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Changes in the accuracy of the genomic estimates obtained by the ssGBLUP and wssGBLUP methods were evaluated using different reference groups. The weighting procedure’s reasonableness of application Pwas considered to improve the accuracy of genomic predictions for meat, fattening and reproduction traits in pigs. Six reference groups were formed to assess the genomic data quantity impact on the accuracy of predicted values (groups of genotyped animals). The datasets included 62,927 records of meat and fattening productivity (fat thickness over 6–7 ribs (BF1, mm)), muscle depth (MD, mm) and precocity up to 100 kg (age, days) and 16,070 observations of reproductive qualities (the number of all born piglets (TNB) and the number of live-born piglets (NBA), according to the results of the first farrowing). The wssGBLUP method has an advantage over ssGBLUP in terms of estimation reliability. When using a small reference group, the difference in the accuracy of ssGBLUP over BLUP AM is from −1.9 to +7.3 percent points, while for wssGBLUP, the change in accuracy varies from +18.2 to +87.3 percent points. Furthermore, the superiority of the wssGBLUP is also maintained for the largest group of genotyped animals: from +4.7 to +15.9 percent points for ssGBLUP and from +21.1 to +90.5 percent points for wssGBLUP. However, for all analyzed traits, the number of markers explaining 5% of genetic variability varied from 71 to 108, and the number of such SNPs varied depending on the size of the reference group (79–88 for BF1, 72–81 for MD, 71–108 for age). The results of the genetic variation distribution have the greatest similarity between groups of about 1000 and about 1500 individuals. Thus, the size of the reference group of more than 1000 individuals gives more stable results for the estimation based on the wssGBLUP method, while using the reference group of 500 individuals can lead to distorted results of GEBV.

The breeding scheme in the Rubia Gallega cattle population is based upon traits measured in farms and slaughterhouses. In recent years, genomic evaluation has been implemented by using a ssGBLUP (single-step Genomic Best Linear Unbiased Prediction). This procedure can reparameterized to perform ssGWAS (single-step Genome Wide Association Studies) by backsolving the SNP (single nucleotide polymorphisms) effects. Therefore, the objective of this study was to identify genomic regions associated with the genetic variability in growth and carcass quality traits. We implemented a ssGBLUP by using a database that included records for Birth Weight (BW-327,350 records-), Weaning Weight (WW-83,818-), Cold Carcass Weight (CCW-91,621-), Fatness (FAT-91,475-) and Conformation (CON-91,609-). The pedigree included 464,373 individuals, 2449 of which were genotyped. After a process of filtering, we ended up using 43,211 SNP markers. We used the GBLUP and SNPBLUP model equivalences to obtain the effects of the SNPs and then calculated the percentage of variance explained by the regions of the genome between 1 Mb. We identified 7 regions of the genome for CCW; 8 regions for BW, WW, FAT and 9 regions for CON, which explained the percentage of variance above 0.5%. Furthermore, a number of the genome regions had pleiotropic effects, located at: BTA1 (131–132 Mb), BTA2 (1–11 Mb), BTA3 (32–33 Mb), BTA6 (36–38 Mb), BTA16 (24–26 Mb), and BTA 21 (56–57 Mb). These regions contain, amongst others, the following candidate genes: NCK1, MSTN, KCNA3, LCORL, NCAPG, and RIN3.

Abstract 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.

Many computations with SNP data including genomic evaluation, parameter estimation, and genome-wide association studies use an inverse of the genomic relationship matrix. The cost of a regular inversion is cubic and is prohibitively expensive for large matrices. Recent studies in cattle demonstrated that the inverse can be computed in almost linear time by recursion on any subset of ∼10,000 individuals. The purpose of this study is to present a theory of why such a recursion works and its implication for other populations. Assume that, because of a small effective population size, the additive information in a genotyped population has a small dimensionality, even with a very large number of SNP markers. That dimensionality is visible as a limited number of effective SNP effects, independent chromosome segments, or the rank of the genomic relationship matrix. Decompose a population arbitrarily into core and noncore individuals, with the number of core individuals equal to that dimensionality. Then, breeding values of noncore individuals can be derived by recursions on breeding values of core individuals, with coefficients of the recursion computed from the genomic relationship matrix. A resulting algorithm for the inversion called “algorithm for proven and young” (APY) has a linear computing and memory cost for noncore animals. Noninfinitesimal genetic architecture can be accommodated through a trait-specific genomic relationship matrix, possibly derived from Bayesian regressions. For populations with small effective population size, the inverse of the genomic relationship matrix can be computed inexpensively for a very large number of genotyped individuals.

