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Key Message: Three computationally efficient algorithms of GP including RHBK, RHDK, and RHPK were developed in approximate genome-based kernel model. The drastically growing amount of genomic information contributes to increasing computational burden of genomic prediction (GP). In this study, we developed three computationally efficient algorithms of GP including RHBK, RHDK, and RHPK in approximate genome-based kernel model, which reduces dimension of genomic data via Nyström approximation and decreases the computational cost significantly thereby. According to the simulation study and real datasets, our three methods demonstrated predictive accuracy similar to or better than RHAPY, GBLUP, and rrBLUP in most cases. They also demonstrated a substantial reduction in computational time compared to GBLUP and rrBLUP in simulation. Due to their advanced computing efficiency, our three methods can be used in a wide range of application scenarios in the future., Competing Interests: Declarations. Conflict of interest: The authors declare that they have no conflict of interest. Ethical approval: Not applicable., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

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/).)

Estimates of dominance variance for growth traits in beef cattle based on pedigree data vary considerably across studies, and the proportion of genetic variance explained by dominance deviations remains largely unknown. The potential benefits of including nonadditive genetic effects in the genomic model combined with the increasing availability of large genomic data sets have recently renewed the interest in including nonadditive genetic effects in genomic evaluation models. The availability of genomic information enables the computation of covariance matrices of dominant genomic relationships among animals, similar to matrices of additive genomic relationships, and in a more straightforward manner than the pedigree-based dominance relationship matrix. Data from 19,357 genotyped American Angus males were used to estimate additive and dominant variance components for 3 growth traits: birth weight, weaning weight, and postweaning gain, and to evaluate the benefit of including dominance effects in beef cattle genomic evaluations. Variance components were estimated using 2 models: the first one included only additive effects (MG) and the second one included both additive and dominance effects (MGD). The dominance deviation variance ranged from 3% to 8% of the additive variance for all 3 traits. Gibbs sampling and REML estimates showed good concordance. Goodness of fit of the models was assessed by a likelihood ratio test. For all traits, MG fitted the data as well as MGD as assessed either by the likelihood ratio test or by the Akaike information criterion. Predictive ability of both models was assessed by cross-validation and did not improve when including dominance effects in the model. There was little evidence of nonadditive genetic variation for growth traits in the American Angus male population as only a small proportion of genetic variation was explained by nonadditive effects. A genomic model including the dominance effect did not improve the model fit. Consequently, including nonadditive effects in the genomic evaluation model is not beneficial for growth traits in the American Angus male population., (© The Author(s) 2019. Published by Oxford University Press on behalf of the American Society of Animal Science.)

Background: The dimensionality of genomic information is limited by the number of independent chromosome segments (M e ), which is a function of the effective population size. This dimensionality can be determined approximately by singular value decomposition of the gene content matrix, by eigenvalue decomposition of the genomic relationship matrix (GRM), or by the number of core animals in the algorithm for proven and young (APY) that maximizes the accuracy of genomic prediction. In the latter, core animals act as proxies to linear combinations of M e . Field studies indicate that a moderate accuracy of genomic selection is achieved with a small dataset, but that further improvement of the accuracy requires much more data. When only one quarter of the optimal number of core animals are used in the APY algorithm, the accuracy of genomic selection is only slightly below the optimal value. This suggests that genomic selection works on clusters of M e ., Results: The simulation included datasets with different population sizes and amounts of phenotypic information. Computations were done by genomic best linear unbiased prediction (GBLUP) with selected eigenvalues and corresponding eigenvectors of the GRM set to zero. About four eigenvalues in the GRM explained 10% of the genomic variation, and less than 2% of the total eigenvalues explained 50% of the genomic variation. With limited phenotypic information, the accuracy of GBLUP was close to the peak where most of the smallest eigenvalues were set to zero. With a large amount of phenotypic information, accuracy increased as smaller eigenvalues were added., Conclusions: A small amount of phenotypic data is sufficient to estimate only the effects of the largest eigenvalues and the associated eigenvectors that contain a large fraction of the genomic information, and a very large amount of data is required to estimate the remaining eigenvalues that account for a limited amount of genomic information. Core animals in the APY algorithm act as proxies of almost the same number of eigenvalues. By using an eigenvalues-based approach, it was possible to explain why the moderate accuracy of genomic selection based on small datasets only increases slowly as more data are added.

Combining breeds in a multibreed evaluation can have a negative impact on prediction accuracy, especially if single nucleotide polymorphism (SNP) effects differ among breeds. The aim of this study was to evaluate the use of a multibreed genomic relationship matrix (G), where SNP effects are considered to be unique to each breed, that is, nonshared. This multibreed G was created by treating SNP of different breeds as if they were on nonoverlapping positions on the chromosome, although, in reality, they were not. This simple setup may avoid spurious Identity by state (IBS) relationships between breeds and automatically considers breed-specific allele frequencies. This scenario was contrasted to a regular multibreed evaluation where all SNPs were shared, that is, the same position, and to single-breed evaluations. Different SNP densities (9k and 45k) and different effective population sizes (Ne) were tested. Five breeds mimicking recent beef cattle populations that diverged from the same historical population were simulated using different selection criteria. It was assumed that quantitative trait locus (QTL) effects were the same over all breeds. For the recent population, generations 1-9 had approximately half of the animals genotyped, whereas all animals in generation 10 were genotyped. Generation 10 animals were set for validation; therefore, each breed had a validation group. Analyses were performed using single-step genomic best linear unbiased prediction. Prediction accuracy was calculated as the correlation between true (T) and genomic estimated breeding values (GEBV). Accuracies of GEBV were lower for the larger Ne and low SNP density. All three evaluation scenarios using 45k resulted in similar accuracies, suggesting that the marker density is high enough to account for relationships and linkage disequilibrium with QTL. A shared multibreed evaluation using 9k resulted in a decrease of accuracy of 0.08 for a smaller Ne and 0.12 for a larger Ne. This loss was mostly avoided when markers were treated as nonshared within the same G matrix. A G matrix with nonshared SNP enables multibreed evaluations without considerably changing accuracy, especially with limited information per breed., (© The Author(s) 2019. Published by Oxford University Press on behalf of the American Society of Animal Science. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

