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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., (The Authors. Published by Elsevier Inc. and Fass Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).)

Single-step genomic BLUP (ssGBLUP) is a method for genomic prediction that integrates matrices of pedigree (A) and genomic (G) relationships into a single unified additive relationship matrix whose inverse is incorporated into a set of mixed model equations (MME) to compute genomic predictions. Pedigree information in dairy cattle is often incomplete. Missing pedigree potentially causes biases and inflation in genomic estimated breeding values (GEBV) obtained with ssGBLUP. Three major issues are associated with missing pedigree in ssGBLUP, namely biased predictions by selection, missing inbreeding in pedigree relationships, and incompatibility between G and A in level and scale. These issues can be solved using a proper model for unknown-parent groups (UPG). The theory behind the use of UPG is well established for pedigree BLUP, but not for ssGBLUP. This study reviews the development of the UPG model in pedigree BLUP, the properties of UPG models in ssGBLUP, and the effect of UPG on genetic trends and genomic predictions. Similarities and differences between UPG and metafounder (MF) models, a generalized UPG model, are also reviewed. A UPG model (QP) derived using a transformation of the MME has a good convergence behavior. However, with insufficient data, the QP model may yield biased genetic trends and may underestimate UPG. The QP model can be altered by removing the genomic relationships linking GEBV and UPG effects from MME. This altered QP model exhibits less bias in genetic trends and less inflation in genomic predictions than the QP model, especially with large data sets. Recently, a new model, which encapsulates the UPG equations into the pedigree relationships for genotyped animals, was proposed in simulated purebred populations. The MF model is a comprehensive solution to the missing pedigree issue. This model can be a choice for multibreed or crossbred evaluations if the data set allows the estimation of a reasonable relationship matrix for MF. Missing pedigree influences genetic trends, but its effect on the predictability of genetic merit for genotyped animals should be negligible when many proven bulls are genotyped. The SNP effects can be back-solved using GEBV from older genotyped animals, and these predicted SNP effects can be used to calculate GEBV for young-genotyped animals with missing parents., (The Authors. Published by Elsevier Inc. and Fass Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).)

The objective of this study was to predict genomic breeding values for milk yield of crossbred dairy cattle under different scenarios using single-step genomic BLUP (ssGBLUP). The data set included 13,880,217 milk yield measurements on 6,830,415 cows. Genotypes of 89,558 Holstein, 40,769 Jersey, and 22,373 Holstein-Jersey crossbred animals were used, of which all Holstein, 9,313 Jersey, and 1,667 crossbred animals had phenotypic records. Genotypes were imputed to 45K SNP markers. The SNP effects were estimated from single-breed evaluations for Jersey (JE), Holstein (HO) and crossbreds (CROSS), and multibreed evaluations including all Jersey and Holstein (JE_HO) or approximately equal proportions of Jersey, Holstein, and crossbred animals (MIX). Indirect predictions (IP) of the validation animals (358 crossbred animals with phenotypes excluded from evaluations) were calculated using the resulting SNP effects. Additionally, breed proportions (BP) of crossbred animals were applied as a weight when IP were estimated based on each pure breed. The predictive ability of IP was calculated as the Pearson correlation between IP and phenotypes of the validation animals adjusted for fixed effects in the model. Regression of adjusted phenotypes on IP was used to assess the inflation of IP. The predictive ability of IP for CROSS, JE, HO, JE_HO, and MIX scenario was 0.50, 0.50, 0.47, 0.50, and 0.46, respectively. Using BP was the least successful, with a predictive ability of 0.32. The inflation of the IP for crossbred animals using CROSS, JE, HO, JE_HO, MIX, and BP scenarios were 1.17, 0.65, 0.55, 0.78, 1.00, and 0.85, respectively. The IP of crossbred animals can be predicted using single-step GBLUP under a scenario that includes purebred genotypes., (The Authors. Published by Elsevier Inc. and Fass Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).)

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 (Δh 2 ), 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 Δh 2 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., (The Authors. Published by Elsevier Inc. and Fass Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).)

