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Selection plans in plant and animal breeding are driven by genetic evaluation. Recent developments suggest using massive genetic marker information, known as “genomic selection.” There is little evidence of its performance, though. We empirically compared three strategies for selection: (1) use of pedigree and phenotypic information, (2) use of genomewide markers and phenotypic information, and (3) the combination of both. We analyzed four traits from a heterogeneous mouse population (http://gscan.well.ox.ac.uk/), including 1884 individuals and 10,946 SNP markers. We used linear mixed models, using extensions of association analysis. Cross-validation techniques were used, providing assumption-free estimates of predictive ability. Sampling of validation and training data sets was carried out across and within families, which allows comparing across- and within-family information. Use of genomewide genetic markers increased predictive ability up to 0.22 across families and up to 0.03 within families. The latter is not statistically significant. These values are roughly comparable to increases of up to 0.57 (across family) and 0.14 (within family) in accuracy of prediction of genetic value. In this data set, within-family information was more accurate than across-family information, and populational linkage disequilibrium was not a completely accurate source of information for genetic evaluation. This fact questions some applications of genomic selection.

Background Gametic variances can be predicted from the outcomes of a genomic prediction for any genotyped individual. This is widely used in plant breeding, applying the utility criterion (UC). This paper aims to examine the conditions to use UC for recurrent selection in livestock. Here, the UC for a selection candidate is the linear combination of the expected value of the future progeny (half of the candidate’s breeding value) and its predicted gametic variance weighted by a coefficient θ to be optimized. Results First, generalizing previous results, we derived analytically the ratio of the variance of the candidate’s gametic variance and that of half of the candidate’s breeding value. This ratio depends strongly on the number of quantitative trait loci (QTL) affecting the trait and, to a lesser extent, on the distribution of QTL allele frequencies: highly unbalanced frequencies and a limited number of QTL (< 10) favor higher values of the ratio. Then, changes in average breeding values and genetic variances when recurrent selection in a population of infinite size is applied were analytically derived and analyzed for selection up to 15 generations: in this ideal situation, after 5 to 10 generations (depending on θ ), the expected breeding values were higher with selection on UC and the genetic variance was always higher than with selection on estimated breeding values. To describe the potential of the UC in more general situations, simulations were applied to a population of 1000 males and 1000 females, with various selection rates, numbers and allele frequencies of QTL, and θ . These simulations were performed assuming independent QTL with known positions and effects. The best values for θ (i.e. providing the best genetic progress) were generally lower than 1, limiting the weight on the gametic variance. As expected from the analytical derivations, the gain in genetic progress from using UC was greatest when there were few QTL and allele frequencies were unbalanced, but they barely exceeded 5%. Conclusions We conclude that the key factor to choose selection on UC rather than on estimated breeding values is the ratio between the variance of the gametic standard deviations and the variance of the breeding values (GEBV), which should be carefully evaluated.

Texel sheep are renowned for their exceptional meatiness. To identify the genes underlying this economically important feature, we performed a whole-genome scan in a Romanov × Texel F2 population. We mapped a quantitative trait locus with a major effect on muscle mass to chromosome 2 and subsequently fine-mapped it to a chromosome interval encompassing the myostatin ( GDF8 ) gene. We herein demonstrate that the GDF8 allele of Texel sheep is characterized by a G to A transition in the 3′ UTR that creates a target site for mir1 and mir206 , microRNAs (miRNAs) that are highly expressed in skeletal muscle. This causes translational inhibition of the myostatin gene and hence contributes to the muscular hypertrophy of Texel sheep. Analysis of SNP databases for humans and mice demonstrates that mutations creating or destroying putative miRNA target sites are abundant and might be important effectors of phenotypic variation.

Background Building an efficient reference population for genomic selection is an issue when the recorded population is small and phenotypes are poorly informed, which is often the case in sheep breeding programs. Using stochastic simulation, we evaluated a genomic design based on a reference population with medium-density genotypes [around 45 K single nucleotide polymorphisms (SNPs)] of dams that were imputed from very low-density genotypes (≤ 1000 SNPs). Methods A population under selection for a maternal trait was simulated using real genotypes. Genetic gains realized from classical selection and genomic selection designs were compared. Genomic selection scenarios that differed in reference population structure (whether or not dams were included in the reference) and genotype quality (medium-density or imputed to medium-density from very low-density) were evaluated. Results The genomic design increased genetic gain by 26% when the reference population was based on sire medium-density genotypes and by 54% when the reference population included both sire and dam medium-density genotypes. When medium-density genotypes of male candidates and dams were replaced by imputed genotypes from very low-density SNP genotypes (1000 SNPs), the increase in gain was 22% for the sire reference population and 42% for the sire and dam reference population. The rate of increase in inbreeding was lower (from − 20 to − 34%) for the genomic design than for the classical design regardless of the genomic scenario. Conclusions We show that very low-density genotypes of male candidates and dams combined with an imputation process result in a substantial increase in genetic gain for small sheep breeding programs.

