Single-step genomic evaluation of milk production traits in Canadian Alpine and Saanen dairy goats

Genomic evaluations are routine in most plant and livestock breeding programs but are used infrequently in dairy goat breeding schemes. In this context, the purpose of this study was to investigate the use of the single-step genomic BLUP method for predicting genomic breeding values for milk production traits (milk, protein, and fat yields; protein and fat percentages) in Canadian Alpine and Saanen dairy goats. There were 6,409 and 12,236 Alpine records and 3,434 and 5,008 Saanen records for each trait in first and later lactations, respectively, and a total of 1,707 genotyped animals (833 Alpine and 874 Saanen). Two validation approaches were used, forward validation (i.e., animals born after 2013 with an average estimated breeding value accuracy from the full data set ≥0.50) and forward cross-validation (i.e., subsets of all animals included in the forward validation were used in successive replications). The forward cross-validation approach resulted in similar validation accuracies (0.55 to 0.66 versus 0.54 to 0.61) and biases (?0.01 to –0.07 versus ?0.03 to 0.11) to the forward validation when averaged across traits. Additionally, both single and multiple-breed analyses were compared, and similar average accuracies and biases were observed across traits. However, there was a small gain in accuracy from the use of multiple-breed models for the Saanen breed. A small gain in validation accuracy for genomically enhanced estimated breeding values (GEBV) relative to pedigree-based estimated breeding values (EBV) was observed across traits for the Alpine breed, but not for the Saanen breed, possibly due to limitations in the validation design, heritability of the traits evaluated, and size of the training populations. Trait-specific gains in theoretical accuracy of GEBV relative to EBV for the validation animals ranged from 17 to 31% in Alpine and 35 to 55% in Saanen, using the cross-validation approach. The GEBV predicted from the full data set were 12 to 16% more accurate than EBV for genotyped animals, but no gains were observed for nongenotyped animals. The largest gains were found for does without lactation records (35–41%) and bucks without daughter records (46–54%), and consequently, the implementation of genomic selection in the Canadian dairy goat population would be expected to increase selection accuracy for young breeding candidates. Overall, this study represents the first step toward implementation of genomic selection in Canadian dairy goat populations.     

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.     

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.     

Single- and multiple-breed genomic evaluations for conformation traits in Canadian Alpine and Saanen dairy goats

Conformation traits are functional traits known to affect longevity, production efficiency, and profitability of dairy goats. However, genetic progress for these traits is expected to be slower than for milk production traits due to the limited number of herds participating in type classification programs, and often lower heritability estimates. Genomic selection substantially accelerates the rate of genetic progress in many species and industries, especially for lowly heritable, difficult, or expensive to measure traits. Therefore, the main objectives of this study were (1) to evaluate the potential benefits of the implementation of single-step genomic evaluations for conformation traits in Canadian Alpine and Saanen dairy goats, and (2) to investigate the effect of the use of single- and multiple-breed training populations. The phenotypes used in this study were linear conformation scores, on a 1-to-9 scale, for 8 traits (i.e., body capacity, dairy character, fore udder, feet and legs, general appearance, rear udder, medial suspensory ligament, and teats) of 5,158 Alpine and 2,342 Saanen does. Genotypes were available for 833 Alpine and 874 Saanen animals. Averaged across all traits, the use of multiple-breed analyses increased validation accuracy for Saanen, and reduced bias of genomically enhanced breeding values (GEBV) for both Alpine and Saanen compared with single-breed analyses. Little benefit was observed from the use of GEBV relative to pedigree-based EBV in terms of validation accuracy and bias, possibly due to limitations in the validation design, but substantial gains of 0.14 to 0.21 (32–50%) were observed in the theoretical accuracy of validation animals when averaged across traits for single- and multiple-breed analyses. Across the whole genotyped population, average gains in theoretical accuracy for GEBV compared with EBV across all traits ranged from 0.15 to 0.17 (32–37%) for Alpine and 0.17 to 0.19 (40–41%) for Saanen, depending on the model used. The largest gains were observed for does without classification records (0.19–0.22 or 50–55%) and bucks without daughter classification records (0.20–0.27 or 57–82%), which have the least information contributing to their traditional EBV. The use of multiple-breed rather than single-breed models was most beneficial for the Saanen breed, which had fewer phenotypic records available for the analyses. These results suggest that the implementation of genomic selection could increase the accuracy of breeding values for conformation traits in Canadian dairy goats.     

