped animals have some computational challenges. In many genomic breeding programs, genomic predictions of young animals should become available for selection decisions in the shortest time possible, which requires either a very effective estimation or an approximation with negligible loss in accuracy. We investigated different procedures for predicting breeding values of young genotyped animals without setting up the full single-step system augmented for the additional genotypes. Methods were based on transmitting the information from single-step breeding values of genotyped animals that took part in the previous full run to young animals, either through genomic relationships or through a marker-based model. The different procedures were tested on real data from the April 2017 run of the German-Austrian official genomic evaluation for Fleckvieh. The data set included 62,559 genotyped animals and was used to run single-step evaluations for 23 conformation traits. A further data set comprising 1,768 young animals was used for interim prediction and we called it the validation set. The reference values for validation were the predicted breeding values of the young animals from a full single-step run containing the genotypes of all 64,327 animals. Correlations between the approximated predictions and those from the full single-step run also containing genotypes from young animals averaged 0.9932 for the best method (from 0.990 to 0.995 across traits). In conclusion, prediction of single-step breeding values for young animals can be well approximated using systems of size equal to the number of markers.     

Hot topic: A unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score

The first national single-step, full-information (phenotype, pedigree, and marker genotype) genetic evaluation was developed for final score of US Holsteins. Data included final scores recorded from 1955 to 2009 for 6,232,548 Holsteins cows. BovineSNP50 (Illumina, San Diego, CA) genotypes from the Cooperative Dairy DNA Repository (Beltsville, MD) were available for 6,508 bulls. Three analyses used a repeatability animal model as currently used for the national US evaluation. The first 2 analyses used final scores recorded up to 2004. The first analysis used only a pedigree-based relationship matrix. The second analysis used a relationship matrix based on both pedigree and genomic information (single-step approach). The third analysis used the complete data set and only the pedigree-based relationship matrix. The fourth analysis used predictions from the first analysis (final scores up to 2004 and only a pedigree-based relationship matrix) and prediction using a genomic based matrix to obtain genetic evaluation (multiple-step approach). Different allele frequencies were tested in construction of the genomic relationship matrix. Coefficients of determination between predictions of young bulls from parent average, single-step, and multiple-step approaches and their 2009 daughter deviations were 0.24, 0.37 to 0.41, and 0.40, respectively. The highest coefficient of determination for a single-step approach was observed when using a genomic relationship matrix with assumed allele frequencies of 0.5. Coefficients for regression of 2009 daughter deviations on parent-average, single-step, and multiple-step predictions were 0.76, 0.68 to 0.79, and 0.86, respectively, which indicated some inflation of predictions. The single-step regression coefficient could be increased up to 0.92 by scaling differences between the genomic and pedigree-based relationship matrices with little loss in accuracy of prediction. One complete evaluation took about 2 h of computing time and 2.7 gigabytes of memory. Computing times for single-step analyses were slightly longer (2%) than for pedigree-based analysis. A national single-step genetic evaluation with the pedigree relationship matrix augmented with genomic information provided genomic predictions with accuracy and bias comparable to multiple-step procedures and could account for any population or data structure. Advantages of single-step evaluations should increase in the future when animals are pre-selected on genotypes.     

Using sequence variants of a QTL region improves the accuracy of genomic evaluation in French Saanen goats

The enhanced availability of sequence data in livestock provides an opportunity for more accurate predictions in routine genomic evaluations. Such evaluations would therefore no longer rely only on the linkage disequilibrium between a chip marker and the causal mutation. The objective of this study was to assess the usefulness of sequence data in Saanen goats (n = 33) to better capture a quantitative trait locus (QTL) on chromosome 19 (CHI19) and improve the accuracy of predictions for 3 milk production traits, 5 type traits, and somatic cell scores. All 1,207 50K genotypes were imputed to the sequence level. Four scenarios, each using a subset of CHI19 imputed variants, were then tested. Sequence-derived information included all CHI19 variants (529,576), all variants in the QTL region (22,269), 178 variants selected in the QTL region and added to an updated chip, or 178 randomly selected variants on CHI19. Two genomic evaluation models were applied: single-step genomic BLUP and weighted single-step genomic BLUP. All scenarios were compared with single-step genomic BLUP using 50K genotypes. Best overall results were obtained using single-step genomic BLUP on 50K genotypes completed with all variants in the QTL region of chromosome 19 (6.2% average increase in accuracy for 9 traits) with the highest accuracy gain for fat yield (17.9%), significant increases for milk (13.7%) and protein yields (12.5%), and type traits associated with CHI19. Despite its association with the QTL region of chromosome 19, the somatic cell score showed decreased accuracy in every alternative scenario. Using all CHI19 variants led to an overall decrease of 4.8% in prediction accuracy. The updated chip was efficient and improved genomic evaluations by 3.1 to 6.4% on average, depending on the scenario. Indeed, information from only a few carefully selected variants increased accuracies for traits of interest when used in a single-step genomic BLUP model. In conclusion, using QTL region variants imputed from sequence data in single-step genomic evaluations represents a promising perspective for such evaluations in dairy goats. Furthermore, using only a limited number of selected variants in QTL regions, as available on SNP chip updates, significantly increases the accuracy for QTL-associated traits without deteriorating the evaluation accuracy for other traits. The latter approach is interesting, as it avoids time-consuming imputation and data formatting processes and provides reliable genotypes.     

