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In 2017, genomic selection was implemented in French dairy goats using the single-step genomic best linear unbiased prediction (ssGBLUP) method, which assumes that all single nucleotide polymorphisms explain the same fraction of genetic variance. However, ssGBLUP is not suitable for protein content, which is controlled by a major gene, i.e. α s 1 casein. This gene explains about 40% of the genetic variation in protein content. In this study, we evaluated the accuracy of genomic prediction using different genomic methods to include the effect of the α s 1 casein gene. Genomic evaluation for protein content was performed with data from the official genetic evaluation on 2955 animals genotyped with the Illumina goat SNP50 BeadChip, 7202 animals genotyped at the α s 1 casein gene and 6,767,490 phenotyped females. Pedigree-based BLUP was compared with regular unweighted ssGBLUP and with three weighted ssGBLUP methods (WssGBLUP, WssGBLUPMax and WssGBLUPSum), which give weights to SNPs according to their effect on protein content. Two other methods were also used: trait-specific marker-derived relationship matrix (TABLUP) using pre-selected SNPs associated with protein content and gene content based on a multiple-trait genomic model that includes α s 1 casein genotypes. We estimated accuracies of predicted genomic estimated breeding values (GEBV) in two populations of goats (Alpine and Saanen). Accuracies of GEBV with ssGBLUP improved by + 5 to + 7 percent points over accuracies from the pedigree-based BLUP model. With the WssGBLUP methods, SNPs that are located close to the α s 1 casein gene had the biggest weights and contributed substantially to the capture of signals from quantitative trait loci. Improvement in accuracy of genomic predictions using the three weighted ssGBLUP methods delivered up to + 6 percent points of accuracy over ssGBLUP. A similar accuracy was obtained for ssGBLUP and TABLUP considering the 20,000 most important SNPs. Incorporating information on the α s 1 casein genotypes based on the gene content method gave similar results as ssGBLUP. The three weighted ssGBLUP methods were efficient for detecting SNPs associated with protein content and for a better prediction of genomic breeding values than ssGBLUP. They also combined fast computing, simplicity and required ssGBLUP to be run only twice.

Background Pedigree-based management of genetic diversity in populations, e.g., using optimal contributions, involves computation of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{Ax}}$$\end{document}Ax type yielding elements (relationships) or functions (usually averages) of relationship matrices. For pedigree-based relationships \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{A}}$$\end{document}A, a very efficient method exists. When all the individuals of interest are genotyped, genomic management can be addressed using the genomic relationship matrix \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{G}}$$\end{document}G; however, to date, the computational problem of efficiently computing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{Gx}}$$\end{document}Gx has not been well studied. When some individuals of interest are not genotyped, genomic management should consider the relationship matrix \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{H}}$$\end{document}H that combines genotyped and ungenotyped individuals; however, direct computation of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{Hx}}$$\end{document}Hx is computationally very demanding, because construction of a possibly huge matrix is required. Our work presents efficient ways of computing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{Gx}}$$\end{document}Gx and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{Hx}}$$\end{document}Hx, with applications on real data from dairy sheep and dairy goat breeding schemes. Results For genomic relationships, an efficient indirect computation with quadratic instead of cubic cost is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{x}} = {\mathbf{Z}}\left( {{\mathbf{Z^{\prime}x}}} \right)/k$$\end{document}x=ZZ′x/k, where Z is a matrix relating animals to genotypes. For the relationship matrix \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{H}}$$\end{document}H, we propose an indirect method based on the difference between vectors \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{Hx}} - {\mathbf{Ax}}$$\end{document}Hx-Ax, which involves computation of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{Ax}}$$\end{document}Ax and of products such as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{Gw}}$$\end{document}Gw and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{A}}_{22}^{ - 1} {\mathbf{w}}$$\end{document}A22-1w, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{w}}$$\end{document}w is a working vector derived from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{x}}$$\end{document}x. The latter computation is the most demanding but can be done using sparse Cholesky decompositions of matrix \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{A}}^{ - 1}$$\end{document}A-1, which allows handling very large genomic and pedigree data files. Studies based on simulations reported in the literature show that the trends of average relationships in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{H}}$$\end{document}H and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{A}}$$\end{document}A differ as genomic selection proceeds. When selection is based on genomic relationships but management is based on pedigree data, the true genetic diversity is overestimated. However, our tests on real data from sheep and goat obtained before genomic selection started do not show this. Conclusions We present efficient methods to compute elements and statistics of the genomic relationships \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{G}}$$\end{document}G and of matrix \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{H}}$$\end{document}H that combines ungenotyped and genotyped individuals. These methods should be useful to monitor and handle genomic diversity.

