Practical implementation of genetic groups in single-step genomic evaluations with Woodbury matrix identity-based genomic relationship inverse.

The growing amount of genomic information in dairy cattle has increased computational and modeling challenges in the single-step evaluations. The computational challenges are due to the dense inverses of genomic (G) and pedigree (A22) relationship matrices of genotyped animals in the single-step mixed model equations. An equivalent mixed model equation is given by single-step genomic BLUP that are based on the T matrix (ssGTBLUP), where these inverses are avoided by expressing G-1 through a product of 2 rectangular matrices, and (A22)-1 through sparse matrix blocks of the inverse of full relationship matrix A-1. A proper way to account genetic groups through unknown parent groups (UPG) after the Quaas-Pollak transformation (QP) is one key factor in a single-step model. When the UPG effects are incompletely accounted, the iterative solving method may have convergence problems. In this study, we investigated computational and predictive performance of ssGTBLUP with residual polygenic (RPG) effect and UPG. The QP transformation used A-1 and, in the complete form, T and (A22)-1 matrices as well. The models were tested with official Nordic Holstein milk production test-day data and model. The results show that UPG can be easily implemented in ssGTBLUP having RPG. The complete QP transformation was computationally feasible when preconditioned conjugate gradient iteration and iteration on data without explicitly setting up G or A22 matrices were used. Furthermore, for good convergence of the preconditioned conjugate gradient method, a complete QP transformation was necessary.

Metafounder approach for single-step genomic evaluations of Red Dairy cattle.

Single-step genomic BLUP (ssGBLUP) is a powerful approach for breeding value prediction in populations with a limited number of genotyped animals. However, conflicting genomic (G) and pedigree (A22) relationship matrices complicate the implementation of ssGBLUP into practice. The metafounder (MF) approach is a recently proposed solution for this problem and has been successfully used on simulated and real multi-breed pig data. Advantages of the method are easily seen across breed evaluations, where pedigrees are traced to several pure breeds, which are thereafter used as MF. Application of the MF method to ruminants is complicated due to multi-breed pedigree structures and the inability to transmit existing unknown parent groups (UPG) to MF. In this study, we apply the MF approach for ssGBLUP evaluation of Finnish Red Dairy cattle treated as a single breed. Relationships among MF were accounted for by a (co)variance matrix (Γ) computed using estimated base population allele frequencies. The attained Γ was used to calculate a relationship matrix A22Γ for the genotyped animals. We tested the influence of SNP selection on the Γ matrix by applying a minor allele frequency (MAF) threshold (ΓMAF) where accepted markers had an MAF ≥0.05. Elements in the ΓMAF matrix were slightly lower than in the Γ matrix. Correlation between diagonal elements of the genomic and pedigree relationship matrices increased from 0.53 (A22) to 0.76 ( A22Γ and [Formula: see text] ). Average diagonal elements of A22Γ and [Formula: see text] matrices increased to the same level as in the G matrix. The ssGBLUP breeding values (GEBV) were solved using either the original 236 or redefined 8 UPG, or 8 MF computed with or without the MAF threshold. For bulls, the GEBV validation test results for the 8 UPG and 8 MF gave the same validation reliability (R2; 0.31) and over-dispersion (0.73, measured by regression coefficient b1). No significant R2 increase was observed in cows. Thus, the MF greatly influenced the pedigree relationship matrices but not the GEBV. Selection of SNP according to MAF had a notable effect on the Γ matrix and made the A22 and G matrices more similar.

Short communication: Multivariate outlier detection for routine Nordic dairy cattle genetic evaluation in the Nordic Holstein and Red population.

It is of practical importance to ensure the data quality from a milk-recording system before use for genetic evaluation. A procedure was developed for detection of multivariate outliers based on an approximation for Mahalanobis distance and was implemented in the Nordic Holstein and Red population. The general target of this procedure is based on the Nordic Cattle Genetic Evaluation yield model, which is a 9-trait model for milk, protein, and fat in the first 3 lactations. The procedure is based on the phenotypic correlation structure as a function of days in milk (DIM) and on computation of trait means and standard deviations within a production year, lactation, and DIM. For each record in the data, a Mahalanobis distance value was computed based on the trait mean and the covariance matrix for the actual production year, lactation, and DIM. A set of cutoff values, ranging from 10 to 100 with steps of 10, for discarding multivariate outliers was investigated. Prediction accuracy was calculated as the Pearson correlations between estimated breeding values predicted by full data set and estimated breeding values predicted by reduced data set for cows without records in the reduced data set and with 1 or more records deleted due to the editing rules on Mahalanobis distance. The results showed that, averaged over all scenarios, gains of 0.005 to 0.048 on prediction accuracy have been obtained by deleting the multivariate outliers. The improvements were more profound for progeny of young bulls compared with progeny of proven bulls. It is easy to implement this multivariate outlier-detection procedure in the routine genetic evaluation for different dairy cattle breeds; however, an optimal cutoff value for Mahalanobis distance needs to be defined to achieve an acceptable compromise between genetic evaluation accuracy and data deletion.

