A comparison of methods to estimate genomic relationships using pedigree and markers in livestock populations

Accurate prediction of breeding values depends on capturing the variability in genome sharing of relatives with the same pedigree relationship. Here, we compare two approaches to set up genomic relationship matrices for precision of genomic relationships (GR) and accuracy of estimated breeding values (GEBV). Real and simulated data (pigs, 60k SNP) were analysed, and GR were estimated using two approaches: (i) identity by state, corrected with either the observed ( G _{VR ‐O} ) or the base population ( G _{VR ‐B} ) allele frequencies and (ii) identity by descent using linkage analysis ( G _{IBD ‐L} ). Estimators were evaluated for precision and empirical bias with respect to true pedigree IBD GR. All three estimators had very low bias. G _{IBD ‐L} displayed the lowest sampling error and the highest correlation with true genome‐shared values. G _{VR ‐B} approximated G _{IBD ‐L} 's correlation and had lower error than G _{VR ‐O} . Accuracy of GEBV for selection candidates was significantly higher when G _{IBD ‐L} was used and identical between G _{VR ‐O} and G _{VR ‐B} . In real data, G _{IBD ‐L} 's sampling standard deviation was the closest to the theoretical value for each pedigree relationship. Use of pedigree to calculate GR improved the precision of estimates and the accuracy of GEBV.     

Effects of a breeding scheme combined by genomic pre‐selection and progeny testing on annual genetic gain in a dairy cattle population

The effectiveness of the incorporation of genomic pre‐selection into dairy cattle progeny testing (GS‐PT) was compared with that of progeny testing (PT) where the fraction of dam to breed bull (DB) selected was 0.01. When the fraction of sires to breed bulls (SB) selected without being progeny tested to produce young bulls (YB) in the next generation was 0.2, the annual genetic gain from GS‐PT was 13% to 43% greater when h² = 0.3 and 16% to 53% greater when h² = 0.1 compared with that from PT. Given h² = 0.3, a selection accuracy of 0.8 for both YB and DB, and selected fractions of 0.117 for YB and 0.04 for DB, GS‐PT produced 40% to 43% greater annual genetic gain than PT. Given h² = 0.1, a selection accuracy of 0.6 for both YB and DB, and selected fractions of 0.117 for YB and 0.04 for DB, annual genetic gain from GS‐PT was 48% to 53% greater than that from PT. When h² = 0.3, progeny testing capacity had little effect on annual genetic gain from GS‐PT. However, when h² = 0.1, annual genetic gain from GS‐PT increased with increasing progeny testing capacity.     

Within‐ and across‐breed imputation of high‐density genotypes in dairy and beef cattle from medium‐ and low‐density genotypes

The objective of this study was to evaluate, using three different genotype density panels, the accuracy of imputation from lower‐ to higher‐density genotypes in dairy and beef cattle. High‐density genotypes consisting of 777 962 single‐nucleotide polymorphisms (SNP) were available on 3122 animals comprised of 269, 196, 710, 234, 719, 730 and 264 Angus, Belgian Blue, Charolais, Hereford, Holstein‐Friesian, Limousin and Simmental bulls, respectively. Three different genotype densities were generated: low density (LD; 6501 autosomal SNPs), medium density (50K; 47 770 autosomal SNPs) and high density (HD; 735 151 autosomal SNPs). Imputation from lower‐ to higher‐density genotype platforms was undertaken within and across breeds exploiting population‐wide linkage disequilibrium. The mean allele concordance rate per breed from LD to HD when undertaken using a single breed or multiple breed reference population varied from 0.956 to 0.974 and from 0.947 to 0.967, respectively. The mean allele concordance rate per breed from 50K to HD when undertaken using a single breed or multiple breed reference population varied from 0.987 to 0.994 and from 0.987 to 0.993, respectively. The accuracy of imputation was generally greater when the reference population was solely comprised of the breed to be imputed compared to when the reference population comprised of multiple breeds, although the impact was less when imputing from 50K to HD compared to imputing from LD.     