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 objective of this study was to investigate the impact of accounting for parent average (PA) and genotyped daughters' average (GDA) on the estimation of deregressed estimated breeding values (dEBVs) used as pseudo-phenotypes in multiple-step genomic evaluations. Genomic estimated breeding values (GEBVs) were predicted, in eight different simulated scenarios, using dEBVs calculated based on four methods. These methods included PA and GDA in the dEBV (VR) or only GDA (VRpa) and excluded both PA and GDA from the dEBV with either all information or only information from PA and GDA (JA and NEW, respectively). In general, VR and NEW showed the lowest and highest GEBV reliabilities across scenarios, respectively. Among all deregression methods, VRpa and NEW provided the most consistent bias estimates across the majority of scenarios, and they significantly yielded the least biased GEBVs. Our results indicate that removing PA and GDA information from dEBVs used in multiple-step genomic evaluations can increase the reliability of GEBVs, when both bulls and their daughters are included in the training population., (© 2019 Blackwell Verlag GmbH.)

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.)

Pooling semen of multiple boars is commonly used in swine production systems. Compared with single boar systems, this technique changes family structure creating maternal half-sib families. The aim of this simulation study was to investigate how pooling semen affects the accuracy of estimating direct and maternal effects for individual piglet birth weight, in purebred pigs. Different scenarios of pooling semen were simulated by allowing the same female to mate from 1 to 6 boars, per insemination, whereas litter size was kept constant (N = 12). In each pooled boar scenario, genomic information was used to construct either the genomic relationship matrix (G) or to reconstruct pedigree in addition to G. Genotypes were generated for 60,000 SNPs evenly distributed across 18 autosomes. From the 5 simulated generations, only animals from generations 3 to 5 were genotyped (N = 36,000). Direct and maternal true breeding values (TBV) were computed as the sum of the effects of the 1,080 QTLs. Phenotypes were constructed as the sum of direct TBV, maternal TBV, an overall mean of 1.25 kg, and a residual effect. The simulated heritabilities for direct and maternal effects were 0.056 and 0.19, respectively, and the genetic correlation between both effects was -0.25. All simulations were replicated 5 times. Variance components and direct and maternal heritability were estimated using average information REML. Predictions were computed via pedigree-based BLUP and single-step genomic BLUP (ssGBLUP). Genotyped littermates in the last generation were used for validation. Prediction accuracies were calculated as correlations between EBV and TBV for direct (accdirect) and maternal (accmat) effects. When boars were known, accdirect were 0.21 (1 boar) and 0.26 (6 boars) for BLUP, whereas for ssGBLUP, they were 0.38 (1 boar) and 0.43 (6 boars). When boars were unknown, accdirect was lower in BLUP but similar in ssGBLUP. For the scenario with known boars, accmat was 0.58 and 0.63 for 1 and 6 boars, respectively, under ssGBLUP. For unknown boars, accmat was 0.63 for 2 boars and 0.62 for 6 boars in ssGBLUP. In general, accdirect and accmat were lower in the single-boar scenario compared with pooled semen scenarios, indicating that a half-sib structure is more adequate to estimate direct and maternal effects. Using pooled semen from multiple boars can help us to improve accuracy of predicting maternal and direct effects when maternal half-sib families are larger than 2., (© The Author(s) 2019. Published by Oxford University Press on behalf of the American Society of Animal Science. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Genomic selection (GS) is routinely applied to many purebreds and lines of farm species. However, this method can be extended to predictions across purebreds as well as for crossbreds. This is useful for swine and poultry, for which selection in nucleus herds is typically performed on purebred animals, whereas the commercial product is the crossbred animal. Single-step genomic BLUP (ssGBLUP) is a widely applied method that can explore the recently developed algorithm for proven and young (APY). The APY allows for greater efficiency in computing BLUP solutions by exploiting the theory of limited dimensionality of genomic information and chromosome segments (Me). This study investigates the predictivity as a proxy for accuracy across and within 2 purebred pig lines and their crosses, under the application of APY in ssGBLUP setup, and different levels of Me overlapping across populations. The data consisted of approximately 210k phenotypic records for 2 traits (T1 and T2) with moderate heritability. Genotypes for 43k SNP markers were available for approximately 46k animals, from which 26k and 16k belong to 2 pure lines (L1 and L2), and approximately 4k are crossbreds. The complete pedigree had more than 720k animals. Different multivariate ssGBLUP models were applied, either with the regular or APY inverse of the genomic relationship matrix (G). The models included a standard bivariate animal model with 3 lines evaluated as 1 joint line, and for each trait individually, a 3-trait animal model with each line treated as a separate trait. Both models provided the same predictivity across and within the lines. Using either of the pure lines data as a training set resulted in a similar predictivity for the crossbreed animals (0.18 to 0.21). Across-line predictive ability was limited to less than half of the maximum predictivity for each line (L1T1 0.33, L1T2 0.25, L2T1 0.35, L2T2 0.36). For crossbred predictions, APY performed equivalently to regular G inverse when the number of core animals was equal to the number of eigenvalues explaining between 98% and 99% of the variance of G (4k to 8k) including all lines. Predictivity across the lines is achievable because of the shared Me between them. The number of those shared segments can be obtained via eigenvalue decomposition of genomic information available for each line., (© The Author(s) 2019. Published by Oxford University Press on behalf of the American Society of Animal Science.)

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.)

