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.     

Genomic evaluation of Brown Swiss dairy cattle with limited national genotype data and integrated external information

This study demonstrated the feasibility of a genomic evaluation for the dairy cattle population for which the small national training population can be complemented with foreign information from international evaluations. National test-day milk yield data records for the Slovenian Brown Swiss cattle population were analyzed. Genomic evaluation was carried out using the single-step genomic best linear unbiased prediction method (ssGBLUP), resulting in genomic estimated breeding values (GEBV). The predominantly female group of genotyped animals, representing the national training population in the single-step genomic evaluation, was further augmented with 7,024 genotypes of foreign progeny-tested sires from an international Brown Swiss InterGenomics genomic evaluation (https://interbull.org/ib/whole_cop). Additionally, the estimated breeding values for the altogether 7,246 genotyped domestic and foreign sires from the 2019 sire multiple across-country evaluation (MACE), were added to the ssGBLUP as external pseudophenotypic information. The ssGBLUP method, with integration of MACE information by avoiding double counting, was then performed, resulting in MACE-enhanced GEBV (GEBVM). The methods were empirically validated with forward prediction. The validation group consisted of 315 domestic males and 1,041 domestic females born after 2012. Increase, inflation, and bias of the GEBV(M) reliability (REL) were assessed for the validation group with a focus on females. All individuals in the validation benefited from genomic evaluations using both methods, but the GEBV(M) REL increased most for the youngest selection candidates. Up to 35 points of GEBV REL could be assigned to national genomic information, and up to 17 points of GEBVM REL could additionally be attributed to the integration of foreign sire genomic and MACE information. Results indicated that the combined foreign progeny-tested sire genomic and external MACE information can be used in the single-step genomic evaluation as an equivalent replacement for domestic phenotypic information. Thus, an equal or slightly higher genomic breeding value REL was obtained sooner than the pedigree-based breeding value REL for the female selection candidates. When the abundant foreign progeny-tested sire genomic and MACE information was used to complement available national genomic and phenotypic information in single-step genomic evaluation, the genomic breeding value REL for young-female selection candidates increased approximately 10 points. Use of international information provides the possibility to upgrade small national training populations and obtain satisfying reliability of genomic breeding values even for the youngest female selection candidates, which will help to increase selection efficiency in the future.     

Application of single-step genomic evaluation using multiple-trait random regression test-day models in dairy cattle

Test-day traits are important for genetic evaluation in dairy cattle and are better modeled by multiple-trait random regression models (RRM). The reliability and bias of genomic estimated breeding values (GEBV) predicted using multiple-trait RRM via single-step genomic best linear unbiased prediction (ssGBLUP) were investigated in the 3 major dairy cattle breeds in Canada (i.e., Ayrshire, Holstein, and Jersey). Individual additive genomic random regression coefficients for the test-day traits were predicted using 2 multiple-trait RRM: (1) one for milk, fat, and protein yields in the first, second, and third lactations, and (2) one for somatic cell score in the first, second, and third lactations. The predicted coefficients were used to derive GEBV for each lactation day and, subsequently, the daily GEBV were compared with traditional daily parent averages obtained by BLUP. To ensure compatibility between pedigree and genomic information for genotyped animals, different scaling factors for combining the inverse of genomic (G^?1) and pedigree (A^?1₂₂) relationship matrices were tested. In addition, the inclusion of only genotypes from animals with accurate breeding values (defined in preliminary analysis) was compared with the inclusion of all available genotypes in the analyzes. The ssGBLUP model led to considerably larger validation reliabilities than the BLUP model without genomic information. In general, scaling factors used to combine the G^?1 and A^?1₂₂ matrices had small influence on the validation reliabilities. However, a greater effect was observed in the inflation of GEBV. Less inflated GEBV were obtained by the ssGBLUP compared with the parent average from traditional BLUP when using optimal scaling factors to combine the G^?1 and A^?1₂₂ matrices. Similar results were observed when including either all available genotypes or only genotypes from animals with accurate breeding values. These findings indicate that ssGBLUP using multiple-trait RRM increases reliability and reduces bias of breeding values of young animals when compared with parent average from traditional BLUP in the Canadian Ayrshire, Holstein, and Jersey breeds.     

