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.     

Performance of genomic selection under a single-step approach in autochthonous Spanish beef cattle populations

This study evaluated different strategies for implementing a single-step genomic selection programme in two autochthonous Spanish beef cattle populations (Pirenaica—Pi and Rubia Gallega—RG). The strategies were compared in terms of accuracy attained under different scenarios by simulating genomic data over the known genealogy. Several genotyping approaches were tested, as well as, other factors like marker density, effective population size, mutation rate and heritability of the trait. The results obtained showed gains in accuracy with respect to pedigree BLUP evaluation in all cases. The greatest benefit was obtained when the candidates to selection had their genotypes included in the evaluation. Moreover, genotyping the individuals with the most accurate predictions maximized the gains but other suboptimal strategies also yielded satisfactory results. Furthermore, the gains in accuracy increased with the marker density reaching a plateau at around 50,000 markers. Likewise, the effective population size and the mutation rate have also shown an effect, both increasing the accuracy with decreasing values of these population parameters. Finally, the results obtained for the RG population showed greater gains compared to the Pi population, probably attributed to the wider implantation of artificial insemination.     

Genomic selection in American mink (Neovison vison) using a single-step genomic best linear unbiased prediction model for size and quality traits graded on live mink

Genomic selection relies on single-nucleotide polymorphisms (SNPs), which are often collected using medium-density SNP arrays. In mink, no such array is available; instead, genotyping by sequencing (GBS) can be used to generate marker information. Here, we evaluated the effect of genomic selection for mink using GBS. We compared the estimated breeding values (EBVs) from single-step genomic best linear unbiased prediction (SSGBLUP) models to the EBV from ordinary pedigree-based BLUP models. We analyzed seven size and quality traits from the live grading of brown mink. The phenotype data consisted of ~20,600 records for the seven traits from the mink born between 2013 and 2016. Genotype data included 2,103 mink born between 2010 and 2014, mostly breeding animals. In total, 28,336 SNP markers from 391 scaffolds were available for genomic prediction. The pedigree file included 29,212 mink. The predictive ability was assessed by the correlation (r) between progeny trait deviation (PTD) and EBV, and the regression of PTD on EBV, using 5-fold cross-validation. For each fold, one-fifth of animals born in 2014 formed the validation set. For all traits, the SSGBLUP model resulted in higher accuracies than the BLUP model. The average increase in accuracy was 15% (between 3% for fur clarity and 28% for body weight). For three traits (body weight, silky appearance of the under wool, and guard hair thickness), the difference in r between the two models was significant (P < 0.05). For all traits, the regression slopes of PTD on EBV from SSGBLUP models were closer to 1 than regression slopes from BLUP models, indicating SSGBLUP models resulted in less bias of EBV for selection candidates than the BLUP models. However, the regression coefficients did not differ significantly. In conclusion, the SSGBLUP model is superior to conventional BLUP model in the accurate selection of superior animals, and, thus, it would increase genetic gain in a selective breeding program. In addition, this study shows that GBS data work well in genomic prediction in mink, demonstrating the potential of GBS for genomic selection in livestock species.     

Efficient approximation of reliabilities for single-step genomic best linear unbiased predictor models with the Algorithm for Proven and Young

The objectives of this study were to develop an efficient algorithm for calculating prediction error variances (PEVs) for genomic best linear unbiased prediction (GBLUP) models using the Algorithm for Proven and Young (APY), extend it to single-step GBLUP (ssGBLUP), and apply this algorithm for approximating the theoretical reliabilities for single- and multiple-trait models in ssGBLUP. The PEV with APY was calculated by block sparse inversion, efficiently exploiting the sparse structure of the inverse of the genomic relationship matrix with APY. Single-step GBLUP reliabilities were approximated by combining reliabilities with and without genomic information in terms of effective record contributions. Multi-trait reliabilities relied on single-trait results adjusted using the genetic and residual covariance matrices among traits. Tests involved two datasets provided by the American Angus Association. A small dataset (Data1) was used for comparing the approximated reliabilities with the reliabilities obtained by the inversion of the left-hand side of the mixed model equations. A large dataset (Data2) was used for evaluating the computational performance of the algorithm. Analyses with both datasets used single-trait and three-trait models. The number of animals in the pedigree ranged from 167,951 in Data1 to 10,213,401 in Data2, with 50,000 and 20,000 genotyped animals for single-trait and multiple-trait analysis, respectively, in Data1 and 335,325 in Data2. Correlations between estimated and exact reliabilities obtained by inversion ranged from 0.97 to 0.99, whereas the intercept and slope of the regression of the exact on the approximated reliabilities ranged from 0.00 to 0.04 and from 0.93 to 1.05, respectively. For the three-trait model with the largest dataset (Data2), the elapsed time for the reliability estimation was 11 min. The computational complexity of the proposed algorithm increased linearly with the number of genotyped animals and with the number of traits in the model. This algorithm can efficiently approximate the theoretical reliability of genomic estimated breeding values in ssGBLUP with APY for large numbers of genotyped animals at a low cost.     