Differences between genomic‐based and pedigree‐based relationships in a chicken population,as a function of quality control and pedigree links among individuals

This work studied differences between expected (calculated from pedigree) and realized (genomic, from markers) relationships in a real population, the influence of quality control on these differences, and their fit to current theory. Data included 4940 pure line chickens across five generations genotyped for 57 636 SNP. Pedigrees (5762 animals) were available for the five generations, pedigree starting on the first one. Three levels of quality control were used. With no quality control, mean difference between realized and expected relationships for different type of relationships was ≤ 0.04 with standard deviation ≤ 0.10. With strong quality control (call rate ≥ 0.9, parent‐progeny conflicts, minor allele frequency and use of only autosomal chromosomes), these numbers reduced to ≤ 0.02 and ≤ 0.04, respectively. While the maximum difference was 1.02 with the complete data, it was only 0.18 with the latest three generations of genotypes (but including all pedigrees). Variation of expected minus realized relationships agreed with theoretical developments and suggests an effective number of loci of 70 for this population. When the pedigree is complete and as deep as the genotypes, the standard deviation of difference between the expected and realized relationships is around 0.04, all categories confounded. Standard deviation of differences larger than 0.10 suggests bad quality control, mistakes in pedigree recording or genotype labelling, or insufficient depth of pedigree.     

Impacts of genotyping strategies on long‐term genetic response in genomic selection

The present study investigated the effects of the choices of animals of reference populations on long‐term responses to genomic selection. Simulated populations comprised 300 individuals and 10 generations of selection practiced for a trait with heritability of 0.1, 0.3 or 0.5. Thirty individuals were randomly selected in the first five generations and selected by estimated breeding values from best linear unbiased prediction (BLUP) and genomic BLUP in the subsequent five generations. The reference populations comprise all animals for all generations (scenario 1), all animals for 6‐10 generations (scenario 2) and 2‐6 generations (scenario 3), and half of the animals for all generations (scenario 4). For all heritability levels, the genetic gains in generation 10 were similar in scenarios 1 and 2. Among scenarios 2 to 4, the highest genetic gains were obtained in scenario 2, with heritabilities of 0.1 and 0.3 as well as scenario 4 with heritability of 0.5. The inbreeding coefficients in scenarios 1, 2 and 4 were lower than those in BLUP, especially within cases with low heritability. These results indicate an appropriate choice of reference population can improve genetic gain and restrict inbreeding even when the reference population size is limited.     

Model averaging for genome‐enabled prediction with reproducing kernel Hilbert spaces: a case study with pig litter size and wheat yield

Predictive ability of yet‐to‐be observed litter size (pig) grain yield (wheat) records of several reproducing kernel Hilbert spaces (RKHS) regression models combining different number of Gaussian or t kernels was evaluated. Predictive performance was assessed as the average (over 50 replicates) predictive correlation in the testing set. Predictions from these models were combined using three different types of model averaging: (i) mean of predicted phenotypes obtained in each model, (ii) weighted average using mean squared error as weight or (iii) using the marginal likelihood as weight. (ii) and (iii) were obtained in a validation set with 5% of the data. Phenotypes consisted of 2598, 1604 and 1879 average litter size records from three commercial pig lines and wheat grain yield of 599 lines evaluated in four macro‐environments. SNPs from the PorcineSNP60 BeadChip and 1447 DArT markers were used as predictors for the pig and wheat data analyses, respectively. Gaussian and univariate t kernels led to same predictive performance. Multikernel RKHS regression models overcame shortcomings of single kernel models (increasing the predictive correlation of RKHS models by 0.05 where 3 Gaussian or t kernels were fitted in the RKHS models simultaneously). None of the proposed averaging strategies improved the predictive correlations attained with single models using multiple kernel fitting.     

Use of genomic recursions and algorithm for proven and young animals for single‐step genomic BLUP analyses – a simulation study

The purpose of this study was to examine accuracy of genomic selection via single‐step genomic BLUP (ssGBLUP) when the direct inverse of the genomic relationship matrix ( G ) is replaced by an approximation of G ^?1 based on recursions for young genotyped animals conditioned on a subset of proven animals, termed algorithm for proven and young animals (APY). With the efficient implementation, this algorithm has a cubic cost with proven animals and linear with young animals. Ten duplicate data sets mimicking a dairy cattle population were simulated. In a first scenario, genomic information for 20k genotyped bulls, divided in 7k proven and 13k young bulls, was generated for each replicate. In a second scenario, 5k genotyped cows with phenotypes were included in the analysis as young animals. Accuracies (average for the 10 replicates) in regular EBV were 0.72 and 0.34 for proven and young animals, respectively. When genomic information was included, they increased to 0.75 and 0.50. No differences between genomic EBV (GEBV) obtained with the regular G ^?1 and the approximated G ^?1 via the recursive method were observed. In the second scenario, accuracies in GEBV (0.76, 0.51 and 0.59 for proven bulls, young males and young females, respectively) were also higher than those in EBV (0.72, 0.35 and 0.49). Again, no differences between GEBV with regular G ^?1 and with recursions were observed. With the recursive algorithm, the number of iterations to achieve convergence was reduced from 227 to 206 in the first scenario and from 232 to 209 in the second scenario. Cows can be treated as young animals in APY without reducing the accuracy. The proposed algorithm can be implemented to reduce computing costs and to overcome current limitations on the number of genotyped animals in the ssGBLUP method.     