The widespread use of sexed semen on US dairy cows and heifers has led to an excess of replacement heifers' calves, and the sale prices for those calves are much lower than in the past. Females not selected to produce the next generation of replacement heifers are increasingly being bred to beef bulls to produce crossbred calves for beef production. The purpose of this study was to investigate the use of beef service sires bred to dairy cows and heifers and to provide a tool for dairy producers to evaluate beef service sires' conception. Sire conception rate (SCR) is a phenotypic evaluation of service sire fertility that is routinely calculated for US dairy bulls. A total of 268,174 breedings were available, which included 36 recognized beef breeds and 7 dairy breeds. Most of the beef-on-dairy inseminations (95.4%) were to Angus (AN) bulls. Because of the limited number of records among other breeds, we restricted our final evaluations to AN service sires bred to Holstein (HO) cows. Service-sire inbreeding and expected inbreeding of resulting embryo were set to zero because pedigree data for AN bulls were unavailable. There were 233,379 breedings from 1,344 AN service sire to 163,919 HO cows. A mean (SD) conception rate of 33.8% (47.3%) was observed compared with 34.3% (47.5%) for breedings with HO sires mated to HO cows. Publishable AN bulls were required to have ≥100 total matings, ≥10 matings in the most recent 12 mo, and breedings in at least 5 herds. Mean SCR reliability was 64.5% for 116 publishable bulls, with a maximum reliability of 99% based on 25,217 breedings. Average SCR was near zero (on AN base) with a range of -5.1 to 4.4. Breedings to HO heifers were also examined, which included 19,437 breedings (443 AN service sire and 15,971 HO heifers). A mean (SD) conception rate of 53.0% (49.9%) was observed, compared with 55.3% (49.7%) for breedings with a HO sire mated to a HO heifer. Beef sires were used more frequently in cows known to be problem breeders, which explains some of the difference in conception rate. Mean service number was 1.92 and 2.87 for HO heifers and 2.13 and 3.04 for HO cows mated to HO and AN sires, respectively. Mating dairy cows and heifers to beef bulls may be profitable if calf prices are higher, fertility is improved, or if practices such as sexed semen, genomic testing, and improved cow productive life allow herd owners to produce both higher quality dairy replacement and increased income from market calves., (The Authors. Published by Elsevier Inc. and Fass Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).)

Functional traits, such as fertility and lactation persistency, are becoming relevant breeding goals for dairy cattle. Fertility is a key element for herd profitability and animal welfare; in particular, calving interval (CIN) is an indicator of female fertility that can be easily recorded. Lactation persistency (LPE; i.e., the ability of a cow to maintain a high milk yield after the lactation peak) is economically important and is related to several other traits, such as feed efficiency, health, and reproduction. The selection of these functional traits is constrained by their low heritability. In this study, variance components for CIN and LPE in the Italian Simmental cattle breed were estimated using genomic and pedigree information under the single-step genomic framework. A data set of 594,257 CIN records (from 275,399 cows) and 285,213 LPE records (from 1563,389 cows) was considered. Phenotypes were limited up to the third parity. The pedigree contained about 2 million animals, and 7,246 genotypes were available. Lactation persistency was estimated using principal component analysis on test day records, with higher values of the second extracted principal component (PC2) values associated with lower LPE, and lower PC2 values associated with higher LPE. Heritability of CIN and LPE were estimated using single-trait repeatability models. A multiple-trait analysis using CIN and production traits (milk, fat, and protein yields) was performed to estimate genetic correlations among these traits. Heritability for CIN in the single-trait model was low (0.06 ± 0.002). Unfavorable genetic correlations were found between CIN and production traits. A measure of LPE was derived using principal component analysis on test day records. The heritability and repeatability of LPE were 0.11 ± 0.004 and 0.20 ± 0.02, respectively. Genetic correlation between CIN and LPE was weak but had a favorable direction. Despite the low heritability estimates, results of the present work suggest the possibility of including these traits in the Italian Simmental breeding program. The use of a single-step approach may provide better results for young genotyped animals without their own phenotypes., (Copyright © 2020 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

