Nonparallel genome changes within subpopulations over time contributed to genetic diversity within the US Holstein population.

Maintaining genetic variation in a population is important for long-term genetic gain. The existence of subpopulations within a breed helps maintain genetic variation and diversity. The 20,990 genotyped animals, representing the breeding animals in the year 2014, were identified as the sires of animals born after 2010 with at least 25 progenies, and females measured for type traits within the last 2 yr of data. K-means clustering with 5 clusters (C1, C2, C3, C4, and C5) was applied to the genomic relationship matrix based on 58,990 SNP markers to stratify the selected candidates into subpopulations. The general higher inbreeding resulting from within-cluster mating than across-cluster mating suggests the successful stratification into genetically different groups. The largest cluster (C4) contained animals that were less related to each animal within and across clusters. The average fixation index was 0.03, indicating that the populations were differentiated, and allele differences across the subpopulations were not due to drift alone. Starting with the selected candidates within each cluster, a family unit was identified by tracing back through the pedigree, identifying the genotyped ancestors, and assigning them to a pseudogeneration. Each of the 5 families (F1, F2, F3, F4, and F5) was traced back for 10 generations, allowing for changes in frequency of individual SNPs over time to be observed, which we call allele frequencies change. Alternative procedures were used to identify SNPs changing in a parallel or nonparallel way across families. For example, markers that have changed the most in the whole population, markers that have changed differently across families, and genes previously identified as those that have changed in allele frequency. The genomic trajectory taken by each family involves selective sweeps, polygenic changes, hitchhiking, and epistasis. The replicate frequency spectrum was used to measure the similarity of change across families and showed that populations have changed differently. The proportion of markers that reversed direction in allele frequency change varied from 0.00 to 0.02 if the rate of change was greater than 0.02 per generation, or from 0.14 to 0.24 if the rate of change was greater than 0.005 per generation within each family. Cluster-specific SNP effects for stature were estimated using only females and applied to obtain indirect genomic predictions for males. Reranking occurs depending on SNP effects used. Additive genetic correlations between clusters show possible differences in populations. Further research is required to determine how this knowledge can be applied to maintain diversity and optimize selection decisions in the future.

Identifying influential sires and distinct clusters of selection candidates based on genomic relationships to reduce inbreeding in the US Holstein.

High relatedness in the US Holstein breed can be attributed to the increased rate of inbreeding that resulted from strong selection and the extensive use of a few bulls via reproductive biotechnology. The objectives of this study were to determine whether clustering could separate selected candidates into genetically different groups and whether such clustering could reduce the expected inbreeding of the next generation. A genomic relationship matrix composed of 1,145 sires with the most registered progeny in the breed born after 1985 was used for principal component analysis and k-means clustering. The 5 clusters reduced the variance by 25% and contained 171 (C1), 252 (C2), 200 (C3), 244 (C4), and 278 (C5) animals, respectively. The 2 most predominant families were C1 and C2, while C4 contained the most international animals. On average, C1 and C5 contained older animals; the average birth year per cluster was 1988 (C1), 1996 (C2 and C3), 1999 (C4), and 1990 (C5). Increasing to 10 clusters allowed the separation of the predominant sons. Statistically significant differences were observed for indices (net merit index, cheese merit index, and fluid merit index), daughter pregnancy rate, and production traits (milk, fat, and protein), with older clusters having lower merit for production but higher for reproduction. K-means clustering was also used for 20,099 animals considered as selection candidates. Based on the reduction in variance achieved by clustering, 5 to 7 clusters were appropriate. The number of animals in each cluster was 3,577 (C1), 3,073 (C2), 3,302 (C3), 5,931 (C4), and 4,216 (C5). The expected inbreeding from within or across cluster mating was calculated using the complete pedigree, assuming the mean inbreeding of animals born in the same year when parents are unknown. Generally, inbreeding was highest within cluster mating and lowest across cluster mating. Even when 10 clusters were used, one cluster always gave low inbreeding in all scenarios. This suggests that this cluster contains animals that differ from all other groups but still contains enough diversity within itself. Based on lower across cluster inbreeding, up to 7 clusters were appropriate. Statistically significant differences in genomic estimated breeding values were found between clusters. The rankings of clusters for different traits were mostly the same except for reproduction and fat. Results show that diversity within the population exists and clustering of selection candidates can reduce the expected inbreeding of the next generations.

