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Abstract Background Single-nucleotide polymorphism (SNP) effects can be backsolved from ssGBLUP genomic estimated breeding values (GEBV) and used for genome-wide association studies (ssGWAS). However, obtaining p-values for those SNP effects relies on the inversion of dense matrices, which poses computational limitations in large genotyped populations. In this study, we present a method to approximate SNP p-values for ssGWAS with many genotyped animals. This method relies on the combination of a sparse approximation of the inverse of the genomic relationship matrix ( $${\mathbf{G}}_{\mathbf{A}\mathbf{P}\mathbf{Y}}^\mathbf{-1}$$ G A P Y - 1 ) built with the algorithm for proven and young ( $$\text{APY}$$ APY ) and an approximation of the prediction error variance of SNP effects which does not require the inversion of the left-hand side (LHS) of the mixed model equations. To test the proposed p-value computing method, we used a reduced genotyped population of 50K genotyped animals and compared the approximated SNP p-values with benchmark p-values obtained with the direct inverse of LHS built with an exact genomic relationship matrix ( $${\mathbf{G}}^\mathbf{-1})$$ G - 1 ) . Then, we applied the proposed approximation method to obtain SNP p-values for a larger genotyped population composed of 450K genotyped animals. Results The same genomic regions on chromosomes 7 and 20 were identified across all p-value computing methods when using 50K genotyped animals. In terms of computational requirements, obtaining p-values with the proposed approximation reduced the wall-clock time by 38 times and the memory requirement by ten times compared to using the exact inversion of the LHS. When the approximation was applied to a population of 450K genotyped animals, two new significant regions on chromosomes 6 and 14 were uncovered, indicating an increase in GWAS detection power when including more genotypes in the analyses. The process of obtaining p-values with the approximation and 450K genotyped individuals took 24.5 wall-clock hours and 87.66GB of memory, which is expected to increase linearly with the addition of noncore genotyped individuals. Conclusions With the proposed method, obtaining p-values for SNP effects in ssGWAS is computationally feasible in large genotyped populations. The computational cost of obtaining p-values in ssGWAS may no longer be a limitation in extensive populations with many genotyped animals.

Abstract Background With the introduction of digital phenotyping and high-throughput data, traits that were previously difficult or impossible to measure directly have become easily accessible, offering the opportunity to enhance the efficiency and rate of genetic gain in animal production. It is of interest to assess how behavioral traits are indirectly related to the production traits during the performance testing period. The aim of this study was to assess the quality of behavior data extracted from day-wise video recordings and estimate the genetic parameters of behavior traits and their phenotypic and genetic correlations with production traits in pigs. Behavior was recorded for 70 days after on-test at about 10 weeks of age and ended at off-test for 2008 female purebred pigs, totaling 119,812 day-wise records. Behavior traits included time spent eating, drinking, laterally lying, sternally lying, sitting, standing, and meters of distance traveled. A quality control procedure was created for algorithm training and adjustment, standardizing recording hours, removing culled animals, and filtering unrealistic records. Results Production traits included average daily gain (ADG), back fat thickness (BF), and loin depth (LD). Single-trait linear models were used to estimate heritabilities of the behavior traits and two-trait linear models were used to estimate genetic correlations between behavior and production traits. The results indicated that all behavior traits are heritable, with heritability estimates ranging from 0.19 to 0.57, and showed low-to-moderate phenotypic and genetic correlations with production traits. Two-trait linear models were also used to compare traits at different intervals of the recording period. To analyze the redundancies in behavior data during the recording period, the averages of various recording time intervals for the behavior and production traits were compared. Overall, the average of the 55- to 68-day recording interval had the strongest phenotypic and genetic correlation estimates with the production traits. Conclusions Digital phenotyping is a new and low-cost method to record behavior phenotypes, but thorough data cleaning procedures are needed. Evaluating behavioral traits at different time intervals offers a deeper insight into their changes throughout the growth periods and their relationship with production traits, which may be recorded at a less frequent basis.

This study aimed to investigate genetic parameters for sow pelvic organ prolapse in purebred and crossbred herds. Pelvic organ prolapse was recorded as normal or prolapsed on the individual sow level across 32 purebred and 8 crossbred farms. In total, 75,162 purebred Landrace sows from a single maternal line were recorded between 2018 and 2023, while 18,988 commercial two-way crossbred (Landrace x Large White) sows were available between 2020 and 2023. There were 5,122,005 animals included in the pedigree. The prolapse in purebreds and crossbreds was considered two different traits in the model. Pedigrees of the crossbred sows were determined based on genotypes through parentage assignment. The average incidence rates were 1.81% and 3.93% for purebreds and crossbreds, respectively. The bivariate model incorporated fixed effects of parity group and region with random effects of contemporary group (farm and mating year and month at the first parity), additive genetic, and residual. Genetic parameter estimates were obtained using BLUPF90+ with the AIREML option. The estimated additive variance was larger in crossbreds than in purebreds. Estimates of heritability in the observed scale were 0.09 (0.006) for purebreds and 0.11 (0.014) for crossbreds, with a genetic correlation of 0.83 using a linear model. Results suggested that including data from crossbreds with higher incidence rate is beneficial and selection to reduce the prolapse incidence in purebred sow herds would also benefit commercial crossbred sow herds.

