Controlling bias in genomic breeding values for young genotyped bulls

Erosion of estimated genomic breeding values with generations is due to long distance associations between markers and QTL

BACKGROUND

Most validation studies of genomic evaluations on candidates (prior to observing phenotypes) present inflation of their predicted breeding values, i.e., regression coefficients of their later observed phenotypes on the early predictions are smaller than one. The aim of this study was to show that this inflation pattern reflects at least partly long-distance associations between markers and quantitative trait loci (QTL) in the reference population and to propose methods to estimate the corresponding "erosion" coefficient.

RESULTS

Across-chromosome linkage disequilibrium (LD) is observed in different dairy cattle breeds, being a result from limited effective population size and from relationships within the reference population. Due to this long distance LD, the estimated SNP effects capture non-zero contributions from distant QTLs, some located on other chromosomes than the SNP itself. Therefore, corresponding SNP effects are partly lost in the next generations and we refer to this loss as "erosion". With the concept of QTL contribution to SNP effects derived from mixed model equations, we show with simulation that this long range LD explains 6-25% of the variance of the estimated genomic breeding values, a proportion that is unchanged when the evaluation model includes a residual polygenic effect. Two methods are proposed to predict this erosion factor assuming known simulated QTL effects. In Method 1, one generation of progeny is simulated from the reference population and the GEBV of these progeny based on SNP effects estimated in this newly simulated generation are regressed on the GEBV of the same progeny based on SNP effects estimated in the reference population. In Method 2 all the QTL contributions to SNP effects are regressed based on SNP-QTL recombination rates and summed to predict the GEBV at the next generation. The regression coefficient of the GEBV based on eroded contributions on the raw GEBV is also an estimate of erosion. An illustration is given with the French Normande female reference bovine population in 2021, showing erosion factors ranging from 0.84 to 0.87.

CONCLUSION

Accounting for erosion is important to avoid inflation and biased predictions. The ways to both reduce inflation and to correct for it in the prediction are discussed.

Optimisation of variance component estimation and genomic prediction in a commercial crossbred population of Duroc x (Landrace x Yorkshire) three-way pigs

Crossbreeding is often used in livestock breeding, and genomic selection (GS) is implemented with the breeding goal of selecting purebreds (PB) with high genetic merit for hybridisation to produce crossbreds (CB) with generally improved performance. Previous studies have demonstrated the practicality and efficiency of using CB progeny from a commercial population as a reference population for GS, where a reference population consisting of extreme phenotypic individuals showed a predictive advantage. However, this completely extreme sampling strategy would significantly overestimate the genetic variance of traits, resulting in a significant inflation of the genomic estimated breeding values (GEBV) of PB candidates. So, we explored and optimised the variance component (VC) estimation and genomic prediction using different sampling strategies in a commercial CB population based on data from a Duroc x (Landrace x Yorkshire) pigs three-way crossbreeding system. We first compared the performance of completely extreme sampling, completely random sampling, and four mixed sampling schemes combining extreme and random sampling for VC estimation and genomic prediction for traits with high, medium, and low heritability (h2 = 0.5, 0.3, and 0.1) at different sample sizes (500-6 500). The results showed that the VC estimated from the reference populations obtained using mixed sampling strategies was more accurate than completely extreme sampling, and the mixed reference populations can carry out more accurate predictions and achieve higher response to selection. Furthermore, we applied an optimisation strategy for the mixed reference populations by solving the mixed model equation based on the VC estimated from only random CB therein, which proved to be very positive for improving the GEBV inflation caused by extreme phenotypic CB, effectively reducing the prediction bias while ensuring the prediction accuracy and response to selection. The combination of accurate VC estimation from random CB and the advantage of extreme phenotypic CB in prediction accuracy allows the mixed reference populations to achieve a superior predictive performance in GS. The optimised strategies can maximise the information from commercial CB populations in livestock genomic breeding.

All-breed single-step genomic best linear unbiased predictor evaluations for fertility traits in US dairy cattle

The US dairy cattle genetic evaluation is currently a multistep process, including multibreed traditional BLUP estimations followed by single-breed SNP effects estimation. Single-step GBLUP (ssGBLUP) combines pedigree and genomic data for all breeds in one analysis. Unknown parent groups (UPG) or metafounders (MF) can be used to address missing pedigree information. Fertility traits are notably difficult to evaluate due to low heritabilities, changing management, and a higher recent emphasis on selection to move in a favorable direction. We assessed bias, dispersion, and accuracy of fertility traits in all-breed US dairy cattle using pedigree-based BLUP (PBLUP) and ssGBLUP with UPG or MF; with 5% or 10% residual polygenic effect. Validation methods included the linear regression method and comparison of early and late deregressed proofs for Holstein and Jersey breeds. By comparing MF or UPG in PBLUP, we observed similar results in terms of bias, dispersion, and correlations between early and recent predictions. When genomics was used, ssGBLUP with MF and 10% residual polygenic effect consistently outperformed other models regarding bias, dispersion, and correlations. Compared with multistep results, ssGBLUP with MF and 10% residual polygenic effect showed less bias and increased correlations but slightly overdispersed estimates. Overall, genomic prediction of fertility traits using ssGBLUP was accurate and unbiased, more so with MF than with UPG.

Optimizing purebred selection to improve crossbred performance

Crossbreeding is a widely adopted practice in the livestock industry, leveraging the advantages of heterosis and breed complementarity. The prediction of Crossbred Performance (CP) often relies on Purebred Performance (PB) due to limited crossbred data availability. However, the effective selection of purebred parents for enhancing CP depends on non-additive genetic effects and environmental factors. These factors are encapsulated in the genetic correlation between crossbred and purebred populations (r p c ). In this study, a two-way crossbreeding simulation was employed to investigate various strategies for integrating data from purebred and crossbred populations. The goal was to identify optimal models that maximize CP across different levels ofr p c . Different scenarios involving the selection of genotyped individuals from purebred and crossbred populations were explored using ssGBLUP (single-step Genomic Best Linear Unbiased Prediction) and ssGBLUP-MF (ssGBLUP with metafounders) models. The findings revealed an increase in prediction accuracy across all scenarios asr p c values increased. Notably, in the scenario incorporating genotypes from both purebred parent breeds and their crossbreds, both ssGBLUP and ssGBLUP-MF models exhibited nearly identical predictive accuracy. This scenario achieved maximum accuracy whenr p c was less than 0.5. However, atr p c = 0.8, ssGBLUP, which exclusively included sire breed genotypes in the training set, achieved the highest overall prediction accuracy at 73.2%. In comparison, the BLUP-UPG (BLUP with unknown parent group) model demonstrated lower accuracy than ssGBLUP and ssGBLUP-MF across allr p c levels. Although ssGBLUP and ssGBLUP-MF did not demonstrate a definitive trend in their respective scenarios, the prediction ability for CP increased when incorporating both crossbred and purebred population genotypes at lower levels of  r p c . Furthermore, whenr p c was high, utilizing paternal genotype for CP predictions emerged as the most effective strategy. Predicted dispersion remained relatively similar in all scenarios, indicating a slight underestimation of breeding values. Overall, ther p c value emerged as a critical factor in predicting CP based on purebred data. However, the optimal model to maximize CP depends on the factors influencingr p c . Consequently, ongoing research aims to develop models that optimize purebred selection, further enhancing CP.

