De-regressed Proofs Research Articles

Computation of deregressed proofs for genomic selection when own phenotypes exist with an application in French show-jumping horses1

Genomic evaluations often use as pseudo-phenotypes corrected means of progeny performances, like daughter yield deviations (DYD) in dairy species. In horse breeding, own performances are also available and performances from other relatives (as half sibs) may play an important part in the EBV because the number of progeny remains low, even for stallions. The first step for genomic selection in horses is therefore to generate pseudo-phenotypes for genomic analysis when parental or own information is considered. This work presents an easy method to compute deregressed EBV from regular pedigree-based genetic evaluations (EBV, reliabilities) to be used in genomic evaluations. The proposed methodology builds deregressed proofs so that they combine own performances (from genotyped individuals) and performances of relatives (outside of the genotyped sample). An application to show jumping horse data is presented. A sample of 908 stallions specialized in show jumping [71% Selle Français (SF), 17% foreign sport horses (FH), 13% Anglo Arab (AA)] were genotyped. Genotyping was performed using the Illumina Equine SNP50 BeadChip, and after quality tests, 44,444 SNP were retained. Two methods were used for genomic evaluation: GBLUP and BayesCπ, and 6 validation data sets were compared, chosen according to breeds SF + FH + AA or SF + FH, family structure (more than 3 half sibs), reliability of sires (>0.97) or sons (>0.72). In spite of a favorable genetic structure [linkage disequilibrium equal to 0.24 at 50 kb pairs], results showed low advantage of genomic evaluation. On the validation sample SF + FH + AA, the correlation between deregressed proofs and GBLUP or BayesCπ predictions was 0.39, 0.37, 0.51 according to the different validation data sets, compared with 0.36, 0.33, 0.53 obtained with BLUP predictions. Correlations were much lower on the SF + FH sample. Research is pursued to understand this low advantage of genomic selection and to improve the methodology for genomic evaluation in this context, which is less favorable than dairy cattle breeding.

Comparison of methods for the implementation of genome-assisted evaluation of Spanish dairy cattle

The aim of this study was to evaluate methods for genomic evaluation of the Spanish Holstein population as an initial step toward the implementation of routine genomic evaluations. This study provides a description of the population structure of progeny tested bulls in Spain at the genomic level and compares different genomic evaluation methods with regard to accuracy and bias. Two Bayesian linear regression models, Bayes-A and Bayesian-LASSO (B-LASSO), as well as a machine learning algorithm, Random-Boosting (R-Boost), and BLUP using a realized genomic relationship matrix (G-BLUP), were compared. Five traits that are currently under selection in the Spanish Holstein population were used: milk yield, fat yield, protein yield, fat percentage, and udder depth. In total, genotypes from 1859 progeny tested bulls were used. The training sets were composed of bulls born before 2005; including 1601 bulls for production and 1574 bulls for type, whereas the testing sets contained 258 and 235 bulls born in 2005 or later for production and type, respectively. Deregressed proofs (DRP) from January 2009 Interbull (Uppsala, Sweden) evaluation were used as the dependent variables for bulls in the training sets, whereas DRP from the December 2011 DRPs Interbull evaluation were used to compare genomic predictions with progeny test results for bulls in the testing set. Genomic predictions were more accurate than traditional pedigree indices for predicting future progeny test results of young bulls. The gain in accuracy, due to inclusion of genomic data varied by trait and ranged from 0.04 to 0.42 Pearson correlation units. Results averaged across traits showed that B-LASSO had the highest accuracy with an advantage of 0.01, 0.03 and 0.03 points in Pearson correlation compared with R-Boost, Bayes-A, and G-BLUP, respectively. The B-LASSO predictions also showed the least bias (0.02, 0.03 and 0.10 SD units less than Bayes-A, R-Boost and G-BLUP, respectively) as measured by mean difference between genomic predictions and progeny test results. The R-Boosting algorithm provided genomic predictions with regression coefficients closer to unity, which is an alternative measure of bias, for 4 out of 5 traits and also resulted in mean squared errors estimates that were 2%, 10%, and 12% smaller than B-LASSO, Bayes-A, and G-BLUP, respectively. The observed prediction accuracy obtained with these methods was within the range of values expected for a population of similar size, suggesting that the prediction method and reference population described herein are appropriate for implementation of routine genome-assisted evaluations in Spanish dairy cattle. R-Boost is a competitive marker regression methodology in terms of predictive ability that can accommodate large data sets.

