Removing data and using metafounders alleviates biases for all traits in Lacaune dairy sheep predictions

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Use of a reduced set of single nucleotide polymorphisms for genetic evaluation of resistance to Salmonella carrier state in laying hens

Chantier qualité GA; Salmonella propagation by apparently healthy chickens could be decreased by the selection and use of chicken lines that are more resistant to carrier state. Using a reduced set of markers, this study investigates, for the first time to the authors' knowledge, the feasibility of a genomic selection approach for resistance to carrier state in hen lines. In this study, commercial laying hen lines were divergently selected for resistance to Salmonella carrier state at 2 different ages: young chicks and adults at the peak of lay. A total of 600 birds were typed with 831 informative SNP markers and artificially infected with Salmonella Enteritidis. Phenotypes were collected 28 d (389 young animals) or 38 d (208 adults) after infection. Two types of variance component analyses, including SNP data or not, were performed and compared. The set of SNP used was efficient in capturing a large part of the genetic variation. Average accuracies from mixed model equations did not change between analyses, showing that using SNP data does not increase information in this data set. These results confirm that genomic selection for Salmonella carrier state resistance in laying hens is promising. Nevertheless, a denser SNP coverage of the genome on a greater number of animals is still needed to assess its feasibility and efficiency

The Dimensionality of Genomic Information and Its Effect on Genomic Prediction

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 (N(e)). The objective of this study was to evaluate these assumptions by simulation. Six populations were simulated with approximate effective population size (N(e)) 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 ∼N(e)L largest eigenvalues, with no information beyond 4N(e)L. Genomic predictions with the APY inverse of the GRM are more accurate than by the regular inverse

Removing data and using metafounders alleviates biases for all traits in Lacaune dairy sheep predictions

Bias in dairy genetic evaluations, when it exists, has to be understood and properly addressed. The origin of biases is not always clear. We analyzed 40 yr of records from the Lacaune dairy sheep breeding program to evaluate the extent of bias, assess possible corrections, and emit hypotheses on its origin. The data set included 7 traits (milk yield, fat and protein contents, somatic cell score, teat angle, udder cleft, and udder depth) with records from 600,000 to 5 million depending on the trait,-1,900,000 animals, and-5,900 genotyped elite artificial insemination rams. For the-8% animals with missing sire, we fit 25 unknown parent groups. We used the linear regression method to compare "partial" and "whole" predictions of young rams before and after progeny testing, with 7 cut-off points, and we obtained estimates of their bias, (over)dispersion, and accuracy in early proofs. We tried (1) several scenarios as follows: multiple or single trait, the "official" (routine) evalua-tion, which is a mixture of both single and multiple trait, and "deletion" of data before 1990; and (2) sev-eral models as follows: BLUP and single-step genomic (SSG)BLUP with fixed unknown parent groups or metafounders, where, for metafounders, their relation-ship matrix gamma was estimated using either a model for inbreeding trend, or base allele frequencies esti-mated by peeling. The estimate of gamma obtained by modeling the inbreeding trend resulted in an estimated increase of inbreeding, based on markers, faster than the pedigree-based one. The estimated genetic trends were similar for most models and scenarios across all traits, but were shrunken when gamma was estimated by peeling. This was due to shrinking of the estimates of metafounders in the latter case. Across scenarios, all traits showed bias, generally as an overestimate of genetic trend for milk yield and an underestimate for the other traits. As for the slope, it showed overdisper-sion of estimated breeding values for all traits. Using multiple-trait models slightly reduced the overestimate of genetic trend and the overdispersion, as did including genomic information (i.e., SSGBLUP) when the gam-ma matrix was estimated by the model for inbreeding trend. However, only deletion of historical data before 1990 resulted in elimination of both kind of biases. The SSGBLUP resulted in more accurate early proofs than BLUP for all traits. We considered that a snowball ef-fect of small errors in each genetic evaluation, combined with selection, may have resulted in biased evaluations. Improving statistical methods reduced some bias but not all, and a simple solution for this data set was to remove historical records

Genomic BLUP including additive and dominant variation in purebreds and F1 crossbreds, with an application in pigs