Definition of metafounders based on population structure analysis

BACKGROUND

Limitations of the concept of identity by descent in the presence of stratification within a breeding population may lead to an incomplete formulation of the conventional numerator relationship matrix ( A ). Combining A with the genomic relationship matrix ( G ) in a single-step approach for genetic evaluation may cause inconsistencies that can be a source of bias in the resulting predictions. The objective of this study was to identify stratification using genomic data and to transfer this information to matrix A , to improve the compatibility of A and G .

METHODS

Using software to detect population stratification (ADMIXTURE), we developed an iterative approach. First, we identified 2 to 40 strata ( k ) with ADMIXTURE, which we then introduced in a stepwise manner into matrix A , to generate matrixA Γ using the metafounder methodology. Improvements in consistency between matrix G andA Γ were evaluated by regression analysis and through the comparison of the overall mean and mean diagonal values of both matrices. The approach was tested on genotype and pedigree information of European and North American Brown Swiss animals (85,249). Analyses with ADMIXTURE were initially performed on the full set of genotypes (S1). In addition, we used an alternative dataset where we avoided sampling of closely related animals (S2).

RESULTS

Results of the regression analyses of standard A on G were - 0.489, 0.780 and 0.647 for intercept, slope and fit of the regression. When analysing S1 data results of the regression forA Γ on G corresponding values were - 0.028, 1.087 and 0.807 for k =7, while there was no clear optimum k . Analyses of S2 gave a clear optimal k =24, with - 0.020, 0.998 and 0.817 as results of the regression. For this k differences in mean and mean diagonal values between both matrices were negligible.

CONCLUSIONS

The derivation of hidden stratification information based on genotyped animals and its integration into A improved compatibility of the resultingA Γ and G considerably compared to the initial situation. In dairy breeding populations with large half-sib families as sub-structures it is necessary to balance the data when applying population structure analysis to obtain meaningful results.

Unknown parent groups and truncated pedigree in single-step genomic evaluations of Murrah buffaloes

Missing pedigree may produce bias in genomic evaluations. Thus, strategies to deal with this problem have been proposed as using unknown parent groups (UPG) or truncated pedigrees. The aim of this study was to investigate the impact of modeling missing pedigree under ssGBLUP evaluations for productive and reproductive traits in dairy buffalos using different approaches: 1) traditional BLUP without UPG (BLUP), 2) traditional BLUP including UPG (BLUP/UPG), 3) ssGBLUP without UPG (ssGBLUP), 4) ssGBLUP including UPG in the A and A22 matrices (ssGBLUP/A_UPG), 5) ssGBLUP including UPG in all elements of the H matrix (ssGBLUP/H_UPG), 6) BLUP with pedigree truncation for the last 3 generations (BLUP/truncated), and 7) ssGBLUP with pedigree truncation for the last 3 generations (ssGBLUP/ truncated). UPGs were not used in the scenarios with truncated pedigree. A total of 3,717, 4,126 and 3,823 records of the first lactation for accumulated 305 d milk yield (MY), age at first calving (AFC) and lactation length (LL), respectively were used. Accuracies ranged from 0.27 for LL (BLUP) to 0.46 for MY (BLUP), bias ranged from -0.62 for MY (ssGBLUP) to 0.0002 for AFC (BLUP/truncated), and dispersion ranged from 0.88 for MY (BLUP/ A_UPG) to 1.13 for LL (BLUP). Genetic trend showed genetic gains for all traits across 20 years of selection and the impact of including either genomic information, UPG or pedigree truncation under GEBV accuracies ranged among the evaluated traits. Overall, methods using UPGs, truncation pedigree and genomic information exhibited potential to improve GEBV accuracies, bias and dispersion for all traits compared with other methods. Truncated scenarios promoted high genetic gains. In small populations with few genotyped animals, combining truncated pedigree or UPG with genomic information is a feasible approach to deal with missing pedigrees.

Combining large broiler populations into a single genomic evaluation: dealing with genetic divergence

Combining breeding populations that have diverged at some point is a conventional practice, particularly in the poultry industry, where generation intervals are short and genetic evaluations should be frequently available. This study aimed to assess the feasibility of combining large, distantly genetically connected broiler populations into a single genomic evaluation within the single-step GBLUP framework. The pedigree data for broiler lines 1 and 2 consisted of 428,790 and 477,488 animals, being 156,088 and 186,387 genotyped, respectively. Phenotypic data for body weight (kg), carcass yield (%), mortality (1 to 2), and feet health (1 to 7) were collected for 397,974 animals in line 1 and 458,881 in line 2. A 4-trait model was employed for the analyses, and genetic differences between the populations were addressed through different approaches: introducing an additional fixed effect accounting for the line of origin (M2) or making each fixed effect origin-specific (M3). Those models were compared against a conventional model (M1) that did not account for animal origin in the evaluation. Unknown parent groups (UPG) and Metafounders (MF) were fit to account for the genetic differences in M1, M2, and M3; they were set based on the animal's line of origin and sex. Accuracy, bias, and dispersion were used to assess the performances of the models using the Linear Regression method. Validations were performed separately within individual lines and collectively after combining the 2 lines to better assess the advantages of combining the 2 populations. Overall, the accuracy increased when the 2 populations were combined compared to the accuracies obtained from evaluating each line individually. Notably, there were no apparent differences among the models regarding accuracy and dispersion. Regarding bias, using models M2 or M3 with UPG yields the least biased estimates in the combined evaluation. Thus, when combining different populations into a single genomic evaluation, accounting for the genetic and non-genetic differences among the lines ensures accurate and less biased predictions.

Multi-line ssGBLUP evaluation using preselected markers from whole-genome sequence data in pigs

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.

Selective genotyping to implement genomic selection in beef cattle breeding

Genomic selection (GS) plays an essential role in livestock genetic improvement programs. In dairy cattle, the method is already a recognized tool to estimate the breeding values of young animals and reduce generation intervals. Due to the different breeding structures of beef cattle, the implementation of GS is still a challenge and has been adopted to a much lesser extent than dairy cattle. This study aimed to evaluate genotyping strategies in terms of prediction accuracy as the first step in the implementation of GS in beef while some restrictions were assumed for the availability of phenotypic and genomic information. For this purpose, a multi-breed population of beef cattle was simulated by imitating the practical system of beef cattle genetic evaluation. Four genotyping scenarios were compared to traditional pedigree-based evaluation. Results showed an improvement in prediction accuracy, albeit a limited number of animals being genotyped (i.e., 3% of total animals in genetic evaluation). The comparison of genotyping scenarios revealed that selective genotyping should be on animals from both ancestral and younger generations. In addition, as genetic evaluation in practice covers traits that are expressed in either sex, it is recommended that genotyping covers animals from both sexes.