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.     

Multibreed genomic evaluation for production traits of dairy cattle in the United States using single-step genomic best linear unbiased predictor

Official multibreed genomic evaluations for dairy cattle in the United States are based on multibreed BLUP evaluation followed by single-breed estimation of SNP effects. Single-step genomic BLUP (ssGBLUP) allows the straight computation of genomic (G)EBV in a multibreed context. This work aimed to develop ssGBLUP multibreed genomic predictions for US dairy cattle using the algorithm for proven and young (APY) to compute the inverse of the genomic relationship matrix. Only purebred Ayrshire (AY), Brown Swiss (BS), Guernsey (GU), Holstein (HO), and Jersey (JE) animals were considered. A 3-trait model with milk (MY), fat (FY), and protein (PY) yields was applied using about 45 million phenotypes recorded from January 2000 to June 2020. The whole data set included about 29.5 million animals, of which almost 4 million were genotyped. All the effects in the model were breed specific, and breed was also considered as fixed unknown parent groups. Evaluations were done for (1) each single breed separately (single); (2) HO and JE together (HO_JE); (3) AY, BS, and GU together (AY_BS_GU); (4) all the 5 breeds together (5_BREEDS). Initially, 15k core animals were used in APY for AY_BS_GU and 5_BREEDS, but larger core sets with more animals from the least represented breeds were also tested. The HO_JE evaluation had a fixed set of 30k core animals, with an equal representation of the 2 breeds, whereas HO and JE single-breed analysis involved 15k core animals. Validation for cows was based on correlations between adjusted phenotypes and (G)EBV, whereas for bulls on the regression of daughter yield deviations on (G)EBV. Because breed was correctly considered in the model, BLUP results for single and multibreed analyses were the same. Under ssGBLUP, predictability and reliability for AY, BS, and GU were on average 7% and 2% lower in 5_BREEDS compared with single-breed evaluations, respectively. However, validation parameters for these 3 breeds became better than in the single-breed evaluations when 45k animals were included in the core set for 5_BREEDS. Evaluations for Holsteins were more stable across scenarios because of the greatest number of genotyped animals and amount of data. Combining AY, BS, and GU into one evaluation resulted in predictions similar to the ones from single breed, especially when using about 30k core animals in APY. The results showed that single-step large-scale multibreed evaluations are computationally feasible, but fine tuning is needed to avoid a reduction in reliability when numerically dominant breeds are combined. Having evaluations for AY, BS, and GU separated from HO and JE may reduce inflation of GEBV for the first 3 breeds.     

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.     

Application of single-step single nucleotide polymorphism best linear unbiased predictor model with unknown-parent groups for type traits in Japanese Holsteins

The objectives of this study were to investigate the computational performance and the predictive ability and bias of a single-step SNP BLUP model (ssSNPBLUP) in genotyped young animals with unknown-parent groups (UPG) for type traits, using national genetic evaluation data from the Japanese Holstein population. The phenotype, genotype, and pedigree data were the same as those used in a national genetic evaluation of linear type traits classified between April 1984 and December 2020. In the current study, 2 data sets were prepared: the full data set containing all entries up to December 2020 and a truncated data set ending with December 2016. Genotyped animals were classified into 3 types: sires with classified daughters (S), cows with records (C), and young animals (Y). The computing performance and prediction accuracy of ssSNPBLUP were compared for the following 3 groups of genotyped animals: sires with classified daughters and young animals (SY); cows with records and young animals (CY); and sires with classified daughters, cows with records, and young animals (SCY). In addition, we tested 3 parameters of residual polygenic variance in ssSNPBLUP (0.1, 0.2, or 0.3). Daughter yield deviations (DYD) for the validation bulls and phenotypes adjusted for all fixed effects and random effects other than animal and residual (Y_adj) for the validation cows were obtained using the full data set from the pedigree-based BLUP model. The regression coefficients of DYD for bulls (or Y_adj for cows) on the genomic estimated breeding value (GEBV) using the truncated data set were used to measure the inflation of the predictions of young animals. The coefficient of determination of DYD on GEBV was used to measure the predictive ability of the predictions for the validation bulls. The reliability of the predictions for the validation cows was calculated as the square of the correlation between Y_adj and GEBV divided by heritability. The predictive ability was highest in the SCY group and lowest in the CY group. However, minimal difference was found in predictive abilities with or without UPG models using different parameters of residual polygenic variance. The regression coefficients approached 1.0 as the parameter of residual polygenic variance increased, but regression coefficients were mostly similar regardless of the use of UPG across the groups of genotyped animals. The ssSNPBLUP model, including UPG, was demonstrated as feasible for implementation in the national evaluation of type traits in Japanese Holsteins.     