Background: Most developments in quantitative genetics theory focus on the study of intra-breed/line concepts. With the availability of massive genomic information, it becomes necessary to revisit the theory for crossbred populations. We propose methods to construct genomic covariances with additive and non-additive (dominance) inheritance in the case of pure lines and crossbred populations. Results: We describe substitution effects and dominant deviations across two pure parental populations and the crossbred population. Gene effects are assumed to be independent of the origin of alleles and allelic frequencies can differ between parental populations. Based on these assumptions, the theoretical variance components (additive and dominant) are obtained as a function of marker effects and allelic frequencies. The additive genetic variance in the crossbred population includes the biological additive and dominant effects of a gene and a covariance term. Dominance variance in the crossbred population is proportional to the product of the heterozygosity coefficients of both parental populations. A genomic BLUP (best linear unbiased prediction) equivalent model is presented. We illustrate this approach by using pig data (two pure lines and their cross, including 8265 phenotyped and genotyped sows). For the total number of piglets born, the dominance variance in the crossbred population represented about 13 % of the total genetic variance. Dominance variation is only marginally important for litter size in the crossbred population. Conclusions: We present a coherent marker-based model that includes purebred and crossbred data and additive and dominant actions. Using this model, it is possible to estimate breeding values, dominant deviations and variance components in a dataset that comprises data on purebred and crossbred individuals. These methods can be exploited to plan assortative mating in pig, maize or other species, in order to generate superior crossbred individuals in terms of performance

A relationship matrix including full pedigree and genomic information

, athens 30602 ‡ instituto Nacional de investigación agropecuaria, las Brujas, Uruguay aBStraCt Dense molecular markers are being used in genetic evaluation for parts of the population. This requires a two-step procedure where pseudo-data (for instance, daughter yield deviations) are computed from full records and pedigree data and later used for genomic evaluation. This results in bias and loss of information. One way to incorporate the genomic information into a full genetic evaluation is by modifying the numerator relationship matrix. A naive proposal is to substitute the relationships of genotyped animals with the genomic relationship matrix. However, this results in incoherencies because the genomic relationship matrix includes information on relationships among ancestors and descendants. In other words, using the pedigree-derived covariance between genotyped and ungenotyped individuals, with the pretense that genomic information does not exist, leads to inconsistencies. It is proposed to condition the genetic value of ungenotyped animals on the genetic value of genotyped animals via the selection index (e.g., pedigree information), and then use the genomic relationship matrix for the latter. This results in a joint distribution of genotyped and ungenotyped genetic values, with a pedigree-genomic relationship matrix H. In this matrix, genomic information is transmitted to the covariances among all ungenotyped individuals. The matrix is (semi)positive definite by construction, which is not the case for the naive approach. Numerical examples and alternative expressions are discussed. Matrix H is suitable for iteration on data algorithms that multiply a vector times a matrix, such as preconditioned conjugated gradients

Frequentist p-values for large-scale-single step genome-wide association, with an application to birth weight in American Angus cattle.

Background: Single-step genomic best linear unbiased prediction (SSGBLUP) is a comprehensive method for genomic prediction. Point estimates of marker effects from SSGBLUP are often used for genome-wide association studies (GWAS) without a formal framework of hypothesis testing. Our objective was to implement p-values for singlemarker GWAS studies within the single-step GWAS (SSGWAS) framework by deriving computational algorithms and procedures, and by applying these to a large beef cattle population. Methods: P-values were obtained based on the prediction error (co)variances for single nucleotide polymorphisms (SNPs), which were obtained from the prediction error (co)variances of genomic predictions based on the inverse of the coefficient matrix and formulas to estimate SNP effects. Results: Computation of p-values took a negligible time for a dataset with almost 2 million animals in the pedigree and 1424 genotyped sires, and no inflation of statistics was observed. The SNPs that passed the Bonferroni threshold of 10-5.9 were the same as those that explained the highest proportion of additive genetic variance, but even at the same significance levels and effects, some of them explained less genetic variance due to lower allele frequency. Conclusions: The use of a p-value for SSGWAS is a very general and efficient strategy to identify quantitative trait loci (QTL). It can be used for complex datasets such as those used in animal breeding, where only a proportion of the pedigreed animals are genotyped

Genomic analysis of dominance effects on milk production and conformation traits in Fleckvieh cattle

