Genomic evaluation of carcass traits of Korean beef cattle Hanwoo using a single-step marker effect model.

Hanwoo beef cattle are well known for the flavor and tenderness of their meat. Genetic improvement programs have been extremely successful over the last 40 yr. Recently, genomic selection was initiated in Hanwoo to enhance genetic progress. Routine genomic evaluation based on the single-step breeding value model was implemented in 2020 for all economically important traits. In this study, we tested a single-step marker effect model for the genomic evaluation of four carcass traits, namely, carcass weight (CW), eye muscle area, backfat thickness, and marbling score. In total, 8,023,666 animals with carcass records were jointly evaluated, including 29,965 genotyped animals. To assess the prediction stability of the single-step model, carcass data from the last 4 yr were removed in a forward validation study. The estimated genomic breeding values (GEBV) of the validation animals and other animals were compared between the truncated and full evaluations. A parallel conventional best linear unbiased prediction (BLUP) evaluation with either the full or the truncated dataset was also conducted for comparison with the single-step model. The estimates of the marker effect from the truncated evaluation were highly correlated with those from the full evaluation, ranging from 0.88 to 0.92. The regression coefficients of the estimates of the marker effect for the full and truncated evaluations were close to their expected value of 1, indicating unbiased estimates for all carcass traits. Estimates of the marker effect revealed three chromosomal regions (chromosomes 4, 6, and 14) harboring the major genes for CW in Hanwoo. For validation of cows or steers, the single-step model had a much higher R2 value for the linear regression model than the conventional BLUP model. Based on the regression intercept and slope of the validation, the single-step evaluation was neither inflated nor deflated. For genotyped animals, the estimated GEBV from the full and truncated evaluations were more correlated than the estimated breeding values from the two conventional BLUP evaluations. The single-step model provided a more accurate and stable evaluation over time.

Hanwoo beef cattle are well known for the flavor and tenderness of their meat. Genetic improvement programs have been successful over the last 40 yr. Recently, genomic selection was initiated in Hanwoo to enhance genetic progress. A routine genomic evaluation based on the single-step breeding value model was implemented in 2020 for all economically important traits. In this study, we tested a single-step marker effect model for the genomic evaluation of four carcass traits. In total, 8,023,666 cows or steers with carcass records were jointly evaluated, including 29,965 genotyped animals. To assess the prediction accuracy of the single-step model, carcass data from the last 4 yr were removed in a forward validation study. Estimated genomic breeding values (GEBV) of validation animals were compared between truncated and full evaluations. A parallel conventional best linear unbiased prediction (BLUP) evaluation with either the full or truncated dataset was conducted for comparison with the single-step model. Plots of the estimates of the marker effect showed three chromosomal regions harboring the major genes for carcass weight in Hanwoo. The single-step model yielded a more accurate and stable evaluation over time than the conventional BLUP model.

Single-step SNPBLUP evaluation in six German beef cattle breeds.

The implementation of genomic selection for six German beef cattle populations was evaluated. Although the multiple-step implementation of genomic selection is the status quo in most national dairy cattle evaluations, the breeding structure of German beef cattle, coupled with the shortcoming and complexity of the multiple-step method, makes single step a more attractive option to implement genomic selection in German beef cattle populations. Our objective was to develop a national beef cattle single-step genomic evaluation in five economically important traits in six German beef cattle populations and investigate its impact on the accuracy and bias of genomic evaluations relative to the current pedigree-based evaluation. Across the six breeds in our study, 461,929 phenotyped and 14,321 genotyped animals were evaluated with a multi-trait single-step model. To validate the single-step model, phenotype data in the last 2 years were removed in a forward validation study. For the conventional and single-step approaches, the genomic estimated breeding values of validation animals and other animals were compared between the truncated and the full evaluations. The correlation of the GEBVs between the full and truncated evaluations in the validation animals was slightly higher in the single-step evaluation. The regression of the full GEBVs on truncated GEBVs was close to the optimal value of 1 for both the pedigree-based and the single-step evaluations. The SNP effect estimates from the truncated evaluation were highly correlated with those from the full evaluation, with values ranging from 0.79 to 0.94. The correlation of the SNP effect was influenced by the number of genotyped animals shared between the full and truncated evaluations. The regression coefficients of the SNP effect of the full evaluation on the truncated evaluation were all close to the expected value of 1, indicating unbiased estimates of the SNP markers for the production traits. The Manhattan plot of the SNP effect estimates identified chromosomal regions harbouring major genes for muscling and body weight in breeds of French origin. Based on the regression intercept and slope of the GEBVs of validation animals, the single-step evaluation was neither inflated nor deflated across the six breeds. Overall, the single-step model resulted in a more accurate and stable evaluation. However, due to the small number of genotyped individuals, the single-step method only provided slightly better results when compared to the pedigree-based method.