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

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

Reducing bias in the dairy cattle single-step genomic evaluation by ignoring bulls without progeny.

The number of genotyped animals has increased rapidly creating computational challenges for genomic evaluation. In animal model BLUP, candidate animals without progeny and phenotype do not contribute information to the evaluation and can be discarded. In theory, genotyped candidate animal without progeny can bring information into single-step BLUP (ssGBLUP) and affect the estimation of other breeding values. We studied the effect of including or excluding genomic information of culled bull calves on genomic breeding values (GEBV) from ssGBLUP. In particular, GEBVs of genotyped bulls with daughters and GEBVs of young bulls selected into AI to be progeny tested (test bulls) were studied. The ssGBLUP evaluation was computed using Nordic test day (TD) model and TD data for the Nordic Red Dairy Cattle. The results indicate that genomic information of culled bull calves does not affect the GEBVs of progeny tested reference animals, but if genotypes of the culled bulls are used in the TD ssGBLUP, the genetic trend in the test bulls is considerably higher compared to the situation when genomic information of the culled bull calves is excluded. It seems that by discarding genomic information of culled bull calves without progeny, upward bias of GEBVs of test bulls is reduced.

Detection of evaluation bias caused by genomic preselection.

The aim of this simulation study was to investigate whether it is possible to detect the effect of genomic preselection on Mendelian sampling (MS) means or variances obtained by the MS validation test. Genomic preselection of bull calves is 1 additional potential source of bias in international evaluations unless adequately accounted for in national evaluations. Selection creates no bias in traditional breeding value evaluation if the data of all animals are included. However, this is not the case with genomic preselection, as it excludes culled bulls. Genomic breeding values become biased if calculated using a multistep procedure instead of, for example, a single-step method. Currently, about 60% of the countries participating in international bull evaluations have already adopted genomic selection in their breeding schemes. The data sent for multiple across-country evaluation can, therefore, be very heterogeneous, and a proper validation method is needed to ensure a fair comparison of the bulls included in international genetic evaluations. To study the effect of genomic preselection, we generated a total of 50 replicates under control and genomic preselection schemes using the structures of the real data and pedigree from a medium-size cow population. A genetic trend of 15% of the genetic standard deviation was created for both schemes. In carrying out the analyses, we used 2 different heritabilities: 0.25 and 0.10. From the start of genomic preselection, all bulls were genomically preselected. Their MS deviations were inflated with a value corresponding to selection of the best 10% of genomically tested bull calves. For cows, the MS deviations were unaltered. The results revealed a clear underestimation of bulls' breeding values (BV) after genomic preselection started, as well as a notable deviation from zero both in true and estimated MS means. The software developed recently for the MS validation test already produces yearly MS means, and they can be used to devise an appropriate test. Mean squared true MS of genomically preselected bulls was clearly inflated. After correcting for the simulated preselection bias, the true genetic variance was smaller than the parametric value used to simulate BV, and also below the variance based on the estimated BV. Based on this study, the lower the trait's heritability, the stronger the bias in estimated BV and MS means and variances. Daughters of genomically preselected bulls had higher true and estimated BV compared with the control scheme and only slightly elevated MS means, but no effect on genetic variances was observed.

Validation of consistency of Mendelian sampling variance.

