La réussite de la reproduction est primordiale pour la rentabilité de l’élevage, elle constitue un préalable indispensable à toute production. L’aptitude à la reproduction d’un animal au cours d’une carrière dépend des caractères de précocité sexuelle, de fertilité et de prolificité, cette dernière pouvant être décomposée en termes de taux d’ovulation et de mortalité embryonnaire. Ces différents aspects font l’objet de recherches en génétique animale et sont intégrés à des degrés divers dans les schémas de sélection, en race pure ou en croisement. La précocité sexuelle et la prolificité doivent être améliorées quand elles sont limitantes, mais certains seuils ne doivent pas être dépassés sous peine de voir se réduire le gain économique espéré. S’intéresser aux composantes de la prolificité devrait en permettre un meilleur contrôle. Une fertilité maximale est toujours recherchée mais elle revêt différentes facettes qui en compliquent son amélioration. Elle est à la fois dépendante du sexe (la fertilité femelle reste souvent la plus limitante) de la technique de reproduction employée (naturelle ou artificielle) et du moment choisi pour la mise à la reproduction (intervalle mise bas - reproduction, saison). Les recherches sur la génétique des caractères de reproduction doivent être poursuivies tout en intégrant les résultats de cartographie génétique.

This review focuses on methods used to predict complex traits. Main characteristics of prediction approaches are given: the deterministic or stochastic nature of prediction, the objects of prediction, the sources of information and the main statistical methods. Sources of information discussed are the traditional genealogies and phenotypes, nucleotide sequences, expression data and epigenetics marks. Statistical methods are presented as successive degrees of generalization from the definition of the conditional expectation as the prediction rule, to best linear unbiased prediction, then Bayesian and, recently, machine learning methods, including meta-methods. We highlight the contributions of Daniel Gianola to this methodological evolution.

The genetic variation of dairy traits for small dairy ruminants is revised. Examples are given on the exploitation of this genetic variation in large populations using a classical polygenic approach (sheep) or taking profit of major genes (goat). The genetic determinism of secondary traits, including meat and functional traits, is also described. Finally, perspectives for new profitable technologies, as molecular genetic and reproductive technology, are discussed.

Genetic prediction for complex traits is usually based on models including individual or marker effects. Alternatively, models can include both the individual and the marker effects. In particular, we studied a model combining effects for base individuals, realized Mendelian sampling in descendants and marker effects. The predictive ability of this model, measured as the correlation between true (simulated) and predicted genetic values, was similar to that of the marker model. As expected, the Mendelian sampling model was worthwhile when markers captured a low fraction of total genetic variance.

Genetic links among individuals are widely used to characterize the diversity of domesticated and natural populations and they also provide complementary information for statistical population summaries. We first discuss the measures used by geneticists based on genealogy and DNA data. The choice of metrics of genetic links should be coherent with the objectives: biodiversity or genotype-phenotype relationships. For the last objective, we evaluate by simulation the interest of genetic distances when the objective is the prediction of individual genetic values and phenotypes using kernel regression. A pseudo-distance based on correlations between marker genotypes of pairs of individual yields better predictions than other classical definition of distances.

Genetic prediction for complex traits is usually based on models including individual (infinitesimal) or marker effects. Here, we concentrate on models including both the individual and the marker effects. In particular, we develop a "Mendelian segregation" model combining infinitesimal effects for base individuals and realized Mendelian sampling in descendants described by the available DNA data. The model is illustrated with an example and the analyses of a public simulated data file. Further, the potential contribution of such models is assessed by simulation. Accuracy, measured as the correlation between true (simulated) and predicted genetic values, was similar for all models compared under different genetic backgrounds. As expected, the segregation model is worthwhile when markers capture a low fraction of total genetic variance.

Cette revue bibliographique couvre deux aspects de la génétique des caprins laitiers : la variabilité génétique des caractères et l’améliorationgénétique. La majorité des connaissances sur le déterminisme génétique des caractères chez les caprins est issue de l’approche«polygénique» car les outils génériques de la génétique moléculaire sont encore limités dans cette espèce. Toutefois, nous discutonsici surtout les résultats sur quelques gènes bien étudiés en caprins, comme ceux des caséines, de la protéine prion et du cornage.Pour l’amélioration génétique, nous rappelons des principes généraux des méthodes de sélection avec ou sans données moléculaires,avant de discuter les programmes de sélection caprine actuels et leurs perspectives.