We investigated the effects of different strategies for genotyping populations on variance components and heritabilities estimated with an animal model under restricted maximum likelihood (REML), genomic REML (GREML), and single-step GREML (ssGREML). A population with 10 generations was simulated. Animals from the last one, two or three generations were genotyped with 45,116 SNP evenly distributed on 27 chromosomes. Animals to be genotyped were chosen randomly or based on EBV. Each scenario was replicated five times. A single trait was simulated with three heritability levels (low, moderate, high). Phenotypes were simulated for only females to mimic dairy sheep and also for both sexes to mimic meat sheep. Variance component estimates from genomic data and phenotypes for one or two generations were more biased than from three generations. Estimates in the scenario without selection were the most accurate across heritability levels and methods. When selection was present in the simulations, the best option was to use genotypes of randomly selected animals. For selective genotyping, heritabilities from GREML were more biased compared to those estimated by ssGREML, because ssGREML was less affected by selective or limited genotyping., (© 2018 Blackwell Verlag GmbH.)

When the environment on which the animals are raised is very diverse, selecting the best sires for different environments may require the use of models that account for genotype by environment interaction (G × E). The main objective of this study was to evaluate the existence of G × E for yearling weight (YW) in Nellore cattle using reaction norm models with only pedigree and pedigree combined with genomic relationships. Additionally, genomic regions associated with each environment gradient were identified. A total of 67,996 YW records were used in reaction norm models to calculate EBV and genomic EBV. The method of choice for genomic evaluations was single-step genomic BLUP (ssGBLUP). Traditional and genomic models were tested on the ability to predict future animal performance. Genetic parameters for YW were obtained with the average information restricted maximum likelihood method, with and without adding genomic information for 5,091 animals. Additive genetic variances explained by windows of 200 adjacent SNP were used to identify genomic regions associated with the environmental gradient. Estimated variance components for the intercept and the slope in traditional and genomic models were similar. In both models, the observed changes in heritabilities and genetic correlations for YW across environments indicate the occurrence of genotype by environment interactions. Both traditional and genomic models were capable of identifying the genotype by environment interaction; however, the inclusion of genomic information in reaction norm models improved the ability to predict animals' future performance by 7.9% on average. The proportion of genetic variance explained by the top SNP window was 0.77% for the regression intercept (BTA5) and 0.82% for the slope (BTA14). Single-step GBLUP seems to be a suitable model to predict genetic values for YW in different production environments.

We investigated the importance of SNP weighting in populations with 2,000 to 25,000 genotyped animals. Populations were simulated with two effective sizes (20 or 100) and three numbers of QTL (10, 50 or 500). Pedigree information was available for six generations; phenotypes were recorded for the four middle generations. Animals from the last three generations were genotyped for 45,000 SNP. Single-step genomic BLUP (ssGBLUP) and weighted ssGBLUP (WssGBLUP) were used to estimate genomic EBV using a genomic relationship matrix (G). The WssGBLUP performed better in small genotyped populations; however, any advantage for WssGBLUP was reduced or eliminated when more animals were genotyped. WssGBLUP had greater resolution for genome-wide association (GWA) as did increasing the number of genotyped animals. For few QTL, accuracy was greater for WssGBLUP than ssGBLUP; however, for many QTL, accuracy was the same for both methods. The largest genotyped set was used to assess the dimensionality of genomic information (number of effective SNP). The number of effective SNP was considerably less in weighted G than in unweighted G. Once the number of independent SNP is well represented in the genotyped population, the impact of SNP weighting becomes less important., (© 2017 Blackwell Verlag GmbH.)

In genomic evaluations, it is desirable to have low computing cost while retaining high accuracy of evaluation for young animals. When the population is large but only few animals have phenotypes, especially for low heritability traits, the convergence rate of BLUP or single-step genomic BLUP (ssGBLUP) can be very slow. This study investigates the effect of pedigree truncation on convergence rate and solutions of ssGBLUP for data exhibiting slow convergence. The data consisted of 216,000, 221,000, 732,000, and 579,000 phenotypes on 4 traits. Heritabilities were less than 0.1 for 2 traits and greater than 0.2 for the other 2 traits. The full pedigree consisted of 2.4 million animals. Genotypes were available for 33,000 animals and consisted of 60,000 SNP. Two bivariate animal models were fit using pedigree-based BLUP or ssGBLUP. Either a regular or the algorithm for proven and young (APY) inverse was used for the genomic relationship matrix. Different pedigree depths were analyzed including full pedigree and 1 to 5 ancestral generations. Pedigree depths were defined as n ancestral generations for animals with phenotypes. The number of animals in the reduced pedigrees varied from 226,000 and 760,000 for 1 generation to 228,000 and 767,000 for 5 generations. Genomic EBV (GEBV) for genotyped animals had correlations greater than 0.99 between runs with the full and reduced pedigrees with 2 to 5 generations. A single generation of pedigree was not sufficient to obtain the same GEBV as full pedigree. The convergence rate was the worst with the full pedigree and generally improved with reduced pedigrees. Using ssGBLUP with the APY inverse improved convergence without affecting accuracy. Reducing pedigrees and the APY are important tools to reduce the computational cost in the implementation of ssGBLUP.

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.)

Background: Most genomic prediction applications in animal breeding use genotypes with tens of thousands of single nucleotide polymorphisms (SNPs). However, modern sequencing technologies and imputation algorithms can generate ultra-high-density genotypes (including millions of SNPs) at an affordable cost. Empirical studies have not produced clear evidence that using ultra-high-density genotypes can significantly improve prediction accuracy. However, (whole-genome) prediction accuracy is not very informative about the ability of a model to capture the genetic signals from specific genomic regions. To address this problem, we propose a simple methodology that detects chromosome regions for which a specific model (e.g., single-step genomic best linear unbiased prediction (ssGBLUP)) may fail to fully capture the genetic signal present in such segments-a phenomenon that we refer to as signal leakage. We propose to detect regions with evidence of signal leakage by testing the association of residuals from a pedigree or a genomic model with SNP genotypes. We discuss how this approach can be used to map regions with signals that are poorly captured by a model and to identify strategies to fix those problems (e.g., using a different prior or increasing marker density). Finally, we explored the proposed approach to scan for signal leakage of different models (pedigree-based, ssGBLUP, and various Bayesian models) applied to growth-related phenotypes (average daily gain and backfat thickness) in pigs., Results: We report widespread evidence of signal leakage for pedigree-based models. Including a percentage of animals with SNP data in ssGBLUP reduced the extent of signal leakage. However, local peaks of missed signals remained in some regions, even when all animals were genotyped. Using variable selection priors solves leakage points that are caused by excessive shrinkage of marker effects. Nevertheless, these models still miss signals in some regions due to low linkage disequilibrium between the SNPs on the array used and causal variants. Thus, we discuss how such problems could be addressed by adding sequence SNPs from those regions to the prediction model., Conclusions: Residual single-marker regression analysis is a simple approach that can be used to detect regional genomic signals that are poorly captured by a model and to indicate ways to fix such problems., (© 2023. ’Institut National de Recherche en Agriculture, Alimentation et Environnement (INRAE).)