Bias in genomic predictions by mating practices for linear type traits in a large-scale genomic evaluation.

The objective of this study was to clarify how bias in genomic predictions is created by investigating a relationship among selection intensity, a change in heritability (Δh2), and assortative mating (ASM). A change in heritability, resulting from selection, reflects the impact that the Bulmer effect has on the reduction in between-family variation, whereas assortative mating impacts the within-family variance or Mendelian sampling variation. A partial data set up to 2014, including 841K genotyped animals, was used to calculate genomic predictions with a single-step genomic model for 18 linear type traits in US Holsteins. A full data set up to 2018, including 2.3 million genotyped animals, was used to calculate benchmark genomic predictions. Inbreeding and unknown parent groups for missing parents of animals were included in the model. Genomic evaluation was performed using 2 different genetic parameters: those estimated 14 yr ago, which have been used in the national genetic evaluation for linear type traits in the United States, and those newly estimated with recent records from 2015 to 2018 and those corresponding pedigrees. Genetic trends for 18 type traits were estimated for bulls with daughters and cows with phenotypes in 2018. Based on selection intensity and mating decisions, these traits can be categorized into 3 groups: (a) high directional selection, (b) moderate selection, and (c) intermediate optimum selection. The first 2 categories can be explained by positive assortative mating, and the last can be explained by negative assortative or disassortative mating. Genetic progress was defined by genetic gain per year based on average standardized genomic predictions for cows from 2000 to 2014. Traits with more genetic progress tended to have more "inflated" genomic predictions (i.e., "inflation" means here that genomic predictions are larger in absolute values than expected, whereas "deflation" means smaller than expected). Heritability estimates for 14 out of 18 traits declined in the last 16 yr, and Δh2 ranged from -0.09 to 0.04. Traits with a greater decline in heritability tended to have more deflated genomic predictions. Biases (inflation or deflation) in genomic predictions were not improved by using the latest genetic parameters, implying that bias in genomic predictions due to preselection was not substantial for a large-scale genomic evaluation. Moreover, the strong selection intensity was not fully responsible for bias in genomic predictions. The directional selection can decrease heritability; however, positive assortative mating, which was strongly associated with large genetic gains, could minimize the decline in heritability for a trait under strong selection and could affect bias in genomic predictions.

Controlling bias in genomic breeding values for young genotyped bulls.

The objectives of this study were to investigate bias in genomic predictions for dairy cattle and to find a practical approach to reduce the bias. The simulated data included phenotypes, pedigrees, and genotypes, mimicking a dairy cattle population (i.e., cows with phenotypes and bulls with no phenotypes) and assuming selection by breeding values or no selection. With the simulated data, genomic estimated breeding values (GEBV) were calculated with a single-step genomic BLUP and compared with true breeding values. Phenotypes and genotypes were simulated in 10 generations and in the last 4 generations, respectively. Phenotypes in the last generation were removed to predict breeding values for those individuals using only genomic and pedigree information. Complete pedigrees and incomplete pedigrees with 50% missing dams were created to construct the pedigree-based relationship matrix with and without inbreeding. With missing dams, unknown parent groups (UPG) were assigned in relationship matrices. Regression coefficients (b1) and coefficients of determination (R2) of true breeding values on (G)EBV were calculated to investigate inflation and accuracy in GEBV for genotyped animals, respectively. In addition to the simulation study, 18 linear type traits of US Holsteins were examined. For the 18 type traits, b1 and R2 of GEBV with full data sets on GEBV with partial data sets for young genotyped bulls were calculated. The results from the simulation study indicated inflation in GEBV for genotyped males that were evaluated with only pedigree and genomic information under BLUP selection. However, when UPG for only pedigree-based relationships were included, the inflation was reduced, accuracy was highest, and genetic trends had no bias. For the linear type traits, when UPG for only pedigree-based relationships were included, the results were generally in agreement with those from the simulation study, implying less bias in genetic trends. However, when including no UPG, UPG in pedigree-based relationships, or UPG in genomic relationships, inflation and accuracy in GEBV were similar. The results from the simulation and type traits suggest that UPG must be defined accurately to be estimable and inbreeding should be included in pedigree-based relationships. In dairy cattle, known pedigree information with inbreeding and estimable UPG plays an important role in improving compatibility between pedigree-based and genomic relationship matrices, resulting in more reliable genomic predictions.