Invited review: Unknown-parent groups and metafounders in single-step genomic BLUP

Single-step genomic BLUP (ssGBLUP) is a method for genomic prediction that integrates matrices of pedigree (A) and genomic (G) relationships into a single unified additive relationship matrix whose inverse is incorporated into a set of mixed model equations (MME) to compute genomic predictions. Pedigree information in dairy cattle is often incomplete. Missing pedigree potentially causes biases and inflation in genomic estimated breeding values (GEBV) obtained with ssGBLUP. Three major issues are associated with missing pedigree in ssGBLUP, namely biased predictions by selection, missing inbreeding in pedigree relationships, and incompatibility between G and A in level and scale. These issues can be solved using a proper model for unknown-parent groups (UPG). The theory behind the use of UPG is well established for pedigree BLUP, but not for ssGBLUP. This study reviews the development of the UPG model in pedigree BLUP, the properties of UPG models in ssGBLUP, and the effect of UPG on genetic trends and genomic predictions. Similarities and differences between UPG and metafounder (MF) models, a generalized UPG model, are also reviewed. A UPG model (QP) derived using a transformation of the MME has a good convergence behavior. However, with insufficient data, the QP model may yield biased genetic trends and may underestimate UPG. The QP model can be altered by removing the genomic relationships linking GEBV and UPG effects from MME. This altered QP model exhibits less bias in genetic trends and less inflation in genomic predictions than the QP model, especially with large data sets. Recently, a new model, which encapsulates the UPG equations into the pedigree relationships for genotyped animals, was proposed in simulated purebred populations. The MF model is a comprehensive solution to the missing pedigree issue. This model can be a choice for multibreed or crossbred evaluations if the data set allows the estimation of a reasonable relationship matrix for MF. Missing pedigree influences genetic trends, but its effect on the predictability of genetic merit for genotyped animals should be negligible when many proven bulls are genotyped. The SNP effects can be back-solved using GEBV from older genotyped animals, and these predicted SNP effects can be used to calculate GEBV for young-genotyped animals with missing parents.     

Differing genetic trend estimates from traditional and genomic evaluations of genotyped animals as evidence of preselection bias in US Holsteins

The objective of this study was to compare genetic trends from single-step genomic BLUP (ssGBLUP) and traditional BLUP models for milk production traits of US Holsteins. Phenotypes were 305-d milk, fat, and protein yields from 21,527,040 cows recorded between January 1990 and August 2015. The pedigree file included 29,651,623 animals and was limited to 3 generations back from recorded or genotyped animals. Genotypes for 764,029 animals were used, and analyses were by a 3-trait repeatability model as used in the US official genetic evaluation. Unknown-parent groups were incorporated into the inverse of a relationship matrix (H^?1 in ssGBLUP and A^?1 in BLUP) with the QP transformation. For ssGBLUP, 18,359 genotyped animals were randomly chosen as core animals to calculate the inverse of the genomic relationship matrix with the APY algorithm. Computations took 6.5 h and 1.4 GB of memory for BLUP, and 13 h and 115 GB of memory for ssGBLUP. For genotyped sires with at least 10 daughters, the average genetic levels for predicted transmitting ability (PTA) and genomic PTA were similar up to 2008, with a higher level for ssGBLUP later (approximately by 36 kg for milk, 2.1 kg for fat, and 1.1 kg for protein for bulls born in 2010). For genotyped cows, the average genetic levels were similar up to 2006, with a higher level for ssGBLUP (approximately by 91 kg for milk, 3.6 kg for fat, and 2.7 kg for protein for cows born in 2012). For all cows, the average levels were slightly higher for ssGBLUP, with much smaller differences than for genotyped cows. Trends for BLUP indicate bias due to genomic preselection for genotyped sires and cows. For official evaluations released in December 2016, traditional PTA had the same trend as multiple-step genomic PTA for both genotyped bulls and cows except for the youngest bulls, who had traditional PTA slightly lower than genomic PTA. For genotyped bulls born in recent years, genetic gain for official traditional and genomic evaluations was similar in contrast to ssGBLUP and BLUP differences. Official PTA for cows were adjusted so that the Mendelian sampling variance was comparable with that for bulls, and those adjustments likely removed bias due to genomic preselection from traditional PTA, especially for genotyped cows. The ssGBLUP method seems to account partially for that bias and is computationally suitable for national evaluations.     