Abstract Background Validation by data truncation is a common practice in genetic evaluations because of the interest in predicting the genetic merit of a set of young selection candidates. Two of the most used validation methods in genetic evaluations use a single data partition: predictivity or predictive ability (correlation between pre-adjusted phenotypes and estimated breeding values (EBV) divided by the square root of the heritability) and the linear regression (LR) method (comparison of “early” and “late” EBV). Both methods compare predictions with the whole dataset and a partial dataset that is obtained by removing the information related to a set of validation individuals. EBV obtained with the partial dataset are compared against adjusted phenotypes for the predictivity or EBV obtained with the whole dataset in the LR method. Confidence intervals for predictivity and the LR method can be obtained by replicating the validation for different samples (or folds), or bootstrapping. Analytical confidence intervals would be beneficial to avoid running several validations and to test the quality of the bootstrap intervals. However, analytical confidence intervals are unavailable for predictivity and the LR method. Results We derived standard errors and Wald confidence intervals for the predictivity and statistics included in the LR method (bias, dispersion, ratio of accuracies, and reliability). The confidence intervals for the bias, dispersion, and reliability depend on the relationships and prediction error variances and covariances across the individuals in the validation set. We developed approximations for large datasets that only need the reliabilities of the individuals in the validation set. The confidence intervals for the ratio of accuracies and predictivity were obtained through the Fisher transformation. We show the adequacy of both the analytical and approximated analytical confidence intervals and compare them versus bootstrap confidence intervals using two simulated examples. The analytical confidence intervals were closer to the simulated ones for both examples. Bootstrap confidence intervals tend to be narrower than the simulated ones. The approximated analytical confidence intervals were similar to those obtained by bootstrapping. Conclusions Estimating the sampling variation of predictivity and the statistics in the LR method without replication or bootstrap is possible for any dataset with the formulas presented in this study.

Abstract Background Whole-genome sequence (WGS) data harbor causative variants that may not be present in standard single nucleotide polymorphism (SNP) chip data. The objective of this study was to investigate the impact of using preselected variants from WGS for single-step genomic predictions in maternal and terminal pig lines with up to 1.8k sequenced and 104k sequence imputed animals per line. Methods Two maternal and four terminal lines were investigated for eight and seven traits, respectively. The number of sequenced animals ranged from 1365 to 1491 for the maternal lines and 381 to 1865 for the terminal lines. Imputation to sequence occurred within each line for 66k to 76k animals for the maternal lines and 29k to 104k animals for the terminal lines. Two preselected SNP sets were generated based on a genome-wide association study (GWAS). Top40k included the SNPs with the lowest p-value in each of the 40k genomic windows, and ChipPlusSign included significant variants integrated into the porcine SNP chip used for routine genotyping. We compared the performance of single-step genomic predictions between using preselected SNP sets assuming equal or different variances and the standard porcine SNP chip. Results In the maternal lines, ChipPlusSign and Top40k showed an average increase in accuracy of 0.6 and 4.9%, respectively, compared to the regular porcine SNP chip. The greatest increase was obtained with Top40k, particularly for fertility traits, for which the initial accuracy based on the standard SNP chip was low. However, in the terminal lines, Top40k resulted in an average loss of accuracy of 1%. ChipPlusSign provided a positive, although small, gain in accuracy (0.9%). Assigning different variances for the SNPs slightly improved accuracies when using variances obtained from BayesR. However, increases were inconsistent across the lines and traits. Conclusions The benefit of using sequence data depends on the line, the size of the genotyped population, and how the WGS variants are preselected. When WGS data are available on hundreds of thousands of animals, using sequence data presents an advantage but this remains limited in pigs.

Abstract Background Identifying true positive variants in genome-wide associations (GWA) depends on several factors, including the number of genotyped individuals. The limited dimensionality of genomic information may give insights into the optimal number of individuals to be used in GWA. This study investigated different discovery set sizes based on the number of largest eigenvalues explaining a certain proportion of variance in the genomic relationship matrix (G). In addition, we investigated the impact on the prediction accuracy by adding variants, which were selected based on different set sizes, to the regular single nucleotide polymorphism (SNP) chips used for genomic prediction. Methods We simulated sequence data that included 500k SNPs with 200 or 2000 quantitative trait nucleotides (QTN). A regular 50k panel included one in every ten simulated SNPs. Effective population size (Ne) was set to 20 or 200. GWA were performed using a number of genotyped animals equivalent to the number of largest eigenvalues of G (EIG) explaining 50, 60, 70, 80, 90, 95, 98, and 99% of the variance. In addition, the largest discovery set consisted of 30k genotyped animals. Limited or extensive phenotypic information was mimicked by changing the trait heritability. Significant and large-effect size SNPs were added to the 50k panel and used for single-step genomic best linear unbiased prediction (ssGBLUP). Results Using a number of genotyped animals corresponding to at least EIG98 allowed the identification of QTN with the largest effect sizes when Ne was large. Populations with smaller Ne required more than EIG98. Furthermore, including genotyped animals with a higher reliability (i.e., a higher trait heritability) improved the identification of the most informative QTN. Prediction accuracy was highest when the significant or the large-effect SNPs representing twice the number of simulated QTN were added to the 50k panel. Conclusions Accurately identifying causative variants from sequence data depends on the effective population size and, therefore, on the dimensionality of genomic information. This dimensionality can help identify the most suitable sample size for GWA and could be considered for variant selection, especially when resources are restricted. Even when variants are accurately identified, their inclusion in prediction models has limited benefits.