Variance of gametic diversity and its application in selection programs.

The variance of gametic diversity ( σgamete2) can be used to find individuals that more likely produce progeny with extreme breeding values. The aim of this study was to obtain this variance for individuals from routine genomic evaluations, and to apply gametic variance in a selection criterion in conjunction with breeding values to improve genetic progress. An analytical approach was developed to estimate σgamete2 by the sum of binomial variances of all individual quantitative trait loci across the genome. Simulation was used to verify the predictability of this variance in a range of scenarios. The accuracy of prediction ranged from 0.49 to 0.85, depending on the scenario and model used. Compared with sequence data, SNP data are sufficient for estimating σgamete2 Results also suggested that markers with low minor allele frequency and the covariance between markers should be included in the estimation. To incorporate σgamete2 into selective breeding programs, we proposed a new index, relative predicted transmitting ability, which better utilizes the genetic potential of individuals than traditional predicted transmitting ability. Simulation with a small genome showed an additional genetic gain of up to 16% in 10 generations, depending on the number of quantitative trait loci and selection intensity. Finally, we applied σgamete2 to the US genomic evaluations for Holstein and Jersey cattle. As expected, the DGAT1 gene had a strong effect on the estimation of σgamete2 for several production traits. However, inbreeding had a small impact on gametic variability, with greater effect for more polygenic traits. In conclusion, gametic variance, a potentially important parameter for selection programs, can be easily computed and is useful for improving genetic progress and controlling genetic diversity.

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.

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

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

Implementation of genomic recursions in single-step genomic best linear unbiased predictor for US Holsteins with a large number of genotyped animals.

The objectives of this study were to develop and evaluate an efficient implementation in the computation of the inverse of genomic relationship matrix with the recursion algorithm, called the algorithm for proven and young (APY), in single-step genomic BLUP. We validated genomic predictions for young bulls with more than 500,000 genotyped animals in final score for US Holsteins. Phenotypic data included 11,626,576 final scores on 7,093,380 US Holstein cows, and genotypes were available for 569,404 animals. Daughter deviations for young bulls with no classified daughters in 2009, but at least 30 classified daughters in 2014 were computed using all the phenotypic data. Genomic predictions for the same bulls were calculated with single-step genomic BLUP using phenotypes up to 2009. We calculated the inverse of the genomic relationship matrix GAPY(-1) based on a direct inversion of genomic relationship matrix on a small subset of genotyped animals (core animals) and extended that information to noncore animals by recursion. We tested several sets of core animals including 9,406 bulls with at least 1 classified daughter, 9,406 bulls and 1,052 classified dams of bulls, 9,406 bulls and 7,422 classified cows, and random samples of 5,000 to 30,000 animals. Validation reliability was assessed by the coefficient of determination from regression of daughter deviation on genomic predictions for the predicted young bulls. The reliabilities were 0.39 with 5,000 randomly chosen core animals, 0.45 with the 9,406 bulls, and 7,422 cows as core animals, and 0.44 with the remaining sets. With phenotypes truncated in 2009 and the preconditioned conjugate gradient to solve mixed model equations, the number of rounds to convergence for core animals defined by bulls was 1,343; defined by bulls and cows, 2,066; and defined by 10,000 random animals, at most 1,629. With complete phenotype data, the number of rounds decreased to 858, 1,299, and at most 1,092, respectively. Setting up GAPY(-1) for 569,404 genotyped animals with 10,000 core animals took 1.3h and 57 GB of memory. The validation reliability with APY reaches a plateau when the number of core animals is at least 10,000. Predictions with APY have little differences in reliability among definitions of core animals. Single-step genomic BLUP with APY is applicable to millions of genotyped animals.