Genomic prediction models have been commonly used in plant breeding but only in reduced datasets comprising a few hundred genotyped individuals. However, pedigree information for an entire breeding population is frequently available, as are historical data on the performance of a large number of selection candidates. The single-step method extends the genomic relationship information from genotyped individuals to pedigree information from a larger number of phenotyped individuals in order to combine relationship information on all members of the breeding population. Furthermore, genomic prediction models that incorporate genotype x environment interactions (G x E) have produced substantial increases in prediction accuracy compared with single-environment genomic prediction models. Our main objective was to show how to use single- step genomic and pedigree models to assess the prediction accuracy of 58,798 CIMMYT wheat (Triticum aestivum L.) lines evaluated in several simulated environments in Ciudad Obregon, Mexico, and to predict the grain yield performance of some of them in several sites in South Asia (India, Pakistan, and Bangladesh) using a reaction norm model that incorporated G x E. Another objective was to describe the statistical and computational challenges encountered when developing the pedigree and single-step models in such large datasets. Results indicate that the genomic prediction accuracy achieved by models using pedigree only, markers only, or both pedigree and markers to predict various environments in India, Pakistan, and Bangladesh is higher (0.25-0.38) than prediction accuracy of models that use only phenotypic prediction (0.20) or do not include the G x E term.

Background Mortality due to cannibalism causes both economic and welfare problems in laying hens. To limit mortality due to cannibalism, laying hens are often beak-trimmed, which is undesirable for animal welfare reasons. Genetic selection is an alternative strategy to increase survival and is more efficient by taking heritable variation that originates from social interactions into account, which are modelled as the so-called indirect genetic effects (IGE). Despite the considerable heritable variation in survival time due to IGE, genetic improvement of survival time in laying hens is still challenging because the detected heritable variation of the trait with IGE is still limited, ranging from 0.06 to 0.26, and individuals that are still alive at the end of the recording period are censored. Furthermore, survival time records are available late in life and only on females. To cope with these challenges, we tested the hypothesis that genomic prediction increases the accuracy of estimated breeding values (EBV) compared to parental average EBV, and increases response to selection for survival time compared to a traditional breeding scheme. We tested this hypothesis in two lines of brown layers with intact beaks, which show cannibalism, and also the hypothesis that the rate of inbreeding per year is lower for genomic selection than for the traditional breeding scheme. Results and discussion The standard deviation of genomic prediction EBV for survival time was around 22 days for both lines, indicating good prospects for selection against mortality in laying hens with intact beaks. Genomic prediction increased the accuracy of the EBV by 35 and 32 % compared to the parent average EBV for the two lines. At the current reference population size, predicted response to selection was 91 % higher when using genomic selection than with the traditional breeding scheme, as a result of a shorter generation interval in males and greater accuracy of selection in females. The predicted rate of inbreeding per generation with truncation selection was substantially lower for genomic selection than for the traditional breeding scheme for both lines. Conclusions Genomic selection for socially affected traits is a promising tool for the improvement of survival time in laying hens with intact beaks. Electronic supplementary material The online version of this article (doi:10.1186/s12711-016-0247-4) contains supplementary material, which is available to authorized users.