Background: The innovations of the "Omics Era" have ushered in significant advancements in genetic improvement of agriculturally important animal species through transforming genetics, genomics and breeding strategies. These advancements were often coordinated, in part, by support provided over 30 years through the 1993–2023 National Research Support Project 8 (NRSP8, National Animal Genome Research Program, NAGRP) and affiliate projects focused on enabling genomic discoveries in livestock, poultry, and aquaculture species. These significant and parallel advances demand strategic planning of future research priorities. This paper, as an output from the May 2023 Aquaculture Genomics, Genetics, and Breeding Workshop, provides an updated status of genomic resources for United States aquaculture species, highlighting major achievements and emerging priorities. Main text: Finfish and shellfish genome and omics resources enhance our understanding of genetic architecture and heritability of performance and production traits. The 2023 Workshop identified present aims for aquaculture genomics/omics research to build on this progress: (1) advancing reference genome assembly quality; (2) integrating multi-omics data to enhance analysis of production and performance traits; (3) developing resources for the collection and integration of phenomics data; (4) creating pathways for applying and integrating genomics information across animal industries; and (5) providing training, extension, and outreach to support the application of genome to phenome. Research focuses should emphasize phenomics data collection, artificial intelligence, identifying causative relationships between genotypes and phenotypes, establishing pathways to apply genomic information and tools across aquaculture industries, and an expansion of training programs for the next-generation workforce to facilitate integration of genomic sciences into aquaculture operations to enhance productivity, competitiveness, and sustainability. Conclusion: This collective vision of applying genomics to aquaculture breeding with focus on the highlighted priorities is intended to facilitate the continued advancement of the United States aquaculture genomics, genetics and breeding research community and industries. Critical challenges ahead include the practical application of genomic tools and analytical frameworks beyond academic and research communities that require collaborative partnerships between academia, government, and industry. The scope of this review encompasses the use of omics tools and applications in the study of aquatic animals cultivated for human consumption in aquaculture settings throughout their life-cycle. [ABSTRACT FROM AUTHOR]

Background: Automatic and continuous recording of vaginal temperature (TV) using wearable sensors causes minimal disruptions to animal behavior and can generate data that enable the evaluation of temporal body temperature variation under heat stress (HS) conditions. However, the genetic basis of TV in lactating sows from a longitudinal perspective is still unknown. The objectives of this study were to define statistical models and estimate genetic parameters for TV in lactating sows using random regression models, and identify genomic regions and candidate genes associated with HS indicators derived from automatically-recorded TV. Results: Heritability estimates for TV ranged from 0.14 to 0.20 over time (throughout the day and measurement period) and from 0.09 to 0.18 along environmental gradients (EG, − 3.5 to 2.2, which correspond to dew point values from 14.87 to 28.19 ˚C). Repeatability estimates of TV over time and along EG ranged from 0.57 to 0.66 and from 0.54 to 0.77, respectively. TV measured from 12h00 to 16h00 had moderately high estimates of heritability (0.20) and repeatability (0.64), indicating that this period might be the most suitable for recording TV for genetic selection purposes. Significant genotype-by-environment interactions (GxE) were observed and the moderately high estimates of genetic correlations between pairs of extreme EG indicate potential re-ranking of selection candidates across EG. Two important genomic regions on chromosomes 10 (59.370–59.998 Mb) and16 (21.548–21.966 Mb) were identified. These regions harbor the genes CDC123, CAMK1d, SEC61A2, and NUDT5 that are associated with immunity, protein transport, and energy metabolism. Across the four time-periods, respectively 12, 13, 16, and 10 associated genomic regions across 14 chromosomes were identified for TV. For the three EG classes, respectively 18, 15, and 14 associated genomic windows were identified for TV, respectively. Each time-period and EG class had uniquely enriched genes with identified specific biological functions, including regulation of the nervous system, metabolism and hormone production. Conclusions: TV is a heritable trait with substantial additive genetic variation and represents a promising indicator trait to select pigs for improved heat tolerance. Moderate GxE for TV exist, indicating potential re-ranking of selection candidates across EG. TV is a highly polygenic trait regulated by a complex interplay of physiological, cellular and behavioral mechanisms. [ABSTRACT FROM AUTHOR]

Background: Hoof structure and health are essential for the welfare and productivity of beef cattle. Therefore, we assessed the genetic and genomic background of foot score traits in American (US) and Australian (AU) Angus cattle and investigated the feasibility of performing genomic evaluations combining data for foot score traits recorded in US and AU Angus cattle. The traits evaluated were foot angle (FA) and claw set (CS). In total, 109,294 and ~ 1.12 million animals had phenotypic and genomic information, respectively. Four sets of analyses were performed: (1) genomic connectedness between US and AU Angus cattle populations and population structure, (2) estimation of genetic parameters, (3) single-step genomic prediction of breeding values, and (4) single-step genome-wide association studies for FA and CS. Results: There was no clear genetic differentiation between US and AU Angus populations. Similar heritability estimates (FA: 0.22–0.24 and CS: 0.22–0.27) and moderate-to-high genetic correlations between US and AU foot scores (FA: 0.61 and CS: 0.76) were obtained. A joint-genomic prediction using data from both populations outperformed within-country genomic evaluations. A genomic prediction model considering US and AU datasets as a single population performed similarly to the scenario accounting for genotype-by-environment interactions (i.e., multiple-trait model considering US and AU records as different traits), even though the genetic correlations between countries were lower than 0.80. Common significant genomic regions were observed between US and AU for FA and CS. Significant single nucleotide polymorphisms were identified on the Bos taurus (BTA) chromosomes BTA1, BTA5, BTA11, BTA13, BTA19, BTA20, and BTA23. The candidate genes identified were primarily from growth factor gene families, including FGF12 and GDF5, which were previously associated with bone structure and repair. Conclusions: This study presents comprehensive population structure and genetic and genomic analyses of foot scores in US and AU Angus cattle populations, which are essential for optimizing the implementation of genomic selection for improved foot scores in Angus cattle breeding programs. We have also identified candidate genes associated with foot scores in the largest Angus cattle populations in the world and made recommendations for genomic evaluations for improved foot score traits in the US and AU. [ABSTRACT FROM AUTHOR]