Genomic information allows for more accurate breeding values for milkability in dual-purpose Italian Simmental cattle

Milkability is a trait related to the milking efficiency of an animal, and it is a component of the herd profitability. Due to its economic importance, milkability is currently included in the selection index of the Italian Simmental cattle breed with a weight of 7.5%. This lowly heritable trait is measured on a subjective scale from 1 to 3 (1 = slow, 3 = fast), and genetic evaluations are performed by pedigree-based BLUP. Genomic information is now available for some animals in the Italian Simmental population, and its inclusion in the genetic evaluation system could increase accuracy of breeding values and genetic progress for milkability. The aim of this study was to test the feasibility and advantages of having a genomic evaluation for this trait in the Italian Simmental population. Phenotypes were available for 131,308 cows. A total of 9,526 animals had genotypes for 42,152 loci; among the genotyped animals, 2,455 were cows with phenotypes, and the other were their relatives. The youngest cows with both phenotypes and genotypes (n = 900) were identified as selection candidates. Variance components and heritability were estimated using pedigree information, whereas genetic and genomic evaluations were carried out using BLUP and single-step genomic BLUP (ssGBLUP), respectively. In addition, a weighted ssGBLUP was assessed using genomic regions from a genome-wide association study. Evaluation models were validated using theoretical and realized accuracies. The estimated heritability for milkability was 0.12 ± 0.01. The mean theoretical accuracies for selection candidates were 0.43 ± 0.08 (BLUP) and 0.53 ± 0.06 (ssGBLUP). The mean realized accuracies based on linear regression statistics were 0.29 (BLUP) and 0.40 (ssGBLUP). No genomic regions were significantly associated with milkability, thus no improvements in accuracy were observed when using weighted ssGBLUP. Results indicated that genomic information could improve the accuracy of breeding values and increase genetic progress for milkability in Italian Simmental.     

Methods for genomic evaluation of a relatively small genotyped dairy population and effect of genotyped cow information in multiparity analyses

Methods for genomic prediction were evaluated for an Israeli Holstein dairy population of 713,686 cows and 1,305 progeny-tested bulls with genotypes. Inclusion of genotypes of 343 elite cows in an evaluation method that considers pedigree, phenotypes, and genotypes simultaneously was also evaluated. Two data sets were available: a complete data set with production records from 1985 through 2011, and a reduced data set with records after 2006 deleted. For each production trait, a multitrait animal model was used to compute traditional genetic evaluations for parities 1 through 3 as separate traits. Evaluations were calculated for the reduced and complete data sets. The evaluations from the reduced data set were used to calculate parent average for validation bulls, which was the benchmark for comparing gain in predictive ability from genomics. Genomic predictions for bulls in 2006 were calculated using a Bayesian regression method (BayesC), genomic BLUP (GBLUP), single-step GBLUP (ssGBLUP), and weighted ssGBLUP (WssGBLUP). Predictions using BayesC and GBLUP were calculated either with or without an index that included parent average. Genomic predictions that included elite cow genotypes were calculated using ssGBLUP and WssGBLUP. Predictive ability was assessed by coefficients of determination (R²) and regressions of predictions of 135 validation bulls with no daughters in 2006 on deregressed evaluations of those bulls in 2011. A reduction in R² and regression coefficients was observed from parities 1 through 3. Fat and protein yields had the lowest R² for all the methods. On average, R² was lowest for parent averages, followed by GBLUP, BayesC, ssGBLUP, and WssGBLUP. For some traits, R² for direct genomic values from BayesC and GBLUP were lower than those for parent averages. Genomic estimated breeding values using ssGBLUP were the least biased, and this method appears to be a suitable tool for genomic evaluation of a small genotyped population, as it automatically accounts for parental index, allows for inclusion of female genomic information without preadjustments in evaluations, and uses the same model as in traditional evaluations. Weighted ssGBLUP has the potential for higher evaluation accuracy.     

