Invited review: Unknown-parent groups and metafounders in single-step genomic BLUP.

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.

A Comprehensive Comparison of Haplotype-Based Single-Step Genomic Predictions in Livestock Populations With Different Genetic Diversity Levels: A Simulation Study.

The level of genetic diversity in a population is inversely proportional to the linkage disequilibrium (LD) between individual single nucleotide polymorphisms (SNPs) and quantitative trait loci (QTLs), leading to lower predictive ability of genomic breeding values (GEBVs) in high genetically diverse populations. Haplotype-based predictions could outperform individual SNP predictions by better capturing the LD between SNP and QTL. Therefore, we aimed to evaluate the accuracy and bias of individual-SNP- and haplotype-based genomic predictions under the single-step-genomic best linear unbiased prediction (ssGBLUP) approach in genetically diverse populations. We simulated purebred and composite sheep populations using literature parameters for moderate and low heritability traits. The haplotypes were created based on LD thresholds of 0.1, 0.3, and 0.6. Pseudo-SNPs from unique haplotype alleles were used to create the genomic relationship matrix ( G ) in the ssGBLUP analyses. Alternative scenarios were compared in which the pseudo-SNPs were combined with non-LD clustered SNPs, only pseudo-SNPs, or haplotypes fitted in a second G (two relationship matrices). The GEBV accuracies for the moderate heritability-trait scenarios fitting individual SNPs ranged from 0.41 to 0.55 and with haplotypes from 0.17 to 0.54 in the most (Ne ≅ 450) and less (Ne < 200) genetically diverse populations, respectively, and the bias fitting individual SNPs or haplotypes ranged between -0.14 and -0.08 and from -0.62 to -0.08, respectively. For the low heritability-trait scenarios, the GEBV accuracies fitting individual SNPs ranged from 0.24 to 0.32, and for fitting haplotypes, it ranged from 0.11 to 0.32 in the more (Ne   ≅ 250) and less (Ne   ≅ 100) genetically diverse populations, respectively, and the bias ranged between -0.36 and -0.32 and from -0.78 to -0.33 fitting individual SNPs or haplotypes, respectively. The lowest accuracies and largest biases were observed fitting only pseudo-SNPs from blocks constructed with an LD threshold of 0.3 (p < 0.05), whereas the best results were obtained using only SNPs or the combination of independent SNPs and pseudo-SNPs in one or two G matrices, in both heritability levels and all populations regardless of the level of genetic diversity. In summary, haplotype-based models did not improve the performance of genomic predictions in genetically diverse populations.

Variance components using genomic information for 2 functional traits in Italian Simmental cattle: Calving interval and lactation persistency.

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

Estimating dominance genetic variances for growth traits in American Angus males using genomic models.

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.

Accuracy of genomic BLUP when considering a genomic relationship matrix based on the number of the largest eigenvalues: a simulation study.

BACKGROUND: The dimensionality of genomic information is limited by the number of independent chromosome segments (Me), 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 Me. 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 Me. 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.

Genomic predictions in purebreds with a multibreed genomic relationship matrix1.

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.

Whole-genome mapping of quantitative trait loci and accuracy of genomic predictions for resistance to columnaris disease in two rainbow trout breeding populations.

BACKGROUND: Columnaris disease (CD) is an emerging problem for the rainbow trout aquaculture industry in the US. The objectives of this study were to: (1) identify common genomic regions that explain a large proportion of the additive genetic variance for resistance to CD in two rainbow trout (Oncorhynchus mykiss) populations; and (2) estimate the gains in prediction accuracy when genomic information is used to evaluate the genetic potential of survival to columnaris infection in each population. METHODS: Two aquaculture populations were investigated: the National Center for Cool and Cold Water Aquaculture (NCCCWA) odd-year line and the Troutlodge, Inc., May odd-year (TLUM) nucleus breeding population. Fish that survived to 21 days post-immersion challenge were recorded as resistant. Single nucleotide polymorphism (SNP) genotypes were available for 1185 and 1137 fish from NCCCWA and TLUM, respectively. SNP effects and variances were estimated using the weighted single-step genomic best linear unbiased prediction (BLUP) for genome-wide association. Genomic regions that explained more than 1% of the additive genetic variance were considered to be associated with resistance to CD. Predictive ability was calculated in a fivefold cross-validation scheme and using a linear regression method. RESULTS: Validation on adjusted phenotypes provided a prediction accuracy close to zero, due to the binary nature of the trait. Using breeding values computed from the complete data as benchmark improved prediction accuracy of genomic models by about 40% compared to the pedigree-based BLUP. Fourteen windows located on six chromosomes were associated with resistance to CD in the NCCCWA population, of which two windows on chromosome Omy 17 jointly explained more than 10% of the additive genetic variance. Twenty-six windows located on 13 chromosomes were associated with resistance to CD in the TLUM population. Only four associated genomic regions overlapped with quantitative trait loci (QTL) between both populations. CONCLUSIONS: Our results suggest that genome-wide selection for resistance to CD in rainbow trout has greater potential than selection for a few target genomic regions that were found to be associated to resistance to CD due to the polygenic architecture of this trait, and because the QTL associated with resistance to CD are not sufficiently informative for selection decisions across populations.