Background: Carcass traits are important in pig breeding programs for improving pork production. Understanding the genetic variants underlies complex phenotypes can help explain trait variation in pigs. In this study, we integrated a weighted single-step genome-wide association study (wssGWAS) and copy number variation (CNV) analyses to map genetic variations and genes associated with loin muscle area (LMA), loin muscle depth (LMD) and lean meat percentage (LMP) in Duroc pigs. Results: Firstly, we performed a genome-wide analysis for CNV detection using GeneSeek Porcine SNP50 Bead chip data of 3770 pigs. A total of 11,100 CNVs were detected, which were aggregated by overlapping 695 CNV regions (CNVRs). Next, we investigated CNVs of pigs from the same population by whole-genome resequencing. A genome-wide analysis of 21 pigs revealed 23,856 CNVRs that were further divided into three categories (851 gain, 22,279 loss, and 726 mixed), which covered 190.8 Mb (~ 8.42%) of the pig autosomal genome. Further, the identified CNVRs were used to determine an overall validation rate of 68.5% for the CNV detection accuracy of chip data. CNVR association analyses identified one CNVR associated with LMA, one with LMD and eight with LMP after applying stringent Bonferroni correction. The wssGWAS identified eight, six and five regions explaining more than 1% of the additive genetic variance for LMA, LMD and LMP, respectively. The CNVR analyses and wssGWAS identified five common regions, of which three regions were associated with LMA and two with LMP. Four genes (DOK7, ARAP1, ELMO2 and SLC13A3) were highlighted as promising candidates according to their function. Conclusions: We determined an overall validation rate for the CNV detection accuracy of low-density chip data and constructed a genomic CNV map for Duroc pigs using resequencing, thereby proving a value genetic variation resource for pig genome research. Furthermore, our study utilized a composite genetic strategy for complex traits in pigs, which will contribute to the study for elucidating the genetic architecture that may be influenced and regulated by multiple forms of variations. [ABSTRACT FROM AUTHOR]

Background: Selection of livestock based on their robustness or sensitivity to environmental variation could help improve the efficiency of production systems, particularly in the light of climate change. Genetic variation in robustness arises from genotype-by-environment (G × E) interactions, with genotypes performing differently when animals are raised in contrasted environments. Understanding the nature of this genetic variation is essential to implement strategies to improve robustness. In this study, our aim was to explore the genetics of robustness in Australian sheep to different growth environments using linear reaction norm models (RNM), with post-weaning weight records of 22,513 lambs and 60 k single nucleotide polymorphisms (SNPs). The use of scale-corrected genomic estimated breeding values (GEBV) for the slope to account for scale-type G × E interactions was also investigated. Results: Additive genetic variance was observed for the slope of the RNM, with genetic correlations between low- and high-growth environments indicating substantial re-ranking of genotypes (0.44–0.49). The genetic variance increased from low- to high-growth environments. The heritability of post-weaning body weight ranged from 0.28 to 0.39. The genetic correlation between intercept and slope of the reaction norm for post-weaning body weight was low to moderate when based on the estimated (co)variance components but was much higher when based on back-solved SNP effects. An initial analysis suggested that a region on chromosome 11 affected both the intercept and the slope, but when the GEBV for the slope were conditioned on the GEBV for the intercept to remove the effect of scale-type G × E interactions on SNP effects for robustness, a single genomic region on chromosome 7 was found to be associated with robustness. This region included genes previously associated with growth traits and disease susceptibility in livestock. Conclusions: This study shows a significant genetic variation in the slope of RNM that could be used for selecting for increased robustness of sheep. Both scale-type and rank-type G × E interactions contributed to variation in the slope. The correction for scale effects of GEBV for the slope should be considered when analysing robustness using RNM. Overall, robustness appears to be a highly polygenic trait. [ABSTRACT FROM AUTHOR]

The review focuses on breeding practices aimed at improving resistance to diseases and health disorders that are associated with better efficiency, welfare and longevity of cows. It is commonly known that diseases like mastitis, foot and claw disorders, metabolic and reproductive issues seriously violate dairy cows' well-being. The cause of prevailing health and fertility deterioration has been the intensive selection merely based on higher milk production starting after the Second World War. Therefore since the last decades of the 20th-century genetic selection programs have been increasingly focused on increasing resistance to diseases and improving fertility traits using several omics techniques, including genomics. The first steps for maintaining the goal of genetic breeding for disease resistance were the introduction of disease data collection at national levels followed by an elaboration of gene evaluation systems. It was proved that diseases exhibit additive genetic variability exploitable in the breeding. For greater breeding efficiency, the indicator traits are used, which were strongly genetically correlated with health traits, have higher heritability, and above all, are usually easily measurable at low cost. Genome-wide association studies have identified several polymorphisms associated with disease liability that could also be used for speeding up of selection efforts. [ABSTRACT FROM AUTHOR]