Genetic parameters between feed-intake-related traits and conformation in 2 separate dairy populations--the Netherlands and United States.

To include feed-intake-related traits in the breeding goal, accurate estimates of genetic parameters of feed intake, and its correlations with other related traits (i.e., production, conformation) are required to compare different options. However, the correlations between feed intake and conformation traits can vary depending on the population. Therefore, the objective was to estimate genetic correlations between 6 feed-intake-related traits and 7 conformation traits within dairy cattle from 2 countries, the Netherlands (NL) and the United States (US). The feed-intake-related traits were dry matter intake (DMI), residual feed intake (RFI), milk energy output (MilkE), milk yield (MY), body weight (BW), and metabolic body weight (MBW). The conformation traits were stature (ST), chest width (CW), body depth (BD), angularity (ANG), rump angle (RA), rump width (RW), and body condition score (BCS). Feed intake data were available for 1,665 cows in NL and for 1,920 cows in US, from 83 nutritional experiments (48 in NL and 35 in US) conducted between 1991 and 2011 in NL and between 2007 and 2013 in US. Additional conformation records from relatives of the animals with DMI records were added to the database, giving a total of 37,241 cows in NL and 28,809 in US with conformation trait information. Genetic parameters were estimated using bivariate animal model analyses. The model included the following fixed effects for feed-intake-related traits: location by experiment-ration, age of cow at calving modeled with a second order polynomial by parity class, location by year-season, and days in milk, and these fixed effects for the conformation traits: herd by classification date, age of cow at classification, and lactation stage at classification. Both models included additive genetic and residual random effects. The highest estimated genetic correlations involving DMI were with CW in both countries (NL=0.45 and US=0.61), followed by ST (NL=0.33 and US=0.57), BD (NL=0.26 and US=0.49), and BCS (NL=0.24 and US=0.46). The MilkE and MY were moderately correlated with ANG in both countries (0.33 and 0.47 in NL, and 0.36 and 0.48 in US). Finally, BW was highly correlated with CW (0.77 in NL and 0.84 in US) and with BCS (0.83 in NL and 0.85 in US). Feed-intake-related traits were moderately to highly genetically correlated with conformation traits (ST, CW, BD, and BCS) in both countries, making them potentially useful as predictors of DMI.

Genotype by environment interactions on culling rates and 305-day milk yield of Holstein cows in 3 US regions.

The objective of this study was to investigate genotype by environment interactions for culling rates and milk production in large and small dairy herds in 3 US regions, using genotypes, pedigree, and phenotypes. Single nucleotide polymorphism (SNP) marker variances were also estimated in these different environments. Culling rates including cow mortality were based on 6 Dairy Herd Improvement termination codes reported by dairy producers. Separate data sets for culling rates and 305-d milk yield were created for large and small dairy herds in the US regions of the Southeast (SE), Southwest (SW), and Northeast (NE) for the first 3 lactation cows that calved between 1999 and 2008. Genomic information from 42,503 SNP markers on 34,506 bulls was included in the analysis to predict genomic estimated breeding value (GEBV) of culling rates and 305-d milk yield with a single-step genomic BLUP using a bivariate threshold-linear model. Cow replacement rates in large SE and NE herds were higher. Heritability estimates of culling rates ranged from 0.03 to 0.11, but the differences were small between large and small herds and among the 3 US regions. Genetic correlations between culling rates and 305-d milk yield were medium to high for cows sold for poor production and reproduction problems. Correlations of GEBV for culling rates among the 3 US regions ranged from 0.34 to 0.92 and were lower between the SW and the other regions, especially in small herds. Correlations of GEBV between large and small herds ranged from 0.44 to 0.90 and were lower in the SW. These results indicate genotype by environment interactions of cow culling rate between the US regions and between large and small herds. Correlations of top 30 SNP marker effects for culling rates between 2 US regions ranged from 0.64 to 0.98 and were higher than those of more SNP marker effects except for a culling reason "sold for dairy purpose." Those correlations between large and small herds ranged from 0.67 to 0.98. High correlations of top SNP marker effects on culling reasons between the US regions and between large and small herds suggest that major markers can be useful for selection in different environments. The SNP variance shown in a marker gene segment on chromosome 14 was strongly associated with milk production in large and small herds in the NE but not in the SE and SW. Marker genes on chromosome 14 also showed a strong association with cow culling rates due to poor production and mortality in large herds in the NE.