The dairy industry is known for its extensive use of artificial insemination, which has resulted in a population where most animals can be traced back to only a few sires. Due to their relatedness to the population, old influential sires could still contribute to the accuracy of genomic predictions. The objective of the study was to identify the impact of historically influential sires on the recent population. This was tested by constructing a genomic relationship matrix using recursion with different sets of sires. Differences in prediction accuracies with different sets are indicative of how important each set is. Recursion coefficients linking young animals to those sets reveal the relative importance of specific sires to the prediction accuracy of recent animals. The data included ∼10 million scores for stature and fore udder attachment (FUA) measured from 1983. Genotypes of 569,404 animals were available. Sire sets included the 100 most popular sires born within different time periods. Computations were with single-step genomic BLUP. In general, the younger sires had higher prediction accuracies than the oldest sires, even though they generally have fewer progeny. The accuracy of evaluation for stature was increased from 0.54 with the most popular sires born before 1981 to 0.69 with sires born from 2001 to 2010, while the accuracy for FUA increased from 0.47 to 0.61. The accuracy achieved using the overall 100 most used sires was 0.66 for stature and 0.58 for FUA. All 100 sires from each period were combined in a subset to determine the importance of each sire relative to all 400 animals in the combined subset. The highest relative impact of a sire that was born within the different time sets was 1.97 for Valiant (before 1981), 1.94 for Blackstar (1981 to 1990), 4.38 for Shottle (1991 to 2000), and 3.09 for Planet (2001 to 2010). The 3 sires among the 400 with the greatest impact were Shottle, Goldwyn (3.73), and Planet. The relative impact of a sire was not strongly related to the number of progeny. For instance, the relative impact of Durham with 34K progeny was 2.29, whereas the impact of O Man with 15K progeny was 3.13. The impact of a sire is also influenced by whether it was used as a sire of sires. Results show that younger sires are more relevant to the accuracy of breeding value prediction in the recent population.

Abstract Background Reliabilities of best linear unbiased predictions (BLUP) of breeding values are defined as the squared correlation between true and estimated breeding values and are helpful in assessing risk and genetic gain. Reliabilities can be computed from the prediction error variances for models with a single base population but are undefined for models that include several base populations and when unknown parent groups are modeled as fixed effects. In such a case, the use of metafounders in principle enables reliabilities to be derived. Methods We propose to compute the reliability of the contrast of an individual’s estimated breeding value with that of a metafounder based on the prediction error variances of the individual and the metafounder, their prediction error covariance, and their genetic relationship. Computation of the required terms demands only little extra work once the sparse inverse of the mixed model equations is obtained, or they can be approximated. This also allows the reliabilities of the metafounders to be obtained. We studied the reliabilities for both BLUP and single-step genomic BLUP (ssGBLUP), using several definitions of reliability in a large dataset with 1,961,687 dairy sheep and rams, most of which had phenotypes and among which 27,000 rams were genotyped with a 50K single nucleotide polymorphism (SNP) chip. There were 23 metafounders with progeny sizes between 100,000 and 2000 individuals. Results In models with metafounders, directly using the prediction error variance instead of the contrast with a metafounder leads to artificially low reliabilities because they refer to a population with maximum heterozygosity. When only one metafounder is fitted in the model, the reliability of the contrast is shown to be equivalent to the reliability of the individual in a model without metafounders. When there are several metafounders in the model, using a contrast with the oldest metafounder yields reliabilities that are on a meaningful scale and very close to reliabilities obtained from models without metafounders. The reliabilities using contrasts with ssGBLUP also resulted in meaningful values. Conclusions This work provides a general method to obtain reliabilities for both BLUP and ssGBLUP when several base populations are included through metafounders.

Single-step genomic best linear unbiased predictor (ssGBLUP) is a methodology for estimating breeding values jointly for genotyped and non-genotyped animals. Since its development in the early 2010s, ssGBLUP faced challenges like modelling missing pedigrees, efficiently computing accuracies, ensuring the compatibility between genomic and pedigree information, implementing large-scale genetic evaluations, and using non-genotyped animals for genome-wide association studies, among others. Because of the extensive research and the availability of efficient software packages, those challenges for ssGBLUP were solved. Nowadays, ssGBLUP is the chosen methodology estimating values in almost all livestock populations. This review aims to report the progress of ssGBLUP, outline the current state of the art, and hypothesise about the future of this methodology.Highlights Single-step genomic BLUP is the most popular methodology for genetic evaluations including genotyped and non-genotyped animals. The development of theories and efficient software allows to use single-step for virtually any real dataset. Continuous research in single-step will allow the use of massive amount of data like video recording, omics, among others.

Evaluations using single-step genomic BLUP require blending the genomic relationship matrix (G) with a positive definite matrix to ensure nonsingularity for solving the mixed model equations. Many organizations blend G with a proportion of the numerator relationship matrix for genotyped animals (A22) to improve stability and possibly add a residual polygenic effect. However, when nearly all the polygenic variance is explained by G, blending with A22 may cause inflation and add excess computing time; thus, blending with an identity matrix (I) multiplied by a small value may be a better solution. The objective of this study was to evaluate changes in reliability and inflation of genomic estimated breeding values, convergence rate, elapsed wall-clock time for blending G with different levels of A22 or I, and develop a more time-efficient blending method. A US Holstein cattle data set was used with 9.7 million animals in the pedigree, 569,404 animals with genotypes, and 10.1 million stature phenotypes. Blending G by adding a small value to the diagonal elements had comparable performance to A22 with fewer rounds to convergence required to solve the system of equations. Reliability and inflation of genomic estimated breeding values ranged from 0.63 to 0.68 and 0.86 to 0.89 for all blending scenarios tested. The current blending default in the BLUPF90 software is to replace G with (1 – β)G + βA22, where β equals 0.05. In this study, β values of 0.30, 0.20, 0.05, 0.01, 0.005, and 0.001 were evaluated with A22 and I. Negligible differences in elapsed computing time between the blending types and levels were observed. Subsequently, the current blending algorithm used in the BLUPF90 family of programs was optimized, reducing the blending time from approximately 2 h to 5 min for A22 and less than 1 s for I. The new time difference between blending with A22 or I is negligible and not computationally critical. The results indicate that blending G with A22 does not have clear advantages over blending with a small proportion of I.