AbstractBackgroundFormulae to predict the precision or accuracy of genomic estimated breeding values (GEBV) are important when modelling selection schemes. Simple versions of such formulae have been proposed in the past, based on a number of simplifying hypotheses, including absence of linkage disequilibrium and linkage between loci, a population made up of unrelated individuals, and that all genetic variability of the trait is explained by the genotyped loci. These formulae were based on approximations that were not always clear. The objective of this paper is to offer a unique framework to derive equations that predict the precision of GEBV from the size of the reference population and the heritability of and number of QTL controlling the quantitative trait.ResultsThe exact formulation of the precision of GEBV involves the expectation of the inverse of a linear function of the genomic matrix, which cannot be calculated from simple algebra but can be approximated using a Taylor polynomial expansion. First order approximations performed better than the initial prediction equations published in the literature. Second order approximations produced almost perfect estimates of precision when compared to results obtained when simulating situations that agreed with the assumptions that were required to derive the precision equations. Using this proposed framework, we present several generalizations, including multi-trait genomic evaluation.ConclusionsAlthough further improvements are needed to account for the complexity of practical situations, the equations proposed here can be used to derive the precision of GEBV when comparing breeding schemes a priori.

Ewes from the Booroola strain of Australian Mérino sheep are characterized by high ovulation rate and litter size. This phenotype is due to the action of the FecBBallele of a major gene named FecB, as determined by statistical analysis of phenotypic data. By genetic analysis of 31 informative half-sib families from heterozygous sires, we showed that the FecB locus is situated in the region of ovine chromosome 6 corresponding to the human chromosome 4q22-23 that contains the bone morphogenetic protein receptor IB (BMPR-IB) gene encoding a member of the transforming growth factor-β (TGF-β) receptor family. A nonconservative substitution (Q249R) in the BMPR-IB coding sequence was found to be associated fully with the hyperprolificacy phenotype of Booroola ewes. In vitro, ovarian granulosa cells from FecBB/FecBBewes were less responsive than granulosa cells from FecB+/FecB+ewes to the inhibitory effect on steroidogenesis of GDF-5 and BMP-4, natural ligands of BMPR-IB. It is suggested that in FecBB/FecBBewes, BMPR-IB would be inactivated partially, leading to an advanced differentiation of granulosa cells and an advanced maturation of ovulatory follicles.

Background Spurious associations between single nucleotide polymorphisms and phenotypes are a major issue in genome-wide association studies and have led to underestimation of type 1 error rate and overestimation of the number of quantitative trait loci found. Many authors have investigated the influence of population structure on the robustness of methods by simulation. This paper is aimed at developing further the algebraic formalization of power and type 1 error rate for some of the classical statistical methods used: simple regression, two approximate methods of mixed models involving the effect of a single nucleotide polymorphism (SNP) and a random polygenic effect (GRAMMAR and FASTA) and the transmission/disequilibrium test for quantitative traits and nuclear families. Analytical formulae were derived using matrix algebra for the first and second moments of the statistical tests, assuming a true mixed model with a polygenic effect and SNP effects. Results The expectation and variance of the test statistics and their marginal expectations and variances according to the distribution of genotypes and estimators of variance components are given as a function of the relationship matrix and of the heritability of the polygenic effect. These formulae were used to compute type 1 error rate and power for any kind of relationship matrix between phenotyped and genotyped individuals for any level of heritability. For the regression method, type 1 error rate increased with the variability of relationships and with heritability, but decreased with the GRAMMAR method and was not affected with the FASTA and quantitative transmission/disequilibrium test methods. Conclusions The formulae can be easily used to provide the correct threshold of type 1 error rate and to calculate the power when designing experiments or data collection protocols. The results concerning the efficacy of each method agree with simulation results in the literature but were generalized in this work. The power of the GRAMMAR method was equal to the power of the FASTA method at the same type 1 error rate. The power of the quantitative transmission/disequilibrium test was low. In conclusion, the FASTA method, which is very close to the full mixed model, is recommended in association mapping studies.

Background Genomic selection is still to be evaluated and optimized in many species. Mathematical modeling of selection schemes prior to their implementation is a classical and useful tool for that purpose. These models include formalization of a number of entities including the precision of the estimated breeding value. To model genomic selection schemes, equations that predict this reliability as a function of factors such as the size of the reference population, its diversity, its genetic distance from the group of selection candidates genotyped, number of markers and strength of linkage disequilibrium are needed. The present paper aims at exploring new approximations of this reliability. Results Two alternative approximations are proposed for the estimation of the reliability of genomic estimated breeding values (GEBV) in the case of non-independence between candidate and reference populations. Both were derived from the Taylor series heuristic approach suggested by Goddard in 2009. A numerical exploration of their properties showed that the series were not equivalent in terms of convergence to the exact reliability, that the approximations may overestimate the precision of GEBV and that they converged towards their theoretical expectations. Formulae derived for these approximations were simple to handle in the case of independent markers. A few parameters that describe the markers’ genotypic variability (allele frequencies, linkage disequilibrium) can be estimated from genomic data corresponding to the population of interest or after making assumptions about their distribution. When markers are not in linkage equilibrium, replacing the real number of markers and QTL by the “effective number of independent loci”, as proposed earlier is a practical solution. In this paper, we considered an alternative, i.e. an “equivalent number of independent loci” which would give a GEBV reliability for unrelated individuals by considering a sub-set of independent markers that is identical to the reliability obtained by considering the full set of markers. Conclusions This paper is a further step towards the development of deterministic models that describe breeding plans based on the use of genomic information. Such deterministic models carry low computational burden, which allows design optimization through intensive numerical exploration.

International audience

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.