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.

Weighted single-step genomic best linear unbiased prediction integrating variants selected from sequencing data by association and bioinformatics analyses

Background

Sequencing data enable the detection of causal loci or single nucleotide polymorphisms (SNPs) highly linked to causal loci to improve genomic prediction. However, until now, studies on integrating such SNPs using a single-step genomic best linear unbiased prediction (ssGBLUP) model are scarce. We investigated the integration of sequencing SNPs selected by association (1262 SNPs) and bioinformatics (2359 SNPs) analyses into the currently used 54K-SNP chip, using three ssGBLUP models which make different assumptions on the distribution of SNP effects: a basic ssGBLUP model, a so-called featured ssGBLUP (ssFGBLUP) model that considered selected sequencing SNPs as a feature genetic component, and a weighted ssGBLUP (ssWGBLUP) model in which the genomic relationship matrix was weighted by the SNP variances estimated from a Bayesian whole-genome regression model, with every 1, 30, or 100 adjacent SNPs within a chromosome region sharing the same variance. We used data on milk production and female fertility in Danish Jersey. In total, 15,823 genotyped and 528,981‬ non-genotyped females born between 1990 and 2013 were used as reference population and 7415 genotyped females and 33,040 non-genotyped females born between 2014 and 2016 were used as validation population.

Results

With basic ssGBLUP, integrating SNPs selected from sequencing data improved prediction reliabilities for milk and protein yields, but resulted in limited or no improvement for fat yield and female fertility. Model performances depended on the SNP set used. When using ssWGBLUP with the 54K SNPs, reliabilities for milk and protein yields improved by 0.028 for genotyped animals and by 0.006 for non-genotyped animals compared with ssGBLUP. However, with the SNP set that included SNPs selected from sequencing data, no statistically significant difference in prediction reliability was observed between the three ssGBLUP models.

Conclusions

In summary, when using 54K SNPs, a ssWGBLUP model with a common weight on the SNPs in a given region is a feasible approach for single-trait genetic evaluation. Integrating relevant SNPs selected from sequencing data into the standard SNP chip can improve the reliability of genomic prediction. Based on such SNP data, a basic ssGBLUP model was suggested since no significant improvement was observed from using alternative models such as ssWGBLUP and ssFGBLUP.

Imputation for sequencing variants preselected to a customized low-density chip

The sequencing variants preselected from association analyses and bioinformatics analyses could improve genomic prediction. In this study, the imputation of sequencing SNPs preselected from major dairy breeds in Denmark-Finland-Sweden (DFS) and France (FRA) was investigated for both contemporary animals and old bulls in Danish Jersey. For contemporary animals, a two-step imputation which first imputed to 54 K and then to 54 K + DFS + FRA SNPs achieved highest accuracy. Correlations between observed and imputed genotypes were 91.6% for DFS SNPs and 87.6% for FRA SNPs, while concordance rates were 96.6% for DFS SNPs and 93.5% for FRA SNPs. The SNPs with lower minor allele frequency (MAF) tended to have lower correlations but higher concordance rates. For old bulls, imputation for DFS and FRA SNPs were relatively accurate even for bulls without progenies (correlations higher than 97.2% and concordance rates higher than 98.4%). For contemporary animals, given limited imputation accuracy of preselected sequencing SNPs especially for SNPs with low MAF, it would be a good strategy to directly genotype preselected sequencing SNPs with a customized SNP chip. For old bulls, given high imputation accuracy for preselected sequencing SNPs with all MAF ranges, it would be unnecessary to re-genotype preselected sequencing SNPs.

Bias in estimates of variance components in populations undergoing genomic selection: a simulation study

Background

After the extensive implementation of genomic selection (GS), the choice of the statistical model and data used to estimate variance components (VCs) remains unclear. A primary concern is that VCs estimated from a traditional pedigree-based animal model (P-AM) will be biased due to ignoring the impact of GS. The objectives of this study were to examine the effects of GS on estimates of VC in the analysis of different sets of phenotypes and to investigate VC estimation using different methods. Data were simulated to resemble the Danish Jersey population. The simulation included three phases: (1) a historical phase; (2) 20 years of conventional breeding; and (3) 15 years of GS. The three scenarios based on different sets of phenotypes for VC estimation were as follows: (1) Pheno₁: phenotypes from only the conventional phase (1–20 years); (2) Pheno_1 + 2: phenotypes from both the conventional phase and GS phase (1–35 years); (3) Pheno₂: phenotypes from only the GS phase (21–35 years). Single-step genomic BLUP (ssGBLUP), a single-step Bayesian regression model (ssBR), and P-AM were applied. Two base populations were defined: the first was the founder population referred to by the pedigree-based relationship (P-base); the second was the base population referred to by the current genotyped population (G-base).