Background Estimates of dominance variance in dairy cattle based on pedigree data vary considerably across traits and amount to up to 50% of the total genetic variance for conformation traits and up to 43% for milk production traits. Using bovine SNP (single nucleotide polymorphism) genotypes, dominance variance can be estimated both at the marker level and at the animal level using genomic dominance effect relationship matrices. Yield deviations of high-density genotyped Fleckvieh cows were used to assess cross-validation accuracy of genomic predictions with additive and dominance models. The potential use of dominance variance in planned matings was also investigated. Results Variance components of nine milk production and conformation traits were estimated with additive and dominance models using yield deviations of 1996 Fleckvieh cows and ranged from 3.3% to 50.5% of the total genetic variance. REML and Gibbs sampling estimates showed good concordance. Although standard errors of estimates of dominance variance were rather large, estimates of dominance variance for milk, fat and protein yields, somatic cell score and milkability were significantly different from 0. Cross-validation accuracy of predicted breeding values was higher with genomic models than with the pedigree model. Inclusion of dominance effects did not increase the accuracy of the predicted breeding and total genetic values. Additive and dominance SNP effects for milk yield and protein yield were estimated with a BLUP (best linear unbiased prediction) model and used to calculate expectations of breeding values and total genetic values for putative offspring. Selection on total genetic value instead of breeding value would result in a larger expected total genetic superiority in progeny, i.e. 14.8% for milk yield and 27.8% for protein yield and reduce the expected additive genetic gain only by 4.5% for milk yield and 2.6% for protein yield. Conclusions Estimated dominance variance was substantial for most of the analyzed traits. Due to small dominance effect relationships between cows, predictions of individual dominance deviations were very inaccurate and including dominance in the model did not improve prediction accuracy in the cross-validation study. Exploitation of dominance variance in assortative matings was promising and did not appear to severely compromise additive genetic gain

Metafounders are related to F st fixation indices and reduce bias in single-step genomic evaluations.

International audienceAbstractBackground Metafounders are pseudo-individuals that encapsulate genetic heterozygosity and relationships within and across base pedigree populations, i.e. ancestral populations. This work addresses the estimation and usefulness of metafounder relationships in single-step genomic best linear unbiased prediction (ssGBLUP).ResultsWe show that ancestral relationship parameters are proportional to standardized covariances of base allelic frequencies across populations, such as Fst\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$F_{\text{st}}$$\end{document} fixation indexes. These covariances of base allelic frequencies can be estimated from marker genotypes of related recent individuals and pedigree. Simple methods for their estimation include naïve computation of allele frequencies from marker genotypes or a method of moments that equates average pedigree-based and marker-based relationships. Complex methods include generalized least squares (best linear unbiased estimator (BLUE)) or maximum likelihood based on pedigree relationships. To our knowledge, methods to infer Fst\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$F_{\text{st}}$$\end{document} coefficients from marker data have not been developed for related individuals. We derived a genomic relationship matrix, compatible with pedigree relationships, that is constructed as a cross-product of {−1,0,1} codes and that is equivalent (apart from scale factors) to an identity-by-state relationship matrix at genome-wide markers. Using a simulation with a single population under selection in which only males and youngest animals are genotyped, we observed that generalized least squares or maximum likelihood gave accurate and unbiased estimates of the ancestral relationship parameter (true value: 0.40) whereas the naïve method and the method of moments were biased (average estimates of 0.43 and 0.35). We also observed that genomic evaluation by ssGBLUP using metafounders was less biased in terms of estimates of genetic trend (bias of 0.01 instead of 0.12), resulted in less overdispersed (0.94 instead of 0.99) and as accurate (0.74) estimates of breeding values than ssGBLUP without metafounders and provided consistent estimates of heritability.ConclusionsEstimation of metafounder relationships can be achieved using BLUP-like methods with pedigree and markers. Inclusion of metafounder relationships reduces bias of genomic predictions with no loss in accuracy

Surgical approach for cardiac surgery in a patient with tracheostoma

The thoracic approach for cardiac surgery in a patient with a tracheostoma can result in difficult problems, such as mediastinitis, stoma necrosis or inadequate operative exposure. We present a distinct approach consisting of an incision at the second intercostal space, transverse sternum transection and longitudinal median sternotomy to the xiphoid process, performed for coronary artery bypass grafting and aortic valve replacement, in a patient with previous tracheotomy. This approach permitted adequate surgical exposure for cardiopulmonary bypass, aortic valve replacement and coronary revascularization procedures