Technical note: adjustment of traditional cow evaluations to improve accuracy of genomic predictions

Genomic evaluations are calculated using deregressed predicted transmitting abilities (PTA) from traditional evaluations to estimate effects of single nucleotide polymorphisms. The direct genomic value (sum of an animal's marker effects) should be consistent with traditional PTA, which is the case for bulls. However, traditional PTA of yield traits (milk, fat, and protein) for genotyped cows are higher than their direct genomic values. To ensure that characteristics of cow PTA for yield traits were more similar to those for bull PTA, mean and variance of cow Mendelian sampling (PTA minus parent average) were adjusted to be similar to those of bulls. The same adjustments were used for all genotyped cows in a breed. To determine gains in reliabilities, predictions were made for bulls with August 2010 evaluations that did not have traditional evaluations in August 2006. By adjusting cow PTA and parent averages of genotyped animals, Holstein and Jersey regressions of August 2010 deregressed PTA on genomic evaluations based on August 2006 data became closer to 1 for the adjusted predictor population compared with the unadjusted predictor population. Evaluation bias was decreased for Holsteins when the predictor population was adjusted. Mean gain in reliability over parent average increased 3.5 percentage points across yield traits for Holsteins and 0.9 percentage points for Jerseys when the predictor population was adjusted. The accuracy of genomic evaluations for Holsteins and Jerseys was increased through better use of information from cows.     

Use of a Bayesian model including QTL markers increases prediction reliability when test animals are distant from the reference population

Relatedness between reference and test animals has an important effect on the reliability of genomic prediction for test animals. Because genomic prediction has been widely applied in practical cattle breeding and bulls have been selected according to genomic breeding value without progeny testing, the sires or grandsires of candidates might not have phenotypic information and might not be in the reference population when the candidates are selected. The objective of this study was to investigate the decreasing trend of the reliability of genomic prediction given distant reference populations, using genomic best linear unbiased prediction (GBLUP) and Bayesian variable selection models with or without including the quantitative trait locus (QTL) markers detected from sequencing data. The data used in this study consisted of 22,242 bulls genotyped using the 54K SNP array from EuroGenomics. Among them, 1,444 Danish bulls born from 2006 to 2010 were selected as test animals. Different reference populations with varying relationships to test animals were created according to pedigree-based relationships. The reference individuals having a relationship with one or more test animals higher than 0.4 (scenario ρ < 0.4), 0.2 (ρ < 0.2), or 0.1 (ρ < 0.1, where ρ = relationship coefficient) were removed from reference sets; these represented the distance between reference and test animals being 2 generations, 3 generations, and 4 generations, respectively. Imputed whole-genome sequencing data of bulls from Denmark were used to conduct a genome-wide association study (GWAS). A small number of significant variants (QTL markers) from the GWAS were added to the array data. To compare the effects of different models, the basic GBLUP model, a Bayesian selection variable model, a GBLUP model with 2 components of genetic effects, and a Bayesian model with pooled array data and QTL markers were used for estimating genomic estimated breeding values (GEBV) of test animals. The reliability of genomic prediction decreased when the test animals were more generations away from the reference population. The reliability of genomic prediction was 0.461 for 1 generation away and 0.396 for 3 generations away, with the same number of individuals in the reference set, using a GBLUP model with chip markers only. The results showed that using the Bayesian method and QTL markers improved the reliability of genomic prediction in all scenarios of relationship between test and reference animals, in a range of 1.3% and 65.1% (4 generations away with only 841 individuals in the reference set). However, most gains were for predictions of milk yield and fat yield. There was little improvement for predictions of protein yield and mastitis, and no improvement for prediction of fertility, except for scenario ρ < 0.1, in which there was a large improvement for predictions of all traits. On the other hand, models including more than 10% polygenic effect decreased prediction reliability when the relationship between test and reference animals was distant.     