Use of different statistical models to predict direct genomic values for productive and functional traits in Italian Holsteins

One of the main issues in genomic selection was the huge unbalance between number of markers and phenotypes available. In this work, principal component analysis is used to reduce the number of predictors for calculating direct genomic breeding values (DGV) for production and functional traits. 2093 Italian Holstein bulls were genotyped with the 54 K Illumina beadchip, and 39,555 SNP markers were retained after data editing. Principal Components (PC) were extracted from SNP matrix, and 15,207 PC explaining 99% of the original variance were retained and used as predictors. Bulls born before 2001 were included in the reference population, younger animals in the test population. A BLUP model was used to estimate the effect of principal component on deregressed proof (DRPF) for 35 traits and results were compared to those obtained by using SNP genotypes as predictors either with BLUP or with Bayes_A models. Correlations between DGV and DRPF did not substantially differ among the three methods except for milk fat content. The lowest prediction bias was obtained for the method based on the use of principal component. Regression coefficients of DRPF on DGV were lower than one for the approach based on the use of PC and higher than one for the other two methods. The use of PC as predictors resulted in a large reduction of number of predictors (approximately 38%) and of computational time that was approximately 2% of the time needed to estimate SNP effects with the other two methods. Accuracies of genomic predictions were in most of cases only slightly higher than those of the traditional pedigree index, probably due to the limited size of the considered population.

Comparison of genomic predictions using medium-density (∼54,000) and high-density (∼777,000) single nucleotide polymorphism marker panels in Nordic Holstein and Red Dairy Cattle populations

This study investigated genomic prediction using medium-density (∼54,000; 54K) and high-density marker panels (∼777,000; 777K), based on data from Nordic Holstein and Red Dairy Cattle (RDC). The Holstein data comprised 4,539 progeny-tested bulls, and the RDC data 4,403 progeny-tested bulls. The data were divided into reference data and test data using October 1, 2001, as a cut-off date (birth date of the bulls). This resulted in about 25% genotyped bulls in the Holstein test data and 20% in the RDC test data. For each breed, 3 data sets of markers were used to predict breeding values: (1) 54K data set with missing genotypes, (2) 54K data set where missing genotypes were imputed, and (3) imputed high-density (HD) marker data set created by imputing the 54K data to the HD data based on 557 bulls genotyped using a 777K single nucleotide polymorphism chip in Holstein, and 706 bulls in RDC. Based on the 3 marker data sets, direct genomic breeding values (DGV) for protein, fertility, and udder health were predicted using a genomic BLUP model (GBLUP) and a Bayesian mixture model with 2 normal distributions. Reliability of DGV was measured as squared correlations between deregressed proofs (DRP) and DGV corrected for reliability of DRP. Unbiasedness was assessed by regression of DRP on DGV, based on the bulls in the test data sets. Averaged over the 3 traits, reliability of DGV based on the HD markers was 0.5% higher than that based on the 54K data in Holstein, and 1.0% higher than that in RDC. In addition, the HD markers led to an improvement of unbiasedness of DGV. The Bayesian mixture model led to 0.5% higher reliability than the GBLUP model in Holstein, but not in RDC. Imputing missing genotypes in the 54K marker data did not improve genomic predictions for most of the traits.