Estimating single nucleotide polymorphism (SNP) effects over time is essential to identify and validate candidate genes (or quantitative trait loci) associated with time-dependent variation of economically important traits and to better understand the underlying mechanisms of lactation biology. Therefore, in this study, we aimed to estimate time-dependent effects of SNP and identifying candidate genes associated with milk (MY), fat (FY), and protein (PY) yields, and somatic cell score (SCS) in the first 3 lactations of Canadian Ayrshire, Holstein, and Jersey breeds, as well as suggest their potential pattern of phenotypic effect over time. Random regression coefficients for the additive direct genetic effect were estimated for each animal using single-step genomic BLUP, based on 2 random regression models: one considering MY, FY, and PY in the first 3 lactations and the other considering SCS in the first 3 lactations. Thereafter, SNP solutions were obtained for random regression coefficients, which were used to estimate the SNP effects over time (from 5 to 305 d in lactation). The top 1% of SNP that showed a high magnitude of SNP effect in at least 1 d in lactation were selected as relevant SNP for further analyses of candidate genes, and clustered according to the trajectory of their SNP effects over time. The majority of SNP selected for MY, FY, and PY increased the magnitude of their effects over time, for all breeds. In contrast, for SCS, most selected SNP decreased the magnitude of their effects over time, especially for the Holstein and Jersey breeds. In general, we identified a different set of candidate genes for each breed, and similar genes were found across different lactations for the same trait in the same breed. For some of the candidate genes, the suggested pattern of phenotypic effect changed among lactations. Among the lactations, candidate genes (and their suggested phenotypic effect over time) identified for the second and third lactations were more similar to each other than for the first lactation. Well-known candidate genes with major effects on milk production traits presented different suggested patterns of phenotypic effect across breeds, traits, and lactations in which they were identified. The candidate genes identified in this study can be used as target genes in studies of gene expression., (Copyright © 2019 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

Causal variants inferred from sequence data analysis are expected to increase accuracy of genomic selection. In this work we evaluated the gain in reliability of genomic predictions, for stature in US Holsteins, when adding selected sequence variants to a pre-existent SNP chip. Two prediction methods were tested: de-regressed proofs assuming heterogeneous (genomic BLUP; GBLUP) residual variances and by single-step GBLUP (ssGBLUP) using actual phenotypes. Phenotypic data included 3,999,631 records for stature on 3,027,304 Holstein cows. Genotypes on 54,087 SNP markers (54k) were available for 26,877 bulls. Additionally, 16,648 selected sequence variants were combined with the 54k markers, for a total of 70,735 (70k) markers. In all methods, SNP in the genomic relationship matrix (G) were unweighted or weighted iteratively, with weights derived either by SNP effects squared or by a nonlinear method that resembles BayesA (nonlinear A). Reliability of genomic predictions were obtained by cross validation. With unweighted G derived from 54k markers, the reliabilities (× 100) were 72.4 for GBLUP and 75.3 for ssGBLUP. With unweighted G derived from 70k markers, the reliabilities were 73.4 and 76.0, respectively. Weighting by nonlinear A changed reliabilities to 73.3, and 75.9, respectively. Addition of selected sequence variants had a small effect on reliabilities. Weighting by quadratic functions reduced reliabilities. Weighting by nonlinear A increased reliabilities for GBLUP but had only a small effect in ssGBLUP. Reliabilities for direct genomic values extracted from ssGBLUP using unweighted G with 54k were higher than reliabilities by any GBLUP. Thus, ssGBLUP seems to capture more information than GBLUP and there is less room for extra reliability. Improvements in GBLUP may be because the weights in G change the covariance structure, which can explain a proportion of the variance that is accounted for when a heterogeneous residual variance is assumed by considering a different number of daughters per bull., (Copyright © 2019 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

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 (b 1 ) and coefficients of determination (R 2 ) 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, b 1 and R 2 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., (Copyright © 2019 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

