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Supplementary Materials to "Partition of the genetic trend of French dairy sheep in Mendelian samplings and long-term contributions" S. Antonios, A. Legarra, R. Pong-Wong, J.M. Astruc, S.T. Rodríguez-Ramilo and Z.G. Vitezica

Supplementary Materials to "Partition of the genetic trend of French dairy sheep in Mendelian samplings and long-term contributions" S. Antonios, A. Legarra, R. Pong-Wong, J.M. Astruc, S.T. Rodríguez-Ramilo and Z.G. Vitezica

For single-step genomic best linear unbiased prediction, the use of so-called metafounders provides a coherent approach for combining pedigree and genomic relationships. Here, maximum likelihood estimation of metafounder parameters is presented. For one breed, the maximum likelihood estimate of metafounder parameter can be determined by solving a cubic equation. For multiple breeds, we provide an expression for the likelihood function, and for numerical maximisation of this function using gradient methods, we express the metafounder relationship matrix as a function of partial relationship matrices and metafounder parameters.

It is now widely accepted that animals’ phenotypes are determined by the host genetic and the microbiome composition. For the genetic evaluation purpose, our objectives are to estimate the heritability and microbiability, and the additive metagenomic effect, assuming that these two components have additive effects. In this study were included, as dairy traits, milk production, fat and protein content; and 16S rRNA gene of rumen bacteria of 795 ewes. Two genomicmodels were used, a first model to predict individual microbiome contribution to phenotypes; and a second model to predict genetic effects on this predicted microbiome contribution. Results showed that the microbiabilities for milk traits were close to zero, and the residual heritabilities were not different from the trait heritabilities. By disentangling the milk traits’ variance explained by the microbiome, we conclude that rumen bacteria abundances do not provide improved genetic evaluation of dairy traits in Lacaune sheep.

International audience; In France, dairy sheep and goats have developed efficient breeding schemes, whose annual genetic gain ranges from 0.10 to 0.27 genetic standard deviation of the total merit index, according to the breeds. From 2015 to 2020, the 5 dairy sheep breeds and 2 main dairy goat breeds have shifted to full genomic programs, based on reference population constituted of AI progeny-tested males. Currently, the breeding goals are similar for almost all the selected breeds and may be per se qualified as balanced, since they include efficiency criteria (milk yield and content), resilience criteria (udder health, resistance to scrapie), and adaptation to mechanic milking in order to mitigate the workload of the farmer in the milking parlour (udder morphology). There are increasing expectations for improving sustainability, robustness and resilience while still increasing efficiency. These new objectives are emphasized by the different stakeholders: the farmers, the industry, but also the consumers, the citizens. Opportunities occur to cope with these requests: a larger efficiency of selection offered by genomic programs allowing to consider new traits to select, new technologies and methods to limit the phenotyping costs (eg. use of MIR spectra), awareness and consent of all stakeholders to bring new challenges at the agenda (climate change, growing resistance to antibiotics or anthelmintics). Various recent or on-going projects (eg. iSAGE, RUSTIC, ARDI, SMARTER) are addressing the topics of adaptation, sustainability, resilience in small ruminants. Through the French dairy sheep and goat illustration, we propose to explore the following ways, that are the core objectives of the on-going SMARTER project: breeding for new efficiency and resilience traits in a context of more agro-ecological systems and pursuit of self-sufficiency in the feeding systems; benefiting from international harmonization and cooperation; tackling the genotype x environment interactions; sharing the ideas and solutions across the wider range of stakeholders.; En France, les brebis et chèvres laitières bénéficient de schémas de sélection efficaces, dont le pro-grès génétique annuel varie, selon la race, entre 0.10 et 0.27 écart-type génétique. De 2015 à 2020, les 5 racesovines laitières et les 2 races caprines en sélection ont basculé vers des schémas de sélection génomiques,basés sur des populations de référence constituées de mâles d’IA testés sur descendance. Actuellement, lesobjectifs de sélection, assez similaires d’une race à l’autre, peuvent être qualifiés d’équilibrés, car ils incluentdes critères de production et d’efficience (quantité et richesse du lait), des critères de résilience (santé de lamamelle, résistance à la tremblante) et d’adaptation à la traite mécanique (morphologie de la mamelle). Desattentes, soutenues par l’ensemble des acteurs des filières, sont fortes pour améliorer la durabilité, la robus-tesse, la résilience tout en améliorant l’efficience des animaux. Des opportunités existent pour traiter ces de-mandes : plus grande efficacité de la sélection offerte par la génomique, nouvelles technologies ou méthodes,prise de conscience et consentement des acteurs pour mettre en avant ces nouveaux challenges (changementclimatique, résistance aux antibiotiques et aux anthelminthiques). Plusieurs projets, récents ou en cours (ex.iSAGE, RUSTIC, ARDI, SMARTER), abordent les questions d’adaptation, de durabilité et de résilience en pe-tits ruminants. Au travers de l’exemple des chèvres et brebis laitières françaises, nous proposons de balise les thèmes suivants, qui sont au cœur du projet SMARTER: la sélection de nouveaux caractères d’efficienceet de résilience dans une contexte d’intérêt croissant pour des systèmes plus agro-écologiques, recherchantplus d’autonomie alimentaire; l’intérêt de l’harmonisation et de la coopération internationale; les interactionsgénotypes x milieu ; la partage des idées et des solutions par un large réseau d’acteurs et d’utilisateurs de lagénétique et de la production de petits ruminant

Additional file 1. Weighted marker effects in APY-SNP-BLUP and numerical illustration of the equivalence between APY-GBLUP and APY-SNP-BLUP with and without a residual polygenic effect.