Modeling missing pedigree in single-step genomic BLUP

The objective was to compare methods of modeling missing pedigree in single-step genomic BLUP (ssGBLUP). Options for modeling missing pedigree included ignoring the missing pedigree, unknown parent groups (UPG) based on A (the numerator relationship matrix) or H (the unified pedigree and genomic relationship matrix), and metafounders. The assumptions for the distribution of estimated breeding values changed with the different models. We simulated data with heritabilities of 0.3 and 0.1 for dairy cattle populations that had more missing pedigrees for animals of lesser genetic merit. Predictions for the youngest generation and UPG solutions were compared with the true values for validation. For both traits, ssGBLUP with metafounders provided accurate and unbiased predictions for young animals while also appropriately accounting for genetic trend. Accuracy was least and bias was greatest for ssGBLUP with UPG for H for the trait with heritability of 0.3 and with UPG for A for the trait with heritability of 0.1. For the trait with heritability of 0.1 and UPG for H, the UPG accuracy (SD) was ?0.49 (0.12), suggesting poor estimates of genetic trend despite having little bias for validations on young, genotyped animals. Problems with UPG estimates were likely caused by the lesser amount of information available for the lower heritability trait. Hence, UPG need to be defined differently based on the trait and amount of information. More research is needed to investigate accounting for UPG in A₂₂ to better account for missing pedigrees for genotyped animals.     

Validation of single-step genomic BLUP random regression test-day models and SNP effects analysis on milk yield in French Saanen goats

The shape of the lactation curve is linked to an animal's health, feed requirements, and milk production throughout the year. Random regression models (RRM) are widely used for genetic evaluation of total milk production throughout the lactation and for milk yield persistency. Genomic information used with the single-step genomic BLUP method (ssGBLUP) substantially improves the accuracy of genomic prediction of breeding values in the main dairy cattle breeds. The aim of this study was to implement an RRM using ssGBLUP for milk yield in Saanen dairy goats in France. The data set consisted of 7,904,246 test-day records from 1,308,307 lactations of Saanen goats collected in France between 2000 and 2017. The performance of this type of evaluation was assessed by applying a validation step with data targeting candidate bucks. The model was compared with a nongenomic evaluation and a traditional evaluation that use cumulated performance throughout the lactation model (LM). The incorporation of genomic information increased correlations between daughter yield deviations (DYD) and estimated breeding values (EBV) obtained with a partial data set for candidate bucks. The LM and the RRM had similar correlation between DYD and EBV. However, the RRM reduced overestimation of EBV and improved the slope of the regression of DYD on EBV obtained at birth. This study shows that a genomic evaluation from a ssGBLUP RRM is possible in dairy goats in France and that RRM performance is comparable to a LM but with the additional benefit of a genomic evaluation of persistency. Variance of adjacent SNPs was studied with LM and RRM following the ssGBLUP. Both approaches converged on approximately the same regions explaining more than 1% of total variance. Regions associated with persistency were also found.     

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.     

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 first step toward genomic selection in the multi-breed French dairy goat population

The objectives of this study were to describe, using the goat SNP50 BeadChip (Illumina Inc., San Diego, CA), molecular data for the French dairy goat population and compare the effect of using genomic information on breeding value accuracy in different reference populations. Several multi-breed (Alpine and Saanen) reference population sizes, including or excluding female genotypes (from 67 males to 677 males, and 1,985 females), were used. Genomic evaluations were performed using genomic best linear unbiased predictor for milk production traits, somatic cell score, and some udder type traits. At a marker distance of 50 kb, the average r² (squared correlation coefficient) value of linkage disequilibrium was 0.14, and persistence of linkage disequilibrium as correlation of r-values among Saanen and Alpine breeds was 0.56. Genomic evaluation accuracies obtained from cross validation ranged from 36 to 53%. Biases of these estimations assessed by regression coefficients (from 0.73 to 0.98) of phenotypes on genomic breeding values were higher for traits such as protein yield than for udder type traits. Using the reference population that included all males and females, accuracies of genomic breeding values derived from prediction error variances (model accuracy) obtained for young buck candidates without phenotypes ranged from 52 to 56%. This was lower than the average pedigree-derived breeding value accuracies obtained at birth for these males from the official genetic evaluation (62%). Adding females to the reference population of 677 males improved accuracy by 5 to 9% depending on the trait considered. Gains in model accuracies of genomic breeding values ranged from 1 to 7%, lower than reported in other studies. The gains in breeding value accuracy obtained using genomic information were not as good as expected because of the limited size (at most 677 males and 1,985 females) and the structure of the 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.     