Hot topic: Use of genomic recursions in single-step genomic best linear unbiased predictor (BLUP) with a large number of genotypes.

The purpose of this study was to evaluate the accuracy of genomic selection in single-step genomic BLUP (ssGBLUP) when the inverse of the genomic relationship matrix (G) is derived by the "algorithm for proven and young animals" (APY). This algorithm implements genomic recursions on a subset of "proven" animals. Only a relationship matrix for animals treated as "proven" needs to be inverted, and the extra costs of adding animals treated as "young" are linear. Analyses involved 10,102,702 final scores on 6,930,618 Holstein cows. Final score, which is a composite of type traits, is popular trait in the United States and was easily available for this study. A total of 100,000 animals with genotypes were used in the analyses and included 23,000 sires (16,000 with >5 progeny), 27,000 cows, and 50,000 young animals. Genomic EBV (GEBV) were calculated with a regular inverse of G, and with the G inverse approximated by APY. Animals in the proven subset included only sires (23,000), sires+cows (50,000), only cows (27,000), or sires with >5 progeny (16,000). The correlations of GEBV with APY and regular GEBV for young genotyped animals were 0.994, 0.995, 0.992, and 0.992, respectively Later, animals in the proven subset were randomly sampled from all genotyped animals in sets of 2,000, 5,000, 10,000, 15,000, and 20,000; each sample was replicated 4 times. Respective correlations were 0.97 (5,000 sample), 0.98 (10,000 sample), and 0.99 (20,000 sample), with minimal difference between samples of the same size. Genomic EBV with APY were accurate when the number of animals used in the subset is between 10,000 and 20,000, with little difference between the ways of creating the subset. Due to the approximately linear cost of APY, ssGBLUP with APY could support any number of genotyped animals without affecting accuracy.

Assigning unknown parent groups to reduce bias in genomic evaluations of final score in US Holsteins.

Assigning unknown parent groups (UPG) in mixed-model equations using single-step genomic BLUP was investigated to reduce bias and to increase accuracy in genomic estimated breeding values (GEBV). The original UPG were defined based on the animal's birth year and the sex of the animal's unknown parents. Combining the last 2 UPG for the animals' birth years and separating the UPG for US and non-US Holsteins were considered in the redefinition. A full data set in the 2011 national genetic evaluation of final score in US Holsteins was used to calculate estimated breeding values (EBV) for validation, and a subset of the 2011 data, which excluded phenotypes recorded after 2007, was used to calculate GEBV for all animals, including 34,500 genotyped bulls. The EBV and GEBV in 2007 were compared with EBV in the 2011 full data. The last group effects for unknown sires and dams were overestimated with the GEBV model using the reduced 2007 data. The genetic trends from EBV in 2011 and GEBV in 2007 with the original UPG in the last few years demonstrated inflation, whereas GEBV with the redefined UPG by combining the last 2 groups showed deflation. On the other hand, the redefined UPG by separating for US and non-US Holsteins reduced the bias in GEBV. Regression coefficients smaller than unity for GEBV for young genotyped bulls with no daughters in 2007 on progeny deviations in 2011 also indicated inflation. The redefining of UPG reduced bias and slightly increased accuracy in GEBV for both US and non-US genotyped bulls. Rank correlations between GEBV in 2007 and in 2011 with the redefined UPG were higher than those with no UPG and the original UPG, especially for non-US bulls. Redefining of UPG in genomic evaluation could improve reliability of GEBV and provide correct genetic trends.

Are evaluations on young genotyped animals benefiting from the past generations?