Additional file 2: Figure S1. Distribution of the minor allele frequencies of the Illumina array-specific SNPs in Scenario 1 and the Affymetrix array-specific SNPs in Scenario 2. Figure S2. Effect of allele frequency on $${2{p}_{j}{q}_{j}\left({q}_{j}-{p}_{j}\right)}^{2}$$ 2 p j q j q j - p j 2 .

Additional file 1: Table S1. Estimates of variance components, standard error (SE) of parameters, − 2 log likelihood (− 2LogL), AIC (Akaike’s Information Criterion) from models MA, MAD, MAD*, MAI, MAID and MAID*. Table S2. Contributed additive genetic variance from the inbreeding depression effect. Table S3. P-value of likelihood ratio test based on model MA. Table S4. P-value of likelihood ratio test based on models MAI, MAD and MAD*. Table S5. P-value of inbreeding depression effect based on the Wald test. Table S6. Average genomic relationships between animals in the imputed and reference sets. Table S7. Converted classical variance components based on the genotypic variance component in models MAD and MAID.

International audience; Abstract Allele substitution effects at quantitative trait loci (QTL) are part of the basis of quantitative genetics theory and applications such as association analysis and genomic prediction. In the presence of nonadditive functional gene action, substitution effects are not constant across populations. We develop an original approach to model the difference in substitution effects across populations as a first order Taylor series expansion from a “focal” population. This expansion involves the difference in allele frequencies and second-order statistical effects (additive by additive and dominance). The change in allele frequencies is a function of relationships (or genetic distances) across populations. As a result, it is possible to estimate the correlation of substitution effects across two populations using three elements: magnitudes of additive, dominance, and additive by additive variances; relationships (Nei’s minimum distances or Fst indexes); and assumed heterozygosities. Similarly, the theory applies as well to distinct generations in a population, in which case the distance across generations is a function of increase of inbreeding. Simulation results confirmed our derivations. Slight biases were observed, depending on the nonadditive mechanism and the reference allele. Our derivations are useful to understand and forecast the possibility of prediction across populations and the similarity of GWAS effects.

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We revisited, in a genomic context, the theory of hybrid genetic evaluation models of hybrid crosses of pure lines, as the current practice is largely based on infinitesimal model assumptions. Expressions for covariances between hybrids due to additive substitution effects and dominance and epistatic deviations were analytically derived. Using dense markers in a GBLUP analysis, it is possible to split specific combining ability into dominance and across-groups epistatic deviations, and to split general combining ability (GCA) into within-line additive effects and within-line additive by additive (and higher order) epistatic deviations. We analyzed a publicly available maize data set of Dent × Flint hybrids using our new model (called GCA-model) up to additive by additive epistasis. To model higher order interactions within GCAs, we also fitted “residual genetic” line effects. Our new GCA-model was compared with another genomic model which assumes a uniquely defined effect of genes across origins. Most variation in hybrids is accounted by GCA. Variances due to dominance and epistasis have similar magnitudes. Models based on defining effects either differently or identically across heterotic groups resulted in similar predictive abilities for hybrids. The currently used model inflates the estimated additive genetic variance. This is not important for hybrid predictions but has consequences for the breeding scheme—e.g. overestimation of the genetic gain within heterotic group. Therefore, we recommend using GCA-model, which is appropriate for genomic prediction and variance component estimation in hybrid crops using genomic data, and whose results can be practically interpreted and used for breeding purposes.

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Additional file 3: Figure S1. Heritability of the gene content along the X-chromosome (X-specific part), when males considered homozygous are coded as {0,2}. A. For all genotyped individuals, B. For genotyped males only. Black and gray dots indicate heritabilities estimated with the pedigree-based relationships using rules specific to the X-chromosome (S) and general rules for the autosomes (A), respectively.

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Additional file 1 Metafounder’s theory as applied to the S matrix, rules and code for this matrix and its inverse.

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Additional file 2: Table S1. Comparison of realized (marker-based) and expected (pedigree-based) additive genetic relationships on the X-chromosome (specific part) for different categories of animals. Table S2. Comparison of realized (marker-based) and expected (pedigree-based) additive genetic relationships on the autosomes (all together) for different categories of animals. Table S3. Comparison of realized (marker-based) and expected (pedigree-based) additive genetic relationships on the BTA2 for different categories of animals.