Technical note: Automatic scaling in single-step genomic BLUP

Single-step genomic BLUP (ssGBLUP) requires compatibility between genomic and pedigree relationships for unbiased and accurate predictions. Scaling the genomic relationship matrix (G) to have the same averages as the pedigree relationship matrix (i.e., scaling by averages) is one way to ensure compatibility. This requires computing both relationship matrices, calculating averages, and changing G, whereas only the inverses of those matrices are needed in the mixed model equations. Therefore, the compatibility process can add extra computing burden. In the single-step Bayesian regression, the scaling is done by including a mean (μ_g) as a fixed effect in the model. The parameter μ_g can be interpreted as the average of the breeding values of the genotyped animals. In this study, such scaling, called automatic, was implemented in ssGBLUP via Quaas-Pollak transformation of the inverse of the relationship matrix used in ssGBLUP (H), which combines the inverses of the pedigree and genomic relationship matrices. Comparisons involved a simulated data set, and the genomic relationship matrix was computed using different allele frequencies either from the current population (i.e., realized allele frequencies), equal among all the loci, or from the base population. For all of the scenarios, we computed bias [defined as the average difference between true breeding values (TBV) and genomic estimated breeding values (GEBV)], accuracy (defined as the correlation between TBV and GEBV), and dispersion (defined as the regression coefficient of GEBV on TBV). With no scaling, the bias expressed in terms of genetic standard deviations was 0.86, 0.64, and 0.58 with realized, equal, and base population allele frequencies, respectively. With scaling by averages, which is currently used in ssGBLUP, bias was 0.07, 0.08, and 0.03, respectively. With automatic scaling, bias was 0.18 regardless of allele frequencies. Accuracies were similar among scaling methods, but about 0.1 lower in the scenario without scaling. The GEBV were more inflated without any scaling, whereas the automatic scaling performed similarly to the scaling by averages. The average dispersion for those methods was 0.94. When μ_g was treated as random, with the variance equal to differences between pedigree and genomic relationships, the bias was the same as with the scaling by averages. The automatic scaling is biased, especially when μ_g is treated as a fixed effect. The bias may be small in real data with fewer generations, when traits are undergoing weak selection, or when the number of genotyped animals is large.     

Breeding value reliabilities for multiple-trait single-step genomic best linear unbiased predictor