Data sets of US Holsteins, Israeli Holsteins, and pigs from PIC (a Genus company, Hendersonville, TN) were used to evaluate the effect of different numbers of generations on ability to predict genomic breeding values of young genotyped animals. The influence of including only 2 generations of ancestors (A2) or all ancestors (Af) was also investigated. A total of 34,506 US Holsteins, 1,305 Israeli Holsteins, and 5,236 pigs were genotyped. The evaluations were computed by traditional BLUP and single-step genomic BLUP, and computing performance was assessed for the latter method. For the 2 Holstein data sets, coefficients of determination (R(2)) and regression (δ) of deregressed evaluations from a full data set with records up to 2011 on estimated breeding values and genomic estimated breeding values from the truncated data sets were computed. The thresholds for data deletion were set by intervals of 5 yr, based on the average generation interval in dairy cattle. For the PIC data set, correlations between corrected phenotypes and estimated or genomic estimated breeding values were used to evaluate predictive ability on young animals born in 2010 and 2011. The reduced data set contained data up to 2009, and the thresholds were set based on an average generation interval of 3 yr. The number of generations that could be deleted without a reduction in accuracy depended on data structure and trait. For US Holsteins, removing 3 and 4 generations of data did not reduce accuracy of evaluations for final score in Af and A2 scenarios, respectively. For Israeli Holsteins, the accuracies for milk, fat, and protein yields were the highest when only phenotypes recorded in 2000 and later were included and full pedigrees were applied. Of the 135 Israeli bulls with genotypes (validation set) and daughter records only in the complete data set, 38 and 97 were sons of Israeli and foreign bulls, respectively. Although more phenotypic data increased the prediction accuracy for sons of Israeli bulls, the reverse was true for sons of foreign bulls. Also, more phenotypic data caused large inflation of genomic estimated breeding values for sons of foreign bulls, whereas the opposite was true with the deletion of all but the most recent phenotypic data. Results for protein and fat percentage were different from those for milk, fat, and protein yields; however, relatively, the changes in coefficients of determination and regression were smaller for percentage traits. For PIC data set, removing data from up to 5 generations did not erode predictive ability for genotyped animals for the 2 reproductive traits used in validation. Given the data used in this study, truncating old data reduces computation requirements but does not decrease the accuracy. For small populations that include local and imported animals, truncation may be beneficial for one group of animals and detrimental to another group.

Short communication: genomic evaluations of final score for US Holsteins benefit from the inclusion of genotypes on cows.

Currently, the US Department of Agriculture Animal Improvement Programs Laboratory utilizes a multi-step procedure in genomic evaluations for US Holstein bulls and cows, with adjustments for cows. We used a single-step procedure to investigate whether adding cows' genotypes could increase reliability in genomic breeding values for bulls while minimizing bias. The first data set to 2007 was used to calculate genomic estimated breeding values (GEBV) for animals, including young genotyped bulls with no daughters and young cows (heifers) with no records in 2007. The second data set to 2011 was used to calculate GEBV for the same animals, including those young bulls with daughters and young cows with records in 2011. Genotypes (42,503 single nucleotide polymorphism markers) for 34,506 bulls and 5,235 cows from 356,413 bulls and 9,245,619 cows in pedigree were used to calculate single-step GEBV (ssGEBV) and multi-step GEBV (msGEBV). Regression coefficients of 2007 GEBV on 2011 progeny deviations and coefficients of determination were used as indicators of bias and reliability in 2007 GEBV for bulls with no daughters and for cows with no records in 2007, using bull genotypes only and using bull and cow genotypes. Parent averages were also calculated from estimated breeding values of parents to compare with GEBV. For genotyped bulls, inflation was larger for ssGEBV than for msGEBV, whereas reliability was higher for ssGEBV. Using all genotyped bulls and cows, reliabilities were increased by 2 to 3%. Use of genotypes of high-profile cows improves reliability in ssGEBV and msGEBV for bulls.

Methods to approximate reliabilities in single-step genomic evaluation.