Abstract Background Although single-step GBLUP (ssGBLUP) is an animal model, SNP effects can be backsolved from genomic estimated breeding values (GEBV). Predicted SNP effects allow to compute indirect prediction (IP) per individual as the sum of the SNP effects multiplied by its gene content, which is helpful when the number of genotyped animals is large, for genotyped animals not in the official evaluations, and when interim evaluations are needed. Typically, IP are obtained for new batches of genotyped individuals, all of them young and without phenotypes. Individual (theoretical) accuracies for IP are rarely reported, but they are nevertheless of interest. Our first objective was to present equations to compute individual accuracy of IP, based on prediction error covariance (PEC) of SNP effects, and in turn, are obtained from PEC of GEBV in ssGBLUP. The second objective was to test the algorithm for proven and young (APY) in PEC computations. With large datasets, it is impossible to handle the full PEC matrix, thus the third objective was to examine the minimum number of genotyped animals needed in PEC computations to achieve IP accuracies that are equivalent to GEBV accuracies. Results Correlations between GEBV and IP for the validation animals using SNP effects from ssGBLUP evaluations were ≥ 0.99. When all available genotyped animals were used for PEC computations, correlations between GEBV and IP accuracy were ≥ 0.99. In addition, IP accuracies were compatible with GEBV accuracies either with direct inversion of the genomic relationship matrix (G) or using the algorithm for proven and young (APY) to obtain the inverse of G. As the number of genotyped animals included in the PEC computations decreased from around 55,000 to 15,000, correlations were still ≥ 0.96, but IP accuracies were biased downwards. Conclusions Theoretical accuracy of indirect prediction can be successfully obtained by computing SNP PEC out of GEBV PEC from ssGBLUP equations using direct or APY G inverse. It is possible to reduce the number of genotyped animals in PEC computations, but accuracies may be underestimated. Further research is needed to approximate SNP PEC from ssGBLUP to limit the computational requirements with many genotyped animals.

Abstract Background Single-step genomic predictions obtained from a breeding value model require calculating the inverse of the genomic relationship matrix $$({\mathbf{G}}^{-1})$$ ( G - 1 ) . The Algorithm for Proven and Young (APY) creates a sparse representation of $${\mathbf{G}}^{-1}$$ G - 1 with a low computational cost. APY consists of selecting a group of core animals and expressing the breeding values of the remaining animals as a linear combination of those from the core animals plus an error term. The objectives of this study were to: (1) extend APY to marker effects models; (2) derive equations for marker effect estimates when APY is used for breeding value models, and (3) show the implication of selecting a specific group of core animals in terms of a marker effects model. Results We derived a family of marker effects models called APY-SNP-BLUP. It differs from the classic marker effects model in that the row space of the genotype matrix is reduced and an error term is fitted for non-core animals. We derived formulas for marker effect estimates that take this error term in account. The prediction error variance (PEV) of the marker effect estimates depends on the PEV for core animals but not directly on the PEV of the non-core animals. We extended the APY-SNP-BLUP to include a residual polygenic effect and accommodate non-genotyped animals. We show that selecting a specific group of core animals is equivalent to select a subspace of the row space of the genotype matrix. As the number of core animals increases, subspaces corresponding to different sets of core animals tend to overlap, showing that random selection of core animals is algebraically justified. Conclusions The APY-(ss)GBLUP models can be expressed in terms of marker effect models. When the number of core animals is equal to the rank of the genotype matrix, APY-SNP-BLUP is identical to the classic marker effects model. If the number of core animals is less than the rank of the genotype matrix, genotypes for non-core animals are imputed as a linear combination of the genotypes of the core animals. For estimating SNP effects, only relationships and estimated breeding values for core animals are needed.

Genomic evaluations in pigs could benefit from using multi-line data along with whole-genome sequencing (WGS) if the data are large enough to represent the variability across populations. The objective of this study was to investigate strategies to combine large-scale data from different terminal pig lines in a multi-line genomic evaluation (MLE) through single-step GBLUP (ssGBLUP) models while including variants preselected from whole-genome sequence (WGS) data. We investigated single-line and multi-line evaluations for five traits recorded in three terminal lines. The number of sequenced animals in each line ranged from 731 to 1,865, with 60k to 104k imputed to WGS. Unknown parent groups (UPG) and metafounders (MF) were explored to account for genetic differences among the lines and improve the compatibility between pedigree and genomic relationships in the MLE. Sequence variants were preselected based on multi-line genome-wide association studies (GWAS) or linkage disequilibrium (LD) pruning. These preselected variant sets were used for ssGBLUP predictions without and with weights from BayesR, and the performances were compared to that of a commercial porcine single-nucleotide polymorphisms (SNP) chip. Using UPG and MF in MLE showed small to no gain in prediction accuracy (up to 0.02), depending on the lines and traits, compared to the single-line genomic evaluation (SLE). Likewise, adding selected variants from the GWAS to the commercial SNP chip resulted in a maximum increase of 0.02 in the prediction accuracy, only for average daily feed intake in the most numerous lines. In addition, no benefits were observed when using preselected sequence variants in multi-line genomic predictions. Weights from BayesR did not help improve the performance of ssGBLUP. This study revealed limited benefits of using preselected whole-genome sequence variants for multi-line genomic predictions, even when tens of thousands of animals had imputed sequence data. Correctly accounting for line differences with UPG or MF in MLE is essential to obtain predictions similar to SLE; however, the only observed benefit of an MLE is to have comparable predictions across lines. Further investigation into the amount of data and novel methods to preselect whole-genome causative variants in combined populations would be of significant interest.