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.     

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.     

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.     

Genomic analysis of claw lesions in Holstein cows: Opportunities for genomic selection,quantitative trait locus detection,and gene identification

Claw lesions are the third most important health issue in dairy cattle, after mastitis and reproductive disorders, and genomic selection is a key component for long-term improvement of claw health. The objectives of this study were to assess the feasibility of a genomic evaluation for claw health in French Holstein cows, explore possibilities to increase evaluation accuracy, and gain a better understanding of the genetic determinism of claw health traits. The data set consisted of 48,685 trimmed Holstein cows, including 9,646 that were genotyped; 478 genotyped sires were also used. Seven claw lesion traits were evaluated using BLUP, genomic BLUP, BayesC, and single-step genomic BLUP, and the accuracies obtained using these approaches were measured through a validation study. The BayesC approach was used to detect quantitative trait locus (QTL) regions associated with the 7 individual traits (digital dermatitis, heel horn erosion, interdigital hyperplasia, sole hemorrhage circumscribed, sole hemorrhage diffused, sole ulcer, and white line fissure) based on their Bayes factor. Annotated genes on these regions were reported. Genomic evaluation approaches generally did not allow for greater accuracies than BLUP, except for single-step genomic BLUP. Accuracies were moderate, but best and worst validation animals were correctly discriminated and showed significant differences in lesion frequencies. A total of 192 QTL regions were identified, including 13 with major evidence or involved for 2 of the traits. A high number of genes were present on these regions, and several had functions associated with the immune system. In particular, the EPYC gene is located close to a major evidence QTL for resistance to digital dermatitis that is also a QTL for interdigital hyperplasia (on chromosome 5, around 20.9 MB) and has been associated with Ehlers-Danlos syndrome in cattle. Genomic selection can be used to improve resistance to individual claw lesions, and several possibilities exist to improve accuracies of genomic evaluations.     

Estimating variance components and breeding values for number of oocytes and number of embryos in dairy cattle using a single-step genomic evaluation

Reproductive technologies such as multiple ovulation and embryo transfer (MOET) and ovum pick-up (OPU) accelerate genetic improvement in dairy breeding schemes. To enhance the efficiency of embryo production, breeding values for traits such as number of oocytes (NoO) and number of MOET embryos (NoM) can help in selection of donors with high MOET or OPU efficiency. The aim of this study was therefore to estimate variance components and (genomic) breeding values for NoO and NoM based on Dutch Holstein data. Furthermore, a 10-fold cross-validation was carried out to assess the accuracy of pedigree and genomic breeding values for NoO and NoM. For NoO, 40,734 OPU sessions between 1993 and 2015 were analyzed. These OPU sessions originated from 2,543 donors, from which 1,144 were genotyped. For NoM, 35,695 sessions between 1994 and 2015 were analyzed. These MOET sessions originated from 13,868 donors, from which 3,716 were genotyped. Analyses were done using only pedigree information and using a single-step genomic BLUP (ssGBLUP) approach combining genomic information and pedigree information. Heritabilities were very similar based on pedigree information or based on ssGBLUP [i.e., 0.32 (standard error = 0.03) for NoO and 0.21 (standard error = 0.01) for NoM with pedigree, 0.31 (standard error = 0.03) for NoO, and 0.22 (standard error = 0.01) for NoM with ssGBLUP]. For animals without their own information as mimicked in the cross-validation, the accuracy of pedigree-based breeding values was 0.46 for NoO and NoM. The accuracies of genomic breeding values from ssGBLUP were 0.54 for NoO and 0.52 for NoM. These results show that including genomic information increases the accuracies. These moderate accuracies in combination with a large genetic variance show good opportunities for selection of potential bull dams.     

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.     

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.     

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.