Boundaries for genotype, phenotype, and pedigree truncation in genomic evaluations in pigs

Historical data collection for genetic evaluation purposes is a common practice in animal populations; however, the larger the dataset, the higher the computing power needed to perform the analyses. Also, fitting the same model to historical and recent data may be inappropriate. Data truncation can reduce the number of equations to solve, consequently decreasing computing costs; however, the large volume of genotypes is responsible for most of the increase in computations. This study aimed to assess the impact of removing genotypes along with phenotypes and pedigree on the computing performance, reliability, and inflation of genomic predicted breeding value (GEBV) from single-step genomic best linear unbiased predictor for selection candidates. Data from two pig lines, a terminal sire (L1) and a maternal line (L2), were analyzed in this study. Four analyses were implemented: growth and "weaning to finish" mortality on L1, pre-weaning and reproductive traits on L2. Four genotype removal scenarios were proposed: removing genotyped animals without phenotypes and progeny (noInfo), removing genotyped animals based on birth year (Age), the combination of noInfo and Age scenarios (noInfo + Age), and no genotype removal (AllGen). In all scenarios, phenotypes were removed, based on birth year, and three pedigree depths were tested: two and three generations traced back and using the entire pedigree. The full dataset contained 1,452,257 phenotypes for growth traits, 324,397 for weaning to finish mortality, 517,446 for pre-weaning traits, and 7,853,629 for reproductive traits in pure and crossbred pigs. Pedigree files for lines L1 and L2 comprised 3,601,369 and 11,240,865 animals, of which 168,734 and 170,121 were genotyped, respectively. In each truncation scenario, the linear regression method was used to assess the reliability and dispersion of GEBV for genotyped parents (born after 2019). The number of years of data that could be removed without harming reliability depended on the number of records, type of analyses (multitrait vs. single trait), the heritability of the trait, and data structure. All scenarios had similar reliabilities, except for noInfo, which performed better in the growth analysis. Based on the data used in this study, considering the last ten years of phenotypes, tracing three generations back in the pedigree, and removing genotyped animals not contributing own or progeny phenotypes, increases computing efficiency with no change in the ability to predict breeding values.

Understanding factors influencing the estimated genetic variance and the distribution of breeding values

This study investigated the main factors influencing the genetic variance and the variance of breeding values (EBV). The first is the variance of genetic values in the base population, and the latter is the variance of genetic values in the population under evaluation. These variances are important as improper variances can lead to systematic bias. The inverse of the genetic relationship matrix (K -1) and the phenotypic variance are the main factors influencing the genetic variance and heritability (h2). These factors and h2 are also the main factors influencing the variance of EBVs. Pedigree- and genomic-based relationship matrices (A and G as K) and phenotypes on 599 wheat lines were used. Also, data were simulated, and a hybrid (genomic-pedigree) relationship matrix (H as K) and phenotypes were used. First, matrix K underwent a transformation (K* = w K + α 11' + β I), and the responses in the mean and variation of diag(K -1) and offdiag(K -1) elements, and genetic variance in the form of h2 were recorded. Then, the original K was inverted, and matrix K -1 underwent the same transformations as K, and the responses in the h2 estimate and the variance of EBVs in the forms of correlation and regression coefficients with the EBVs estimated based on the original K -1 were recorded. In response to weighting K by w, the estimated genetic variance changed by 1/w. We found that μ(diag(K)) - μ(offdiag(K)) influences the genetic variance. As such, α did not change the genetic variance, and increasing β increased the estimated genetic variance. Weighting K -1 by w was equivalent to weighting K by 1/w. Using the weighted K -1 together with its corresponding h2, EBVs remained unchanged, which shows the importance of using variance components that are compatible with the K -1. Increasing β I added to K -1 increased the estimated genetic variance, and the effect of α 11' was minor. We found that larger variation of diag(K -1) and higher concentration of offdiag(K -1) around the mean (0) are responsible for lower h2 estimate and variance of EBVs.

Accounting for population structure in genomic predictions of Eucalyptus globulus

Genetic groups have been widely adopted in tree breeding to account for provenance effects within pedigree-derived relationship matrices. However, provenances or genetic groups have not yet been incorporated into single-step genomic BLUP (“HBLUP”) analyses of tree populations. To quantify the impact of accounting for population structure in Eucalyptus globulus, we used HBLUP to compare breeding value predictions from models excluding base population effects and models including either fixed genetic groups or the marker-derived proxies, also known as metafounders. Full-sib families from 2 separate breeding populations were evaluated across 13 sites in the “Green Triangle” region of Australia. Gamma matrices (Γ) describing similarities among metafounders reflected the geographic distribution of populations and the origins of 2 land races were identified. Diagonal elements of Γ provided population diversity or allelic covariation estimates between 0.24 and 0.56. Genetic group solutions were strongly correlated with metafounder solutions across models and metafounder effects influenced the genetic solutions of base population parents. The accuracy, stability, dispersion, and bias of model solutions were compared using the linear regression method. Addition of genomic information increased accuracy from 0.41 to 0.47 and stability from 0.68 to 0.71, while increasing bias slightly. Dispersion was within 0.10 of the ideal value (1.0) for all models. Although inclusion of metafounders did not strongly affect accuracy or stability and had mixed effects on bias, we nevertheless recommend the incorporation of metafounders in prediction models to represent the hierarchical genetic population structure of recently domesticated populations.

Impact of genomic preselection on subsequent genetic evaluations with ssGBLUP using real data from pigs

Background

Empirically assessing the impact of preselection on genetic evaluation of preselected animals requires comparing scenarios that take different approaches into account, including scenarios without preselection. However, preselection is almost always performed in animal breeding programs, so it is difficult to have a dataset without preselection. Hence, most studies on preselection have used simulated datasets, and have concluded that genomic estimated breeding values (GEBV) from subsequent single-step genomic best linear unbiased prediction (ssGBLUP) evaluations are unbiased. The aim of this study was to investigate the impact of genomic preselection (GPS) on accuracy and bias in subsequent ssGBLUP evaluations, using data from a commercial pig breeding program.

Methods

We used data on average daily gain during performance testing, average daily gain throughout life, backfat thickness, and loin depth from one sire line and one dam line of pigs. As these traits have different weights in the breeding goals of the two lines, we analyzed the lines separately. For each line, we implemented a reference GPS scenario that kept all available data, against which the next two scenarios were compared. We then implemented two other scenarios with additional layers of GPS by removing all animals without progeny either (i) only in the validation generation, or (ii) in all generations. We conducted subsequent ssGBLUP evaluations for each GPS scenario, using all the data remaining after implementing the GPS scenario. Accuracy and bias were computed by comparing GEBV against progeny yield deviations of validation animals.

Results

Results for all traits and in both lines showed a marginal loss in accuracy due to the additional layers of GPS. Average accuracies across all GPS scenarios in the two lines were 0.39, 0.47, 0.56, and 0.60, for average daily gain during performance testing and throughout life, backfat thickness, and loin depth, respectively. Biases were largely absent, and when present, did not differ greatly between the GPS scenarios.

Conclusions

We conclude that the impact of preselection on accuracy and bias in subsequent ssGBLUP evaluations of selection candidates in pigs is generally minimal. We expect this conclusion to apply for other animal breeding programs as well, since preselection of any type or intensity generally has the same effect in animal breeding programs.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12711-022-00727-5.

Correcting for base-population differences and unknown parent groups in single-step genomic predictions of Norwegian Red Cattle

Bias and inflation in genomic evaluation with the single-step methods have been reported in several studies. Incompatibility between the base-populations of the pedigree-based and the genomic relationship matrix (G) could be a reason for these biases. Inappropriate ways of accounting for missing parents could be another reason for biases in genetic evaluations with or without genomic information. To handle these problems, we fitted and evaluated a fixed covariate (J) that contains ones for genotyped animals and zeros for unrelated non-genotyped animals, or pedigree-based regression coefficients for related non-genotyped animals. We also evaluated alternative ways of fitting the J covariate together with genetic groups on biases and stability of breeding value estimates, and of including it into G as a random effect. In a whole vs. partial data set comparison, four scenarios were investigated for the partial data: genotypes missing, phenotypes missing, both genotypes and phenotypes missing, and pedigree missing. Fitting J either as fixed or random reduced level-bias and inflation and increased stability of genomic predictions as compared to the basic model where neither J nor genetic groups were fitted. In most models, genomic predictions were largely biased for scenarios with missing genotype and phenotype information. The biases were reduced for models which combined group and J effects. Models with these corrected group covariates performed better than the recently published model where genetic groups were encapsulated and fitted as random via the Quaas and Pollak transformation. In our Norwegian Red cattle data, a model which combined group and J regression coefficients was preferred because it showed least bias and highest stability of genomic predictions across the scenarios.