Reliability of predictions from single-step genomic BLUP (ssGBLUP) can be calculated by matrix inversion, but that is not feasible for large data sets. Two methods of approximating reliability were developed based on the decomposition of a function of reliability into contributions from records, pedigrees, and genotypes. Those contributions can be expressed in record or daughter equivalents. The first approximation method involved inversion of a matrix that contains inverses of the genomic relationship matrix and the pedigree relationship matrix for genotyped animals. The second approximation method involved only the diagonal elements of those inverses. The 2 approximation methods were tested with a simulated data set. The correlations between ssGBLUP and approximated contributions from genomic information were 0.92 for the first approximation method and 0.56 for the second approximation method; contributions were inflated by 62 and 258%, respectively. The respective correlations for reliabilities were 0.98 and 0.72. After empirical correction for inflation, those correlations increased to 0.99 and 0.89. Approximations of reliabilities of predictions by ssGBLUP are accurate and computationally feasible for populations with up to 100,000 genotyped animals. A critical part of the approximations is quality control of information from single nucleotide polymorphisms and proper scaling of the genomic relationship matrix.

Potential gains in lifetime net merit from genomic testing of cows, heifers, and calves on commercial dairy farms.

The objective of this study was to quantify the gains in genetic potential of replacement females that could be achieved by using genomic testing to facilitate selection and culling decisions on commercial dairy farms. Data were simulated for 100 commercial dairy herds, each with 1,850 cows, heifers, and calves. Parameters of the simulation were based on the US Holstein population, and assumed reliabilities of traditional and genomic predictions matched reliabilities of animals that have been genotyped to date. Selection of the top 10, 20, 30, …, 90% of animals within each age group was based on parent averages and predicted transmitting abilities with or without genomic testing of all animals or subsets of animals that had been presorted by traditional predictions. Average gains in lifetime net merit breeding value of selected females due to genomic testing, minus prorated costs of genotyping the animals and their unselected contemporaries, ranged from $28 (top 90% selected) to $259 (top 20% selected) for heifer calves with no pedigrees, $14 (top 90% selected) to $121 (top 10% selected) for heifer calves with known sires, and $7 (top 90% selected) to $87 (top 20% selected) for heifer calves with full pedigrees. In most cases, gains in genetic merit of selected heifer calves far exceeded prorated genotyping costs, and gains were greater for animals with missing or incomplete pedigree information. Gains in genetic merit due to genomic testing were smaller for lactating cows that had phenotypic records, and in many cases, these gains barely exceeded or failed to exceed genotyping costs. Strategies based on selective genotyping of the top, middle, or bottom 50% of animals after presorting by traditional parent averages or predicted transmitting abilities were cost effective, particularly when pedigrees or phenotypes were available and a relatively small proportion of animals were to be selected or culled. Based on these results, it appears that routine genotyping of heifer calves or yearling heifers can be a cost-effective strategy for enhancing the genetic level of replacement females on commercial dairy farms. Increasing the accuracy of predicted breeding values for young females with genomic testing might lead to synergies with other management tools and strategies, such as propagating genetically superior females using advanced reproductive technologies or selling excess females that were generated by the use of sex-enhanced semen.

International genetic evaluation of Holstein bulls for overall type traits and body condition score.