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.     

Genomic evaluation using SNP‐ and haplotype‐based genomic relationship matrices in a closed line of Duroc pigs

A simulation analysis and real phenotype analysis were performed to evaluate the impact of three different relationship matrices on heritability estimation and prediction accuracy in a closed‐line breeding of Duroc pigs. The numerator relationship matrix (NRM), single nucleotide polymorphism (SNP)‐based genomic relationship matrix (GRM) (G_S), and haplotype‐based GRM (G_H) were applied in this study. We used PorcineSNP60 genotype array data (38 114 SNPs) of 831 Duroc pigs with four selection traits. In both heritability estimation and prediction accuracy, the accuracy depended on the number of animals with records. For heritability estimation, a large difference in the results among three relationship matrices was not shown, but the trend of the estimated heritabilities between GRMs, that is G_S < G_H, was shown in this population. For the accuracy of prediction values in test animals, the accuracies of prediction values obtained by two GRMs were higher than that by the NRM in this population. The accuracies obtained by GRMs using animals with no records were lower than that by the NRM using animals with their performance records, but were close to that by the NRM using animals with full‐sib testing records.     

Improving production efficiency in the presence of genotype by environment interactions in pig genomic selection breeding programmes

We simulated a genomic selection pig breeding schemes containing nucleus and production herds to improve feed efficiency of production pigs that were cross‐breed. Elite nucleus herds had access to high‐quality feed, and production herds were fed low‐quality feed. Feed efficiency in the nucleus herds had a heritability of 0.3 and 0.25 in the production herds. It was assumed the genetic relationships between feed efficiency in the nucleus and production were low (r_g = 0.2), medium (r_g = 0.5) and high (r_g = 0.8). In our alternative breeding schemes, different proportion of production animals were recorded for feed efficiency and genotyped with high‐density panel of genetic markers. Genomic breeding value of the selection candidates for feed efficiency was estimated based on three different approaches. In one approach, genomic breeding value was estimated including nucleus animals in the reference population. In the second approach, the reference population was containing a mixture of nucleus and production animals. In the third approach, the reference population was only consisting of production herds. Using a mixture reference population, we generated 40–115% more genetic gain in the production environment as compared to only using nucleus reference population that were fed high‐quality feed sources when the production animals were offspring of the nucleus animals. When the production animals were grand offspring of the nucleus animals, 43–104% more genetic gain was generated. Similarly, a higher genetic gain generated in the production environment when mixed reference population was used as compared to only using production animals. This was up to 19 and 14% when the production animals were offspring and grand offspring of nucleus animals, respectively. Therefore, in genomic selection pig breeding programmes, feed efficiency traits could be improved by properly designing the reference population.     

Evaluation of the utility of diagonal elements of the genomic relationship matrix as a diagnostic tool to detect mislabelled genotyped animals in a broiler chicken population

This study explored distributions of diagonal elements of genomic relationship matrix (G), evaluated the utility of G as a diagnostic tool to detect mislabelled animals in a genomic dataset and evaluated the effect of mislabelled animals on the accuracy of genomic evaluation. Populations of 10 000 animals were simulated with 60 000 SNP varying in allele frequency at each locus between 0.02 and 0.98. Diagonal elements of G were distributed with a single peak (mean = 1.00 ± 0.03) and ranged from 0.84 through 1.36. Mixed populations were also simulated: 7 000 animals with frequencies of second alleles ranging from 0.02 through 0.98 were combined with 1750 or 7000 animals with frequencies of second alleles ranging from 0.0 through 1.0. The resulting distributions of diagonal elements of G were bimodal. Body weight at 6 weeks was provided by Cobb-Vantress for broiler chickens, of which 3285 were genotyped for 57 636 SNP. Analysis used a combined genomic and pedigree relationship matrix; G was scaled using current allele frequencies. The distribution of diagonal elements was multimodal and ranged from 0.54 to 3.23. Animals with diagonal elements >1.5 were identified as coming from another chicken line or as having low call rates. Removal of mislabelled animals increased accuracy by 0.01. For the studied type of population, diagonal elements of G may be a useful tool to help identify mislabelled animals or secondary populations.     