The use of multi-trait across-country evaluation (MACE) and the exchange of genomic information among countries allows national breeding programs to combine foreign and national data to increase the size of the training populations and potentially increase accuracy of genomic prediction of breeding values. By including genotyped and nongenotyped animals simultaneously in the evaluation, the single-step genomic BLUP (GBLUP) approach has the potential to deliver more accurate and less biased genomic evaluations. A single-step genomic BLUP approach, which enables integration of data from MACE evaluations, can be used to obtain genomic predictions while avoiding double-counting of information. The objectives of this study were to apply a single-step approach that simultaneously includes domestic and MACE information for genomic evaluation of workability traits in Canadian Holstein cattle, and compare the results obtained with this methodology with those obtained using a multi-step approach (msGBLUP). By including MACE bulls in the training population, msGBLUP led to an increase in reliability of genomic predictions of 4.8 and 15.4% for milking temperament and milking speed, respectively, compared with a traditional evaluation using only pedigree and phenotypic information. Integration of MACE data through a single-step approach (ssGBLUP IM ) yielded the highest reliabilities compared with other considered methods. Integration of MACE data also helped reduce bias of genomic predictions. When using ssGBLUP IM , the bias of genomic predictions decreased by half compared with msGBLUP using domestic and MACE information. Therefore, the reliability and bias of genomic predictions for both traits improved substantially when a single-step approach was used for evaluation compared with a multi-step approach. The use of a single-step approach with integration of MACE information provides an alternative to the current method used in Canadian genomic evaluations., (Copyright © 2019 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

An important goal in animal breeding is to improve longitudinal traits; that is, traits recorded multiple times during an individual's lifetime or physiological cycle. Longitudinal traits were first genetically evaluated based on accumulated phenotypic expression, phenotypic expression at specific time points, or repeatability models. Until now, the genetic evaluation of longitudinal traits has mainly focused on using random regression models (RRM). Random regression models enable fitting random genetic and environmental effects over time, which results in higher accuracy of estimated breeding values compared with other statistical approaches. In addition, RRM provide insights about temporal variation of biological processes and the physiological implications underlying the studied traits. Despite the fact that genomic information has substantially contributed to increase the rates of genetic progress for a variety of economically important traits in several livestock species, less attention has been given to longitudinal traits in recent years. However, including genomic information to evaluate longitudinal traits using RRM is a feasible alternative to yield more accurate selection and culling decisions, because selection of young animals may be based on the complete pattern of the production curve with higher accuracy compared with the use of traditional parent average (i.e., without genomic information). Moreover, RRM can be used to estimate SNP effects over time in genome-wide association studies. Thus, by analyzing marker associations over time, regions with higher effects at specific points in time are more likely to be identified. Despite the advances in applications of RRM in genetic evaluations, more research is needed to successfully combine RRM and genomic information. Future research should provide a better understanding of the temporal variation of biological processes and their physiological implications underlying the longitudinal traits., (Copyright © 2019 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

We performed genome-wide association analyses for milk, fat, and protein yields and somatic cell score based on lactation stages in the first 3 parities of Canadian Ayrshire, Holstein, and Jersey cattle. The genome-wide association analyses were performed considering 3 different lactation stages for each trait and parity: from 5 to 95, from 96 to 215, and from 216 to 305 d in milk. Effects of single nucleotide polymorphisms (SNP) for each lactation stage, trait, parity, and breed were estimated by back-solving the direct breeding values estimated using the genomic best linear unbiased predictor and single-trait random regression test-day models containing only the fixed population average curve and the random genomic curves. To identify important genomic regions related to the analyzed lactation stages, traits, parities and breeds, moving windows (SNP-by-SNP) of 20 adjacent SNP explaining more than 0.30% of total genetic variance were selected for further analyses of candidate genes. A lower number of genomic windows with a relatively higher proportion of the explained genetic variance was found in the Holstein breed compared with the Ayrshire and Jersey breeds. Genomic regions associated with the analyzed traits were located on 12, 8, and 15 chromosomes for the Ayrshire, Holstein, and Jersey breeds, respectively. Especially for the Holstein breed, many of the identified candidate genes supported previous reports in the literature. However, well-known genes with major effects on milk production traits (e.g., diacylglycerol O-acyltransferase 1) showed contrasting results among lactation stages, traits, and parities of different breeds. Therefore, our results suggest evidence of differential sets of candidate genes underlying the phenotypic expression of the analyzed traits across breeds, parities, and lactation stages. Further functional studies are needed to validate our findings in independent populations., (Copyright © 2019 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