Prediction ability for growth and maternal traits using SNP arrays based on different marker densities in Nellore cattle using the ssGBLUP

This study aimed to investigate the prediction ability for growth and maternal traits using different low-density customized SNP arrays selected by informativeness and distribution of markers across the genome employing single-step genomic BLUP (ssGBLUP). Phenotypic records for adjusted weight at 210 and 450 days of age were utilized. A total of 945 animals were genotyped with high-density chip, and 267 individuals born after 2008 were selected as validation population. We evaluated 11 scenarios using five customized density arrays (40 k, 20 k, 10 k, 5 k and 2 k) and the HD array was used as desirable scenario. The GEBV predictions and BIF (Beef Improvement Federation) accuracy were obtained with BLUPF90 family programs. Linear regression was used to evaluate the prediction ability, inflation, and bias of GEBV of each customized array. An overestimation of partial GEBVs in contrast with complete GEBVs and increase of BIF accuracy with the density arrays diminished were observed. For all traits, the prediction ability was higher as the array density increased and it was similar with customized arrays higher than 10 k SNPs. Level of inflation was lower as the density array increased of and was higher for MW210 effect. The bias was susceptible to overestimation of GEBVs when the density customized arrays decreased. These results revealed that the BIF accuracy is sensible to overestimation using low-density customized arrays while the prediction ability with least 10,000 informative SNPs obtained from the Illumina BovineHD BeadChip shows accurate and less biased predictions. Low-density customized arrays under ssGBLUP method could be feasible and cost-effective in genomic selection.

Development of genomic predictions for Angus cattle in Brazil incorporating genotypes from related American sires

Genomic prediction has become the new standard for genetic improvement programs, and currently, there is a desire to implement this technology for the evaluation of Angus cattle in Brazil. Thus, the main objective of this study was to assess the feasibility of evaluating young Brazilian Angus (BA) bulls and heifers for 12 routinely recorded traits using single-step genomic BLUP (ssGBLUP) with and without genotypes from American Angus (AA) sires. The second objective was to obtain estimates of effective population size (Ne) and linkage disequilibrium (LD) in the Brazilian Angus population. The dataset contained phenotypic information for up to 277,661 animals belonging to the Promebo breeding program, pedigree for 362,900, of which 1,386 were genotyped for 50k, 77k, and 150k single nucleotide polymorphism (SNP) panels. After imputation and quality control, 61,666 SNPs were available for the analyses. In addition, genotypes from 332 American Angus (AA) sires widely used in Brazil were retrieved from the AA Association database to be used for genomic predictions. Bivariate animal models were used to estimate variance components, traditional EBV, and genomic EBV (GEBV). Validation was carried out with the linear regression method (LR) using young-genotyped animals born between 2013 and 2015 without phenotypes in the reduced dataset and with records in the complete dataset. Validation animals were further split into progeny of BA and AA sires to evaluate if their progenies would benefit by including genotypes from AA sires. The Ne was 254 based on pedigree and 197 based on LD, and the average LD (±SD) and distance between adjacent single nucleotide polymorphisms (SNPs) across all chromosomes were 0.27 (±0.27) and 40743.68 bp, respectively. Prediction accuracies with ssGBLUP outperformed BLUP for all traits, improving accuracies by, on average, 16% for BA young bulls and heifers. The GEBV prediction accuracies ranged from 0.37 (total maternal for weaning weight and tick count) to 0.54 (yearling precocity) across all traits, and dispersion (LR coefficients) fluctuated between 0.92 and 1.06. Inclusion of genotyped sires from the AA improved GEBV accuracies by 2%, on average, compared to using only the BA reference population. Our study indicated that genomic information could help us to improve GEBV accuracies and hence genetic progress in the Brazilian Angus population. The inclusion of genotypes from American Angus sires heavily used in Brazil just marginally increased the GEBV accuracies for selection candidates.

Single-step genomic evaluation of milk production traits in Canadian Alpine and Saanen dairy goats

Genomic evaluations are routine in most plant and livestock breeding programs but are used infrequently in dairy goat breeding schemes. In this context, the purpose of this study was to investigate the use of the single-step genomic BLUP method for predicting genomic breeding values for milk production traits (milk, protein, and fat yields; protein and fat percentages) in Canadian Alpine and Saanen dairy goats. There were 6,409 and 12,236 Alpine records and 3,434 and 5,008 Saanen records for each trait in first and later lactations, respectively, and a total of 1,707 genotyped animals (833 Alpine and 874 Saanen). Two validation approaches were used, forward validation (i.e., animals born after 2013 with an average estimated breeding value accuracy from the full data set ≥0.50) and forward cross-validation (i.e., subsets of all animals included in the forward validation were used in successive replications). The forward cross-validation approach resulted in similar validation accuracies (0.55 to 0.66 versus 0.54 to 0.61) and biases (-0.01 to -0.07 versus -0.03 to 0.11) to the forward validation when averaged across traits. Additionally, both single and multiple-breed analyses were compared, and similar average accuracies and biases were observed across traits. However, there was a small gain in accuracy from the use of multiple-breed models for the Saanen breed. A small gain in validation accuracy for genomically enhanced estimated breeding values (GEBV) relative to pedigree-based estimated breeding values (EBV) was observed across traits for the Alpine breed, but not for the Saanen breed, possibly due to limitations in the validation design, heritability of the traits evaluated, and size of the training populations. Trait-specific gains in theoretical accuracy of GEBV relative to EBV for the validation animals ranged from 17 to 31% in Alpine and 35 to 55% in Saanen, using the cross-validation approach. The GEBV predicted from the full data set were 12 to 16% more accurate than EBV for genotyped animals, but no gains were observed for nongenotyped animals. The largest gains were found for does without lactation records (35-41%) and bucks without daughter records (46-54%), and consequently, the implementation of genomic selection in the Canadian dairy goat population would be expected to increase selection accuracy for young breeding candidates. Overall, this study represents the first step toward implementation of genomic selection in Canadian dairy goat populations.

Validation of single-step genomic predictions using the linear regression method for milk yield and heat tolerance in a Thai-Holstein population

Background and Aim:

Genomic selection improves accuracy and decreases the generation interval, increasing the selection response. This study was conducted to assess the benefits of using single-step genomic best linear unbiased prediction (ssGBLUP) for genomic evaluations of milk yield and heat tolerance in Thai-Holstein cows and to test the value of old phenotypic data to maintain the accuracy of predictions.

Materials and Methods:

The dataset included 104,150 milk yield records collected from 1999 to 2018 from 15,380 cows. The pedigree contained 33,799 animals born between 1944 and 2016, of which 882 were genotyped. Analyses were performed with and without genomic information using ssGBLUP and BLUP, respectively. Statistics for bias, dispersion, the ratio of accuracies, and the accuracy of estimated breeding values were calculated using the linear regression (LR) method. A partial dataset excluded the phenotypes of the last generation, and 66 bulls were identified as validation individuals.