Experiences from international sire evaluation indicate that the multiple-trait across-country evaluation method is sensitive to changes in genetic variance over time. Top bulls from birth year classes with inflated genetic variance will benefit, hampering reliable ranking of bulls. However, none of the methods available today enable countries to validate their national evaluation models for heterogeneity of genetic variance. We describe a new validation method to fill this gap comprising the following steps: estimating within-year genetic variances using Mendelian sampling and its prediction error variance, fitting a weighted linear regression between the estimates and the years under study, identifying possible outliers, and defining a 95% empirical confidence interval for a possible trend in the estimates. We tested the specificity and sensitivity of the proposed validation method with simulated data using a real data structure. Moderate (M) and small (S) size populations were simulated under 3 scenarios: a control with homogeneous variance and 2 scenarios with yearly increases in phenotypic variance of 2 and 10%, respectively. Results showed that the new method was able to estimate genetic variance accurately enough to detect bias in genetic variance. Under the control scenario, the trend in genetic variance was practically zero in setting M. Testing cows with an average birth year class size of more than 43,000 in setting M showed that tolerance values are needed for both the trend and the outlier tests to detect only cases with a practical effect in larger data sets. Regardless of the magnitude (yearly increases in phenotypic variance of 2 or 10%) of the generated trend, it deviated statistically significantly from zero in all data replicates for both cows and bulls in setting M. In setting S with a mean of 27 bulls in a year class, the sampling error and thus the probability of a false-positive result clearly increased. Still, overall estimated genetic variance was close to the parametric value. Only rather strong trends in genetic variance deviated statistically significantly from zero in setting S. Results also showed that the new method was sensitive to the quality of the approximated reliabilities of breeding values used in calculating the prediction error variance. Thus, we recommend that only animals with a reliability of Mendelian sampling higher than 0.1 be included in the test and that low heritability traits be analyzed using bull data sets only.

Solving efficiently large single-step genomic best linear unbiased prediction models.

Single-step genomic BLUP (ssGBLUP) requires a dense matrix of the size equal to the number of genotyped animals in the coefficient matrix of mixed model equations (MME). When the number of genotyped animals is high, solving time of MME will be dominated by this matrix. The matrix is the difference of two inverse relationship matrices: genomic (G) and pedigree (A22 ). Different approaches were used to ease computations, reduce computing time and improve numerical stability. Inverse of A22 can be computed as A22-1=A22-A21A11-1A12 where Aij , i, j = 1,2, are sparse sub-matrices of A-1 , and numbers 1 and 2 refer to non-genotyped and genotyped animals, respectively. Inversion of A11 was avoided by three alternative approaches: iteration on pedigree (IOP), matrix iteration in memory (IM), and Cholesky decomposition by CHOLMOD library (CM). For the inverse of G, the APY (algorithm for proven and young) approach using Cholesky decomposition was formulated. Different approaches to choose the APY core were compared. These approaches were tested on a joint genetic evaluation of the Nordic Holstein cattle for fertility traits and had 81,031 genotyped animals. Computing time per iteration was 1.19 min by regular ssGBLUP, 1.49 min by IOP, 1.32 min by IM, and 1.21 min by CM. In comparison with the regular ssGBLUP, the total computing time decreased due to omitting the inversion of the relationship matrix A22 . When APY used 10,000 (20,000) animals in the core, the computing time per iteration was at most 0.44 (0.63) min by all the APY alternatives. A core of 10,000 animals in APY gave GEBVs sufficiently close to those by regular ssGBLUP but needed only 25% of the total computing time. The developed approaches to invert the two relationship matrices are expected to allow much higher number of genotyped animals than was used in this study.

Effect of cow reference group on validation reliability of genomic evaluation.

We studied the effect of including genomic data for cows in the reference population of single-step evaluations. Deregressed individual cow genetic evaluations (DRP) from milk production evaluations of Nordic Red Dairy cattle were used to estimate the single-step breeding values. Validation reliability and bias of the evaluations were calculated with four data sets including different amount of DRP record information from genotyped cows in the reference population. The gain in reliability was from 2% to 4% units for the production traits, depending on the used DRP data and the amount of genomic data. Moreover, inclusion of genotyped bull dams and their genotyped daughters seemed to create some bias in the single-step evaluation. Still, genotyping cows and their inclusion in the reference population is advantageous and should be encouraged.

Sharing reference data and including cows in the reference population improve genomic predictions in Danish Jersey.