The effects of 2 deleterious recessive haplotypes on reproduction performance of Ayrshire cattle, Ayrshire Haplotype 1 (AH1) and Ayrshire Haplotype 2 (AH2), were investigated in Canadian Ayrshire cattle. We calculated their phenotypic effects on stillbirth (SB) rate and 56-d nonreturn rate (NRR) by estimating the interaction of service sire carrier status with maternal grandsire carrier status using the official Canadian evaluation models for those 2 traits. The interaction term included 9 subclasses for the 3 possible statuses of each bull: haplotype carrier, noncarrier, or not genotyped. For AH1, 394 carriers and 1,433 noncarriers were available, whereas 313 carriers and 1,543 noncarriers were available for the AH2 haplotype. The number of matings considered for SB was 34,312 for heifers (first parity) and 115,935 for cows (later parities). For NRR, 49,479 matings for heifers and 160,528 for cows were used to estimate the haplotype effects. We observed a negative effect of AH1 on SB rates, which was 2.0% higher for matings of AH1-carrier sires to dams that had an AH1-carrier sire; this effect was found for both heifers and cows. However, AH1 had small, generally nonsignificant effects on NRR. The AH2 haplotype had a substantial negative effect on NRR, with 5.1% more heifers and 4.0% more cows returning to service, but the effects on SB rates were inconsistent and mostly small effects. Our results validate the harmful effects of AH1 and AH2 on reproduction traits in the Canadian Ayrshire population. This information will be of great interest for the dairy industry, allowing producers to make mating decisions that would reduce reproductive losses., (Copyright © 2019 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

The purpose of this study was to determine whether multi-country genomic evaluation can be accomplished by multiple-trait genomic best linear unbiased predictor (GBLUP) without sharing genotypes of important animals. Phenotypes and genotypes with 40k SNP were simulated for 25,000 animals, each with 4 traits assuming the same genetic variance and 0.8 genetic correlations. The population was split into 4 subpopulations corresponding to 4 countries, one for each trait. Additionally, a prediction population was created from genotyped animals that were not present in the individual countries but were related to each country's population. Genomic estimated breeding values were computed for each country and subsequently converted to SNP effects. Phenotypes were reconstructed for the prediction population based on the SNP effects of a country and the prediction animals' genotypes. The prediction population was used as the basis for the international evaluation, enabling bull comparisons without sharing genotypes and only sharing SNP effects. The computations were such that SNP effects computed within-country or in the prediction population were the same. Genomic estimated breeding values were calculated by single-trait GBLUP for within-country and multiple-trait GBLUP for multi-country predictions. The true accuracy for the prediction population with reconstructed phenotypes was at most 0.02 less than the accuracy with the original data. The differences increased when countries were assumed unequally sized. However, accuracies by multiple-trait GBLUP with the prediction population were always greater than accuracies from any single within-country prediction. Multi-country genomic evaluations by multiple-trait GBLUP are possible without using original genotypes at a cost of lower accuracy compared with explicitly combining countries' data., (Copyright © 2019 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