Results:

Bias was considerable for BLUP (0.44) but negligible (−0.04) for ssGBLUP; dispersion was similar for both techniques (0.84 vs. 1.06 for BLUP and ssGBLUP, respectively). The ratio of accuracies was 0.33 for BLUP and 0.97 for ssGBLUP, indicating more stable predictions for ssGBLUP. The accuracy of predictions was 0.18 for BLUP and 0.36 for ssGBLUP. Excluding the first 10 years of phenotypic data (i.e., 1999-2008) decreased the accuracy to 0.09 for BLUP and 0.32 for ssGBLUP. Genomic information doubled the accuracy and increased the persistence of genomic estimated breeding values when old phenotypes were removed.

Conclusion:

The LR method is useful for estimating accuracies and bias in complex models. When the population size is small, old data are useful, and even a small amount of genomic information can substantially improve the accuracy. The effect of heat stress on first parity milk yield is small.

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.

Metafounders May Reduce Bias in Composite Cattle Genomic Predictions

Metafounders are pseudo-individuals that act as proxies for animals in base populations. When metafounders are used, individuals from different breeds can be related through pedigree, improving the compatibility between genomic and pedigree relationships. The aim of this study was to investigate the use of metafounders and unknown parent groups (UPGs) for the genomic evaluation of a composite beef cattle population. Phenotypes were available for scrotal circumference at 14 months of age (SC14), post weaning gain (PWG), weaning weight (WW), and birth weight (BW). The pedigree included 680,551 animals, of which 1,899 were genotyped for or imputed to around 30,000 single-nucleotide polymorphisms (SNPs). Evaluations were performed based on pedigree (BLUP), pedigree with UPGs (BLUP_UPG), pedigree with metafounders (BLUP_MF), single-step genomic BLUP (ssGBLUP), ssGBLUP with UPGs for genomic and pedigree relationship matrices (ssGBLUP_UPG) or only for the pedigree relationship matrix (ssGBLUP_UPGA), and ssGBLUP with metafounders (ssGBLUP_MF). Each evaluation considered either four or 10 groups that were assigned based on breed of founders and intermediate crosses. To evaluate model performance, we used a validation method based on linear regression statistics to obtain accuracy, stability, dispersion, and bias of (genomic) estimated breeding value [(G)EBV]. Overall, relationships within and among metafounders were stronger in the scenario with 10 metafounders. Accuracy was greater for models with genomic information than for BLUP. Also, the stability of (G)EBVs was greater when genomic information was taken into account. Overall, pedigree-based methods showed lower inflation/deflation (regression coefficients close to 1.0) for SC14, WWM, and BWD traits. The level of inflation/deflation for genomic models was small and trait-dependent. Compared with regular ssGBLUP, ssGBLUP_MF4 displayed regression coefficient closer to one SC14, PWG, WWM, and BWD. Genomic models with metafounders seemed to be slightly more stable than models with UPGs based on higher similarity of results with different numbers of groups. Further, metafounders can help to reduce bias in genomic evaluations of composite beef cattle populations without reducing the stability of GEBVs.

Across-country genomic predictions in Norwegian and New Zealand Composite sheep populations with similar development history

The goal of this study was to assess the feasibility of across-country genomic predictions in Norwegian White Sheep (NWS) and New Zealand Composite (NZC) sheep populations with similar development history. Different training populations were evaluated (i.e., including only NWS or NZC, or combining both populations). Predictions were performed using the actual phenotypes (normalized) and the single-step GBLUP via Bayesian inference. Genotyped NWS animals born in 2016 (N = 267) were used to assess the accuracy and bias of genomic estimated breeding values (GEBVs) predicted for birth weight (BW), weaning weight (WW), carcass weight (CW), EUROP carcass classification (EUC), and EUROP fat grading (EUF). The accuracy and bias of GEBVs differed across traits and training population used. For instance, the GEBV accuracies ranged from 0.13 (BW) to 0.44 (EUC) for GEBVs predicted including only NWS, from 0.06 (BW) to 0.15 (CW) when including only NZC, and from 0.10 (BW) to 0.41 (EUC) when including both NWS and NZC animals in the training population. The regression coefficients used to assess the spread of GEBVs (bias) ranged from 0.26 (BW) to 0.64 (EUF) for only NWS, 0.10 (EUC) to 0.52 (CW) for only NZC, and from 0.42 (WW) to 2.23 (EUC) for both NWS and NZC in the training population. Our findings suggest that across-country genomic predictions based on ssGBLUP might be possible for NWS and NZC, especially for novel traits.

Accuracy of genomic breeding values and predictive ability for postweaning liveweight and age at first calving in a Nellore cattle population with missing sire information

The multiple sire system (MSS) is a common mating scheme in extensive beef production systems. However, MSS does not allow paternity identification and lead to inaccurate genetic predictions. The objective of this study was to investigate the implementation of single-step genomic BLUP (ssGBLUP) in different scenarios of uncertain paternity in the evaluation for 450-day adjusted liveweight (W450) and age at first calving (AFC) in a Nellore cattle population. To estimate the variance components using BLUP and ssGBLUP, the relationship matrix (A) with different proportions of animals with missing sires (MS) (scenarios 0, 25, 50, 75, and 100% of MS) was created. The genotyped animals with MS were randomly chosen, and ten replicates were performed for each scenario and trait. Five groups of animals were evaluated in each scenario: PHE, all animals with phenotypic records in the population; SIR, proven sires; GEN, genotyped animals; YNG, young animals without phenotypes and progeny; and YNGEN, young genotyped animals. The additive genetic variance decreased for both traits as the proportion of MS increased in the population when using the regular REML. When using the ssGBLUP, accuracies ranged from 0.13 to 0.47 for W450 and from 0.10 to 0.25 for AFC. For both traits, the prediction ability of the direct genomic value (DGV) decreased as the percentage of MS increased. These results emphasize that indirect prediction via DGV of young animals is more accurate when the SNP effects are derived from ssGBLUP with a reference population with known sires. The ssGBLUP could be applied in situations of uncertain paternity, especially when selecting young animals. This methodology is shown to be accurate, mainly in scenarios with a high percentage of MS.

Genomic selection in Gir cattle using female reference population

When a sizeable reference population of proven bulls is not available for implementing Genomic selection for a particular trait, and when a recording of certain traits on large scale is difficult, the use of a female reference population is recommended. Gir, one of the important milk purpose cattle breeds of India falls under this category. There is no large scale Progeny Testing (PT) programme in Gir, so proven bulls based on daughter performance in large numbers are not available. Considering the constraints, a genomic BLUP (GBLUP) model was implemented based on recorded cow reference population in Gir breed. Cows (3491) and 23 bulls were genotyped using INDUSCHIP for this purpose. Due to non-availability of pedigreed data, conventional breeding values (BV) of bulls and their reliabilities were not known. For comparison, assumed theoretical reliability of BV of a bull selected based on its dam's yield was compared with reliability obtained for genomic breeding value (GBV) using a GBLUP model. The reliability estimates for GBVs were 4 times higher than that for BVs. The predictive ability of the model was demonstrated by measuring the correlation between corrected phenotypes and GBVs for animals whose records were masked in a five-fold cross-validation study. The correlation was around 0.45 showing reasonable predictability of the GBLUP model. The GBVs were not biased. The regression coefficient between the corrected phenotype and GBV was 1.045. The present study demonstrates that it is feasible to implement genomic selection in Gir cattle in Indian conditions using a female reference population. It is expected that the bulls can be selected with around 4 fold more accuracy than the current method of selecting based on their dams' yield accelerating expected genetic growth in Gir cattle.