Invited review: Reliability computation from the animal model era to the single-step genomic model era.

The calculation of exact reliabilities involving the inversion of mixed model equations poses a heavy computational challenge when the system of equations is large. This has prompted the development of different approximation methods. We give an overview of the various methods and computational approaches in calculating reliability from the era before the animal model to the era of single-step genomic models. The different methods are discussed in terms of modeling, development, and applicability in large dairy cattle populations. The paper also describes the problems faced in reliability computation. Many details dispersed throughout the literature are presented in this paper. It is clear that a universal solution applicable to every model and input data may not be possible, but we point out several efficient and accurate algorithms developed recently for a variety of very large genomic evaluations.

MetaGS: an accurate method to impute and combine SNP effects across populations using summary statistics.

BACKGROUND: Meta-analysis describes a category of statistical methods that aim at combining the results of multiple studies to increase statistical power by exploiting summary statistics. Different industries that use genomic prediction do not share their raw data due to logistic or privacy restrictions, which can limit the size of their reference populations and creates a need for a practical meta-analysis method. RESULTS: We developed a meta-analysis, named MetaGS, that duplicates the results of multi-trait best linear unbiased prediction (mBLUP) analysis without accessing raw data. MetaGS exploits the correlations among different populations to produce more accurate population-specific single nucleotide polymorphism (SNP) effects. The method improves SNP effect estimations for a given population depending on its relations to other populations. MetaGS was tested on milk, fat and protein yield data of Australian Holstein and Jersey cattle and it generated very similar genomic estimated breeding values to those produced using the mBLUP method for all traits in both breeds. One of the major difficulties when combining SNP effects across populations is the use of different variants for the populations, which limits the applications of meta-analysis in practice. We solved this issue by developing a method to impute missing summary statistics without using raw data. Our results showed that imputing summary statistics can be done with high accuracy (r > 0.9) even when more than 70% of the SNPs were missing with a minimal effect on prediction accuracy. CONCLUSIONS: We demonstrated that MetaGS can replace the mBLUP model when raw data cannot be shared, which can lead to more flexible collaborations compared to the single-trait BLUP model.

Assessing the degree of stratification between closely related Holstein-Friesian populations.

Genomic information is an important part of the routine evaluation of dairy cattle and provides the wide availability of animals genotyped using single nucleotide polymorphism (SNP) microarrays. We analyzed 2243 Polish and 2294 German Holstein-Friesian bulls genotyped using the Illumina BovineSNP50 BeadChip. For each bull, estimated breeding values (EBVs) calculated from national routine genetic evaluation were available for production traits and for somatic cell score (SCS). Separately for each population, we estimated SNP haplotypes, pairwise linkage disequilibrium (LD), and SNP effects. The SNP genetic covariance between both populations was estimated using a bivariate mixed model. The average LD was lower in the Polish than in the German population and, with increasing genomic distance, LD decays 1.7 times more rapidly in German than in Polish cattle. The comparison of SNP allele frequencies for base populations estimated separately using Polish and German data revealed a very good agreement. The comparison of genetic effects corresponding to various window lengths defined in bp emerged a systematic pattern: regardless of the length of the compared region, few significant differences were found for production traits, while many were observed for SCS. For each trait, the German population had much higher SNP variances than the Polish population and the genetic covariance estimates were all positive. Depending on traits' inheritance mode, the additive genetic variation can be stored in many genes following the infinitesimal model (like for SCS) or distributed between genes with high effects and the polygenic "background" (like for production traits). Accounting for those differences has implications on the prospective international genomic evaluation.