Test-day traits are important for genetic evaluation in dairy cattle and are better modeled by multiple-trait random regression models (RRM). The reliability and bias of genomic estimated breeding values (GEBV) predicted using multiple-trait RRM via single-step genomic best linear unbiased prediction (ssGBLUP) were investigated in the 3 major dairy cattle breeds in Canada (i.e., Ayrshire, Holstein, and Jersey). Individual additive genomic random regression coefficients for the test-day traits were predicted using 2 multiple-trait RRM: (1) one for milk, fat, and protein yields in the first, second, and third lactations, and (2) one for somatic cell score in the first, second, and third lactations. The predicted coefficients were used to derive GEBV for each lactation day and, subsequently, the daily GEBV were compared with traditional daily parent averages obtained by BLUP. To ensure compatibility between pedigree and genomic information for genotyped animals, different scaling factors for combining the inverse of genomic (G -1 ) and pedigree (A -1 22 ) relationship matrices were tested. In addition, the inclusion of only genotypes from animals with accurate breeding values (defined in preliminary analysis) was compared with the inclusion of all available genotypes in the analyzes. The ssGBLUP model led to considerably larger validation reliabilities than the BLUP model without genomic information. In general, scaling factors used to combine the G -1 and A -1 22 matrices had small influence on the validation reliabilities. However, a greater effect was observed in the inflation of GEBV. Less inflated GEBV were obtained by the ssGBLUP compared with the parent average from traditional BLUP when using optimal scaling factors to combine the G -1 and A -1 22 matrices. Similar results were observed when including either all available genotypes or only genotypes from animals with accurate breeding values. These findings indicate that ssGBLUP using multiple-trait RRM increases reliability and reduces bias of breeding values of young animals when compared with parent average from traditional BLUP in the Canadian Ayrshire, Holstein, and Jersey breeds., (Copyright © 2019 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

In Canada, reproductive disorders known to affect the profitability of dairy cattle herds have been recorded by producers on a voluntary basis since 2007. Previous studies have shown the feasibility of using producer-recorded health data for genetic evaluations. Despite low heritability estimates and limited availability of phenotypic information, sufficient genetic variation has been observed for those traits to indicate that genetic progress, although slow, can be achieved. Pedigree- and genomic-based analyses were performed on producer-recorded health data of reproductive disorders, including retained placenta (RETP), metritis (METR), and cystic ovaries (CYST) using traditional BLUP and single-step genomic BLUP. Genome-wide association studies and functional analyses were carried out to unravel significant genomic regions and biological pathways, and to better understand the genetic mechanisms underlying RETP, METR, and CYST. Heritability estimates (posterior standard deviation in parentheses) were 0.02 (0.003), 0.01 (0.004), and 0.02 (0.003) for CYST, METR, and RETP, respectively. A moderate to strong genetic correlation of 0.69 (0.102) was found between METR and RETP. Averaged over all traits, sire proof reliabilities increased by approximately 11 percentage points with the incorporation of genomic data using a multiple-trait linear model. Biological pathways and associated genes underlying the studied traits were identified and will contribute to a better understanding of the biology of these 3 health disorders in dairy cattle., (Copyright © 2019 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

Application of random regression models (RRM) in a 2-step genomic prediction might be a feasible way to select young animals based on the complete pattern of the lactation curve. In this context, the prediction reliability and bias of genomic estimated breeding value (GEBV) for milk, fat, and protein yields and somatic cell score over days in milk (DIM) using a 2-step genomic approach were investigated. In addition, the effect of including cows in the training and validation populations was investigated. Estimated breeding values for each DIM (from 5 to 305 d) from the first 3 lactations of Holstein animals were deregressed and used as pseudophenotypes in the second step. Individual additive genomic random regression coefficients for each trait were predicted using RRM and genomic best linear unbiased prediction and further used to derive GEBV for each DIM. Theoretical reliabilities of GEBV obtained by the RRM were slightly higher than theoretical reliabilities obtained by the accumulated yield up to 305 d (P305). However, validation reliabilities estimated for GEBV using P305 were higher than for GEBV using RRM. For all traits, higher theoretical and validation reliabilities were estimated when incorporating genomic information. Less biased GEBV estimates were found when using RRM compared with P305, and different validation reliability and bias patterns for GEBV over time were observed across traits and lactations. Including cows in the training population increased the theoretical reliabilities and bias of GEBV; nonetheless, the inclusion of cows in the validation population does not seem to affect the regression coefficients and the theoretical reliabilities. In summary, the use of RRM in 2-step genomic prediction produced fairly accurate GEBV over the entire lactation curve for all analyzed traits. Thus, selecting young animals based on the pattern of lactation curves seems to be a feasible alternative in genomic selection of Holstein cattle for milk production traits., (Copyright © 2019 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