Approximate multistep methods to calculate reliabilities for estimated breeding values in large genetic evaluations were developed for single-trait (ST-R²A) and multitrait (MT-R²A) single-step genomic BLUP (ssGBLUP) models. First, a traditional animal model was used to estimate the amount of nongenomic information for the genotyped animals. Second, this information was used with genomic data in a genomic BLUP model (genomic BLUP/SNP-BLUP) to approximate the total amount of information and ssGBLUP reliabilities for the genotyped animals. Finally, reliabilities for the nongenotyped animals were calculated using a traditional animal model where the increased information due to genomic data for the genotyped animals is accounted for by including pseudo-record counts for the genotyped animals. The approaches were tested using a multiple-trait ssGBLUP model on 2 data sets. The first data set (data 1) was small enough such that exact ssGBLUP model reliabilities could be computed by inversion and compared with the approximation method reliabilities. Data 1 had 46,535 first-, 35,290 second-, and 23,780 third-lactation 305-d milk yield records from 47,124 Finnish Red dairy cows. The pedigree comprised 64,808 animals, of which 19,757 were genotyped. We examined the efficiency of the MT-R²A approximation on a large data set (data 2) derived from the joint Nordic (Danish, Finnish, and Swedish) Holstein dairy cattle data. Data 2 had 17.8 million 305-d milk records from 8.3 million cows and first 3 lactations. The pedigree had 11 million animals of which 274,145 were genotyped on 46,342 SNP markers. For data 1, correlations between the exact ssGBLUP model and the ST-R²A for the genotyped (nongenotyped) animals were 0.995 (0.987), 0.965 (0.984), and 0.950 (0.983) for first, second, and third lactation, respectively. Correspondingly, correlations between exact ssGBLUP reliabilities and MT-R²A for the genotyped (nongenotyped) animals were 0.995 (0.993), 0.992 (0.991), and 0.990 (0.990) for first, second, and third lactation, respectively. The regression coefficients (b₁) of ssGBLUP reliability on ST-R²A for the genotyped (nongenotyped) animals ranged from 0.87 (0.94) for first lactation to 0.68 (0.93) for third lactation, whereas for MT-R²A they were between 0.91 (0.99) for first lactation to 0.89 (0.99) for third lactation. Correspondingly, the intercepts varied from 0.11 (0.05) to 0.3 (0.06) for ST-R²A and from 0.06 (0.01) to 0.07 (0.02) for MT-R²A. The computing time for the approximation method was approximately 12% of that required by the direct exact approach. In conclusion, the developed approximate approach allows calculating estimated breeding value reliabilities in the ssGBLUP model even for large data sets.     

Assessment of accuracy of genomic prediction for French Lacaune dairy sheep

Genomic selection in Lacaune dairy sheep was investigated based on genotypes from the OvineSNP50 BeadChip (Illumina Inc., San Diego, CA). Historical artificial insemination progeny-tested rams formed a population of 2,892 genotyped rams. Additional ungenotyped rams and females were included by single-step genomic BLUP (ssGBLUP). Three prediction strategies were tried: pseudo-BLUP (using all rams and daughter yield deviations), pseudo-ssGBLUP (using all rams and daughter yield deviations), and regular ssGBLUP (using all phenotypes and pedigree in an animal model). The population linkage disequilibrium was determined, with an average squared correlation coefficient of 0.11 for markers closer than 0.1 cM (lower than in dairy cattle). The estimated effective population is 370 individuals. Gain in accuracy of genomic selection over parent averages ranged from 0.10 to 0.20. Highest accuracies and lowest bias were found using regular ssGBLUP. Transition to a genomic breeding scheme is possible but costs need to be carefully evaluated.     

Accuracy of breeding values in small genotyped populations using different sources of external information—A simulation study

Genetically linked small and large dairy cattle populations were simulated to test the effect of different sources of information from foreign populations on the accuracy of predicting breeding values for young animals in a small population. A large dairy cattle population (P_L) with >20 generations was simulated, and a small subpopulation (P_S) with 3 generations was formed as a related population, including phenotypes and genomic information. Predicted breeding values for young animals in the small population were calculated using BLUP and single-step genomic BLUP (ssGBLUP) in 4 different scenarios: (S1) 3,166 phenotypes, 22,855 pedigree animals, and 1,000 to 6,000 genotypes for P_S; (S2) S1 plus genomic estimated breeding value (GEBV) for 4,475 sires from P_L as external information; (S3) S1 plus 221,580 phenotypes, 402,829 pedigree animals, and 53,558 genotypes for P_L; and (S4) single nucleotide polymorphism (SNP) effects calculated based on P_L data. The ability to predict true breeding value was assessed in the youngest third of the genotyped animals in the small population. When data only from the small population were used and 1,000 animals were genotyped, the accuracy of GEBV was only 1 point greater than the estimated breeding value accuracy (0.32 vs. 0.31). Adding external GEBV for sires from P_L did not considerably increase accuracy (0.33 vs. 0.32 in S1). Combining phenotypes, pedigree, and genotypes for P_S and P_L was beneficial for predicting accuracy of GEBV in the small population, and the prediction accuracy of GEBV in this scenario was 0.38 compared with 0.31 from estimated breeding values. When SNP effects from P_L were used to predict GEBV for young genotyped animals from P_S, accuracy was greatest (0.56). With 6,000 genotyped animal in P_S, accuracy was greatest (0.61) with the combined populations. In a small population with few genotypes, the highest accuracy of evaluation may be obtained by using SNP effects derived from a related large population.     