The genetic structure of longevity in dairy cows.

Longevity of dairy cows is determined by culling. Previous studies have shown that culling of dairy cows is not an unambiguous trait but rather the result of several reasons including diseases and selection decisions. The relative importance of these reasons is not stable over time, implying that genetic background of culling may vary over lifetime. Data of 7.6 million German Holstein cows were used to assess the detailed genetic correlation structure among 18 survival traits defined for the first 3 parities. Differences of genetic factors which determine survival of different production periods were found, showing a pattern with 3 genetically distinct periods within each parity: early lactation (calving until d 59), mid lactation (d 60 to 299), and late lactation (d 300 until next calving). Survival in first and later parities were found to be slightly genetically different from each other. The identified patterns were in good accordance with distributions of reasons for disposal, and correlations of estimated breeding values of survival traits for different periods to production and functional traits were generally plausible compared with literature regarding effects on the risk of culling. The study shows that genetic background of survival is variable not only across but also within parities. The results of the study can help developing more accurate models for routine genetic evaluations of longevity that account for nonunity genetic correlations between survival of different periods.

Prediction of expected genetic variation within groups of offspring for innovative mating schemes.

BACKGROUND: Experience from progeny-testing indicates that the mating of popular bull sires that have high estimated breeding values with excellent dams does not guarantee the production of offspring with superior breeding values. This is explained partly by differences in the standard deviation of gamete breeding values (SDGBV) between animals at the haplotype level. The SDGBV depends on the variance of the true effects of single nucleotide polymorphisms (SNPs) and the degree of heterozygosity. Haplotypes of 58 035 Holstein animals were used to predict and investigate expected SDGBV for fat yield, protein yield, somatic cell score and the direct genetic effect for stillbirth. RESULTS: Differences in SDGBV between animals were detected, which means that the groups of offspring of parents with low SDGBV will be more homogeneous than those of parents with high SDGBV, although the expected mean breeding values of the progeny will be the same. SDGBV was negatively correlated with genomic and pedigree inbreeding coefficients and a small loss of SDGBV over time was observed. Sires that had relatively low mean gamete breeding values but high SDGBV had a higher probability of producing extremely positive offspring than sires that had a high mean gamete breeding value and low SDGBV. CONCLUSIONS: An animal's SDGBV can be estimated based on genomic information and used to design specific genomic mating plans. Estimated SDGBV are an additional tool for mating programs, which allows breeders to identify and match mating partners using specific haplotype information.

Error rate for imputation from the Illumina BovineSNP50 chip to the Illumina BovineHD chip.

BACKGROUND: Imputation of genotypes from low-density to higher density chips is a cost-effective method to obtain high-density genotypes for many animals, based on genotypes of only a relatively small subset of animals (reference population) on the high-density chip. Several factors influence the accuracy of imputation and our objective was to investigate the effects of the size of the reference population used for imputation and of the imputation method used and its parameters. Imputation of genotypes was carried out from 50,000 (moderate-density) to 777,000 (high-density) SNPs (single nucleotide polymorphisms). METHODS: The effect of reference population size was studied in two datasets: one with 548 and one with 1289 Holstein animals, genotyped with the Illumina BovineHD chip (777 k SNPs). A third dataset included the 548 animals genotyped with the 777 k SNP chip and 2200 animals genotyped with the Illumina BovineSNP50 chip. In each dataset, 60 animals were chosen as validation animals, for which all high-density genotypes were masked, except for the Illumina BovineSNP50 markers. Imputation was studied in a subset of six chromosomes, using the imputation software programs Beagle and DAGPHASE. RESULTS: Imputation with DAGPHASE and Beagle resulted in 1.91% and 0.87% allelic imputation error rates in the dataset with 548 high-density genotypes, when scale and shift parameters were 2.0 and 0.1, and 1.0 and 0.0, respectively. When Beagle was used alone, the imputation error rate was 0.67%. If the information obtained by Beagle was subsequently used in DAGPHASE, imputation error rates were slightly higher (0.71%). When 2200 moderate-density genotypes were added and Beagle was used alone, imputation error rates were slightly lower (0.64%). The least imputation errors were obtained with Beagle in the reference set with 1289 high-density genotypes (0.41%). CONCLUSIONS: For imputation of genotypes from the 50 k to the 777 k SNP chip, Beagle gave the lowest allelic imputation error rates. Imputation error rates decreased with increasing size of the reference population. For applications for which computing time is limiting, DAGPHASE using information from Beagle can be considered as an alternative, since it reduces computation time and increases imputation error rates only slightly.