A single-step genomic model with direct estimation of marker effects

Compared with the currently widely used multi-step genomic models for genomic evaluation, single-step genomic models can provide more accurate genomic evaluation by jointly analyzing phenotypes and genotypes of all animals and can properly correct for the effect of genomic preselection on genetic evaluations. The objectives of this study were to introduce a single-step genomic model, allowing a direct estimation of single nucleotide polymorphism (SNP) effects, and to develop efficient computing algorithms for solving equations of the single-step SNP model. We proposed an alternative to the current single-step genomic model based on the genomic relationship matrix by including an additional step for estimating the effects of SNP markers. Our single-step SNP model allowed flexible modeling of SNP effects in terms of the number and variance of SNP markers. Moreover, our single-step SNP model included a residual polygenic effect with trait-specific variance for reducing inflation in genomic prediction. A kernel calculation of the SNP model involved repeated multiplications of the inverse of the pedigree relationship matrix of genotyped animals with a vector, for which numerical methods such as preconditioned conjugate gradients can be used. For estimating SNP effects, a special updating algorithm was proposed to separate residual polygenic effects from the SNP effects. We extended our single-step SNP model to general multiple-trait cases. By taking advantage of a block-diagonal (co)variance matrix of SNP effects, we showed how to estimate multivariate SNP effects in an efficient way. A general prediction formula was derived for candidates without phenotypes, which can be used for frequent, interim genomic evaluations without running the whole genomic evaluation process. We discussed various issues related to implementation of the single-step SNP model in Holstein populations with an across-country genomic reference population.     

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.     

Short communication: Genomic prediction using different single-step methods in the Finnish red dairy cattle population

Single-step genomic prediction models utilizing both genotyped and nongenotyped animals are likely to become the prevailing tool in genetic evaluations of livestock. Various single-step prediction models have been proposed, based either on estimation of individual marker effects or on direct prediction via a genomic relationship matrix. In this study, a classical pedigree-based animal model, a regular single-step genomic BLUP (ssGBLUP) model, algorithm for proven and young (APY) with 2 strategies for choosing core animals, and a single-step Bayesian regression (ssBR) model were compared for 305-d production traits (milk, fat, protein) in the Finnish red dairy cattle population. A residual polygenic effect with 10% of total genetic variance was included in the single-step models to reduce inflation of genomic predictions. Validation reliability was calculated as the squared Pearson correlation coefficient between genomically enhanced breeding value (GEBV) and yield deviation for masked records for 2,056 validation cows from the last year in the data set investigated. The results showed that gains of 0.02 to 0.04 on validation reliability were achieved by using single-step methods compared with the classical animal model. The regular ssGBLUP model and ssBR model with an extra polygenic effect yielded the same results. The APY methods yielded similar reliabilities as the regular ssGBLUP and ssBR. Exact prediction error variance of GEBV could be obtained by ssBR to avoid any approximation methods used for ssGBLUP when inversion left-hand side of mixed model equations is computationally infeasible for large data sets.     

Genomic breeding value estimation using genetic markers, inferred ancestral haplotypes, and the genomic relationship matrix

With the introduction of new single nucleotide polymorphism (SNP) chips of various densities, more and more genotype data sets will include animals genotyped for only a subset of the SNP. Imputation techniques based on unobserved ancestral haplotypes may be used to infer missing genotypes. These ancestral haplotypes may also be used in the genomic prediction model, instead of using the SNP. This may increase the reliability of predictions because the ancestral haplotype may capture more linkage disequilibrium with quantitative trait loci than SNP. The aim of this paper was to study whether using unobserved ancestral haplotypes in a genomic prediction model would provide more reliable genomic predictions than using SNP, and to determine how many loci in the genomic prediction model would be redundant. Genotypes of 8,960 bulls and cows for 39,557 SNP were analyzed with a hidden Markov model to associate each individual at each locus to 2 ancestral haplotypes. The number of ancestral haplotypes per locus was fixed at 10, 15, or 20. Subsequently, a validation study was performed in which the phenotypes of 3,251 progeny-tested bulls for 16 traits were used in a genomic prediction model to predict the estimated breeding values of at least 753 validation bulls. The squared correlation between genomic prediction and deregressed daughter performance estimated breeding value, when averaged across traits, was slightly higher when 15 or 20 ancestral haplotypes per locus were used in the prediction model instead of the SNP genotypes, whereas the prediction model using a genomic relationship matrix gave the lowest squared correlations. The number of redundant loci [i.e., loci that had less than 18 jumps (0.1%) from one ancestral haplotype to another ancestral haplotype at the next locus], was 18,793 (48%), which means that only 20,764 loci would need to be included in the genomic prediction model. This provides opportunities for greatly decreasing computer requirements of genomic evaluations with very large numbers of markers.     