The study documents the procedures used to estimate genetic correlations among countries for overall conformation (OCS), overall udder (OUS), overall feet and legs (OFL), and body condition score (BCS) of Holstein sires. Major differences in traits definition are discussed, in addition to the use of international breeding values (IBV) among countries involved in international genetic evaluations, and similarities among countries through hierarchical clustering. Data were available for populations from 20 countries for OCS and OUS, 18 populations for OFL, and 11 populations for BCS. The IBV for overall traits and BCS were calculated using a multi-trait across-country evaluation model. Distance measures, obtained from genetic correlations, were used as input values in the cluster analysis. Results from surveys sent to countries participating in international genetic evaluation for conformation traits showed that different ways of defining traits are used: the overall traits were either computed from linear or composite traits or defined as general characteristics. For BCS, populations were divided into 2 groups: one scored and evaluated BCS, and one used a best predictor. In general, populations were well connected except for Estonia and French Red Holstein. The average number of common bulls for the overall traits ranged from 19 (OCS and OUS of French Red Holstein) to 514 (OFL of United States), and for BCS from 17 (French Red Holstein) to 413 (the Netherlands). The average genetic correlation (range) across countries was 0.75 (0.35 to 0.95), 0.80 (0.41 to 0.95), and 0.68 (0.12 to 0.89) for OCS, OUS, and OFL, respectively. Genetic correlations among countries that used angularity as best predictor for BCS and countries that scored BCS were negative. The cluster analysis provided a clear picture of the countries distances; differences were due to trait definition, trait composition, and weights in overall traits, genetic ties, and genotype by environment interactions. Harmonization of trait definition and increasing genetic ties could improve genetic correlations across countries and reduce the distances. In each national selection index, all countries, except Estonia and New Zealand, included at least one overall trait, whereas none included BCS. Out of 18 countries, 9 have started genomic evaluation of conformation traits. The first were Canada, France, New Zealand, and United States in 2009, followed by Switzerland, Germany, and the Netherlands in 2010, and Australia and Denmark-Finland-Sweden (joint evaluation) in 2011. Six countries are planning to start soon.

Multiple-trait genomic evaluation of linear type traits using genomic and phenotypic data in US Holsteins.

Currently, the USDA uses a single-trait (ST) model with several intermediate steps to obtain genomic evaluations for US Holsteins. In this study, genomic evaluations for 18 linear type traits were obtained with a multiple-trait (MT) model using a unified single-step procedure. The phenotypic type data on up to 18 traits were available for 4,813,726 Holsteins, and single nucleotide polymorphism markers from the Illumina BovineSNP50 genotyping Beadchip (Illumina Inc., San Diego, CA) were available on 17,293 bulls. Genomic predictions were computed with several genomic relationship matrices (G) that assumed different allele frequencies: equal, base, current, and current scaled. Computations were carried out with ST and MT models. Procedures were compared by coefficients of determination (R(2)) and regression of 2004 prediction of bulls with no daughters in 2004 on daughter deviations of those bulls in 2009. Predictions for 2004 also included parent averages without the use of genomic information. The R(2) for parent averages ranged from 10 to 34% for ST models and from 12 to 35% for MT models. The average R(2) for all G were 34 and 37% for ST and MT models, respectively. All of the regression coefficients were <1.0, indicating that estimated breeding values in 2009 of 1,307 genotyped young bulls' parents tended to be biased. The average regression coefficients ranged from 0.74 to 0.79 and from 0.75 to 0.80 for ST and MT models, respectively. When the weight for the inverse of the numerator relationship matrix (A(-1)) for genotyped animals was reduced from 1 to 0.7, R(2) remained almost identical while the regression coefficients increased by 0.11-0.26 and 0.12-0.23 for ST and MT models, respectively. The ST models required about 5s per iteration, whereas MT models required 3 (6) min per iteration for the regular (genomic) model. The MT single-step approach is feasible for 18 linear type traits in US Holstein cattle. Accuracy for genomic evaluation increases when switching ST models to MT models. Inflation of genomic evaluations for young bulls could be reduced by choosing a small weight for the A(-1) for genotyped bulls.

Multiple trait genomic evaluation of conception rate in Holsteins.

A national data set of artificial inseminations in US Holsteins was used to obtain genetic evaluations for conception rate (CR). The objective of this study was to investigate the feasibility and resulting accuracy from using all available phenotypic, pedigree, and genomic information. Evaluations were performed by regular BLUP or by BLUP with the traditional pedigree and genomic relationships combined in a unified single-step procedure (SSP). Genetic parameters of CR in the first 3 parities were estimated with data from New York State only. Heritability estimates were around 2% and genetic correlations between CR in different parities were >0.73. The R(2) obtained with the SSP were almost twice as large as those achieved with regular BLUP. Computing the SSP took 2h, and it was 33% slower than a regular BLUP. A multiple-trait evaluation of CR using the SSP is both possible and advantageous.