Small reference populations limit the accuracy of genomic prediction in numerically small breeds, such like Danish Jersey. The objective of this study was to investigate two approaches to improve genomic prediction by increasing size of reference population in Danish Jersey. The first approach was to include North American Jersey bulls in Danish Jersey reference population. The second was to genotype cows and use them as reference animals. The validation of genomic prediction was carried out on bulls and cows, respectively. In validation on bulls, about 300 Danish bulls (depending on traits) born in 2005 and later were used as validation data, and the reference populations were: (1) about 1050 Danish bulls, (2) about 1050 Danish bulls and about 1150 US bulls. In validation on cows, about 3000 Danish cows from 87 young half-sib families were used as validation data, and the reference populations were: (1) about 1250 Danish bulls, (2) about 1250 Danish bulls and about 1150 US bulls, (3) about 1250 Danish bulls and about 4800 cows, (4) about 1250 Danish bulls, 1150 US bulls and 4800 Danish cows. Genomic best linear unbiased prediction model was used to predict breeding values. De-regressed proofs were used as response variables. In the validation on bulls for eight traits, the joint DK-US bull reference population led to higher reliability of genomic prediction than the DK bull reference population for six traits, but not for fertility and longevity. Averaged over the eight traits, the gain was 3 percentage points. In the validation on cows for six traits (fertility and longevity were not available), the gain from inclusion of US bull in reference population was 6.6 percentage points in average over the six traits, and the gain from inclusion of cows was 8.2 percentage points. However, the gains from cows and US bulls were not accumulative. The total gain of including both US bulls and Danish cows was 10.5 percentage points. The results indicate that sharing reference data and including cows in reference population are efficient approaches to increase reliability of genomic prediction. Therefore, genomic selection is promising for numerically small population.

Single-step genomic model improved reliability and reduced the bias of genomic predictions in Danish Jersey.

A bias in the trend of genomic estimated breeding values (GEBV) was observed in the Danish Jersey population where the trend of GEBV was smaller than the deregressed proofs for individuals in the validation population. This study attempted to improve the prediction reliability and reduce the bias of predicted genetic trend in Danish Jersey. The data consisted of 1,238 Danish Jersey bulls and 611,695 cows. All bulls were genotyped with the 54K chip, and 1,744 cows were genotyped with either 7K chips (1,157 individuals) or 54K chips (587 individuals). The trait used in the analysis was protein yield. All cows with EBV were used in a single-step approach. Deregressed proofs were used as the response variable. Four alternative approaches were compared with genomic best linear unbiased prediction (GBLUP) model with bulls in the reference data (GBLUPBull): (1) GBLUP with both bulls and genotyped cows in the reference data; (2) GBLUP including a year of birth effect; (3) GEBV from a GBLUP model that accounted for the difference of EBV between dams and maternal grandsires; and (4) using a single-step approach. The results indicated all 4 alternatives could reduce the bias of predicted genetic trend and that the single-step approach performed best. However, not all these approaches improved reliability or reduced inflation of GEBV. The reliability was 0.30 and regression coefficients of deregressed proofs on GEBV were 0.69 in the scenario GBLUPBull. When genotyped cows were included in the reference population, the regression coefficients decreased to 0.59 but the reliability increased to 0.35. If a year effect was included in the model, the prediction reliability decreased to 0.29 and the regression coefficient improved to 0.75. The method in which GEBV were adjusted for the difference between dam EBV and maternal grandsire EBV led to much lower regression coefficients though the reliability increased to 0.4. The single-step approach improved both the reliability, to 0.38 and regression coefficient to 0.78. Therefore, the bias in genetic trend was reduced. The results suggest that implementing the single-step approach is an effective way to improve genomic prediction in Danish Jersey cattle.

Including different groups of genotyped females for genomic prediction in a Nordic Jersey population.

