The availability of genomewide dense markers brings opportunities and challenges to breeding programs. An important question concerns the ways in which dense markers and pedigrees, together with phenotypic records, should be used to arrive at predictions of genetic values for complex traits. If a large number of markers are included in a regression model, marker-specific shrinkage of regression coefficients may be needed. For this reason, the Bayesian least absolute shrinkage and selection operator (LASSO) (BL) appears to be an interesting approach for fitting marker effects in a regression model. This article adapts the BL to arrive at a regression model where markers, pedigrees, and covariates other than markers are considered jointly. Connections between BL and other marker-based regression models are discussed, and the sensitivity of BL with respect to the choice of prior distributions assigned to key parameters is evaluated using simulation. The proposed model was fitted to two data sets from wheat and mouse populations, and evaluated using crossvalidation methods. Results indicate that inclusion of markers in the regression further improved the predictive ability of models. An R program that implements the proposed model is freely available.

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 genomicassisted 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.

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.T HIS work evaluates the empirical performance of the so-called genomewide selection strategy for markerassisted selection (MAS) in a mouse population, using massive molecular marker information. MAS techniques are advocated as a tool for more efficient selection schemes in plant and animal populations (Dekkers and Hospital 2002). In general, MAS techniques are based on tracing the inheritance of the quantitative trait loci (QTL) of interest throughout the pedigree with the help of molecular markers. However, the use of MAS techniques in animal populations is still not much extended, because of its complexity in practice (Boichard et al. 2006) and relatively small additional gains. For example, Chamberlain and Goddard (2006) estimated by cross-validation an increase in prediction accuracy over pedigree index (no use of MAS) of, at best, 0.02. Recent developments in massive single-nucleotide polymorphism (SNP) marker genotyping increased the interest for MAS techniques. Dense marker maps capture much richer information, including not only recombination events in the genotyped pedigree (i.e., linkage analysis) but also the populational linkage disequilibrium pattern in the genome, i.e., the possibility of predicting alleles at some loci on the basis of alleles in other (possibly close) loci. This allows for a much finer description of the genome.

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.

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.