Abstract Background The algorithm for proven and young (APY) has been suggested as a solution for recursively computing a sparse representation for the inverse of a large genomic relationship matrix (G). In APY, a subset of genotyped individuals is used as the core and the remaining genotyped individuals are used as noncore. Size and definition of the core are relevant research subjects for the application of APY, especially given the ever-increasing number of genotyped individuals. Methods The aim of this study was to investigate several core definitions, including the most popular animals (MPA) (i.e., animals with high contributions to the genetic pool), the least popular males (LPM), the least popular females (LPF), a random set (Rnd), animals evenly distributed across genealogical paths (Ped), unrelated individuals (Unrel), or based on within-family selection (Fam), or on decomposition of the gene content matrix (QR). Each definition was evaluated for six core sizes based on prediction accuracy of single-step genomic best linear unbiased prediction (ssGBLUP) with APY. Prediction accuracy of ssGBLUP with the full inverse of G was used as the baseline. The dataset consisted of 357k pedigreed Duroc pigs with 111k pigs with genotypes and ~ 220k phenotypic records. Results When the core size was equal to the number of largest eigenvalues explaining 50% of the variation of G (n = 160), MPA and Ped core definitions delivered the highest average prediction accuracies (~ 0.41−0.53). As the core size increased to the number of eigenvalues explaining 99% of the variation in G (n = 7320), prediction accuracy was nearly identical for all core types and correlations with genomic estimated breeding values (GEBV) from ssGBLUP with the full inversion of G were greater than 0.99 for all core definitions. Cores that represent all generations, such as Rnd, Ped, Fam, and Unrel, were grouped together in the hierarchical clustering of GEBV. Conclusions For small core sizes, the definition of the core matters; however, as the size of the core reaches an optimal value equal to the number of largest eigenvalues explaining 99% of the variation of G, the definition of the core becomes arbitrary.

ABSTRACT: 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.

Abstract Background Understanding whether genomic selection has been effective in livestock and when the results of genomic selection became visible are essential questions which we have addressed in this paper. Three criteria were used to identify practices of breeding programs over time: (1) the point of divergence of estimated genetic trends based on pedigree-based best linear unbiased prediction (BLUP) versus single-step genomic BLUP (ssGBLUP), (2) the point of divergence of realized Mendelian sampling (RMS) trends based on BLUP and ssGBLUP, and (3) the partition of genetic trends into that contributed by genotyped and non-genotyped individuals and by males and females. Methods We used data on 282,035 animals from a commercial maternal line of pigs, of which 32,856 were genotyped for 36,612 single nucleotide polymorphisms (SNPs) after quality control. Phenotypic data included 228,427, 101,225, and 11,444 records for birth weight, average daily gain in the nursery, and feed intake, respectively. Breeding values were predicted in a multiple-trait framework using BLUP and ssGBLUP. Results The points of divergence of the genetic and RMS trends estimated by BLUP and ssGBLUP indicated that genomic selection effectively started in 2019. Partitioning the overall genetic trends into that for genotyped and non-genotyped individuals revealed that the contribution of genotyped animals to the overall genetic trend increased rapidly from ~ 74% in 2016 to 90% in 2019. The contribution of the female pathway to the genetic trend also increased since genomic selection was implemented in this pig population, which reflects the changes in the genotyping strategy in recent years. Conclusions Our results show that an assessment of breeding program practices can be done based on the point of divergence of genetic and RMS trends between BLUP and ssGBLUP and based on the partitioning of the genetic trend into contributions from different selection pathways. However, it should be noted that genetic trends can diverge before the onset of genomic selection if superior animals are genotyped retroactively. For the pig population example, the results showed that genomic selection was effective in this population.

The aim of this study was to test the feasibility of genomic selection in the Italian Mediterranean water buffalo, which is farmed mainly in the south Italy for milk, and mozzarella, production. A total of 498 animals were genotyped at 49,164 loci. Test day records (80,417) of milk (MY), fat (FY) and protein (PY) yields from 4127 cows, born between 1975 and 2009, were analysed in a three-trait model. Cows born in 2008 and 2009 with phenotypes and genotypes were selected as validation animals (n = 50). Variance components (VC) were estimated with BLUP and ssGBLUP. Heritabilities for BLUP were 0.25 ± 0.02 (MY), 0.16 ± 0.01 (FY) and 0.25 ± 0.01 (PY). Breeding values were computed using BLUP and ssGBLUP, using VC estimated from BLUP. ssGBLUP was applied in five scenarios, each with a different number of genotypes available: (A) bulls (35); (B) validation cows (50); (C) bulls and validation cows (85); (D) all genotyped cows (463); (E) all genotypes (498). Model validation was performed using the LR method: correlation, accuracy, dispersion, and bias statistics were calculated. Average correlations were 0.71 ± 0.02 and 0.82 ± 0.01 for BLUP and ssGBLUP-E, respectively. Accuracies were also higher in ssGBLUP-E (0.75 ± 0.03) compared to BLUP (0.57 ± 0.03). The best dispersions (i.e. closer to 1) were found for ssGBLUP-C. The use of genotypes only for the 35 bulls did not change the validation values compared to BLUP. Results of the present study, even if based on small number of animals, showed that the inclusion of genotypes of females can improve breeding values accuracy in the Italian Buffalo.Highlights The genotypes of males did not improve the predictions. Genotypes of females improve breeding values accuracy. Slight increase in prediction accuracy with weighted ssGBLUP.