Accuracy of GEBV of sires based on pooled allele frequency of their progeny

Despite decreasing genotyping costs, in some cases individually genotyping animals is not economically feasible (e.g., in small ruminants). An alternative is to pool DNA, using the pooled allele frequency (PAF) to garner information on performance. Still, the use of PAF for prediction (estimation of genomic breeding values; GEBVs) has been limited. Two potential sources of error on accuracy of GEBV of sires, obtained from PAF of their progeny themselves lacking pedigree information, were tested: (i) pool construction error (unequal contribution of DNA from animals in pools), and (ii) technical error (variability when reading the array). Pooling design (random, extremes, K-means), pool size (5, 10, 25, 50, and 100 individuals), and selection scenario (random, phenotypic) also were considered. These factors were tested by simulating a sheep population. Accuracy of GEBV-the correlation between true and estimated values-was not substantially affected by pool construction or technical error, or selection scenario. A significant interaction, however, between pool size and design was found. Still, regardless of design, mean accuracy was higher for pools of 10 or less individuals. Mean accuracy of GEBV was 0.174 (SE 0.001) for random pooling, and 0.704 (SE 0.004) and 0.696 (SE 0.004) for extreme and K-means pooling, respectively. Non-random pooling resulted in moderate accuracy of GEBV. Overall, pooled genotypes can be used in conjunction with individual genotypes of sires for moderately accurate predictions of their genetic merit with little effect of pool construction or technical error.

Practical implementation of genetic groups in single-step genomic evaluations with Woodbury matrix identity-based genomic relationship inverse

The growing amount of genomic information in dairy cattle has increased computational and modeling challenges in the single-step evaluations. The computational challenges are due to the dense inverses of genomic (G) and pedigree (A₂₂) relationship matrices of genotyped animals in the single-step mixed model equations. An equivalent mixed model equation is given by single-step genomic BLUP that are based on the T matrix (ssGTBLUP), where these inverses are avoided by expressing G^-1 through a product of 2 rectangular matrices, and (A₂₂)^-1 through sparse matrix blocks of the inverse of full relationship matrix A^-1. A proper way to account genetic groups through unknown parent groups (UPG) after the Quaas-Pollak transformation (QP) is one key factor in a single-step model. When the UPG effects are incompletely accounted, the iterative solving method may have convergence problems. In this study, we investigated computational and predictive performance of ssGTBLUP with residual polygenic (RPG) effect and UPG. The QP transformation used A^-1 and, in the complete form, T and (A₂₂)^-1 matrices as well. The models were tested with official Nordic Holstein milk production test-day data and model. The results show that UPG can be easily implemented in ssGTBLUP having RPG. The complete QP transformation was computationally feasible when preconditioned conjugate gradient iteration and iteration on data without explicitly setting up G or A₂₂ matrices were used. Furthermore, for good convergence of the preconditioned conjugate gradient method, a complete QP transformation was necessary.

Genomic studies of milk-related traits in water buffalo (Bubalus bubalis) based on single-step genomic best linear unbiased prediction and random regression models

Genomic selection has been widely implemented in many livestock breeding programs, but it remains incipient in buffalo. Therefore, this study aimed to (1) estimate variance components incorporating genomic information in Murrah buffalo; (2) evaluate the performance of genomic prediction for milk-related traits using single- and multitrait random regression models (RRM) and the single-step genomic best linear unbiased prediction approach; and (3) estimate longitudinal SNP effects and candidate genes potentially associated with time-dependent variation in milk, fat, and protein yields, as well as somatic cell score (SCS) in multiple parities. The data used to estimate the genetic parameters consisted of a total of 323,140 test-day records. The average daily heritability estimates were moderate (0.35 ± 0.02 for milk yield, 0.22 ± 0.03 for fat yield, 0.42 ± 0.03 for protein yield, and 0.16 ± 0.03 for SCS). The highest heritability estimates, considering all traits studied, were observed between 20 and 280 d in milk (DIM). The genetic correlation estimates at different DIM among the evaluated traits ranged from -0.10 (156 to 185 DIM for SCS) to 0.61 (36 to 65 DIM for fat yield). In general, direct selection for any of the traits evaluated is expected to result in indirect genetic gains for milk yield, fat yield, and protein yield but also increase SCS at certain lactation stages, which is undesirable. The predicted RRM coefficients were used to derive the genomic estimated breeding values (GEBV) for each time point (from 5 to 305 DIM). In general, the tuning parameters evaluated when constructing the hybrid genomic relationship matrices had a small effect on the GEBV accuracy and a greater effect on the bias estimates. The SNP solutions were back-solved from the GEBV predicted from the Legendre random regression coefficients, which were then used to estimate the longitudinal SNP effects (from 5 to 305 DIM). The daily SNP effect for 3 different lactation stages were performed considering 3 different lactation stages for each trait and parity: from 5 to 70, from 71 to 150, and from 151 to 305 DIM. Important genomic regions related to the analyzed traits and parities that explain more than 0.50% of the total additive genetic variance were selected for further analyses of candidate genes. In general, similar potential candidate genes were found between traits, but our results suggest evidence of differential sets of candidate genes underlying the phenotypic expression of the traits across parities. These results contribute to a better understanding of the genetic architecture of milk production traits in dairy buffalo and reinforce the relevance of incorporating genomic information to genetically evaluate longitudinal traits in dairy buffalo. Furthermore, the candidate genes identified can be used as target genes in future functional genomics studies.

Genomic predictions for yield traits in US Holsteins with unknown parent groups

The objective of this study was to assess the reliability and bias of estimated breeding values (EBV) from traditional BLUP with unknown parent groups (UPG), genomic EBV (GEBV) from single-step genomic BLUP (ssGBLUP) with UPG for the pedigree relationship matrix (A) only (SS_UPG), and GEBV from ssGBLUP with UPG for both A and the relationship matrix among genotyped animals (A₂₂; SS_UPG2) using 6 large phenotype-pedigree truncated Holstein data sets. The complete data included 80 million records for milk, fat, and protein yields from 31 million cows recorded since 1980. Phenotype-pedigree truncation scenarios included truncation of phenotypes for cows recorded before 1990 and 2000 combined with truncation of pedigree information after 2 or 3 ancestral generations. A total of 861,525 genotyped bulls with progeny and cows with phenotypic records were used in the analyses. Reliability and bias (inflation/deflation) of GEBV were obtained for 2,710 bulls based on deregressed proofs, and on 381,779 cows born after 2014 based on predictivity (adjusted cow phenotypes). The BLUP reliabilities for young bulls varied from 0.29 to 0.30 across traits and were unaffected by data truncation and number of generations in the pedigree. Reliabilities ranged from 0.54 to 0.69 for SS_UPG and were slightly affected by phenotype-pedigree truncation. Reliabilities ranged from 0.69 to 0.73 for SS_UPG2 and were unaffected by phenotype-pedigree truncation. The regression coefficient of bull deregressed proofs on (G)EBV (i.e., GEBV and EBV) ranged from 0.86 to 0.90 for BLUP, from 0.77 to 0.94 for SS_UPG, and was 1.00 ± 0.03 for SS_UPG2. Cow predictivity ranged from 0.22 to 0.28 for BLUP, 0.48 to 0.51 for SS_UPG, and 0.51 to 0.54 for SS_UPG2. The highest cow predictivities for BLUP were obtained with the most extreme truncation, whereas for SS_UPG2, cow predictivities were also unaffected by phenotype-pedigree truncations. The regression coefficient of cow predictivities on (G)EBV was 1.02 ± 0.02 for SS_UPG2 with the most extreme truncation, which indicated the least biased predictions. Computations with the complete data set took 17 h with BLUP, 58 h with SS_UPG, and 23 h with SS_UPG2. The same computations with the most extreme phenotype-pedigree truncation took 7, 36, and 15 h, respectively. The SS_UPG2 converged in fewer rounds than BLUP, whereas SS_UPG took up to twice as many rounds. Thus, the ssGBLUP with UPG assigned to both A and A₂₂ provided accurate and unbiased evaluations, regardless of phenotype-pedigree truncation scenario. Old phenotypes (before 2000 in this data set) did not affect the reliability of predictions for young selection candidates, especially in SS_UPG2.