The success and sustainability of a breeding program incorporating genomic information is largely dependent on the accuracy of predictions. For low heritability traits, large training populations are required to achieve high accuracies of genomic estimated breeding values (GEBV). By including genotyped and nongenotyped animals simultaneously in the evaluation, the single-step genomic BLUP (ssGBLUP) approach has the potential to deliver more accurate and less biased genomic evaluations. The aim of this study was to compare the accuracy and bias of genomic predictions for various traits in Canadian Holstein cattle using ssGBLUP and multi-step genomic BLUP (msGBLUP) under different strategies, such as (1) adding genomic information of cows in the analysis, (2) testing different adjustments of the genomic relationship matrix, and (3) using a blending approach to obtain GEBV from msGBLUP. The following genomic predictions were evaluated regarding accuracy and bias: (1) GEBV estimated by ssGBLUP; (2) direct genomic value estimated by msGBLUP with polygenic effects of 5 and 20%; and (3) GEBV calculated by a blending approach of direct genomic value with estimated breeding values using polygenic effects of 5 and 20%. The effect of adding genomic information of cows in the evaluation was also assessed for each approach. When genomic information was included in the analyses, the average improvement in observed reliability of predictions was observed to be 7 and 13 percentage points for reproductive and workability traits, respectively, compared with traditional BLUP. Absolute deviation from 1 of the regression coefficient of the linear regression of de-regressed estimated breeding values on genomic predictions went from 0.19 when using traditional BLUP to 0.22 when using the msGBLUP method, and to 0.14 when using the ssGBLUP method. The use of polygenic weight of 20% in the msGBLUP slightly improved the reliability of predictions, while reducing the bias. A similar trend was observed when a blending approach was used. Adding genomic information of cows increased reliabilities, while decreasing bias of genomic predictions when using the ssGBLUP method. Differences between using a training population with cows and bulls or with only bulls for the msGBLUP method were small, likely due to the small number of cows included in the analysis. Predictions for lowly heritable traits benefit greatly from genomic information, especially when all phenotypes, pedigrees, and genotypes are used in a single-step approach., (Copyright © 2018 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

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., (Copyright © 2017 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

Genetically linked small and large dairy cattle populations were simulated to test the effect of different sources of information from foreign populations on the accuracy of predicting breeding values for young animals in a small population. A large dairy cattle population (P L ) with >20 generations was simulated, and a small subpopulation (P S ) with 3 generations was formed as a related population, including phenotypes and genomic information. Predicted breeding values for young animals in the small population were calculated using BLUP and single-step genomic BLUP (ssGBLUP) in 4 different scenarios: (S1) 3,166 phenotypes, 22,855 pedigree animals, and 1,000 to 6,000 genotypes for P S ; (S2) S1 plus genomic estimated breeding value (GEBV) for 4,475 sires from P L as external information; (S3) S1 plus 221,580 phenotypes, 402,829 pedigree animals, and 53,558 genotypes for P L ; and (S4) single nucleotide polymorphism (SNP) effects calculated based on P L data. The ability to predict true breeding value was assessed in the youngest third of the genotyped animals in the small population. When data only from the small population were used and 1,000 animals were genotyped, the accuracy of GEBV was only 1 point greater than the estimated breeding value accuracy (0.32 vs. 0.31). Adding external GEBV for sires from P L did not considerably increase accuracy (0.33 vs. 0.32 in S1). Combining phenotypes, pedigree, and genotypes for P S and P L was beneficial for predicting accuracy of GEBV in the small population, and the prediction accuracy of GEBV in this scenario was 0.38 compared with 0.31 from estimated breeding values. When SNP effects from P L were used to predict GEBV for young genotyped animals from P S , accuracy was greatest (0.56). With 6,000 genotyped animal in P S , accuracy was greatest (0.61) with the combined populations. In a small population with few genotypes, the highest accuracy of evaluation may be obtained by using SNP effects derived from a related large population., (Copyright © 2017 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

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., (Copyright © 2016 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)