Genomic prediction of lactation curves for milk,fat, protein,and somatic cell score in Holstein cattle

Application of random regression models (RRM) in a 2-step genomic prediction might be a feasible way to select young animals based on the complete pattern of the lactation curve. In this context, the prediction reliability and bias of genomic estimated breeding value (GEBV) for milk, fat, and protein yields and somatic cell score over days in milk (DIM) using a 2-step genomic approach were investigated. In addition, the effect of including cows in the training and validation populations was investigated. Estimated breeding values for each DIM (from 5 to 305 d) from the first 3 lactations of Holstein animals were deregressed and used as pseudophenotypes in the second step. Individual additive genomic random regression coefficients for each trait were predicted using RRM and genomic best linear unbiased prediction and further used to derive GEBV for each DIM. Theoretical reliabilities of GEBV obtained by the RRM were slightly higher than theoretical reliabilities obtained by the accumulated yield up to 305 d (P305). However, validation reliabilities estimated for GEBV using P305 were higher than for GEBV using RRM. For all traits, higher theoretical and validation reliabilities were estimated when incorporating genomic information. Less biased GEBV estimates were found when using RRM compared with P305, and different validation reliability and bias patterns for GEBV over time were observed across traits and lactations. Including cows in the training population increased the theoretical reliabilities and bias of GEBV; nonetheless, the inclusion of cows in the validation population does not seem to affect the regression coefficients and the theoretical reliabilities. In summary, the use of RRM in 2-step genomic prediction produced fairly accurate GEBV over the entire lactation curve for all analyzed traits. Thus, selecting young animals based on the pattern of lactation curves seems to be a feasible alternative in genomic selection of Holstein cattle for milk production traits.     

Alternative SNP weighting for single-step genomic best linear unbiased predictor evaluation of stature in US Holsteins in the presence of selected sequence variants

Causal variants inferred from sequence data analysis are expected to increase accuracy of genomic selection. In this work we evaluated the gain in reliability of genomic predictions, for stature in US Holsteins, when adding selected sequence variants to a pre-existent SNP chip. Two prediction methods were tested: de-regressed proofs assuming heterogeneous (genomic BLUP; GBLUP) residual variances and by single-step GBLUP (ssGBLUP) using actual phenotypes. Phenotypic data included 3,999,631 records for stature on 3,027,304 Holstein cows. Genotypes on 54,087 SNP markers (54k) were available for 26,877 bulls. Additionally, 16,648 selected sequence variants were combined with the 54k markers, for a total of 70,735 (70k) markers. In all methods, SNP in the genomic relationship matrix (G) were unweighted or weighted iteratively, with weights derived either by SNP effects squared or by a nonlinear method that resembles BayesA (nonlinear A). Reliability of genomic predictions were obtained by cross validation. With unweighted G derived from 54k markers, the reliabilities (× 100) were 72.4 for GBLUP and 75.3 for ssGBLUP. With unweighted G derived from 70k markers, the reliabilities were 73.4 and 76.0, respectively. Weighting by nonlinear A changed reliabilities to 73.3, and 75.9, respectively. Addition of selected sequence variants had a small effect on reliabilities. Weighting by quadratic functions reduced reliabilities. Weighting by nonlinear A increased reliabilities for GBLUP but had only a small effect in ssGBLUP. Reliabilities for direct genomic values extracted from ssGBLUP using unweighted G with 54k were higher than reliabilities by any GBLUP. Thus, ssGBLUP seems to capture more information than GBLUP and there is less room for extra reliability. Improvements in GBLUP may be because the weights in G change the covariance structure, which can explain a proportion of the variance that is accounted for when a heterogeneous residual variance is assumed by considering a different number of daughters per bull.     