Results

In general, both the ssGBLUP and ssBR models with all the phenotypic and genotypic information (Pheno_1 + 2) yielded biased estimates of additive genetic variance compared to the P-base model. When the phenotypes from the conventional breeding phase were excluded (Pheno₂), P-AM led to underestimation of the genetic variance of P-base. Compared to the VCs of G-base, when phenotypes from the conventional breeding phase (Pheno₂) were ignored, the ssBR model yielded unbiased estimates of the total genetic variance and marker-based genetic variance, whereas the residual variance was overestimated.

Conclusions

The results show that neither of the single-step models (ssGBLUP and ssBR) can precisely estimate the VCs for populations undergoing GS. Overall, the best solution for obtaining unbiased estimates of VCs is to use P-AM with phenotypes from the conventional phase or phenotypes from both the conventional and GS phases.

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.

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.

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.

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.

A 660-Kb deletion with antagonistic effects on fertility and milk production segregates at high frequency in Nordic Red cattle: additional evidence for the common occurrence of balancing selection in livestock

In dairy cattle, the widespread use of artificial insemination has resulted in increased selection intensity, which has led to spectacular increase in productivity. However, cow fertility has concomitantly severely declined. It is generally assumed that this reduction is primarily due to the negative energy balance of high-producing cows at the peak of lactation. We herein describe the fine-mapping of a major fertility QTL in Nordic Red cattle, and identify a 660-kb deletion encompassing four genes as the causative variant. We show that the deletion is a recessive embryonically lethal mutation. This probably results from the loss of RNASEH2B, which is known to cause embryonic death in mice. Despite its dramatic effect on fertility, 13%, 23% and 32% of the animals carry the deletion in Danish, Swedish and Finnish Red Cattle, respectively. To explain this, we searched for favorable effects on other traits and found that the deletion has strong positive effects on milk yield. This study demonstrates that embryonic lethal mutations account for a non-negligible fraction of the decline in fertility of domestic cattle, and that associated positive effects on milk yield may account for part of the negative genetic correlation. Our study adds to the evidence that structural variants contribute to animal phenotypic variation, and that balancing selection might be more common in livestock species than previously appreciated.

We report the identification of a large deletion encompassing four genes and the demonstration of its negative effect on fertility in Nordic Red dairy cattle. We show that this deletion is recessively lethal (homozygous embryos die) and therefore, when carrier cows are mated to carrier bulls, there is a high risk of embryonic mortality. As a result, chances of insemination failure are higher for such matings. Surprisingly, despite its negative effect, the deletion is frequent in Nordic Red cattle. We show that this high frequency may be a consequence of the fact that the deletion is associated with increased milk production and therefore selected for. Due to increased levels of inbreeding resulting from the widespread use of artificial insemination, such recessive lethal alleles may account for a non-negligible fraction of the reduction in fertility observed in cattle.

Novel harmful recessive haplotypes identified for fertility traits in Nordic Holstein cattle

Using genomic data, lethal recessives may be discovered from haplotypes that are common in the population but never occur in the homozygote state in live animals. This approach only requires genotype data from phenotypically normal (i.e. live) individuals and not from the affected embryos that die. A total of 7,937 Nordic Holstein animals were genotyped with BovineSNP50 BeadChip and haplotypes including 25 consecutive markers were constructed and tested for absence of homozygotes states. We have identified 17 homozygote deficient haplotypes which could be loosely clustered into eight genomic regions harboring possible recessive lethal alleles. Effects of the identified haplotypes were estimated on two fertility traits: non-return rates and calving interval. Out of the eight identified genomic regions, six regions were confirmed as having an effect on fertility. The information can be used to avoid carrier-by-carrier mattings in practical animal breeding. Further, identification of causative genes/polymorphisms responsible for lethal effects will lead to accurate testing of the individuals carrying a lethal allele.

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 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.

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.