Compared with traditional selection, the use of genomic information tends to increase the accuracy of estimated breeding values (EBV). The cause of this increase is, however, unknown. To explore this phenomenon, this study investigated whether the increase in accuracy when moving from traditional (AA) to genomic selection (GG) was mainly due to genotyping the reference population (GA) or the evaluated animals (AG). In it, a combined relationship matrix for simultaneous use of genotyped and ungenotyped animals was applied. A simulated data set reflected the dairy cattle population. Four differently designed (i.e., different average relationships within the reference population) small reference populations and 3 heritability levels were considered. The animals in the reference populations had high, moderate, low, and random (RND) relationships. The evaluated animals were juveniles. The small reference populations simulated difficult or expensive to measure traits (i.e., methane emission). The accuracy of selection was expressed as the reliability of (genomic) EBV and was predicted based on selection index theory using relationships. Connectedness between the reference populations and evaluated animals was calculated using the prediction error variance. Average (genomic) EBV reliabilities increased with heritability and with a decrease in the average relationship within the reference population. Reliabilities in AA and AG were lower than those in GG and were higher than those in GA (respectively, 0.039, 0.042, 0.052, and 0.048 for RND and a heritability of 0.01). Differences between AA and GA were small. Average connectedness with all animals in the reference population for all scenarios and reference populations ranged from 0.003 to 0.024; it was lowest when the animals were not genotyped (AA; e.g., 0.004 for RND) and highest when all the animals were genotyped (GG; e.g., 0.024 for RND). Differences present across designs of the reference populations were very small. Genomic relationships among animals in the reference population might be less important than those for the evaluated animals with no phenotypic observations. Thus, the main origin of the gain in accuracy when using genomic selection is due to genotyping the evaluated animals. However, genotyping only one group of animals will always yield less accurate estimates.

Genomic selection (GS) permits accurate breeding values to be obtained for young animals, shortening the generation interval and accelerating the genetic gain, thereby leading to reduced costs for proven bulls. Genotyping a large number of animals using high-density single nucleotide polymorphism marker arrays is nevertheless expensive, and therefore, a method to reduce the costs of GS is desired. The aim of this study was to investigate an influence of enlarging the reference population, with either genotyped animals or individuals with predicted genotypes, on the accuracy of genomic estimated breeding values. A dairy cattle population was simulated in which proven bulls with 100 daughters were used as a reference population for GS. Phenotypic records were simulated for bulls with heritability equal to the reliability of daughter yield deviations based on 100 daughters. The simulated traits represented heritabilities at the level of individual daughter performance of 0.3, 0.05, and 0.01. Three scenarios were considered in which (1) the reference population consisted of 1,000 genotyped animals, (2) 1,000 ungenotyped animals were added to the reference population, and (3) the 1,000 animals added in scenario 2 were genotyped in addition to the 1,000 animals from scenario 1. Genotypes for ungenotyped animals were predicted with an average accuracy of 0.58. Additionally, an adjustment of the diagonal elements of the G matrix was proposed for animals with predicted genotypes. The accuracy of genomic estimated breeding values for juvenile animals was the highest for the scenario with 2,000 genotyped animals, being 0.90, 0.79, and 0.60 for the heritabilities of 0.3, 0.05, and 0.01, respectively. Accuracies did not differ significantly between the scenario with 1,000 genotyped animals only and the scenario in which 1,000 ungenotyped animals were added and the adjustment of the G matrix was applied. The absence of significant increase in the accuracy of genomic estimated breeding values was attributed to the low accuracy of predicted genotypes. Although the differences were not significant, the difference between scenario 1 and 2 increased with decreasing heritability. Without the adjustment of the diagonal elements of the G matrix, accuracy decreased. Results suggest that inclusion of ungenotyped animals is only expected to enhance the accuracy of GS when the unknown genotypes can be predicted with high accuracy.