Accuracy of breeding values when using and ignoring the polygenic effect in genomic breeding value estimation with a marker density of one SNP per cM

Genomic selection is based on breeding values that are estimated using genome-wide dense marker maps. The objective of this paper was to investigate the effect of including or ignoring the polygenic effect on the accuracy of total genomic breeding values, when there is coverage of the genome with approximately one SNP per cM. The importance of the polygenic effect might differ for high and low heritability traits, and might depend on the design of the reference dataset. Hence, different scenarios were evaluated using stochastic simulation. Accuracies of the total breeding value of juvenile selection candidates depended on the number of animals included in the reference data. When excluding polygenic effects, those accuracies ranged from 0.38 to 0.55 and from 0.73 to 0.79 for traits with heritabilities of 10 and 50%, respectively. Accuracies were improved by including a polygenic effect in the model for the low heritability trait, when the LD-measure r2 between adjacent markers became smaller than approximately 0.10, while for the high heritability trait there was already a small improvement at r2 between adjacent markers of 0.14. In all situations, the estimated total genetic variance was underestimated, particularly when the polygenic effect was excluded from the model. The haplotype variance was less underestimated when more animals were added in the reference dataset.     

Determining the stability of accuracy of genomic estimated breeding values in future generations in commercial pig populations

Genomic information has a limited dimensionality (number of independent chromosome segments [M_e]) related to the effective population size. Under the additive model, the persistence of genomic accuracies over generations should be high when the nongenomic information (pedigree and phenotypes) is equivalent to M_e animals with high accuracy. The objective of this study was to evaluate the decay in accuracy over time and to compare the magnitude of decay with varying quantities of data and with traits of low and moderate heritability. The dataset included 161,897 phenotypic records for a growth trait (GT) and 27,669 phenotypic records for a fitness trait (FT) related to prolificacy in a population with dimensionality around 5,000. The pedigree included 404,979 animals from 2008 to 2020, of which 55,118 were genotyped. Two single-trait models were used with all ancestral data and sliding subsets of 3-, 2-, and 1-generation intervals. Single-step genomic best linear unbiased prediction (ssGBLUP) was used to compute genomic estimated breeding values (GEBV). Estimated accuracies were calculated by the linear regression (LR) method. The validation population consisted of single generations succeeding the training population and continued forward for all generations available. The average accuracy for the first generation after training with all ancestral data was 0.69 and 0.46 for GT and FT, respectively. The average decay in accuracy from the first generation after training to generation 9 was −0.13 and −0.19 for GT and FT, respectively. The persistence of accuracy improves with more data. Old data have a limited impact on the predictions for young animals for a trait with a large amount of information but a bigger impact for a trait with less information.     

Selection of core animals in the Algorithm for Proven and Young using a simulation model

The Algorithm for Proven and Young (APY) enables the implementation of single‐step genomic BLUP (ssGBLUP) in large, genotyped populations by separating genotyped animals into core and non‐core subsets and creating a computationally efficient inverse for the genomic relationship matrix ( G ). As APY became the choice for large‐scale genomic evaluations in BLUP‐based methods, a common question is how to choose the animals in the core subset. We compared several core definitions to answer this question. Simulations comprised a moderately heritable trait for 95,010 animals and 50,000 genotypes for animals across five generations. Genotypes consisted of 25,500 SNP distributed across 15 chromosomes. Genotyping errors and missing pedigree were also mimicked. Core animals were defined based on individual generations, equal representation across generations, and at random. For a sufficiently large core size, core definitions had the same accuracies and biases, even if the core animals had imperfect genotypes. When genotyped animals had unknown parents, accuracy and bias were significantly better (p ≤ .05) for random and across generation core definitions.     

Accuracies of estimated breeding values from ordinary genetic evaluations do not reflect the correlation between true and estimated breeding values in selected populations

The accuracy of estimated breeding values (EBVs) is an important parameter in livestock genetic improvement. It is used to calculate response to selection and to express the credibility of individual EBVs. Although it is well-known that selection reduces accuracy, this effect is not well-studied and accuracies from genetic evaluations are not adjusted for selection. This work investigates the effect of selection on accuracy of EBVs estimated using best linear unbiased predictors. Results show that accuracies in a selected population may be considerably smaller than the ordinary accuracy from genetic evaluation. Accuracy of the parent average is dramatically reduced by selection, up to a factor of three. Expressions for equilibrium accuracies in selected populations are presented and depend only on the unselected accuracy and the intensity of selection. Thus, schemes with the same unselected accuracy and intensity of selection also have the same equilibrium accuracy and response to selection. At the same unselected accuracy, therefore, schemes based on between-family information do not show greater reduction in response and accuracy because of the Bulmer effect. An example shows that benefit of genomic selection may be underestimated when the effect of selection on accuracy is ignored. Finally, this work argues that the SE of an EBV and the correlation between true and EBVs are different things, and that accuracies should not be adjusted for selection when they primarily serve to indicate the SEs of EBVs.     