Improving accuracy of direct and maternal genetic effects in genomic evaluations using pooled boar semen: a simulation study1.

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.

Optimized Histological Preparation of Ovary for Ovariole Counting in Africanized Honey Bee Queens (Hymenoptera: Apidae).

Techniques for counting ovariole number in virgin and mated Apis mellifera L. queens have been described in previous studies. Having a systematic and fast way to collect this measurement can help accelerate bee breeding programs, because selection decisions can be taken faster. The aim of this work was to develop an efficient histological method to preserve ovaries that allows assessing the number of ovarioles in newly emerged virgin queens, and also in mated queens, in a shorter time than the methods already published. The proposed method resulted in images suitable for ovariole counting in both newly emerged and mated queens, and the total histological process took less than 10 h. This method provides the optimization of the histological procedure for research breeding programs that use ovariole number as selection criteria for improving reproduction and production traits.

Crossbred evaluations using single-step genomic BLUP and algorithm for proven and young with different sources of data1.

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.

Bias in heritability estimates from genomic restricted maximum likelihood methods under different genotyping strategies.

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.

Variance and covariance estimates for resistance to bacterial cold water disease and columnaris disease in two rainbow trout breeding populations1.

Family-based selective breeding can be an effective strategy for controlling diseases in aquaculture. This study aimed to estimate (co)variance components for resistance to bacterial cold water disease (BCWD) and columnaris disease (CD) in two unrelated rainbow trout nucleus breeding populations: the USDA, ARS, National Center for Cool and Cold Water Aquaculture odd-year line (ARS-Fp-R), which has been subjected to five generations of selection for improved resistance to BCWD, and the Troutlodge, Inc., May-spawning odd-year line (TLUM), which has been selected for improved growth performance but not for disease resistance. A total of 46,805 and 27,821 pedigree records were available from both populations, respectively. Between 44 and 138 families per generation and population were evaluated under controlled BCWD and CD challenges, providing 32,311 and 17,861 phenotypic records for BCWD resistance, and 13,603 and 9,413 for CD resistance, in the ARS-Fp-R and TLUM populations, respectively. A two-trait animal threshold model assuming an underlying normal distribution for the binary survival phenotypes was used to estimate (co)variance components separately for each population. Resistance to BCWD (h2 = 0.27 ± 0.04 and 0.43 ± 0.08) and CD (h2 = 0.23 ± 0.07 and 0.34 ± 0.09) was moderately heritable in the ARS-Fp-R and TLUM populations, respectively. The genetic correlation between the resistance to BCWD and CD was favorably positive in the ARS-Fp-R (0.40 ± 0.17) and TLUM (0.39 ± 0.18) populations. These findings suggest that both disease resistance traits can be improved simultaneously even if genetic selection pressure is applied to only one of the two traits.

Development of genomic predictions for harvest and carcass weight in channel catfish.

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.

Accurate genomic predictions for BCWD resistance in rainbow trout are achieved using low-density SNP panels: Evidence that long-range LD is a major contributing factor.