Systems involving many variables are important in population and quantitative genetics, for example, in multi-trait prediction of breeding values and in exploration of multi-locus associations. We studied departures of the joint distribution of sets of genetic variables from independence. New measures of association based on notions of statistical distance between distributions are presented. These are more general than correlations, which are pairwise measures, and lack a clear interpretation beyond the bivariate normal distribution. Our measures are based on logarithmic (Kullback-Leibler) and on relative distances between distributions. Indexes of association are developed and illustrated for quantitative genetics settings in which the joint distribution of the variables is either multivariate normal or multivariate-t, and we show how the indexes can be used to study linkage disequilibrium in a two-locus system with multiple alleles and present applications to systems of correlated beta distributions. Two multivariate beta and multivariate beta-binomial processes are examined, and new distributions are introduced: the GMS-Sarmanov multivariate beta and its beta-binomial counterpart.

Genomic selection aims to increase accuracy and to decrease generation intervals, thus increasing genetic gains in animal breeding. Using real data of the French Lacaune dairy sheep breed, the purpose of this study was to compare the observed accuracies of genomic estimated breeding values using different models (infinitesimal only, markers only, and joint estimation of infinitesimal and marker effects) and methods [BLUP, Bayes Cπ, partial least squares (PLS), and sparse PLS]. The training data set included results of progeny tests of 1,886 rams born from 1998 to 2006, whereas the validation set had results of 681 rams born in 2007 and 2008. The 3 lactation traits studied (milk yield, fat content, and somatic cell scores) had heritabilities varying from 0.14 to 0.41. The inclusion of molecular information, as compared with traditional schemes, increased accuracies of estimated breeding values of young males at birth from 18 up to 25%, according to the trait. Accuracies of genomic methods varied from 0.4 to 0.6, according to the traits, with minor differences among genomic approaches. In Bayes Cπ, the joint estimation of marker and infinitesimal effects had a slightly favorable effect on the accuracies of genomic estimated breeding values, and were especially beneficial for somatic cell counts, the less heritable trait. Inclusion of infinitesimal effects also improved slopes of predictive regression equations. Methods that select markers implicitly (Bayes Cπ and sparse PLS) were advantageous for some models and traits, and are of interest for further quantitative trait loci studies.

This review covers two parts of dairy goat genetics: genetic variation of traits and genetic improvement. Most knowledge on the genetic determinism of goat traits comes from polygenic analyses since generic molecular tools have been limited in this species. There are, however, some genes well studied at the molecular level such as milk casein and prion protein genes, whose effects on phenotypes are also discussed. In the genetic improvement chapter, we summarize the general principles of animal breeding, with and without the use of molecular data, before a discussion on the present practices and perspectives of dairy goat selection.

Goat milk somatic cell counts have been collected for several years in France by the national milk recording organization. Information is used for health management; because repeatedly elevated somatic cell counts are a good indirect predictor of intramammary infection. Genetic parameters were estimated for 67,882 and 49,709 primiparous goats of the dairy Alpine and Saanen breeds, respectively, with complete information for milk somatic cell counts and milk production traits. About 40% of the goats had additional information for 11 udder type traits scored by official classifiers of the breeders' association CAPGENES. Estimates were obtained by REML with an animal model. The studied trait was lactation somatic cell score (LSCS), the weighted mean of somatic cell score (log-transformed SCC) adjusted for lactation stage. Heritability of LSCS was 0.20 and 0.24 in the Alpine and Saanen breeds, respectively. Relationships with milk production and udder type traits were additionally estimated by using multitrait analyses. Heritability estimates in first lactation ranged from 0.30 to 0.35 for lactation milk, fat, and protein yields; from 0.60 to 0.67 for fat and protein contents; and from 0.22 to 0.50 for udder type traits. Genetic correlations of somatic cell score with milk production traits were generally low, ranging from -0.13 to 0.12. Slightly more negative correlations were estimated for fat content: -0.18 and -0.20 in Saanen and Alpine breeds, respectively. Lactation somatic cell score was genetically correlated with udder floor position (r(g) = -0.24 and -0.19 in the Alpine and Saanen breeds, respectively), and, in Saanen, teat length, teat width, and teat form (r(g) = 0.29, 0.34 and -0.27, respectively). These results suggest that a reduction in somatic cell count can be achieved by selection while still improving milk production and udder type and teat traits.