Efficient selection against categorically scored hip dysplasia in dogs is possible using best linear unbiased prediction and optimum contribution selection: a simulation study

Breeding to reduce the prevalence of categorically scored hip dysplasia (HD), based on phenotypic assessment of radiographic hip status, has had limited success. The aim of this study was to evaluate two selection strategies for improved hip status: truncation selection based on phenotypic record versus best linear unbiased prediction (BLUP), using stochastic simulation and selection scenarios resembling those in real dog populations. In addition, optimum contribution selection (OCS) was evaluated. Two traits were considered: HD (as a categorical trait with five classes and a heritability of 0.45 on the liability scale) and a continuous trait (with a heritability of 0.25) intended to represent other characteristics in the breeding goal. A population structure mimicking that in real dog populations was modelled. The categorical nature of HD caused a considerably lower genetic gain compared to simulating HD as a continuous trait. Genetic gain was larger for BLUP selection than for phenotypic selection in all scenarios. However, BLUP selection resulted in higher rates of inbreeding. By applying OCS, the rate of inbreeding was lowered to about the same level as phenotypic selection but with increased genetic improvement. For efficient selection against HD, use of BLUP breeding values should be prioritized. In small populations, BLUP should be used together with OCS or similar strategy to maintain genetic variation.     

Interplay between heritability,genetic correlation and economic weighting in a selection index with and without genomic information

The availability of genomic information demands proper evaluation on how the kind (phenotypic versus genomic) and the amount of information influences the interplay of heritability (h²), genetic correlation () and economic weighting of traits with regard to the standard deviation of the index (σ_I). As σ_I is directly proportional to response to selection, it was the chosen parameter for comparing the indices. Three selection indices incorporating conventional and genomic information for a two trait (i and j) breeding goal were compared. Information sources were chosen corresponding to pig breeding applications. Index I incorporating an own performance in trait j served as reference scenario. In index II, additional information in both traits was contributed by a varying number of full‐sibs (2, 7, 50). In index III, the conventional own performance in trait j was combined with genomic information for both traits. The number of animals in the reference population (N_P = 1000, 5000, 10 000) and thus the accuracy of GBVs were varied. With more information included in the index, σ_I became more independent of , and relative economic weighting. This applied for index II (more full‐sibs) and for index III (more accurate GBVs). Standard deviations of index II with seven full‐sibs and index III with N_P = 1000 were similar when both traits had the same heritability. If the heritability of trait j was reduced ( = 0.1), σ_I of index III with N_P = 1000 was clearly higher than for index II with seven full‐sibs. When enhancing the relative economic weight of trait j, the decrease in σ_I of the conventional full‐sib index was much stronger than for index III. Our results imply that N_P = 1000 can be considered a minimum size for a reference population in pig breeding. These conclusions also hold for comparing the accuracies of the indices.     

Comparison of selection based on phenotype,selection index and best linear unbiased prediction using data from a closed broiler line

1. Selection based on three methods of estimating breeding values, Best Linear Unbiased Prediction (BLUP), selection index (SI), and phenotype (SP) were compared for three traits, juvenile body weight (JW), percentage breast meat yield (BM) and hen‐day rate of egg production (EP) using records provided by a commercial broiler breeding company.

2. Product moment correlations were calculated between breeding values estimated by each method and averaged across sexes. A mean correlation of 0.69 was obtained between selection on SP and BLUP for JW. Mean correlations of 0.88 and 0.68 and 0.87 were obtained between SI and BLUP for the traits JW, EP and BM, respectively.

3. A mean estimated genetic response of 77.7% was obtained with SP for JW relative to BLUP in the absence of restrictions on the selection of close relatives. Estimated genetic responses of 90.7%, 66.9% and 88.4% were obtained by SI relative to BLUP for JW, EP and BM, respectively.

4. Applying restrictions on the selection of close relatives resulted in slight decreases in estimated responses but not in the respective ranking of the selection methods.

5. The results indicate that BLUP could provide commercial breeders with increased selection responses compared to index selection, in particular for traits of low heritability and where relatively few animals possess performance records.     