Impacts of both reference population size and inclusion of a residual polygenic effect on the accuracy of genomic prediction.

BACKGROUND: The purpose of this work was to study the impact of both the size of genomic reference populations and the inclusion of a residual polygenic effect on dairy cattle genetic evaluations enhanced with genomic information. METHODS: Direct genomic values were estimated for German Holstein cattle with a genomic BLUP model including a residual polygenic effect. A total of 17,429 genotyped Holstein bulls were evaluated using the phenotypes of 44 traits. The Interbull genomic validation test was implemented to investigate how the inclusion of a residual polygenic effect impacted genomic estimated breeding values. RESULTS: As the number of reference bulls increased, both the variance of the estimates of single nucleotide polymorphism effects and the reliability of the direct genomic values of selection candidates increased. Fitting a residual polygenic effect in the model resulted in less biased genome-enhanced breeding values and decreased the correlation between direct genomic values and estimated breeding values of sires in the reference population. CONCLUSIONS: Genetic evaluation of dairy cattle enhanced with genomic information is highly effective in increasing reliability, as well as using large genomic reference populations. We found that fitting a residual polygenic effect reduced the bias in genome-enhanced breeding values, decreased the correlation between direct genomic values and sire's estimated breeding values and made genome-enhanced breeding values more consistent in mean and variance as is the case for pedigree-based estimated breeding values.

Use of direct and iterative solvers for estimation of SNP effects in genome-wide selection.

The aim of this study was to compare iterative and direct solvers for estimation of marker effects in genomic selection. One iterative and two direct methods were used: Gauss-Seidel with Residual Update, Cholesky Decomposition and Gentleman-Givens rotations. For resembling different scenarios with respect to number of markers and of genotyped animals, a simulated data set divided into 25 subsets was used. Number of markers ranged from 1,200 to 5,925 and number of animals ranged from 1,200 to 5,865. Methods were also applied to real data comprising 3081 individuals genotyped for 45181 SNPs. Results from simulated data showed that the iterative solver was substantially faster than direct methods for larger numbers of markers. Use of a direct solver may allow for computing (co)variances of SNP effects. When applied to real data, performance of the iterative method varied substantially, depending on the level of ill-conditioning of the coefficient matrix. From results with real data, Gentleman-Givens rotations would be the method of choice in this particular application as it provided an exact solution within a fairly reasonable time frame (less than two hours). It would indeed be the preferred method whenever computer resources allow its use.

Use of direct and iterative solvers for estimation of SNP effects in genome-wide selection

The aim of this study was to compare iterative and direct solvers for estimation of marker effects in genomic selection. One iterative and two direct methods were used: Gauss-Seidel with Residual Update, Cholesky Decomposition and Gentleman-Givens rotations. For resembling different scenarios with respect to number of markers and of genotyped animals, a simulated data set divided into 25 subsets was used. Number of markers ranged from 1,200 to 5,925 and number of animals ranged from 1,200 to 5,865. Methods were also applied to real data comprising 3081 individuals genotyped for 45181 SNPs. Results from simulated data showed that the iterative solver was substantially faster than direct methods for larger numbers of markers. Use of a direct solver may allow for computing (co)variances of SNP effects. When applied to real data, performance of the iterative method varied substantially, depending on the level of ill-conditioning of the coefficient matrix. From results with real data, Gentleman-Givens rotations would be the method of choice in this particular application as it provided an exact solution within a fairly reasonable time frame (less than two hours). It would indeed be the preferred method whenever computer resources allow its use.

Data transformation for rank reduction in multi-trait MACE model for international bull comparison.