Across breed multi‐trait random regression genomic predictions in the Nordic Red dairy cattle

The current study evaluates reliability of genomic predictions in selection candidates using multi-trait random regression model, which accounts for interactions between marker effects and breed of origin in the Nordic Red dairy cattle (RDC). The population structure of the RDC is admixed. Data consisted of individual animal breed proportions calculated from the full pedigree, deregressed proofs (DRP) of published estimated breeding values (EBV) for yield traits and genotypic data for 37,595 single nucleotide polymorphic markers. The analysed data included 3330 bulls in the reference population and 812 bulls that were used for validation. Direct genomic breeding values (DGV) were estimated using the model under study, which accounts for breed effects and also with GBLUP, which assume uniform population. Validation reliability was calculated as a coefficient of determination from weighted regression of DRP on DGV (rDRP,DGV 2), scaled by the mean reliability of DRP. Using the breed-specific model increased the reliability of DGV by 2 and 3% for milk and protein, respectively, when compared to homogeneous population GBLUP. The exception was for fat, where there was no gain in reliability. Estimated validation reliabilities were low for milk (0.32) and protein (0.32) and slightly higher (0.42) for fat.

Comparison on genomic predictions using three GBLUP methods and two single-step blending methods in the Nordic Holstein population

BackgroundA single-step blending approach allows genomic prediction using information of genotyped and non-genotyped animals simultaneously. However, the combined relationship matrix in a single-step method may need to be adjusted because marker-based and pedigree-based relationship matrices may not be on the same scale. The same may apply when a GBLUP model includes both genomic breeding values and residual polygenic effects. The objective of this study was to compare single-step blending methods and GBLUP methods with and without adjustment of the genomic relationship matrix for genomic prediction of 16 traits in the Nordic Holstein population.MethodsThe data consisted of de-regressed proofs (DRP) for 5 214 genotyped and 9 374 non-genotyped bulls. The bulls were divided into a training and a validation population by birth date, October 1, 2001. Five approaches for genomic prediction were used: 1) a simple GBLUP method, 2) a GBLUP method with a polygenic effect, 3) an adjusted GBLUP method with a polygenic effect, 4) a single-step blending method, and 5) an adjusted single-step blending method. In the adjusted GBLUP and single-step methods, the genomic relationship matrix was adjusted for the difference of scale between the genomic and the pedigree relationship matrices. A set of weights on the pedigree relationship matrix (ranging from 0.05 to 0.40) was used to build the combined relationship matrix in the single-step blending method and the GBLUP method with a polygenetic effect.ResultsAveraged over the 16 traits, reliabilities of genomic breeding values predicted using the GBLUP method with a polygenic effect (relative weight of 0.20) were 0.3% higher than reliabilities from the simple GBLUP method (without a polygenic effect). The adjusted single-step blending and original single-step blending methods (relative weight of 0.20) had average reliabilities that were 2.1% and 1.8% higher than the simple GBLUP method, respectively. In addition, the GBLUP method with a polygenic effect led to less bias of genomic predictions than the simple GBLUP method, and both single-step blending methods yielded less bias of predictions than all GBLUP methods.ConclusionsThe single-step blending method is an appealing approach for practical genomic prediction in dairy cattle. Genomic prediction from the single-step blending method can be improved by adjusting the scale of the genomic relationship matrix.

Investigation of reliability of genomic predictions in the admixed Nordic Red dairy cattle

The success of genomic selection (GS) in small breeds which are likely to have admixed structures has been minimal. This is because accuracy of GS depends on the extent of linkage disequilibrium (LD) between markers and quantitative trait loci (QTL) and LD depends on the genetic structure of the population and marker density. In the current study, we evaluate reliability of genomic predictions in young unproven bulls, when interactions between marker effects and breed of origin are accounted for in the Nordic Red dairy cattle (RDC). The population structure of the RDC is admixed. Data consisted of animal breed proportions calculated from the full pedigree, deregressed proofs (DRP) of published estimated breeding values (EBV) for yield traits and genotypic data for 37,595 SNP markers. Direct genomic breeding values (DGV) were estimated using 2 models, one accounting for breed-specific effects and other assuming uniform population. Validation reliabilities were calculated as the squared correlation between DRP and DGV (r2DRP, DGV), corrected by the mean reliability ofDRP. Using the breed-specific model increased the reliability of DGV by 2% and 3% for milk and protein, respectively, when compared to homogeneous population GBLUP model. The exception was for fat, where there was no gain in reliability. Estimated validation reliabilities were low for milk (0.32) and protein (0.32) and slightly higher (0.42) for fat.

