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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.

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.

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.

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.

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 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.

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 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%.