Since many countries use multiple lactation random regression test day models in national evaluations for milk production traits, a random regression multiple across-country evaluation (MACE) model permitting a variable number of correlated traits per country should be used in international dairy evaluations. In order to reduce the number of within country traits for international comparison, three different MACE models were implemented based on German daughter yield deviation data and compared to the random regression MACE. The multiple lactation MACE model analysed daughter yield deviations on a lactation basis reducing the rank from nine random regression coefficients to three lactations. The lactation breeding values were very accurate for old bulls, but not for the youngest bulls with daughters with short lactations. The other two models applied principal component analysis as the dimension reduction technique: one based on eigenvalues of a genetic correlation matrix and the other on eigenvalues of a combined lactation matrix. The first one showed that German data can be transformed from nine traits to five eigenfunctions without losing much accuracy in any of the estimated random regression coefficients. The second one allowed performing rank reductions to three eigenfunctions without having the problem of young bulls with daughters with short lactations.

Statistical aspects of genetic association testing in small samples, based on selective DNA pooling data in the arctic fox.

We analysed data from a selective DNA pooling experiment with 130 individuals of the arctic fox (Alopex lagopus), which originated from 2 different types regarding body size. The association between alleles of 6 selected unlinked molecular markers and body size was tested by using univariate and multinomial logistic regression models, applying odds ratio and test statistics from the power divergence family. Due to the small sample size and the resulting sparseness of the data table, in hypothesis testing we could not rely on the asymptotic distributions of the tests. Instead, we tried to account for data sparseness by (i) modifying confidence intervals of odds ratio; (ii) using a normal approximation of the asymptotic distribution of the power divergence tests with different approaches for calculating moments of the statistics; and (iii) assessing P values empirically, based on bootstrap samples. As a result, a significant association was observed for 3 markers. Furthermore, we used simulations to assess the validity of the normal approximation of the asymptotic distribution of the test statistics under the conditions of small and sparse samples.

Multivariate mixed inheritance models for QTL detection on porcine chromosome 6.

A series of multivariate mixed-inheritance models is fitted to the data from an outbred-line pig cross commercially used in Norway. Each model accommodates information on polygenic (co)variances between F2 individuals and their F1 parents across the five traits through incorporation of a random animal effect. Considered traits relate to meat quality and are chosen following up the results from a previous evaluation, in which a putative quantitative trait locus (QTL) was identified on chromosome six that affects the amount of intramuscular fat (IMF), meat percentage, meat tenderness and smell intensity (Grindflek et al., 2001). An additional trait included in the model, based on results of other studies, is the backfat thickness. The analysed material comprises data scored for 305 F2 individuals, whereas marker information is available for F1 and F2 generations. Based on the results of the multivariate analysis with the mixed-inheritance model, it was possible to conclude that the evidence for QTLs for meat percentage, meat tenderness and smell intensity in the study of Grindflek et al. (2001) do not represent separate QTLs, but is caused by the fact that the applied pre-adjustment of trait values for polygenic effects failed properly to remove the polygenic variation. The QTL effect on IMF on chromosome six was confirmed.

Application of a mixed inheritance model to the detection of quantitative trait loci in swine.

The primary goal of this study was to investigate statistical properties of a mixed inheritance model for the localization of quantitative trait loci (QTL). This is based on the analysis of phenotypic data for the amount of intramuscular fat (IMF) scored on 305 individuals originating from a cross between Duroc and Norwegian Landrace breeds. Marker genotype information is available for F1 and F2 generations. Statistical procedures compared involve i) the interval mapping, ii) the composite interval mapping, iii) a regression method, and iv) a mixed inheritance model accounting for a random animal additive genetic effect and relationships between individuals. The basic statistical properties of the latter approach are then assessed using Monte Carlo simulations showing slight unconservativeness as compared to chi(2)2df and reasonable power to detect QTL of moderate effects. In the analysis of IMF data, the significant evidence for the existing QTL is detected on chromosome 6. A chromosomal region recommended for a second-step fine mapping analysis is identified between markers SW1823 and S0228, based on three types of confidence intervals derived by using: i) the Jackknife algorithm, ii) the numerical variance approximation, and iii) the LOD score approach. The Jackknife algorithm was additionally used to quantify each family's contribution to the test statistic and to the estimate of QTL position.