A Bayesian nonparametric form of regression based on Dirichlet process priors is adapted to the analysis of quantitative traits possibly affected by cryptic forms of gene action, and to the context of SNP-assisted genomic selection, where the main objective is to predict a genomic signal on phenotype. The procedure clusters unknown genotypes into groups with distinct genetic values, but in a setting in which the number of clusters is unknown a priori, so that standard methods for finite mixture analysis do not work. The central assumption is that genetic effects follow an unknown distribution with some "baseline" family, which is a normal process in the cases considered here. A Bayesian analysis based on the Gibbs sampler produces estimates of the number of clusters, posterior means of genetic effects, a measure of credibility in the baseline distribution, as well as estimates of parameters of the latter. The procedure is illustrated with a simulation representing two populations. In the first one, there are 3 unknown QTL, with additive, dominance and epistatic effects; in the second, there are 10 QTL with additive, dominance and additive × additive epistatic effects. In the two populations, baseline parameters are inferred correctly. The Dirichlet process model infers the number of unique genetic values correctly in the first population, but it produces an understatement in the second one; here, the true number of clusters is over 900, and the model gives a posterior mean estimate of about 140, probably because more replication of genotypes is needed for correct inference. The impact on inferences of the prior distribution of a key parameter (M), and of the extent of replication, was examined via an analysis of mean body weight in 192 paternal half-sib families of broiler chickens, where each sire was genotyped for nearly 7,000 SNPs. In this small sample, it was found that inference about the number of clusters was affected by the prior distribution of M. For a set of combinations of parameters of a given prior distribution, the effects of the prior dissipated when the number of replicate samples per genotype was increased. Thus, the Dirichlet process model seems to be useful for gauging the number of QTLs affecting the trait: if the number of clusters inferred is small, probably just a few QTLs code for the trait. If the number of clusters inferred is large, this may imply that standard parametric models based on the baseline distribution may suffice. However, priors may be influential, especially if sample size is not large and if only a few genotypic configurations have replicate phenotypes in the sample.

Genomic prediction of phenotypes relies on the stab ility of marker (SNP) effects on phenotypes along time and across the population whe re pr diction is to be performed. In the context of farm animal genetics, one major factor a ffects the reliability of prediction: the changes in the association between markers and phen otyp s along generations and across structures created by directional selection.

The phenotypic observation of some reproduction traits (e.g., insemination success, interval from lambing to insemination) is the result of environmental and genetic factors acting on 2 individuals: the male and female involved in a mating couple. In animal genetics, the main approach (called additive model) proposed for studying such traits assumes that the phenotype is linked to a purely additive combination, either on the observed scale for continuous traits or on some underlying scale for discrete traits, of environmental and genetic effects affecting the 2 individuals. Statistical models proposed for studying human fecundability generally consider reproduction outcomes as the product of hypothetical unobservable variables. Taking inspiration from these works, we propose a model (product threshold model) for studying a binary reproduction trait that supposes that the observed phenotype is the product of 2 unobserved phenotypes, 1 for each individual. We developed a Gibbs sampling algorithm for fitting a Bayesian product threshold model including additive genetic effects and showed by simulation that it is feasible and that it provides good estimates of the parameters. We showed that fitting an additive threshold model to data that are simulated under a product threshold model provides biased estimates, especially for individuals with high breeding values. A main advantage of the product threshold model is that, in contrast to the additive model, it provides distinct estimates of fixed effects affecting each of the 2 unobserved phenotypes.

The use of all available molecular markers in statistical models for prediction of quantitative traits has led to what could be termed a genomic-assisted selection paradigm in animal and plant breeding. This article provides a critical review of some theoretical and statistical concepts in the context of genomic-assisted genetic evaluation of animals and crops. First, relationships between the (Bayesian) variance of marker effects in some regression models and additive genetic variance are examined under standard assumptions. Second, the connection between marker genotypes and resemblance between relatives is explored, and linkages between a marker-based model and the infinitesimal model are reviewed. Third, issues associated with the use of Bayesian models for marker-assisted selection, with a focus on the role of the priors, are examined from a theoretical angle. The sensitivity of a Bayesian specification that has been proposed (called "Bayes A") with respect to priors is illustrated with a simulation. Methods that can solve potential shortcomings of some of these Bayesian regression procedures are discussed briefly.