Background: Copy number variation (CNV) is an important source of genetic variation that has a significant influence on phenotypic diversity, economically important traits and the evolution of livestock species. In this study, the genome-wide CNV distribution characteristics of 32 fine-wool sheep from three breeds were analyzed using resequencing. Results: A total of 1,747,604 CNVs were detected in this study, and 7228 CNV regions (CNVR) were obtained after merging overlapping CNVs; these regions accounted for 2.17% of the sheep reference genome. The average length of the CNVRs was 4307.17 bp. "Deletion" events took place more frequently than "duplication" or "both" events. The CNVRs obtained overlapped with previously reported sheep CNVRs to variable extents (4.39–55.46%). Functional enrichment analysis showed that the CNVR-harboring genes were mainly involved in sensory perception systems, nutrient metabolism processes, and growth and development processes. Furthermore, 1855 of the CNVRs were associated with 166 quantitative trait loci (QTL), including milk QTLs, carcass QTLs, and health-related QTLs, among others. In addition, the 32 fine-wool sheep were divided into horned and polled groups to analyze for the selective sweep of CNVRs, and it was found that the relaxin family peptide receptor 2 (RXFP2) gene was strongly influenced by selection. Conclusions: In summary, we constructed a genomic CNV map for Chinese indigenous fine-wool sheep using resequencing, thereby providing a valuable genetic variation resource for sheep genome research, which will contribute to the study of complex traits in sheep. [ABSTRACT FROM AUTHOR]

Residual feed intake (RFI) is the most used measure of feed efficiency. However, considering the importance of concentrates in the ration, a new index, the residual concentrate intake (RCI), was here defined. RCI aims to measure the individual efficiency in converting the concentrate into animal products. Brown Swiss young bulls (N = 736) were genotyped at 41,183 loci. Animals were housed in pens equipped with an automatic feeding system able to recognise the animal and record the concentrate intake. The diet consisted of concentrate and hay (ad libitum). The new RCI index was calculated as the residuals of the linear regression of concentrate intake on metabolic live weight and average daily gain. Animals were ranked according to their corrected RCI and divided into low (LRCI) and high phenotypes (HRCI). A low heritability (0.06 ± 0.03) was estimated using only genomics for this new index. Results from multivariate (M-GWAS) and Bayesian (B-GWAS) approaches were combined to identify SNP associated with RCI. The M-GWAS selected 698 SNPs potentially associated, whereas no significant markers were obtained in B-GWAS. Markers in the last approach were ranked according to their posterior inclusion probability and the first 698 were retained. Only SNPs in common between sorted B-GWAS and M-GWAS (N = 11) were considered associated with RCI. A total of 48 candidate genes were retrieved near these SNPs. Most of them were previously reported to be associated with feed efficiency and RFI. The combined use of multivariate and Bayesian techniques allow to identify SNPs associated with the investigated trait. RCI could be promising to select animals 48 candidate genes were found associated with RCI Multivariate technique allowed to identify significant SNPs [ABSTRACT FROM AUTHOR]

Genome sequences for hundreds of mammalian species are available, but an understanding of their genomic regulatory regions, which control gene expression, is only beginning. A comprehensive prediction of potential active regulatory regions is necessary to functionally study the roles of the majority of genomic variants in evolution, domestication, and animal production. We developed a computational method to predict regulatory DNA sequences (promoters, enhancers, and transcription factor binding sites) in production animals (cows and pigs) and extended its broad applicability to other mammals. The method utilizes human regulatory features identified from thousands of tissues, cell lines, and experimental assays to find homologous regions that are conserved in sequences and genome organization and are enriched for regulatory elements in the genome sequences of other mammalian species. Importantly, we developed a filtering strategy, including a machine learning classification method, to utilize a very small number of species-specific experimental datasets available to select for the likely active regulatory regions. The method finds the optimal combination of sensitivity and accuracy to unbiasedly predict regulatory regions in mammalian species. Furthermore, we demonstrated the utility of the predicted regulatory datasets in cattle for prioritizing variants associated with multiple production and climate change adaptation traits and identifying potential genome editing targets. [ABSTRACT FROM AUTHOR]

Genomic selection has been widely used for complex quantitative trait in farm animals. Estimations of breeding values for slaughter traits are most important to beef cattle industry, and it is worthwhile to investigate prediction accuracies of genomic selection for these traits. In this study, we assessed genomic predictive abilities for average daily gain weight (ADG), live weight (LW), carcass weight (CW), dressing percentage (DP), lean meat percentage (LMP) and retail meat weight (RMW) using Illumina Bovine 770K SNP Beadchip in Chinese Simmental cattle. To evaluate the abilities of prediction, marker effects were estimated using genomic BLUP (GBLUP) and three parallel Bayesian models, including multiple chains parallel BayesA, BayesB and BayesCπ (PBayesA, PBayesB and PBayesCπ). Training set and validation set were divided by random allocation, and the predictive accuracies were evaluated using 5-fold cross validations. We found the accuracies of genomic predictions ranged from 0.195±0.084 (GBLUP for LMP) to 0.424±0.147 (PBayesB for CW). The average accuracies across traits were 0.327±0.085 (GBLUP), 0.335±0.063 (PBayesA), 0.347±0.093 (PBayesB) and 0.334±0.077 (PBayesCπ), respectively. Notably, parallel Bayesian models were more accurate than GBLUP across six traits. Our study suggested that genomic selections with multiple chains parallel Bayesian models are feasible for slaughter traits in Chinese Simmental cattle. The estimations of direct genomic breeding values using parallel Bayesian methods can offer important insights into improving prediction accuracy at young ages and may also help to identify superior candidates in breeding programs. [ABSTRACT FROM AUTHOR]