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.     

Genomic analysis of cow mortality and milk production using a threshold-linear model

The objective of this study was to investigate the feasibility of genomic evaluation for cow mortality and milk production using a single-step methodology. Genomic relationships between cow mortality and milk production were also analyzed. Data included 883,887 (866,700) first-parity, 733,904 (711,211) second-parity, and 516,256 (492,026) third-parity records on cow mortality (305-d milk yields) of Holsteins from Northeast states in the United States. The pedigree consisted of up to 1,690,481 animals including 34,481 bulls genotyped with 36,951 SNP markers. Analyses were conducted with a bivariate threshold-linear model for each parity separately. Genomic information was incorporated as a genomic relationship matrix in the single-step BLUP. Traditional and genomic estimated breeding values (GEBV) were obtained with Gibbs sampling using fixed variances, whereas reliabilities were calculated from variances of GEBV samples. Genomic EBV were then converted into single nucleotide polymorphism (SNP) marker effects. Those SNP effects were categorized according to values corresponding to 1 to 4 standard deviations. Moving averages and variances of SNP effects were calculated for windows of 30 adjacent SNP, and Manhattan plots were created for SNP variances with the same window size. Using Gibbs sampling, the reliability for genotyped bulls for cow mortality was 28 to 30% in EBV and 70 to 72% in GEBV. The reliability for genotyped bulls for 305-d milk yields was 53 to 65% to 81 to 85% in GEBV. Correlations of SNP effects between mortality and 305-d milk yields within categories were the highest with the largest SNP effects and reached >0.7 at 4 standard deviations. All SNP regions explained less than 0.6% of the genetic variance for both traits, except regions close to the DGAT1 gene, which explained up to 2.5% for cow mortality and 4% for 305-d milk yields. Reliability for GEBV with a moderate number of genotyped animals can be calculated by Gibbs samples. Genomic information can greatly increase the reliability of predictions not only for milk but also for mortality. The existence of a common region on Bos taurus autosome 14 affecting both traits may indicate a major gene with a pleiotropic effect on milk and mortality.     

Comparison of genomic predictions using genomic relationship matrices built with different weighting factors to account for locus-specific variances

Various models have been used for genomic prediction. Bayesian variable selection models often predict more accurate genomic breeding values than genomic BLUP (GBLUP), but GBLUP is generally preferred for routine genomic evaluations because of low computational demand. The objective of this study was to achieve the benefits of both models using results from Bayesian models and genome-wide association studies as weights on single nucleotide polymorphism (SNP) markers when constructing the genomic matrix (G-matrix) for genomic prediction. The data comprised 5,221 progeny-tested bulls from the Nordic Holstein population. The animals were genotyped using the Illumina Bovine SNP50 BeadChip (Illumina Inc., San Diego, CA). Weighting factors in this investigation were the posterior SNP variance, the square of the posterior SNP effect, and the corresponding minus base-10 logarithm of the marker association P-value [−log₁₀(P)] of a t-test obtained from the analysis using a Bayesian mixture model with 4 normal distributions, the square of the estimated SNP effect, and the corresponding −log₁₀(P) of a t-test obtained from the analysis using a classical genome-wide association study model (linear regression model). The weights were derived from the analysis based on data sets that were 0, 1, 3, or 5 yr before performing genomic prediction. In building a G-matrix, the weights were assigned either to each marker (single-marker weighting) or to each group of approximately 5 to 150 markers (group-marker weighting). The analysis was carried out for milk yield, fat yield, protein yield, fertility, and mastitis. Deregressed proofs (DRP) were used as response variables to predict genomic estimated breeding values (GEBV). Averaging over the 5 traits, the Bayesian model led to 2.0% higher reliability of GEBV than the GBLUP model with an original unweighted G-matrix. The superiority of using a GBLUP with weighted G-matrix over GBLUP with an original unweighted G-matrix was the largest when using a weighting factor of posterior variance, resulting in 1.7 percentage points higher reliability. The second best weighting factors were −log₁₀ (P-value) of a t-test corresponding to the square of the posterior SNP effect from the Bayesian model and −log₁₀ (P-value) of a t-test corresponding to the square of the estimated SNP effect from the linear regression model, followed by the square of estimated SNP effect and the square of the posterior SNP effect. In addition, group-marker weighting performed better than single-marker weighting in terms of reducing bias of GEBV, and also slightly increased prediction reliability. The differences between weighting factors and scenarios were larger in prediction bias than in prediction accuracy. Finally, weights derived from a data set having a lag up to 3 yr did not reduce reliability of GEBV. The results indicate that posterior SNP variance estimated from a Bayesian mixture model is a good alternative weighting factor, and common weights on group markers with a size of 30 markers is a good strategy when using markers of the 50,000-marker (50K) chip. In a population with gradually increasing reference data, the weights can be updated once every 3 yr.     