Comparison of a single-step with a multistep single nucleotide polymorphism best linear unbiased predictor model for genomic evaluation of conformation traits in German Holsteins

Genomic evaluation based on a single-step model uses all available data of phenotype, genotype, and pedigree; therefore, it should provide unbiased genomic breeding values with a higher correlation of prediction than the current multistep genomic model. Since 2019, a mixed reference population of cows and bulls has been applied to the routine multistep genomic evaluation in German Holsteins. For a fair comparison between the single-step and multistep genomic models, the same phenotype, genotype, and pedigree data were used. Because of its simple structure of the standard multitrait animal model used for German Holstein conventional evaluation, conformation traits were chosen as the first trait group to test a single-step SNP BLUP model for the large, genotyped population of German Holsteins. Genotype, phenotype, and pedigree data were taken from the official August 2020 conventional and genomic evaluation. Because of the same trait definition in national and multiple across-country evaluation for the conformation traits, deregressed multiple across-country evaluation estimated breeding value (EBV) of foreign bulls were treated as a new source of data for the same trait in the genomic evaluations. Due to a short history of female genotyping in Germany, the last 3 yr of youngest cows and bulls were deleted, instead of 4 yr, to perform a genomic validation. In comparison to the multistep genomic model, the single-step SNP BLUP model resulted in a higher correlation and greater variance of genomic EBV according to 798 national validation bulls. The regression of genomic prediction of the current, full evaluation on the earlier, truncated evaluation was slightly closer to 1 than the multistep model. For the validation bulls or youngest genomic artificial insemination bulls, correlation of genomic EBV between the 2 models was, on average, 0.95 across all the conformation traits. We did not find overprediction of young animals by the single-step SNP BLUP model for the conformation traits in German Holsteins.     

Are evaluations on young genotyped animals benefiting from the past generations?

Data sets of US Holsteins, Israeli Holsteins, and pigs from PIC (a Genus company, Hendersonville, TN) were used to evaluate the effect of different numbers of generations on ability to predict genomic breeding values of young genotyped animals. The influence of including only 2 generations of ancestors (A2) or all ancestors (Af) was also investigated. A total of 34,506 US Holsteins, 1,305 Israeli Holsteins, and 5,236 pigs were genotyped. The evaluations were computed by traditional BLUP and single-step genomic BLUP, and computing performance was assessed for the latter method. For the 2 Holstein data sets, coefficients of determination (R²) and regression (δ) of deregressed evaluations from a full data set with records up to 2011 on estimated breeding values and genomic estimated breeding values from the truncated data sets were computed. The thresholds for data deletion were set by intervals of 5 yr, based on the average generation interval in dairy cattle. For the PIC data set, correlations between corrected phenotypes and estimated or genomic estimated breeding values were used to evaluate predictive ability on young animals born in 2010 and 2011. The reduced data set contained data up to 2009, and the thresholds were set based on an average generation interval of 3 yr. The number of generations that could be deleted without a reduction in accuracy depended on data structure and trait. For US Holsteins, removing 3 and 4 generations of data did not reduce accuracy of evaluations for final score in Af and A2 scenarios, respectively. For Israeli Holsteins, the accuracies for milk, fat, and protein yields were the highest when only phenotypes recorded in 2000 and later were included and full pedigrees were applied. Of the 135 Israeli bulls with genotypes (validation set) and daughter records only in the complete data set, 38 and 97 were sons of Israeli and foreign bulls, respectively. Although more phenotypic data increased the prediction accuracy for sons of Israeli bulls, the reverse was true for sons of foreign bulls. Also, more phenotypic data caused large inflation of genomic estimated breeding values for sons of foreign bulls, whereas the opposite was true with the deletion of all but the most recent phenotypic data. Results for protein and fat percentage were different from those for milk, fat, and protein yields; however, relatively, the changes in coefficients of determination and regression were smaller for percentage traits. For PIC data set, removing data from up to 5 generations did not erode predictive ability for genotyped animals for the 2 reproductive traits used in validation. Given the data used in this study, truncating old data reduces computation requirements but does not decrease the accuracy. For small populations that include local and imported animals, truncation may be beneficial for one group of animals and detrimental to another group.     