Abstract Background Genomic selection has been successfully implemented in many livestock and crop species. The genomic best linear unbiased predictor (GBLUP) approach, assigning equal variance to all SNP effects, is one of the reference methods. When large-effect variants contribute to complex traits, it has been shown that genomic prediction methods that assign a higher variance to subsets of SNP effects can achieve higher prediction accuracy. We herein compared the efficiency of several such approaches, including the Adaptive MultiBLUP (AM-BLUP) that uses local genomic relationship matrices (GRM) to automatically identify and weight genomic regions with large effects, to predict genetic merit in Belgian Blue beef cattle. Results We used a population of approximately 10,000 genotyped cows and their phenotypes for 14 traits, mostly related to muscular development and body dimensions. According to the trait, we found that 4 to 25% of the genetic variance could be associated with 2 to 12 genomic regions harbouring large-effect variants. Noteworthy, three previously identified recessive deleterious variants presented heterozygote advantage and were among the most significant SNPs for several traits. The AM-BLUP resulted in increased reliability of genomic predictions compared to GBLUP (+ 2%), but Bayesian methods proved more efficient (+ 3%). Overall, the reliability gains remained thus limited although higher gains were observed for skin thickness, a trait affected by two genomic regions having particularly large effects. Higher accuracies than those from the original AM-BLUP were achieved when applying the Bayesian Sparse Linear Mixed Model to pre-select groups of SNPs with large effects and subsequently use their estimated variance to build a weighted GRM. Finally, the single-step GBLUP performed best and could be further improved (+ 3% prediction accuracy) by using these weighted GRM. Conclusions The AM-BLUP is an attractive method to automatically identify and weight genomic regions with large effects on complex traits. However, the method was less accurate than Bayesian methods. Overall, weighted methods achieved modest accuracy gains compared to GBLUP. Nevertheless, the computational efficiency of the AM-BLUP might be valuable at higher marker density, including with whole-genome sequencing data. Furthermore, weighted GRM are particularly useful to account for large variance loci in the single-step GBLUP.

Abstract 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.

Abstract Background Genetic improvement of honey bees is more difficult compared to other livestock, due to the very different reproductive behavior. Estimation of breeding values requires specific adjustment and the use of sires in the pedigree is only possible when mating of queens and drones is strictly controlled. In the breeding program of the National Registry for Italian Queen Breeders and Bee Producers the paternal contribution is mostly unknown. As stronger modeling may compensate for the lack of pedigree information, we tested two models that differed in the way the direct and maternal effects were considered. The two models were tested using 4003 records for honey yield, defensive and swarming behaviors of Italian honey bee queens produced between 2002 and 2014. The first model accounted for the direct genetic effect of worker bees and the genetic maternal effect of the queen, whereas model 2 considered the direct genetic effect of the queen without maternal effect. The analyses were performed by linear (honey production) and threshold (defensive and swarming behavior) single-trait models; estimated genetic correlations among traits were obtained by a three-trait linear-threshold model. Results For all traits, the highest predictability (correlation between breeding values estimated with and without performance records) was obtained with model 2, where direct genetic effect of queens was considered. With this model, heritability estimates were 0.26 for honey yield, 0.36 for defensive behavior, and 0.34 for swarming behavior. Multi-trait estimation resulted in similar or higher heritability estimates for all traits. A low, positive genetic correlation (0.19) was found between honey yield and defensive behavior, whereas the genetic correlation between honey yield and swarming behavior was moderate (0.41). A strong, positive genetic correlation was found between defensive and swarming behaviors (0.62). Predictability for multi-trait evaluations was higher for honey yield (0.46) and defensive behavior (0.30) but almost identical for swarming behavior (0.45) compared to corresponding single-trait predictability. Conclusions Multi-trait evaluation using a model that accounts for the direct genetic effect of queen was the best approach for breeding value estimation of Italian honey bees. The results suggest a new direction for selection of linear and categorical traits in breeding programs where drone origin is unknown.