Accuracy of genomic evaluation with weighted single-step genomic best linear unbiased prediction for milk production traits,udder type traits,and somatic cell scores in French dairy goats

Genomic evaluation of French dairy goats is routinely conducted using the single-step genomic BLUP (ssGBLUP) method. This method has the advantage of simultaneously using all phenotypes, pedigrees, and genotypes. However, ssGBLUP assumes that all SNP explain the same amount of genetic variance, which is unlikely in the case of traits whose major genes or QTL are segregating. In this study, we investigated the effect of weighted ssGBLUP and its alternatives, which give more weight to SNP associated with the trait, on the accuracy of genomic evaluation of milk production, udder type traits, and somatic cell scores. The data set included 2,955 genotyped animals and 2,543,680 pedigree animals. The number of phenotypes varied with the trait. The accuracy of genomic evaluation was assessed on 205 genotyped Alpine and 146 genotyped Saanen goats born between 2009 and 2012. For traits with unknown QTL, weighted ssGBLUP was less accurate than, or as accurate as, ssGBLUP. For traits with identified QTL (i.e., QTL only present in the Saanen breed), weighted ssGBLUP outperformed ssGBLUP by between 2 and 14%.     

Invited review: Genomic selection in dairy cattle: Progress and challenges

A new technology called genomic selection is revolutionizing dairy cattle breeding. Genomic selection refers to selection decisions based on genomic breeding values (GEBV). The GEBV are calculated as the sum of the effects of dense genetic markers, or haplotypes of these markers, across the entire genome, thereby potentially capturing all the quantitative trait loci (QTL) that contribute to variation in a trait. The QTL effects, inferred from either haplotypes or individual single nucleotide polymorphism markers, are first estimated in a large reference population with phenotypic information. In subsequent generations, only marker information is required to calculate GEBV. The reliability of GEBV predicted in this way has already been evaluated in experiments in the United States, New Zealand, Australia, and the Netherlands. These experiments used reference populations of between 650 and 4,500 progeny-tested Holstein-Friesian bulls, genotyped for approximately 50,000 genome-wide markers. Reliabilities of GEBV for young bulls without progeny test results in the reference population were between 20 and 67%. The reliability achieved depended on the heritability of the trait evaluated, the number of bulls in the reference population, the statistical method used to estimate the single nucleotide polymorphism effects in the reference population, and the method used to calculate the reliability. A common finding in 3 countries (United States, New Zealand, and Australia) was that a straightforward BLUP method for estimating the marker effects gave reliabilities of GEBV almost as high as more complex methods. The BLUP method is attractive because the only prior information required is the additive genetic variance of the trait. All countries included a polygenic effect (parent average breeding value) in their GEBV calculation. This inclusion is recommended to capture any genetic variance not associated with the markers, and to put some selection pressure on low-frequency QTL that may not be captured by the markers. The reliabilities of GEBV achieved were significantly greater than the reliability of parental average breeding values, the current criteria for selection of bull calves to enter progeny test teams. The increase in reliability is sufficiently high that at least 2 dairy breeding companies are already marketing bull teams for commercial use based on their GEBV only, at 2 yr of age. This strategy should at least double the rate of genetic gain in the dairy industry. Many challenges with genomic selection and its implementation remain, including increasing the accuracy of GEBV, integrating genomic information into national and international genetic evaluations, and managing long-term genetic gain.