Background: Genomic predictions from BayesA and BayesB use training data that include animals with both phenotypes and genotypes. Single-step methodologies allow additional information from non-genotyped relatives to be included in the analysis. The single-step genomic best linear unbiased prediction (SSGBLUP) method uses a relationship matrix computed from marker and pedigree information, in which missing genotypes are imputed implicitly. Single-step Bayesian regression (SSBR) extends SSGBLUP to BayesB-like models using explicitly imputed genotypes for non-genotyped individuals. Methods: Carcass records included 988 genotyped Hanwoo steers with 35,882 SNPs and 1438 non-genotyped steers that were measured for back-fat thickness (BFT), carcass weight (CWT), eye-muscle area, and marbling score (MAR). Single-trait pedigree-based BLUP, Bayesian methods using only genotyped individuals, SSGBLUP and SSBR methods were compared using cross-validation. Results: Methods using genomic information always outperformed pedigree-based BLUP when the same phenotypic data were modeled from either genotyped individuals only or both genotyped and non-genotyped individuals. For BFT and MAR, accuracies were higher with single-step methods than with BayesB, BayesC and BayesCπ. Gains in accuracy with the single-step methods ranged from +0.06 to +0.09 for BFT and from +0.05 to +0.07 for MAR. For CWT, SSBR always outperformed the corresponding Bayesian methods that used only genotyped individuals. However, although SSGBLUP incorporated information from non-genotyped individuals, prediction accuracies were lower with SSGBLUP than with BayesC (π = 0.9999) and BayesB (π = 0.98) for CWT because, for this particular trait, there was a benefit from the mixture priors of the effects of the single nucleotide polymorphisms. Conclusions: Single-step methods are the preferred approaches for prediction combining genotyped and nongenotyped animals. Alternative priors allow SSBR to outperform SSGBLUP in some cases. [ABSTRACT FROM AUTHOR]

Background: A genomic relationship matrix (GRM) can be inverted efficiently with the Algorithm for Proven and Young (APY) through recursion on a small number of core animals. The number of core animals is theoretically linked to effective population size (Ne). In a simulation study, the optimal number of core animals was equal to the number of largest eigenvalues of GRM that explained 98% of its variation. The purpose of this study was to find the optimal number of core animals and estimate Ne for different species. Methods: Datasets included phenotypes, pedigrees, and genotypes for populations of Holstein, Jersey, and Angus cattle, pigs, and broiler chickens. The number of genotyped animals varied from 15,000 for broiler chickens to 77,000 for Holsteins, and the number of single-nucleotide polymorphisms used for genomic prediction varied from 37,000 to 61,000. Eigenvalue decomposition of the GRM for each population determined numbers of largest eigenvalues corresponding to 90, 95, 98, and 99% of variation. Results: The number of eigenvalues corresponding to 90% (98%) of variation was 4527 (14,026) for Holstein, 3325 (11,500) for Jersey, 3654 (10,605) for Angus, 1239 (4103) for pig, and 1655 (4171) for broiler chicken. Each trait in each species was analyzed using the APY inverse of the GRM with randomly selected core animals, and their number was equal to the number of largest eigenvalues. Realized accuracies peaked with the number of core animals corresponding to 98% of variation for Holstein and Jersey and closer to 99% for other breed/species. Ne was estimated based on comparisons of eigenvalue decomposition in a simulation study. Assuming a genome length of 30 Morgan, Ne was equal to 149 for Holsteins, 101 for Jerseys, 113 for Angus, 32 for pigs, and 44 for broilers. Conclusions: Eigenvalue profiles of GRM for common species are similar to those in simulation studies although they are affected by number of genotyped animals and genotyping quality. For all investigated species, the APY required less than 15,000 core animals. Realized accuracies were equal or greater with the APY inverse than with regular inversion. Eigenvalue analysis of GRM can provide a realistic estimate of Ne. [ABSTRACT FROM AUTHOR]

Background: The mixed linear model employed for genomic best linear unbiased prediction (GBLUP) includes the breeding value for each animal as a random effect that has a mean of zero and a covariance matrix proportional to the genomic relationship matrix (Ggg), where the inverse of Ggg is required to set up the usual mixed model equations (MME). When only some animals have genomic information, genomic predictions can be obtained by an extension known as single-step GBLUP, where the covariance matrix of breeding values is constructed by combining the pedigree-based additive relationship matrix with Ggg. The inverse of the combined relationship matrix can be obtained efficiently, provided Ggg can be inverted. In some livestock species, however, the number Ng of animals with genomic information exceeds the number of marker covariates used to compute Ggg, and this results in a singular Ggg. For such a case, an efficient and exact method to obtain GBLUP and single-step GBLUP is presented here. Results: Exact methods are already available to obtain GBLUP when Ggg is singular, but these require working with large dense matrices. Another approach is to modify Ggg to make it nonsingular by adding a small value to all its diagonals or regressing it towards the pedigree-based relationship matrix. This, however, results in the inverse of Ggg being dense and difficult to compute as Ng grows. The approach presented here recognizes that the number r of linearly independent genomic breeding values cannot exceed the number of marker covariates, and the mixed linear model used here for genomic prediction only fits these r linearly independent breeding values as random effects. Conclusions: The exact method presented here was compared to Apy-GBLUP and to Apy single-step GBLUP, both of which are approximate methods that use a modified Ggg that has a sparse inverse which can be computed efficiently. In a small numerical example, predictions from the exact approach and Apy were almost identical, but the MME from Apy had a condition number about 1000 times larger than that from the exact approach, indicating ill-conditioning of the MME from Apy. The practical application of exact SSGBLUP is not more difficult than implementation of Apy. [ABSTRACT FROM AUTHOR]

Genomic selection, that is based on the prediction of the breeding value (the genomic breeding value or GEBV) of the animals considering genomic information, is changing breeding strategies and approaches in dairy cattle and in several other livestock species. The starting points for the application of genomic selection in pigs were the development of a first commercial single-nucleotide polymorphism panel for high throughput genotyping, the sequencing of the pig genome and the application of statistical and methodological approaches first developed in dairy cattle and then adapted to the peculiarities of the pig breeding industry. In this review, we focused on the specific applications of the genomic selection in pigs, considering its limits, its advantages and its perspectives throughout an analysis of the simulation studies and field applications already available targeting many different traits (with high and low heritability). In addition, we presented an overview of the problems related to the implementation of genomic selection in crossbred and multi-breed pig populations and the potential solutions taking into account the economic aspects that should be faced in including genomic selection in pig breeding programmes. [ABSTRACT FROM PUBLISHER]