The evolution of the prevalence of classical scrapie in sheep in Great Britain using surveillance data between 2005 and 2012

After the decline of the Bovine Spongiform Encephalopathy (BSE) epidemic in Great Britain (GB), scrapie remains the most prevalent animal Transmissible Spongiform Encephalopathy (TSE) present in GB. A number of control measures have been implemented for classical scrapie, and since 2005 there has been a large reduction in the number of observed cases. The objective of this study is to estimate two measures of disease frequency using up to date surveillance data collected during and after the implementation of different control measures established since 2004, and breeding for resistance schemes that ran from 2001 until 2009. This would enable an assessment of the effectiveness of both the breeding for resistance programme and the compulsory eradication measures in reducing the prevalence of scrapie in GB. Evaluation of the sensitivity of the rapid post-mortem test for scrapie indicated that it detected scrapie in the last 25% of the incubation period. A back-calculation model was developed to estimate the prevalence of infection at animal and flock-level. The results of the model indicated a mean drop of infection prevalence of 31% each year, leading to a 90% drop in infection prevalence between 2005, with an estimate of 5737 infected sheep in GB in 2012.     

Genomic selection in multi‐environment plant breeding trials using a factor analytic linear mixed model

Genomic selection (GS) is a statistical and breeding methodology designed to improve genetic gain. It has proven to be successful in animal breeding; however, key points of difference have not been fully considered in the transfer of GS from animal to plant breeding. In plant breeding, individuals (varieties) are typically evaluated across a number of locations in multiple years (environments) in formally designed comparative experiments, called multi‐environment trials (METs). The design structure of individual trials can be complex and needs to be modelled appropriately. Another key feature of MET data sets is the presence of variety by environment interaction (VEI), that is the differential response of varieties to a change in environment. In this paper, a single‐step factor analytic linear mixed model is developed for plant breeding MET data sets that incorporates molecular marker data, appropriately accommodates non‐genetic sources of variation within trials and models VEI. A recently developed set of selection tools, which are natural derivatives of factor analytic models, are used to facilitate GS for a motivating data set from an Australian plant breeding company. The power and versatility of these tools is demonstrated for the variety by environment and marker by environment effects.     

Additional considerations to the use of single‐step genomic predictions in a dominance setting

Recent publications indicate that single‐step models are suitable to estimate breeding values, dominance deviations and total genetic values with acceptable quality. Additive single‐step methods implicitly extend known number of allele information from genotyped to non‐genotyped animals. This theory is well derived in an additive setting. It was recently shown, at least empirically, that this basic strategy can be extended to dominance with reasonable prediction quality. Our study addressed two additional issues. It illustrated the theoretical basis for extension and validated genomic predictions to dominance based on single‐step genomic best linear unbiased prediction theory. This development was then extended to include inbreeding into dominance relationships, which is a currently not yet solved issue. Different parametrizations of dominance relationship matrices were proposed. Five dominance single‐step inverse matrices were tested and described as C¹ , C² , C³ , C⁴ and C⁵ . Genotypes were simulated for a real pig population (n = 11,943 animals). In order to avoid any confounding issues with additive effects, pseudo‐records including only dominance deviations and residuals were simulated. SNP effects of heterozygous genotypes were summed up to generate true dominance deviations. We added random noise to those values and used them as phenotypes. Accuracy was defined as correlation between true and predicted dominance deviations. We conducted five replicates and estimated accuracies in three sets: between all ( S₁ ), non‐genotyped ( S₂ ) and inbred non‐genotyped ( S₃ ) animals. Potential bias was assessed by regressing true dominance deviations on predicted values. Matrices accounting for inbreeding ( C³ , C⁴ and C⁵ ) best fit. Accuracies were on average 0.77, 0.40 and 0.46 in S₁ , S₂ and S₃ , respectively. In addition, C³ , C⁴ and C⁵ scenarios have shown better accuracies than C¹ and C² , and dominance deviations were less biased. Better matrix compatibility (accuracy and bias) was observed by re‐scaling diagonal elements to 1 minus the inbreeding coefficient ( C⁵ ).