International audience; Background: All progeny-tested bucks from the two main French dairy goat breeds (Alpine and Saanen) were genotyped with the Illumina goat SNP50 BeadChip. The reference population consisted of 677 bucks and 148 selection candidates. With the two-step approach based on genomic best linear unbiased prediction (GBLUP), prediction accuracy of candidates did not outperform that of the parental average. We investigated a GBLUP method based on a single-step approach, with or without blending of the two breeds in the reference population.Methods: Three models were used: (1) a multi-breed model, in which Alpine and Saanen breeds were considered as a single breed; (2) a within-breed model, with separate genomic evaluation per breed; and (3) a multiple-trait model, in which a trait in the Alpine was assumed to be correlated to the same trait in the Saanen breed, using three levels of between-breed genetic correlations (ρ): ρ = 0, ρ = 0.99, or estimated ρ. Quality of genomic predictions was assessed on progeny-tested bucks, by cross-validation of the Pearson correlation coefficients for validation accuracy and the regression coefficients of daughter yield deviations (DYD) on genomic breeding values (GEBV). Model-based estimates of average accuracy were calculated on the 148 candidates.Results: The genetic correlations between Alpine and Saanen breeds were highest for udder type traits, ranging from 0.45 to 0.76. Pearson correlations with the single-step approach were higher than previously reported with a two-step approach. Correlations between GEBV and DYD were similar for the three models (within-breed, multi-breed and multiple traits). Regression coefficients of DYD on GEBV were greater with the within-breed model and multiple-trait model with ρ = 0.99 than with the other models. The single-step approach improved prediction accuracy of candidates from 22 to 37% for both breeds compared to the two-step method.Conclusions: Using a single-step approach with GBLUP, prediction accuracy of candidates was greater than that based on parent average of official evaluations and accuracies obtained with a two-step approach. Except for regression coefficients of DYD on GEBV, there were no significant differences between the three models.

Genome-enhanced genotypic evaluations are becoming popular in several livestock species. For this purpose, the combination of the pedigree-based relationship matrix with a genomic similarities matrix between individuals is a common approach. However, the weight placed on each matrix has been so far established with ad hoc procedures, without formal estimation thereof. In addition, when using marker- and pedigree-based relationship matrices together, the resulting combined relationship matrix needs to be adjusted to the same scale in reference to the base population. This study proposes a semi-parametric Bayesian method for combining marker- and pedigree-based information on genome-enabled predictions. A kernel matrix from a reproducing kernel Hilbert spaces regression model was used to combine genomic and genealogical information in a semi-parametric scenario, avoiding inversion and adjustment complications. In addition, the weights on marker- versus pedigree-based information were inferred from a Bayesian model with Markov chain Monte Carlo. The proposed method was assessed involving a large number of SNPs and a large reference population. Five phenotypes, including production and type traits of dairy cattle were evaluated. The reliability of the genome-based predictions was assessed using the correlation, regression coefficient and mean squared error between the predicted and observed values. The results indicated that when a larger weight was given to the pedigree-based relationship matrix the correlation coefficient was lower than in situations where more weight was given to genomic information. Importantly, the posterior means of the inferred weight were near the maximum of 1. The behavior of the regression coefficient and the mean squared error was similar to the performance of the correlation, that is, more weight to the genomic information provided a regression coefficient closer to one and a smaller mean squared error. Our results also indicated a greater accuracy of genomic predictions when using a large reference population. © 2014 Rodríguez-Ramilo et al.

Background Efficient, robust, and accurate genotype imputation algorithms make large-scale application of genomic selection cost effective. An algorithm that imputes alleles or allele probabilities for all animals in the pedigree and for all genotyped single nucleotide polymorphisms (SNP) provides a framework to combine all pedigree, genomic, and phenotypic information into a single-stage genomic evaluation. Methods An algorithm was developed for imputation of genotypes in pedigreed populations that allows imputation for completely ungenotyped animals and for low-density genotyped animals, accommodates a wide variety of pedigree structures for genotyped animals, imputes unmapped SNP, and works for large datasets. The method involves simple phasing rules, long-range phasing and haplotype library imputation and segregation analysis. Results Imputation accuracy was high and computational cost was feasible for datasets with pedigrees of up to 25 000 animals. The resulting single-stage genomic evaluation increased the accuracy of estimated genomic breeding values compared to a scenario in which phenotypes on relatives that were not genotyped were ignored. Conclusions The developed imputation algorithm and software and the resulting single-stage genomic evaluation method provide powerful new ways to exploit imputation and to obtain more accurate genetic evaluations.