Previously accurate genomic predictions for Bacterial cold water disease (BCWD) resistance in rainbow trout were obtained using a medium-density single nucleotide polymorphism (SNP) array. Here, the impact of lower-density SNP panels on the accuracy of genomic predictions was investigated in a commercial rainbow trout breeding population. Using progeny performance data, the accuracy of genomic breeding values (GEBV) using 35K, 10K, 3K, 1K, 500, 300 and 200 SNP panels as well as a panel with 70 quantitative trait loci (QTL)-flanking SNP was compared. The GEBVs were estimated using the Bayesian method BayesB, single-step GBLUP (ssGBLUP) and weighted ssGBLUP (wssGBLUP). The accuracy of GEBVs remained high despite the sharp reductions in SNP density, and even with 500 SNP accuracy was higher than the pedigree-based prediction (0.50-0.56 versus 0.36). Furthermore, the prediction accuracy with the 70 QTL-flanking SNP (0.65-0.72) was similar to the panel with 35K SNP (0.65-0.71). Genomewide linkage disequilibrium (LD) analysis revealed strong LD (r2  ≥ 0.25) spanning on average over 1 Mb across the rainbow trout genome. This long-range LD likely contributed to the accurate genomic predictions with the low-density SNP panels. Population structure analysis supported the hypothesis that long-range LD in this population may be caused by admixture. Results suggest that lower-cost, low-density SNP panels can be used for implementing genomic selection for BCWD resistance in rainbow trout breeding programs.

Incorporation of causative quantitative trait nucleotides in single-step GBLUP.

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%.

Dimensionality of genomic information and performance of the Algorithm for Proven and Young for different livestock species.

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 (N e ). 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 N e 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. N e was estimated based on comparisons of eigenvalue decomposition in a simulation study. Assuming a genome length of 30 Morgan, N e 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 N e .

The Dimensionality of Genomic Information and Its Effect on Genomic Prediction.

The genomic relationship matrix (GRM) can be inverted by the algorithm for proven and young (APY) based on recursion on a random subset of animals. While a regular inverse has a cubic cost, the cost of the APY inverse can be close to linear. Theory for the APY assumes that the optimal size of the subset (maximizing accuracy of genomic predictions) is due to a limited dimensionality of the GRM, which is a function of the effective population size (Ne). The objective of this study was to evaluate these assumptions by simulation. Six populations were simulated with approximate effective population size (Ne) from 20 to 200. Each population consisted of 10 nonoverlapping generations, with 25,000 animals per generation and phenotypes available for generations 1-9. The last 3 generations were fully genotyped assuming genome length L = 30. The GRM was constructed for each population and analyzed for distribution of eigenvalues. Genomic estimated breeding values (GEBV) were computed by single-step GBLUP, using either a direct or an APY inverse of GRM. The sizes of the subset in APY were set to the number of the largest eigenvalues explaining x% of variation (EIGx, x = 90, 95, 98, 99) in GRM. Accuracies of GEBV for the last generation with the APY inverse peaked at EIG98 and were slightly lower with EIG95, EIG99, or the direct inverse. Most information in the GRM is contained in ∼NeL largest eigenvalues, with no information beyond 4NeL Genomic predictions with the APY inverse of the GRM are more accurate than by the regular inverse.

Accuracy of estimated breeding values with genomic information on males, females, or both: an example on broiler chicken.

BACKGROUND: As more and more genotypes become available, accuracy of genomic evaluations can potentially increase. However, the impact of genotype data on accuracy depends on the structure of the genotyped cohort. For populations such as dairy cattle, the greatest benefit has come from genotyping sires with high accuracy, whereas the benefit due to adding genotypes from cows was smaller. In broiler chicken breeding programs, males have less progeny than dairy bulls, females have more progeny than dairy cows, and most production traits are recorded for both sexes. Consequently, genotyping both sexes in broiler chickens may be more advantageous than in dairy cattle. METHODS: We studied the contribution of genotypes from males and females using a real dataset with genotypes on 15 723 broiler chickens. Genomic evaluations used three training sets that included only males (4648), only females (8100), and both sexes (12 748). Realized accuracies of genomic estimated breeding values (GEBV) were used to evaluate the benefit of including genotypes for different training populations on genomic predictions of young genotyped chickens. RESULTS: Using genotypes on males, the average increase in accuracy of GEBV over pedigree-based EBV for males and females was 12 and 1 percentage points, respectively. Using female genotypes, this increase was 1 and 18 percentage points, respectively. Using genotypes of both sexes increased accuracies by 19 points for males and 20 points for females. For two traits with similar heritabilities and amounts of information, realized accuracies from cross-validation were lower for the trait that was under strong selection. CONCLUSIONS: Overall, genotyping males and females improves predictions of all young genotyped chickens, regardless of sex. Therefore, when males and females both contribute to genetic progress of the population, genotyping both sexes may be the best option.