Comparison of models for missing pedigree in single-step genomic prediction

Pedigree information is often missing for some animals in a breeding program. Unknown-parent groups (UPGs) are assigned to the missing parents to avoid biased genetic evaluations. Although the use of UPGs is well established for the pedigree model, it is unclear how UPGs are integrated into the inverse of the unified relationship matrix (H-inverse) required for single-step genomic best linear unbiased prediction. A generalization of the UPG model is the metafounder (MF) model. The objectives of this study were to derive 3 H-inverses and to compare genetic trends among models with UPG and MF H-inverses using a simulated purebred population. All inverses were derived using the joint density function of the random breeding values and genetic groups. The breeding values of genotyped animals (u2) were assumed to be adjusted for UPG effects (g) using matrix Q2 as u2∗=u2+Q2g before incorporating genomic information. The Quaas-Pollak-transformed (QP) H-inverse was derived using a joint density function of u2∗ and g updated with genomic information and assuming nonzero cov(u2∗,g'). The modified QP (altered) H-inverse also assumes that the genomic information updates u2∗ and g, but cov(u2∗,g')=0. The UPG-encapsulated (EUPG) H-inverse assumed genomic information updates the distribution of u2∗. The EUPG H-inverse had the same structure as the MF H-inverse. Fifty percent of the genotyped females in the simulation had a missing dam, and missing parents were replaced with UPGs by generation. The simulation study indicated that u2∗ and g in models using the QP and altered H-inverses may be inseparable leading to potential biases in genetic trends. Models using the EUPG and MF H-inverses showed no genetic trend biases. These 2 H-inverses yielded the same genomic EBV (GEBV). The predictive ability and inflation of GEBVs from young genotyped animals were nearly identical among models using the QP, altered, EUPG, and MF H-inverses. Although the choice of H-inverse in real applications with enough data may not result in biased genetic trends, the EUPG and MF H-inverses are to be preferred because of theoretical justification and possibility to reduce biases.

Avoiding preselection bias in subsequent single-step genomic BLUP evaluations of genomically preselected animals

In animal breeding, parents of the next generation are usually selected in multiple stages, and the initial stages of this selection are called preselection. Preselection reduces the information available for subsequent evaluation of preselected animals and this sometimes leads to bias. The objective of this study was to establish the minimum information required to subsequently evaluate genomically preselected animals without bias arising from preselection, with single-step genomic best linear unbiased prediction (ssGBLUP). We simulated a nucleus of a breeding program in which a recent population of 15 generations was produced. In each generation, parents of the next generation were selected in a single-stage selection based on pedigree BLUP. However, in generation 15, 10% of male and 15% of female offspring were preselected on their genomic estimated breeding values (GEBV). These GEBV were estimated using ssGBLUP, including the pedigree of all animals in generations 0-15, genotypes of all animals in generations 13-15 and phenotypes of all animals in generations 11-14. In subsequent ssGBLUP evaluation of these preselected animals, genotypes and phenotypes from various groups of animals were excluded one after another. We found that GEBV of the preselected animals were only estimated without preselection bias when genotypes and phenotypes of all animals in generations 13 and 14 and of the preselected animals were included in the subsequent evaluation. We also found that genotypes of the animals discarded at preselection only helped in reducing preselection bias in GEBV of their preselected sibs when genotypes of their parents were absent or excluded from the subsequent evaluation. We concluded that to prevent preselection bias in subsequent ssGBLUP evaluation of genomically preselected animals, information representative of the reference data used in the evaluation at preselection and genotypes and phenotypes of the preselected animals are needed in the subsequent evaluation.

Beef trait genetic parameters based on old and recent data and its implications for genomic predictions in Italian Simmental cattle

This study aimed to evaluate the changes in variance components over time to identify a subset of data from the Italian Simmental (IS) population that would yield the most appropriate estimates of genetic parameters and breeding values for beef traits to select young bulls. Data from bulls raised between 1986 and 2017 were used to estimate genetic parameters and breeding values for four beef traits (average daily gain [ADG], body size [BS], muscularity [MUS], and feet and legs [FL]). The phenotypic mean increased during the years of the study for ADG, but it decreased for BS, MUS, and FL. The complete dataset (ALL) was divided into four generational subsets (Gen1, Gen2, Gen3, and Gen4). Additionally, ALL was divided into two larger subsets: the first one (OLD) combined data from Gen1 and Gen2 to represent the starting population, and the second one (CUR) combined data from Gen3 and Gen4 to represent a subpopulation with stronger ties to the current population. Genetic parameters were estimated with a four-trait genomic animal model using a single-step genomic average information restricted maximum likelihood algorithm. Heritability estimates from ALL were 0.26 ± 0.03 for ADG, 0.33 ± 0.04 for BS, 0.55 ± 0.03 for MUS, and 0.23 ± 0.03 for FL. Higher heritability estimates were obtained with OLD and ALL than with CUR. Considerable changes in heritability existed between Gen1 and Gen4 due to fluctuations in both additive genetic and residual variances. Genetic correlations also changed over time, with some values moving from positive to negative or even to zero. Genetic correlations from OLD were stronger than those from CUR. Changes in genetic parameters over time indicated that they should be updated regularly to avoid biases in genomic estimated breeding values (GEBV) and low selection accuracies. GEBV estimated using CUR variance components were less biased and more consistent than those estimated with OLD and ALL variance components. Validation results indicated that data from recent generations produced genetic parameters that more appropriately represent the structure of the current population, yielding accurate GEBV to select young animals and increasing the likelihood of higher genetic gains.