Population structure or genetic relatedness should be considered in genome association studies to avoid spurious association. The most used methods for genome-wide association studies (GWAS) account for population structure but are limited to genotyped individuals with phenotypes. Single-step GWAS (ssGWAS) can use phenotypes from non-genotyped relatives; however, its ability to account for population structure has not been explored. Here we investigate the equivalence among ssGWAS, efficient mixed-model association expedited (EMMAX), and genomic best linear unbiased prediction GWAS (GBLUP-GWAS), and how they differ from the single-SNP analysis without correction for population structure (SSA-NoCor). We used simulated, structured populations that mimicked fish, beef cattle, and dairy cattle populations with 1040, 5525, and 1,400 genotyped individuals, respectively. Larger populations were also simulated that had up to 10-fold more genotyped animals. The genomes were composed by 29 chromosomes, each harboring one QTN, and the number of simulated SNPs was 35,000 for the fish and 65,000 for the beef and dairy cattle populations. Males and females were genotyped in the fish and beef cattle populations, whereas only males had genotypes in the dairy population. Phenotypes for a trait with heritability varying from 0.25 to 0.35 were available in both sexes for the fish population, but only for females in the beef and dairy cattle populations. In the latter, phenotypes of daughters were projected into genotyped sires (i.e., deregressed proofs) before applying EMMAX and SSA-NoCor. Although SSA-NoCor had the largest number of true positive SNPs among the four methods, the number of false negatives was two–fivefold that of true positives. GBLUP-GWAS and EMMAX had a similar number of true positives, which was slightly smaller than in ssGWAS, although the difference was not significant. Additionally, no significant differences were observed when deregressed proofs were used as pseudo-phenotypes in EMMAX compared to daughter phenotypes in ssGWAS for the dairy cattle population. Single-step GWAS accounts for population structure and is a straightforward method for association analysis when only a fraction of the population is genotyped and/or when phenotypes are available on non-genotyped relatives.

Abstract Background Single-step genomic best linear unbiased prediction (SSGBLUP) is a comprehensive method for genomic prediction. Point estimates of marker effects from SSGBLUP are often used for genome-wide association studies (GWAS) without a formal framework of hypothesis testing. Our objective was to implement p-values for single-marker GWAS studies within the single-step GWAS (SSGWAS) framework by deriving computational algorithms and procedures, and by applying these to a large beef cattle population. Methods P-values were obtained based on the prediction error (co)variances for single nucleotide polymorphisms (SNPs), which were obtained from the prediction error (co)variances of genomic predictions based on the inverse of the coefficient matrix and formulas to estimate SNP effects. Results Computation of p-values took a negligible time for a dataset with almost 2 million animals in the pedigree and 1424 genotyped sires, and no inflation of statistics was observed. The SNPs that passed the Bonferroni threshold of 10−5.9 were the same as those that explained the highest proportion of additive genetic variance, but even at the same significance levels and effects, some of them explained less genetic variance due to lower allele frequency. Conclusions The use of a p-value for SSGWAS is a very general and efficient strategy to identify quantitative trait loci (QTL). It can be used for complex datasets such as those used in animal breeding, where only a proportion of the pedigreed animals are genotyped.

Abstract Background Catfish farming is the largest segment of US aquaculture and research is ongoing to improve production efficiency, including genetic selection programs to improve economically important traits. The objectives of this study were to investigate the use of genomic selection to improve breeding value accuracy and to identify major single nucleotide polymorphisms (SNPs) associated with harvest weight and residual carcass weight in a channel catfish population. Phenotypes were available for harvest weight (n = 27,160) and residual carcass weight (n = 6020), and 36,365 pedigree records were available. After quality control, genotypes for 54,837 SNPs were available for 2911 fish. Estimated breeding values (EBV) were obtained with traditional pedigree-based best linear unbiased prediction (BLUP) and genomic (G)EBV were estimated with single-step genomic BLUP (ssGBLUP). EBV and GEBV prediction accuracies were evaluated using different validation strategies. The ability to predict future performance was calculated as the correlation between EBV or GEBV and adjusted phenotypes. Results Compared to the pedigree BLUP, ssGBLUP increased predictive ability up to 28% and 36% for harvest weight and residual carcass weight, respectively; and GEBV were superior to EBV for all validation strategies tested. Breeding value inflation was assessed as the regression coefficient of adjusted phenotypes on breeding values, and the results indicated that genomic information reduced breeding value inflation. Genome-wide association studies based on windows of 20 adjacent SNPs indicated that both harvest weight and residual carcass weight have a polygenic architecture with no major SNPs (the largest SNPs explained 0.96 and 1.19% of the additive genetic variation for harvest weight and residual carcass weight respectively). Conclusions Genomic evaluation improves the ability to predict future performance relative to traditional BLUP and will allow more accurate identification of genetically superior individuals within catfish families.

Abstract Background Much effort is put into identifying causative quantitative trait nucleotides (QTN) in animal breeding, empowered by the availability of dense single nucleotide polymorphism (SNP) information. Genomic selection using traditional SNP information is easily implemented for any number of genotyped individuals using single-step genomic best linear unbiased predictor (ssGBLUP) with the algorithm for proven and young (APY). Our aim was to investigate whether ssGBLUP is useful for genomic prediction when some or all QTN are known. Methods Simulations included 180,000 animals across 11 generations. Phenotypes were available for all animals in generations 6 to 10. Genotypes for 60,000 SNPs across 10 chromosomes were available for 29,000 individuals. The genetic variance was fully accounted for by 100 or 1000 biallelic QTN. Raw genomic relationship matrices (GRM) were computed from (a) unweighted SNPs, (b) unweighted SNPs and causative QTN, (c) SNPs and causative QTN weighted with results obtained with genome-wide association studies, (d) unweighted SNPs and causative QTN with simulated weights, (e) only unweighted causative QTN, (f–h) as in (b–d) but using only the top 10% causative QTN, and (i) using only causative QTN with simulated weight. Predictions were computed by pedigree-based BLUP (PBLUP) and ssGBLUP. Raw GRM were blended with 1 or 5% of the numerator relationship matrix, or 1% of the identity matrix. Inverses of GRM were obtained directly or with APY. Results Accuracy of breeding values for 5000 genotyped animals in the last generation with PBLUP was 0.32, and for ssGBLUP it increased to 0.49 with an unweighted GRM, 0.53 after adding unweighted QTN, 0.63 when QTN weights were estimated, and 0.89 when QTN weights were based on true effects known from the simulation. When the GRM was constructed from causative QTN only, accuracy was 0.95 and 0.99 with blending at 5 and 1%, respectively. Accuracies simulating 1000 QTN were generally lower, with a similar trend. Accuracies using the APY inverse were equal or higher than those with a regular inverse. Conclusions Single-step GBLUP can account for causative QTN via a weighted GRM. Accuracy gains are maximum when variances of causative QTN are known and blending is at 1%.