Genomic prediction for Nordic Red Cattle using one-step and selection index blending

This study investigated the accuracy of direct genomic breeding values (DGV) using a genomic BLUP model, genomic enhanced breeding values (GEBV) using a one-step blending approach, and GEBV using a selection index blending approach for 15 traits of Nordic Red Cattle. The data comprised 6,631 bulls of which 4,408 bulls were genotyped using Illumina Bovine SNP50 BeadChip (Illumina, San Diego, CA). To validate reliability of genomic predictions, about 20% of the youngest genotyped bulls were taken as test data set. Deregressed proofs (DRP) were used as response variables for genomic predictions. Reliabilities of genomic predictions in the validation analyses were measured as squared correlations between DRP and genomic predictions corrected for reliability of DRP, based on the bulls in the test data sets. A set of weighting (scaling) factors was used to construct the combined relationship matrix among genotyped and nongenotyped bulls for one-step blending, and to scale DGV and its expected reliability in the selection index blending. Weighting (scaling) factors had a small influence on reliabilities of GEBV, but a large influence on the variation of GEBV. Based on the validation analyses, averaged over the 15 traits, the reliability of DGV for bulls without daughter records was 11.0 percentage points higher than the reliability of conventional pedigree index. Further gain of 0.9 percentage points was achieved by combining information from conventional pedigree index using the selection index blending, and gain of 1.3 percentage points was achieved by combining information of genotyped and nongenotyped bulls simultaneously applying the one-step blending. These results indicate that genomic selection can greatly improve the accuracy of preselection for young bulls in Nordic Red population, and the one-step blending approach is a good alternative to predict GEBV in practical genetic evaluation program.

Reliabilities of genomic estimated breeding values in Danish Jersey

In order to optimize the use of genomic selection in breeding plans, it is essential to have reliable estimates of the genomic breeding values. This study investigated reliabilities of direct genomic values (DGVs) in the Jersey population estimated by three different methods. The validation methods were (i) fivefold cross-validation and (ii) validation on the most recent 3 years of bulls. The reliability of DGV was assessed using squared correlations between DGV and deregressed proofs (DRPs). In the recent 3-year validation model, estimated reliabilities were also used to assess the reliabilities of DGV. The data set consisted of 1003 Danish Jersey bulls with conventional estimated breeding values (EBVs) for 14 different traits included in the Nordic selection index. The bulls were genotyped for Single-nucleotide polymorphism (SNP) markers using the Illumina 54 K chip. A Bayesian method was used to estimate the SNP marker effects. The corrected squared correlations between DGV and DRP were on average across all traits 0.04 higher than the squared correlation between DRP and the pedigree index. This shows that there is a gain in accuracy due to incorporation of marker information compared with parent index pre-selection only. Averaged across traits, the estimates of reliability of DGVs ranged from 0.20 for validation on the most recent 3 years of bulls and up to 0.42 for expected reliabilities. Reliabilities from the cross-validation were on average 0.24. For the individual traits, the reliability varied from 0.12 (direct birth) to 0.39 (milk). Bulls whose sires were included in the reference group had an average reliability of 0.25, whereas the bulls whose sires were not included in the reference group had an average reliability that was 0.05 lower.

QTL detection from regression analysis of ‘generalized de‐regressed proof’ information

QTL detection using the regression of phenotypes on transmission probability is largely used when large families are available. In three generations designs, the use of a 'de-regressed proof' as a phenotype to be analysed was proposed by Weller et al. (1990) and Tribout et al. (2008). Our work generalizes this approach. A score (that we define as a 'generalized de-regressed proof') is described, which combines performance phenotypes recorded in multigenerational offspring of genotyped individuals. Estimation of the QTL effect on this score with a simple regression is unbiased. The link between this score and the BLUP animal model of the polygenic effect is demonstrated. The theory is developed and two simple examples illustrate how this technique can be implemented.