Accounting for genetic architecture in single‐ and multipopulation genomic prediction using weights from genomewide association studies in pigs

We studied the effect of including GWAS results on the accuracy of single‐ and multipopulation genomic predictions. Phenotypes (backfat thickness) and genotypes of animals from two sire lines (SL1, n = 1146 and SL3, n = 1264) were used in the analyses. First, GWAS were conducted for each line and for a combined data set (both lines together) to estimate the genetic variance explained by each SNP. These estimates were used to build matrices of weights (D), which was incorporated into a GBLUP method. Single population evaluated with traditional GBLUP had accuracies of 0.30 for SL1 and 0.31 for SL3. When weights were employed in GBLUP, the accuracies for both lines increased (0.32 for SL1 and 0.34 for SL3). When a multipopulation reference set was used in GBLUP, the accuracies were higher (0.36 for SL1 and 0.32 for SL3) than in single‐population prediction. In addition, putting together the multipopulation reference set and the weights from the combined GWAS provided even higher accuracies (0.37 for SL1, and 0.34 for SL3). The use of multipopulation predictions and weights estimated from a combined GWAS increased the accuracy of genomic predictions.     

Genome‐wide association study and genomic evaluation of feed efficiency traits in Japanese Black cattle using single‐step genomic best linear unbiased prediction method

The objectives of this study were to better understand the genetic architecture and the possibility of genomic evaluation for feed efficiency traits by (i) performing genome‐wide association studies (GWAS), and (ii) assessing the accuracy of genomic evaluation for feed efficiency traits, using single‐step genomic best linear unbiased prediction (ssGBLUP)‐based methods. The analyses were performed in residual feed intake (RFI), residual body weight gain (RG), and residual intake and body weight gain (RIG) during three different fattening periods. The phenotypes from 4,578 Japanese Black steers, which were progenies of 362 progeny‐tested bulls and the genotypes from the bulls were used in this study. The results of GWAS showed that a total of 16, 8, and 12 gene ontology terms were related to RFI, RG, and RIG, respectively, and the candidate genes identified in RFI and RG were involved in olfactory transduction and the phosphatidylinositol signaling system, respectively. The realized reliabilities of genomic estimated breeding values were low to moderate in the feed efficiency traits. In conclusion, ssGBLUP‐based method can lead to understand some biological functions related to feed efficiency traits, even with small population with genotypes, however, an alternative strategy will be needed to enhance the reliability of genomic evaluation.     

Comparison of heritabilities of dairy traits in Australian Holstein‐Friesian cattle from genomic and pedigree data and implications for genomic evaluations

The reliability of genomic evaluations depends on the proportion of genetic variation explained by the DNA markers. In this study, we have estimated the proportion of variance in daughter trait deviations (DTDs) of dairy bulls explained by 45 993 genome wide single‐nucleotide poly‐ morphism (SNP) markers for 29 traits in Australian Holstein‐Friesian dairy cattle. We compare these proportions to the proportion of variance in DTDs explained by the additive relationship matrix derived from the pedigree, as well as the sum of variance explained by both pedigree and marker information when these were fitted simultaneously. The propor‐ tion of genetic variance in DTDs relative to the total genetic variance (the total genetic variance explained by the genomic relationships and pedigree relationships when both were fitted simultaneously) varied from 32% for fertility to approximately 80% for milk yield traits. When fitting genomic and pedigree relationships simultaneously, the variance unexplained (i.e. the residual variance) in DTDs of the total variance for most traits was reduced compared to fitting either individually, suggesting that there is not complete overlap between the effects. The proportion of genetic variance accounted by the genomic relationships can be used to modify the blending equations used to calculate genomic estimated breeding value (GEBV) from direct genomic breeding value (DGV) and parent average. Our results, from a validation population of young dairy bulls with DTD, suggest that this modification can improve the reliability of GEBV by up to 5%.     

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.     

Estimation of variance and genomic prediction using genotypes imputed from low‐density marker subsets for carcass traits in Japanese black cattle

The influence of genotype imputation using low‐density single nucleotide polymorphism (SNP) marker subsets on the genomic relationship matrix (G matrix), genetic variance explained, and genomic prediction (GP) was investigated for carcass weight and marbling score in Japanese Black fattened steers, using genotype data of approximately 40,000 SNPs. Genotypes were imputed using equally spaced SNP subsets of different densities. Two different linear models were used. The first (model 1) incorporated one G matrix, while the second (model 2) used two different G matrices constructed using the selected and remaining SNPs. When using model 1, the estimated additive genetic variance was always larger when using all SNPs obtained via genotype imputation than when using only equally spaced SNP subsets. The correlations between the genomic estimated breeding values obtained using genotype imputation with at least 3,000 SNPs and those using all available SNPs without imputation were higher than 0.99 for both traits. While additive genetic variance was likely to be partitioned with model 2, it did not enhance the accuracy of GP compared with model 1. These results indicate that genotype imputation using an equally spaced low‐density panel of an appropriate size can be used to produce a cost‐effective, valid GP.