Effect of imputing markers from a low-density chip on the reliability of genomic breeding values in Holstein populations

The purpose of this study was to investigate the imputation error and loss of reliability of direct genomic values (DGV) or genomically enhanced breeding values (GEBV) when using genotypes imputed from a 3,000-marker single nucleotide polymorphism (SNP) panel to a 50,000-marker SNP panel. Data consisted of genotypes of 15,966 European Holstein bulls from the combined EuroGenomics reference population. Genotypes with the low-density chip were created by erasing markers from 50,000-marker data. The studies were performed in the Nordic countries (Denmark, Finland, and Sweden) using a BLUP model for prediction of DGV and in France using a genomic marker-assisted selection approach for prediction of GEBV. Imputation in both studies was done using a combination of the DAGPHASE 1.1 and Beagle 2.1.3 software. Traits considered were protein yield, fertility, somatic cell count, and udder depth. Imputation of missing markers and prediction of breeding values were performed using 2 different reference populations in each country: either a national reference population or a combined EuroGenomics reference population. Validation for accuracy of imputation and genomic prediction was done based on national test data. Mean imputation error rates when using national reference animals was 5.5 and 3.9% in the Nordic countries and France, respectively, whereas imputation based on the EuroGenomics reference data set gave mean error rates of 4.0 and 2.1%, respectively. Prediction of GEBV based on genotypes imputed with a national reference data set gave an absolute loss of 0.05 in mean reliability of GEBV in the French study, whereas a loss of 0.03 was obtained for reliability of DGV in the Nordic study. When genotypes were imputed using the EuroGenomics reference, a loss of 0.02 in mean reliability of GEBV was detected in the French study, and a loss of 0.06 was observed for the mean reliability of DGV in the Nordic study. Consequently, the reliability of DGV using the imputed SNP data was 0.38 based on national reference data, and 0.48 based on EuroGenomics reference data in the Nordic validation, and the reliability of GEBV using the imputed SNP data was 0.41 based on national reference data, and 0.44 based on EuroGenomics reference data in the French validation.     

Reliability of genomic prediction for German Holsteins using imputed genotypes from low-density chips

With the availability of single nucleotide polymorphism (SNP) marker chips, such as the Illumina BovineSNP50 BeadChip (50K), genomic evaluation has been routinely implemented in dairy cattle breeding. However, for an average dairy producer, total costs associated with the 50K chip are still too high to have all the cows genotyped and genomically evaluated. To study the accuracy of cheaper low-density chips, genotypes were simulated for 2 low-density chips, the Illumina Bovine3K BeadChip (3K) and BovineLD BeadChip (6K), according to their original marker maps. Simulated missing genotypes of the 50K chip were imputed using the programs Beagle and Findhap. Three genotype data sets were used to study imputation accuracy: the EuroGenomics data set, with 14,405 reference bulls (data set I); the smaller EuroGenomics data set, with 11,670 older reference bulls (data set II); and the data set of all genotyped German Holsteins, with 31,597 reference animals (data set III). Imputed genotypes were compared with their original ones to calculate allele error rate for validation animals in the 3 data sets. To evaluate the loss in accuracy of genomic prediction when using imputed genotypes, a genomic evaluation was conducted only for EuroGenomics data set II. Furthermore, combined genome-enhanced breeding values calculated from the original and imputed genotypes were compared. Allele error rate for EuroGenomics data set II was highest for the Findhap program on the 3K chip (3.3%) and lowest for the Beagle program on the 6K chip (0.6%). Across the data sets, Beagle was shown to be about 2 times as accurate as Findhap. Compared with the real 50K genotypes, the reduction in reliability of the genomic prediction when using the imputed genotypes was highest for Findhap on the 3K chip (5.3%) and lowest for Beagle on the 6K chip (1%) when averaged over the 12 evaluated traits. Differences in genome-enhanced breeding values of the original and imputed genotypes were largest for Findhap on the 3K chip, whereas Beagle on the 6K chip had the smallest difference. The low-density chip, 6K, gave markedly higher imputation accuracy and more accurate genomic prediction than the 3K chip. On the basis of the relatively small reduction in accuracy of genomic prediction, we would recommend the BovineLD 6K chip for large-scale genotyping as long as its costs are acceptable to breeders.