Investigation of three strategies for an international genetic evaluation of beef cattle weaning weight

Weaning weights from 83 389 Limousin calves born between 1993 and 2002 in France and the Trans-Tasman block (Australia/New Zealand) were analysed to compare different strategies for running an international genetic evaluation for the breed. These records were a subset of the complete data for both countries and comprised a sample of herds that had recorded progeny of sires used across both countries. Genetic and phenotypic parameters for weaning weight were estimated within the countries. The estimates of direct genetic heritabilities were higher in France than in the Trans-Tasman block (0.31 vs. 0.22), while direct-maternal genetic correlations were less negative in the Trans-Tasman block (-0.10) than in France (-0.21). Different strategies for an international evaluation were studied, and the correlations between the estimated breeding values (EBV) of national evaluations and these strategies were derived. The international evaluation strategies were a) an animal model on raw performance data with non unity genetic correlations and heterogeneous residual and genetic variances across countries; b) the same animal model applied to pre-corrected (for fixed effects) performance data; and c) a sire model on de-regressed proofs (MACE). Estimates of the genetic correlations between weaning weight in both countries were 0.86 (0.80) for direct (maternal) genetic effects for the first strategy. Estimation of variance components by MACE appeared to be very sensitive to the sample of bulls and their reliability approximations. Variance component estimates obtained using pre-corrected data were inconsistent with estimates on raw data. However, the EBV predicted using pre-corrected data and parameters estimated from the raw data were similar to those predicted from raw data. Correlations between national and international EBV were always high (> 0.90) for sires, whichever genetic effect (direct or maternal) or international evaluation model was considered. The ranking of the bulls in the top 100 is of primary interest in terms of international genetic evaluation. In this study, some re-ranking of sires was observed for the top 100 bulls between countries and between the three international evaluation models. Thus, the origin of top sires may vary according to the implemented international evaluation strategy.

Comparison of estimated breeding values, daughter yield deviations and de‐regressed proofs within a whole genome scan for QTL

An important issue in quantitative trait loci (QTL) detection is the use of phenotypic measurement as a dependent variable. Daughter yield deviations (DYDs) as the unit of choice are not available for all traits of interest. The use of de‐regressed proofs (DRPFs) of estimated breeding values (EBVs) is an alternative to using daughter yield deviations. The objective of this study was to examine possible differences between DYDs and DRPFs within the use of QTL detection. The pedigree used was part of the granddaughter design of the German QTL effort. Consisting marker maps for livestock species were derived from all available data of 16 German Holstein paternal half‐sib families with a total of 872 sires. The number of progeny ranged from 19 to 127. A whole genome scan was performed using weighted and unweighted multimarker regression with DYDs, DRPFs and EBVs as dependent variables for the traits milk, fat and protein yields. Results were compared with respect to the number of QTL detected. A similar number of QTL was detected with DRPFs and DYDs. Also, when dependent variables were weighted according to the variance of the trait, a higher number of QTL was detected at the desired level of significance as compared to using unweighted variables.

Dependent Variables in International Sire Evaluations

Abstract Stochastic simulation was used to assess the suitability of alternative dependent variables in international sire evaluation. Three such variables were considered: daughter yield deviations (DYD), national proofs (ETA), and de-regressed national proofs (DPRF). Data from two dairy cattle populations considering 10 generations were simulated. Genetic ties necessary for a joint evaluation of the two populations were established with bull exchange in each generation. De-regressed national proofs were the best and ETA were the worst in estimating genetic difference between the two populations and ranking bulls across country. Further, de-regressed national proofs can be easily computed and, contrary to DYD, are always available. De-regressed national proofs are recommended as dependent variables in across country sire evaluation.