Genomic selection refers to the use of genotypic information for predicting breeding values of selection candidates. A prediction formula is calibrated with the genotypes and phenotypes of reference individuals constituting the calibration set. The size and the composition of this set are essential parameters affecting the prediction reliabilities. The objective of this study was to maximize reliabilities by optimizing the calibration set. Different criteria based on the diversity or on the prediction error variance (PEV) derived from the realized additive relationship matrix-best linear unbiased predictions model (RA-BLUP) were used to select the reference individuals. For the latter, we considered the mean of the PEV of the contrasts between each selection candidate and the mean of the population (PEVmean) and the mean of the expected reliabilities of the same contrasts (CDmean). These criteria were tested with phenotypic data collected on two diversity panels of maize (Zea mays L.) genotyped with a 50k SNPs array. In the two panels, samples chosen based on CDmean gave higher reliabilities than random samples for various calibration set sizes. CDmean also appeared superior to PEVmean, which can be explained by the fact that it takes into account the reduction of variance due to the relatedness between individuals. Selected samples were close to optimality for a wide range of trait heritabilities, which suggests that the strategy presented here can efficiently sample subsets in panels of inbred lines. A script to optimize reference samples based on CDmean is available on request.A MONG the different methods that use molecular markers for selection, genomic selection (GS) has received considerable attention in the last decade. The objective of this approach is to predict the breeding values of candidates based on their molecular marker genotypes. A prediction formula is developed using the genotypes and phenotypes of reference individuals forming a calibration set (Meuwissen

Among the several linkage disequilibrium measures known to capture different features of the non-independence between alleles at different loci, the most commonly used for diallelic loci is the r 2 measure. In the present study, we tackled the problem of the bias of r 2 estimate, which results from the sample structure and/or the relatedness between genotyped individuals. We derived two novel linkage disequilibrium measures for diallelic loci that are both extensions of the usual r 2 measure. The first one, r S 2 , uses the population structure matrix, which consists of information about the origins of each individual and the admixture proportions of each individual genome. The second one, r V 2 , includes the kinship matrix into the calculation. These two corrections can be applied together in order to correct for both biases and are defined either on phased or unphased genotypes. We proved that these novel measures are linked to the power of association tests under the mixed linear model including structure and kinship corrections. We validated them on simulated data and applied them to real data sets collected on Vitis vinifera plants. Our results clearly showed the usefulness of the two corrected r 2 measures, which actually captured 'true' linkage disequilibrium unlike the usual r 2 measure.