Single-step genomic evaluation became a standard procedure in livestock breeding, and the main reason is the ability to combine all pedigree, phenotypes, and genotypes available into one single evaluation, without the need of post-analysis processing. Therefore, the incorporation of data on genotyped and non-genotyped animals in this method is straightforward. Since 2009, two main implementations of single-step were proposed. One is called single-step genomic best linear unbiased prediction (ssGBLUP) and uses single nucleotide polymorphism (SNP) to construct the genomic relationship matrix; the other is the single-step Bayesian regression (ssBR), which is a marker effect model. Under the same assumptions, both models are equivalent. In this review, we focus solely on ssGBLUP. The implementation of ssGBLUP into the BLUPF90 software suite was done in 2009, and since then, several changes were made to make ssGBLUP flexible to any model, number of traits, number of phenotypes, and number of genotyped animals. Single-step GBLUP from the BLUPF90 software suite has been used for genomic evaluations worldwide. In this review, we will show theoretical developments and numerical examples of ssGBLUP using SNP data from regular chips to sequence data.

The purpose of this study was to identify genomic regions associated with carcass traits in an experimental Nelore cattle population. The studied data set contained 2,306 ultrasound records for longissimus muscle area (LMA), 1,832 for backfat thickness (BF), and 1,830 for rump fat thickness (RF). A high-density SNP panel (BovineHD BeadChip assay 700k, Illumina Inc., San Diego, CA) was used for genotyping. After genomic data quality control, 437,197 SNPs from 761 animals were available, of which 721 had phenotypes for LMA, 669 for BF, and 718 for RF. The SNP solutions were estimated using a single-step genomic BLUP approach (ssGWAS), which calculated the variance for windows of 50 consecutive SNPs and the regions that accounted for more than 0.5% of the additive genetic variance were used to search for candidate genes. The results indicated that 12, 18, and 15 different windows were associated to LMA, BF, and RF, respectively. Confirming the polygenic nature of the studied traits, 43, 65, and 53 genes were found in those associated windows, respectively for LMA, BF, and RF. Among the candidate genes, some of them, which already had their functions associated with the expression of energy metabolism, were found associated with fat deposition in this study. In addition, ALKBH3 and HSD17B12 genes, which are related in fibroblast death and metabolism of steroids, were found associated with LMA. The results presented here should help to better understand the genetic and physiologic mechanism regulating the muscle tissue deposition and subcutaneous fat cover expression of Zebu animals. The identification of candidate genes should contribute for Zebu breeding programs in order to consider carcass traits as selection criteria in their genetic evaluation.

Genomic Best Linear Unbiased Predictor (GBLUP) assumes equal variance for all single nucleotide polymorphisms (SNP). When traits are influenced by major SNP, Bayesian methods have the advantage of SNP selection. To overcome the limitation of GBLUP, unequal variance or weights for all SNP are applied in a method called weighted GBLUP (WGBLUP). If only a fraction of animals is genotyped, single-step WGBLUP (WssGBLUP) can be used. Default weights in WGBLUP or WssGBLUP are obtained iteratively based on single SNP effect squared (u^2) and/or heterozygosity. When the weights are optimal, prediction accuracy and ability to detect major SNP are maximized. The objective was to develop optimal weights for WGBLUP-based methods. We evaluated 5 new procedures that accounted for locus-specific or windows-specific variance to maximize accuracy of predicting genomic estimated breeding value (GEBV) and SNP effect. Simulated datasets consisted of phenotypes for 13,000 animals, including 1,540 animals genotyped for 45,000 SNP. Scenarios with 5, 100 and 500 simulated quantitative trait loci (QTL) were considered. The 5 new procedures for SNP weighting were: 1) u^2 plus a constant equal to the weight of the top SNP; 2) from a heavy-tailed distribution (similar to BayesA); 3) for every 20 SNP in a window along the whole genome, the largest effect (u^2) among them; 4) the mean effect of every 20 SNP; and 5) the summation of every 20 SNP. Those methods were compared to the default WssGBLUP, GBLUP, BayesB, and BayesC. WssGBLUP methods were evaluated over 10 iterations. The accuracy of predicting GEBV was the correlation between true and estimated genomic breeding values for 300 genotyped animals from the last generation. The ability to detect the simulated QTL was also investigated. For most of the QTL scenarios, the accuracies obtained with all WssGBLUP procedures were higher compared to those from BayesB and BayesC, partly due to automatic inclusion of parent average in the former. Manhattan plots had higher resolution with 5 and 100 QTL. Using a common weight for a window of 20 SNP that sums or averages the SNP variance enhances accuracy of predicting GEBV and provides accurate estimation of marker effects.