Core-dependent changes in genomic predictions using the Algorithm for Proven and Young in single-step genomic best linear unbiased prediction

Single-step genomic best linear unbiased prediction with the Algorithm for Proven and Young (APY) is a popular method for large-scale genomic evaluations. With the APY algorithm, animals are designated as core or noncore, and the computing resources to create the inverse of the genomic relationship matrix (GRM) are reduced by inverting only a portion of that matrix for core animals. However, using different core sets of the same size causes fluctuations in genomic estimated breeding values (GEBVs) up to one additive standard deviation without affecting prediction accuracy. About 2% of the variation in the GRM is noise. In the recursion formula for APY, the error term modeling the noise is different for every set of core animals, creating changes in breeding values. While average changes are small, and correlations between breeding values estimated with different core animals are close to 1.0, based on the normal distribution theory, outliers can be several times bigger than the average. Tests included commercial datasets from beef and dairy cattle and from pigs. Beyond a certain number of core animals, the prediction accuracy did not improve, but fluctuations decreased with more animals. Fluctuations were much smaller than the possible changes based on prediction error variance. GEBVs change over time even for animals with no new data as genomic relationships ties all the genotyped animals, causing reranking of top animals. In contrast, changes in nongenomic models without new data are small. Also, GEBV can change due to details in the model, such as redefinition of contemporary groups or unknown parent groups. In particular, increasing the fraction of blending of the GRM with a pedigree relationship matrix from 5% to 20% caused changes in GEBV up to 0.45 SD, with a correlation of GEBV > 0.99. Fluctuations in genomic predictions are part of genomic evaluation models and are also present without the APY algorithm when genomic evaluations are computed with updated data. The best approach to reduce the impact of fluctuations in genomic evaluations is to make selection decisions not on individual animals with limited individual accuracy but on groups of animals with high average accuracy.

Bias in genomic predictions by mating practices for linear type traits in a large-scale genomic evaluation

The objective of this study was to clarify how bias in genomic predictions is created by investigating a relationship among selection intensity, a change in heritability (Δh²), and assortative mating (ASM). A change in heritability, resulting from selection, reflects the impact that the Bulmer effect has on the reduction in between-family variation, whereas assortative mating impacts the within-family variance or Mendelian sampling variation. A partial data set up to 2014, including 841K genotyped animals, was used to calculate genomic predictions with a single-step genomic model for 18 linear type traits in US Holsteins. A full data set up to 2018, including 2.3 million genotyped animals, was used to calculate benchmark genomic predictions. Inbreeding and unknown parent groups for missing parents of animals were included in the model. Genomic evaluation was performed using 2 different genetic parameters: those estimated 14 yr ago, which have been used in the national genetic evaluation for linear type traits in the United States, and those newly estimated with recent records from 2015 to 2018 and those corresponding pedigrees. Genetic trends for 18 type traits were estimated for bulls with daughters and cows with phenotypes in 2018. Based on selection intensity and mating decisions, these traits can be categorized into 3 groups: (a) high directional selection, (b) moderate selection, and (c) intermediate optimum selection. The first 2 categories can be explained by positive assortative mating, and the last can be explained by negative assortative or disassortative mating. Genetic progress was defined by genetic gain per year based on average standardized genomic predictions for cows from 2000 to 2014. Traits with more genetic progress tended to have more "inflated" genomic predictions (i.e., "inflation" means here that genomic predictions are larger in absolute values than expected, whereas "deflation" means smaller than expected). Heritability estimates for 14 out of 18 traits declined in the last 16 yr, and Δh² ranged from -0.09 to 0.04. Traits with a greater decline in heritability tended to have more deflated genomic predictions. Biases (inflation or deflation) in genomic predictions were not improved by using the latest genetic parameters, implying that bias in genomic predictions due to preselection was not substantial for a large-scale genomic evaluation. Moreover, the strong selection intensity was not fully responsible for bias in genomic predictions. The directional selection can decrease heritability; however, positive assortative mating, which was strongly associated with large genetic gains, could minimize the decline in heritability for a trait under strong selection and could affect bias in genomic predictions.

Single-Step Genomic Evaluations from Theory to Practice: Using SNP Chips and Sequence Data in BLUPF90

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.

Current status of genomic evaluation

Early application of genomic selection relied on SNP estimation with phenotypes or de-regressed proofs (DRP). Chips of 50k SNP seemed sufficient for an accurate estimation of SNP effects. Genomic estimated breeding values (GEBV) were composed of an index with parent average, direct genomic value, and deduction of a parental index to eliminate double counting. Use of SNP selection or weighting increased accuracy with small data sets but had minimal to no impact with large data sets. Efforts to include potentially causative SNP derived from sequence data or high-density chips showed limited or no gain in accuracy. After the implementation of genomic selection, EBV by BLUP became biased because of genomic preselection and DRP computed based on EBV required adjustments, and the creation of DRP for females is hard and subject to double counting. Genomic selection was greatly simplified by single-step genomic BLUP (ssGBLUP). This method based on combining genomic and pedigree relationships automatically creates an index with all sources of information, can use any combination of male and female genotypes, and accounts for preselection. To avoid biases, especially under strong selection, ssGBLUP requires that pedigree and genomic relationships are compatible. Because the inversion of the genomic relationship matrix (G) becomes costly with more than 100k genotyped animals, large data computations in ssGBLUP were solved by exploiting limited dimensionality of genomic data due to limited effective population size. With such dimensionality ranging from 4k in chickens to about 15k in cattle, the inverse of G can be created directly (e.g., by the algorithm for proven and young) at a linear cost. Due to its simplicity and accuracy, ssGBLUP is routinely used for genomic selection by the major chicken, pig, and beef industries. Single step can be used to derive SNP effects for indirect prediction and for genome-wide association studies, including computations of the P-values. Alternative single-step formulations exist that use SNP effects for genotyped or for all animals. Although genomics is the new standard in breeding and genetics, there are still some problems that need to be solved. This involves new validation procedures that are unaffected by selection, parameter estimation that accounts for all the genomic data used in selection, and strategies to address reduction in genetic variances after genomic selection was implemented.

Multi-Trait Genomic Prediction Improves Predictive Ability for Dry Matter Yield and Water-Soluble Carbohydrates in Perennial Ryegrass

In perennial ryegrass (Lolium perenne L), annual and seasonal dry matter yield (DMY) and nutritive quality of herbage are high-priority traits targeted for improvement through selective breeding. Genomic prediction (GP) has proven to be a valuable tool for improving complex traits and may be further enhanced through the use of multi-trait (MT) prediction models. In this study, we evaluated the relative performance of MT prediction models to improve predictive ability for DMY and key nutritive quality traits, using two different training populations (TP1, n = 463 and TP2, n = 517) phenotyped at multiple locations. MT models outperformed single-trait (ST) models by 24% to 59% for DMY and 67% to 105% for nutritive quality traits, such as low, high, and total WSC, when a correlated secondary trait was included in both the training and test set (MT-CV2) or in the test set alone (MT-CV3) (trait-assisted genomic selection). However, when a secondary trait was included in training set and not the test set (MT-CV1), the predictive ability was not statistically significant (p > 0.05) compared to the ST model. We evaluated the impact of training set size when using a MT-CV2 model. Using a highly correlated trait (r_g = 0.88) as the secondary trait in the MT-CV2 model, there was no loss in predictive ability for DMY even when the training set was reduced to 50% of its original size. In contrast, using a weakly correlated secondary trait (r_g = 0.56) in the MT-CV2 model, predictive ability began to decline when the training set size was reduced by only 11% from its original size. Using a ST model, genomic predictive ability in a population unrelated to the training set was poor (r_p = -0.06). However, when using an MT-CV2 model, the predictive ability was positive and high (r_p = 0.76) for the same population. Our results demonstrate the first assessment of MT models in forage species and illustrate the prospects of using MT genomic selection in forages, and other outcrossing plant species, to accelerate genetic gains for complex agronomical traits, such as DMY and nutritive quality characteristics.