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

Most of the genomic studies in plants and animals have used additive models for studying genetic parameters and prediction accuracies. In this study, we used genomic models with additive and nonadditive effects to analyze the genetic architecture of growth and wood traits in an open-pollinated (OP) population of Eucalyptus pellita. We used two progeny trials consisting of 5742 trees from 244 OP families to estimate genetic parameters and to test genomic prediction accuracies of three growth traits (diameter at breast height - DBH, total height - Ht and tree volume - Vol) and kraft pulp yield (KPY). From 5742 trees, 468 trees from 28 families were genotyped with 2023 pre-selected markers from candidate genes. We used the pedigree-based additive best linear unbiased prediction (ABLUP) model and two marker-based models (single-step genomic BLUP – ssGBLUP and genomic BLUP – GBLUP) to estimate the genetic parameters and compare the prediction accuracies. Analyses with the two genomic models revealed large dominant effects influencing the growth traits but not KPY. Theoretical breeding value accuracies were higher with the dominance effect in ssGBLUP model for the three growth traits. Accuracies of cross-validation with random folding in the genotyped trees have ranged from 0.60 to 0.82 in different models. Accuracies of ABLUP were lower than the genomic models. Accuracies ranging from 0.50 to 0.76 were observed for within family cross-validation predictions with low relationships between training and validation populations indicating part of the functional variation is captured by the markers through short-range linkage disequilibrium (LD). Within-family phenotype predictive abilities and prediction accuracies of genetic values with dominance effects are higher than the additive models for growth traits indicating the importance of dominance effects in predicting phenotypes and genetic values. This study demonstrates the importance of genomic approaches in OP families to study nonadditive effects. To capture the LD between markers and the quantitative trait loci (QTL) it may be important to use informative markers from candidate genes.

Abstract 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.

Background Planting tested forest reproductive material is crucial to ensure the increased resilience of intensively managed productive stands for timber and wood product markets under climate change scenarios. Single-step Genomic Best Linear Unbiased Prediction (ssGBLUP) analysis is a cost-effective option for using genomic tools to enhance the accuracy of predicted breeding values and genetic parameter estimation in forest tree species. Here, we tested the efficiency of ssGBLUP in a tropical multipurpose tree species, Cordia africana, by partial population genotyping. A total of 8070 trees from three breeding seedling orchards (BSOs) were phenotyped for height. We genotyped 6.1% of the phenotyped individuals with 4373 single nucleotide polymorphisms. The results of ssGBLUP were compared with pedigree-based best linear unbiased prediction (ABLUP) and genomic best linear unbiased prediction (GBLUP), based on genetic parameters, theoretical accuracy of breeding values, selection candidate ranking, genetic gain, and predictive accuracy and prediction bias. Results Genotyping a subset of the study population provided insights into the level of relatedness in BSOs, allowing better genetic management. Due to the inbreeding detected within the genotyped provenances, we estimated genetic parameters both with and without accounting for inbreeding. The ssGBLUP model showed improved performance in terms of additive genetic variance and theoretical breeding value accuracy. Similarly, ssGBLUP showed improved predictive accuracy and lower bias than the pedigree-based relationship matrix (ABLUP). Conclusions This study of C. africana , a species in decline due to deforestation and selective logging, revealed inbreeding depression. The provenance exhibiting the highest level of inbreeding had the poorest overall performance. The use of different relationship matrices and accounting for inbreeding did not substantially affect the ranking of candidate individuals. This is the first study of this approach in a tropical multipurpose tree species, and the analysed BSOs represent the primary effort to breed C. africana .

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.

Background The traditional way to estimate variance components (VC) is based on the animal model using a pedigree-based relationship matrix ( A ) (A-AM). After genomic selection was introduced into breeding programs, it was anticipated that VC estimates from A-AM would be biased because the effect of selection based on genomic information is not captured. The single-step method (H-AM), which uses an H matrix as (co)variance matrix, can be used as an alternative to estimate VC. Here, we compared VC estimates from A-AM and H-AM and investigated the effect of genomic selection, genotyping strategy and genotyping proportion on the estimation of VC from the two methods, by analyzing a dataset from a commercial broiler line and a simulated dataset that mimicked the broiler population. Results VC estimates from H-AM were severely overestimated with a high proportion of selective genotyping, and overestimation increased as proportion of genotyping increased in the analysis of both commercial and simulated data. This bias in H-AM estimates arises when selective genotyping is used to construct the H -matrix, regardless of whether selective genotyping is applied or not in the selection process. For simulated populations under genomic selection, estimates of genetic variance from A-AM were also significantly overestimated when the effect of genomic selection was strong. Our results suggest that VC estimates from H-AM under random genotyping have the expected values. Predicted breeding values from H-AM were inflated when VC estimates were biased, and inflation differed between genotyped and ungenotyped animals, which can lead to suboptimal selection decisions. Conclusions We conclude that VC estimates from H-AM are biased with selective genotyping, but are close to expected values with random genotyping.VC estimates from A-AM in populations under genomic selection are also biased but to a much lesser degree. Therefore, we recommend the use of H-AM with random genotyping to estimate VC for populations under genomic selection. Our results indicate that it is still possible to use selective genotyping in selection, but then VC estimation should avoid the use of genotypes from one side only of the distribution of phenotypes. Hence, a dual genotyping strategy may be needed to address both selection and VC estimation.