Including genotyped females in a reference population (RP) is an obvious way to increase the RP in genomic selection, especially for dairy breeds of limited population size. However, the incorporation of these females must be conducted cautiously because of the potential preferential treatment of the genotyped cows and lower reliabilities of phenotypes compared with the proven pseudo-phenotypes of bulls. Breeding organizations in Denmark, Finland, and Sweden have implemented a female-genotyping project with the possibility of genotyping entire herds using the low-density (LD) chip. In the present study, 5 scenarios for building an RP were investigated in the Nordic Jersey population: (1) bulls only, (2) bulls with females from the LD project, (3) bulls with females from the LD project plus non-LD project females genotyped before their first calving, (4) bulls with females from the LD project plus non-LD project females genotyped after their first calving, and (5) bulls with all genotyped females. The genomically enhanced breeding value (GEBV) was predicted for 8 traits in the Nordic total merit index through a genomic BLUP model using deregressed proof (DRP) as the response variable in all scenarios. In addition, (daughter) yield deviation and raw phenotypic data were studied as response variables for comparison with the DRP, using stature as a model trait. The validation population was formed using a cut-off birth year of 2005 based on the genotyped Nordic Jersey bulls with DRP. The average increment in reliability of the GEBV across the 8 traits investigated was 1.9 to 4.5 percentage points compared with using only bulls in the RP (scenario 1). The addition of all the genotyped females to the RP resulted in the highest gain in reliability (scenario 5), followed by scenario 3, scenario 2, and scenario 4. All scenarios led to inflated GEBV because the regression coefficients are less than 1. However, scenario 2 and scenario 3 led to less bias of genomic predictions than scenario 5, with regression coefficients showing less deviation from scenario 1. For the study on stature, the daughter yield deviation/daughter yield deviation performed slightly better than the DRP as the response variable in the genomic BLUP (GBLUP) model. Therefore, adding unselected females in the RP could significantly improve the reliabilities and tended to reduce the prediction bias compared with adding selectively genotyped females. Although the DRP has performed robustly so far, the use of raw data is recommended with a single-step model as an optimal solution for future genomic evaluations.

Short communication: Improving accuracy of Jersey genomic evaluations in the United States and Denmark by sharing reference population bulls.

The effect on prediction accuracy for Jersey genomic evaluations of Danish and US bulls from using a larger reference population was assessed. Each country contributed genotypes from 1,157 Jersey bulls to the reference population of the other. Data were separated into reference (US only, Danish only, and combined US-Danish) and validation (US only and Danish only) populations. Depending on trait (milk, fat, and protein yields and component percentages; productive life; somatic cell score; daughter pregnancy rate; 14 conformation traits; and net merit), the US reference population included 2,720 to 4,772 bulls and cows with traditional evaluations as of August 2009; the Danish reference population included 635 to 996 bulls. The US validation population included 442 to 712 bulls that gained a traditional evaluation between August 2009 and December 2013; the Danish validation population included 105 to 196 bulls with multitrait across-country evaluations on the US scale by December 2013. Genomic predicted transmitting abilities (GPTA) were calculated on the US scale using a selection index that combined direct genomic predictions with either traditional predicted transmitting ability for the reference population or traditional parent averages (PA) for the validation population and a traditional evaluation based only on genotyped animals. Reliability for GPTA was estimated from the reference population and August 2009 traditional PA and PA reliability. For prediction of December 2013 deregressed daughter deviations on the US scale, mean August 2009 GPTA reliability for Danish validation bulls was 0.10 higher when based on the combined US-Danish reference population than when the reference population included only Danish bulls; for US validation bulls, mean reliability increased by 0.02 when Danish bulls were added to the US reference population. Exchanging genotype data to increase the size of the reference population is an efficient approach to increasing the accuracy of genomic prediction when the reference population is small.

Single-step genomic evaluation using multitrait random regression model and test-day data.

The objectives of this study were to evaluate the feasibility of use of the test-day (TD) single-step genomic BLUP (ssGBLUP) using phenotypic records of Nordic Red Dairy cows. The critical point in ssGBLUP is how genomically derived relationships (G) are integrated with population-based pedigree relationships (A) into a combined relationship matrix (H). Therefore, we also tested how different weights for genomic and pedigree relationships affect ssGBLUP, validation reliability, and validation regression coefficients. Deregressed proofs for 305-d milk, protein, and fat yields were used for a posteriori validation. The results showed that the use of phenotypic TD records in ssGBLUP is feasible. Moreover, the TD ssGBLUP model gave considerably higher validation reliabilities and validation regression coefficients than the TD model without genomic information. No significant differences were found in validation reliability between the different TD ssGBLUP models according to bootstrap confidence intervals. However, the degree of inflation in genomic enhanced breeding values is affected by the method used in construction of the H matrix. The results showed that ssGBLUP provides a good alternative to the currently used multi-step approach but there is a great need to find the best option to combine pedigree and genomic information in the genomic matrix.

Economic basis for the Nordic Total Merit Index.