Background: Genomic selection and estimation of genomic breeding values (GBV) are widely used in cattle and plant breeding. Several studies have attempted to detect population subdivision by investigating the structure of the genomic relationship matrix G. However, the question of how these effects influence GBV estimation using genomic best linear unbiased prediction (GBLUP) has received little attention. Methods: We propose a simple method to decompose G into two independent covariance matrices, one describing the covariance that results from systematic differences in allele frequencies between groups at the pedigree base (GA*) and the other describing genomic relationships (GS) corrected for these differences. Using this decomposition and Fst statistics, we examined whether observed genetic distances between genotyped subgroups within populations resulted from the heterogeneous genetic structure present at the base of the pedigree and/or from breed divergence. Using this decomposition, we tested three models in a forward prediction validation scenario on six traits using Brown Swiss and dual-purpose Fleckvieh cattle data. Model 0 (M0) used both components and is equivalent to the model using the standard G-matrix. Model 1 (M1) used GS only and model 2 (M2), an extension of M1, included a fixed genetic group effect. Moreover, we analyzed the matrix of contributions of each base group (Q) and estimated the effects and prediction errors of each base group using M0 and M1. Results: The proposed decomposition of G helped to examine the relative importance of the effects of base groups and segregation in a given population. We found significant differences between the effects of base groups for each breed. In forward prediction, differences between models in terms of validation reliability of estimated direct genomic values were small but predictive power was consistently lowest for M1. The relative advantage of M0 or M2 in prediction depended on breed, trait and genetic composition of the validation group. Our approach presents a general analogy with the use of genetic groups in conventional animal models and provides proof that standard GBLUP using G yields solutions equivalent to M0, where base groups are considered as correlated random effects within the additive genetic variance assigned to the genetic base. [ABSTRACT FROM AUTHOR]

Background: It becomes clear that the increase in the density of marker panels and even the use of sequence data didn't result in any meaningful increase in the accuracy of genomic selection (GS) using either regression (RM) or variance component (VC) approaches. This is in part due to the limitations of current methods. Association model are well over-parameterized and suffer from severe co-linearity and lack of statistical power. Even when the variant effects are not directly estimated using VC based approaches, the genomic relationships didn't improve after the marker density exceeded a certain threshold. SNP prioritization-based fixation index (FST) scores were used to track the majority of significant QTL and to reduce the dimensionality of the association model. Results: Two populations with average LD between adjacent markers of 0.3 (P1) and 0.7 (P2) were simulated. In both populations, the genomic data consisted of 400 K SNP markers distributed on 10 chromosomes. The density of simulated genomic data mimics roughly 1.2 million SNP markers in the bovine genome. The genomic relationship matrix (G) was calculated for each set of selected SNPs based on their FST score and similar numbers of SNPs were selected randomly for comparison. Using all 400 K SNPs, 46% of the off-diagonal elements (OD) were between − 0.01 and 0.01. The same portion was 31, 23 and 16% when 80 K, 40 K and 20 K SNPs were selected based on FST scores. For randomly selected 20 K SNP subsets, around 33% of the OD fell within the same range. Genomic similarity computed using SNPs selected based on FST scores was always higher than using the same number of SNPs selected randomly. Maximum accuracies of 0.741 and 0.828 were achieved when 20 and 10 K SNPs were selected based on FST scores in P1 and P2, respectively. Conclusions: Genomic similarity could be maximized by the decrease in the number of selected SNPs, but it also leads to a decrease in the percentage of genetic variation explained by the selected markers. Finding the balance between these two parameters could optimize the accuracy of GS in the presence of high density marker panels. [ABSTRACT FROM AUTHOR]

Background: The single-step single nucleotide polymorphism best linear unbiased prediction (ssSNPBLUP) method, such as single-step genomic BLUP (ssGBLUP), simultaneously analyses phenotypic, pedigree, and genomic information of genotyped and non-genotyped animals. In contrast to ssGBLUP, SNP effects are fitted explicitly as random effects in the ssSNPBLUP model. Similarly, principal components associated with the genomic information can be fitted explicitly as random effects in a single-step principal component BLUP (ssPCBLUP) model to remove noise in genomic information. Single-step genomic BLUP is solved efficiently by using the preconditioned conjugate gradient (PCG) method. Unfortunately, convergence issues have been reported when solving ssSNPBLUP by using PCG. Poor convergence may be linked with poor spectral condition numbers of the preconditioned coefficient matrices of ssSNPBLUP. These condition numbers, and thus convergence, could be improved through the deflated PCG (DPCG) method, which is a two-level PCG method for ill-conditioned linear systems. Therefore, the first aim of this study was to compare the properties of the preconditioned coefficient matrices of ssGBLUP and ssSNPBLUP, and to document convergence patterns that are obtained with the PCG method. The second aim was to implement and test the efficiency of a DPCG method for solving ssSNPBLUP and ssPCBLUP. Results: For two dairy cattle datasets, the smallest eigenvalues obtained for ssSNPBLUP (ssPCBLUP) and ssGBLUP, both solved with the PCG method, were similar. However, the largest eigenvalues obtained for ssSNPBLUP and ssPCBLUP were larger than those for ssGBLUP, which resulted in larger condition numbers and in slow convergence for both systems solved by the PCG method. Different implementations of the DPCG method led to smaller condition numbers, and faster convergence for ssSNPBLUP and for ssPCBLUP, by deflating the largest unfavourable eigenvalues. Conclusions: Poor convergence of ssSNPBLUP and ssPCBLUP when solved by the PCG method are related to larger eigenvalues and larger condition numbers in comparison to ssGBLUP. These convergence issues were solved with a DPCG method that annihilates the effect of the largest unfavourable eigenvalues of the preconditioned coefficient matrix of ssSNPBLUP and of ssPCBLUP on the convergence of the PCG method. It resulted in a convergence pattern, at least, similar to that of ssGBLUP. [ABSTRACT FROM AUTHOR]