Within a group of cooperating countries, all breeding animals are judged according to the same criteria if a joint breeding goal is applied in these countries. This makes it easier for dairy farmers to compare national and foreign elite bulls and may lead to more selection across borders. However, a joint breeding goal is only an advantage if the countries share the same production environment. In this study, we investigated whether the development of a joint breeding goal for each of the major dairy cattle breeds across Denmark, Finland, and Sweden would be an advantage compared with national breeding goals. For that purpose, economic values for all breeding goal traits in the 3 countries were derived, and estimated rank correlations between bulls selected for a national breeding goal and a joint breeding goal were compared. The economic values within country were derived by means of an objective bio-economic model, and the basic situation in each of the 3 production environments was based on an average dairy cattle herd with regard to production system, production level, and management strategy. The common Nordic economic values for each trait were calculated as the average of that specific trait in each of the 3 production environments. Balanced breeding goals were obtained in all situations because the derived economic values for traits related to health, fertility, milk production, and longevity were sizeable. For both Nordic Red Dairy Cattle and Nordic Holstein, the estimated rank correlations between bulls selected for a national breeding goal and a joint breeding goal were very high. Thus, a joint breeding goal within breed is feasible for Denmark, Finland, and Sweden.

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.

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.

Evaluation of the inheritance of the complex vertebral malformation syndrome by breeding studies.

To investigate the congenital complex vertebral malformation syndrome (CVM) in Holstein calves, two breeding studies were performed including 262 and 363 cows, respectively. Cows were selected from the Danish Cattle Database based on pedigree and insemination records. Selected cows were progeny of sires with an established heterozygous CVM genotype and pregnant after insemination with semen from another sire with heterozygous CVM genotype. Following calving the breeders should state, if the calf was normal and was requested to submit dead calves for necropsy. In both studies, significantly fewer CVM affected calves than expected were obtained; a finding probably reflecting extensive intrauterine mortality in CVM affected foetuses. The findings illustrate increased intrauterine mortality as a major potential bias in observational studies of inherited disorders.

Genetic relationship between body condition score, dairy character, mastitis, and diseases other than mastitis in first-parity Danish Holstein cows.

The aim of this study was to explore the possibilities of using body condition score (BCS) or dairy character (DC) as indicators of mastitis and diseases other than mastitis in first-parity Danish Holsteins. The dataset included 28,948 observations on conformation scores and 365,136 disease observations. The analysis was performed using a multitrait linear sire model. Heritability estimates for BCS and DC were moderate (0.25 and 0.22), and heritability estimates for mastitis and diseases other than mastitis were low (0.038 and 0.022). Between BCS and diseases other than mastitis, the genetic correlation was -0.22, whereas the genetic correlation was -0.16 between BCS and mastitis. The genetic correlation between DC and diseases other than mastitis was 0.43, and between DC and mastitis it was 0.27. The genetic correlation between BCS and DC was -0.61. Residual correlations were close to 0, except between BCS and DC (-0.37). Including DC as an indicator of diseases other than mastitis will increase the accuracy of the predicted breeding value for diseases, especially when the progeny group is small. Using BCS as an additional indicator of diseases did not increase the accuracy. Breeding for less DC will increase resistance to diseases.

Genetic analysis of body condition score in first-parity Danish Holstein cows.

The aim of this study was to test whether genetic components for body condition score (BCS) changed during lactation in first-parity Danish Holsteins. Data were extracted from the national conformation scoring system and consisted of 28,948 records from 3894 herds. Cows were scored once during lactation for BCS on a scale from 1 to 9 with increments of 1. The majority of records were made from d 30 to 150 of lactation. Mean BCS was 4.28 +/- 0.98. Body condition score was lowest in wk 8 to 10 from calving. A multivariate sire model with BCS recordings in six lactation stages treated as different traits was used to analyze the data. In addition, a random regression sire model was used to evaluate the changes in BCS as continuous functions of lactation stage. Estimates of heritability from the multivariate approach ranged from 0.14 to 0.29, and the estimated genetic correlations between BCS at different lactation stages were all higher than 0.82. The random regression model was based on Legendre polynomials (LP) specified on days in milk at scoring. To evaluate the change in mean BCS during lactation, the fixed part of the model included a fifth-order LP on the effect of days in milk at scoring. The highest order of fit used for the sire effect was a third-order LP, but based on likelihood ratio tests this could be reduced to a 0 order, i.e., a model with only the intercept term for the sire effect. This means that the genetic variation is constant over the investigated part of the lactation. Therefore, BCS can be considered the same trait during lactation, and a simple sire model can be used for prediction of breeding values.