The study provided comparative insight into genetic evaluation performed using: (1) the traditional BLUP approach based on pedigree data and (2) the unified approach based on both pedigree and marker data. In this study, we investigated the accuracy of overall, direct and maternal estimated breeding values as well as the influence of heritability of the trait and the genetic correlation between maternal and direct effects on the accuracy.
It has been reported in honey bees that most economically important traits have low to medium heritability [27–29]. Therefore, we also simulated heritabilities in the same range. The extremely negative estimates of genetic correlation between maternal and direct effects have often been questioned (; Ehrhardt and Bienefeld, unpublished results), therefore, we simulated a general value of correlation of −0.46 which exists in other species as well [31–33] and compared it to a case with no correlation between maternal and direct effects.
Unlike previous studies [6, 7, 34], our study takes into account the influence of maternal and direct effects. We observed that the accuracy of overall estimated breeding values (Table 3) increased considerably with the unified approach for all scenarios of heritability and correlation with significant P-values (< 0.05). A higher gain in the accuracy of overall estimated breeding values was observed for juvenile animals. It is desired that the gain in accuracy is higher for juvenile animals as they are the subsequent candidates for selection. This may consequently help speeding up the selection procedure as a result of reduction in the generation interval. Similar gain in accuracy was reported in other studies. For example, in another study , the accuracy of estimated breeding values for genotyped female pigs was reported to be 0.22 with the pedigree based approach whereas it ranged from 0.28 to 0.49 with the unified approach depending on the G matrix. Likewise, Christensen and Lund  reported an accuracy of 0.66 with the one-step unified approach and 0.35 with the pedigree based approach.
In our study, the accuracies of maternal and direct estimated breeding values for the pedigree based approach (PED_BLUP) with maternal and direct heritability of 0.15 were 0.38 and 0.41 at no correlation and 0.21 and 0.19 at a correlation of −0.46, respectively. In an earlier pedigree based study by Roehe and Kennedy , the accuracy of maternal and direct estimated breeding values was reported to be 0.21 (0.21) and 0.38 (0.28) for the case of no correlation and 0.19 (0.18) and 0.31 (0.23) for a negative correlation of −0.5 in female (male) pigs for maternal and direct heritability of 0.05 and 0.1, respectively. These estimates were based on a pedigree based complete animal model with maternal effects. The difference in the accuracies between our study and to that reported by Roehe and Kennedy  can be a result of dissimilarities between the two studies such as the construction of the numerator relationship matrix, value of simulated maternal and direct heritability, random selection of the individuals, number of generations simulated, population structure and size. Nonetheless, the comparison of results of the pedigree based approach with the study from Roehe and Kennedy  helps to assess and validate the values of accuracy of maternal and direct estimated breeding values obtained in our study. In our study, the accuracies of maternal and direct estimated breeding values were higher for the UNI_BLUP approach as compared to the PED_BLUP approach, but the difference between UNI_BLUP and PED_BLUP approaches were not significant for some cases (Table 4). Thus, in order to achieve maximum gain from implementing the unified approach, a proper investigation into the cost benefits and the relative improvement in genetic gain is required for traits selected solely on the basis of maternal or direct breeding values. Nevertheless, the sum of maternal and direct effects is still the most important criterion for selection and the use of only direct or maternal effects is not helpful for the honey bee.
A complexity associated with the estimation of breeding values for maternally influenced traits is that negative correlation between maternal and direct effects severely impedes the response to selection [35, 36]. Additionally, it leads to a decrease in the total genetic variance resulting in lowered accuracies. As shown in the results, the accuracy of estimated breeding values improved significantly in case of negative correlation with the unified approach as compared to the pedigree based approach. We propose that the extra gain from genomic selection (versus pedigree-BLUP) is larger, when the correlations between direct and maternal effects are negative, compared to scenarios with positive correlations. This is because some of the markers capture maternal (direct) genetic differences, induced by loci without pleiotropic direct (maternal) effects. These parts of the genetic variation are of special interest in case of negative correlations between direct and maternal effects, since they provide, at least partially, opportunity for achieving both maternal and direct genetic gain in the desired direction. In contrast to this, each positive maternal (direct) gain stemming from pleiotropic loci is counterbalanced by a negative direct (maternal) one. Obviously, this kind of distinction does not matter at all in case of positive correlations and is even impossible to be exploited with only pedigree information at hand. So, genomic selection offers special advantages in cases, where maternal and direct effects are negatively correlated through the pleiotropic action of common loci, a phenomenon probably deserving more attention and research also in other species. Additionally, the increase in accuracies can be attributed to the genomic matrix which is able to provide a more precise measure of genetic relatedness. The numerator relationship matrix uses pedigree information to derive the probability of genes to be identical by descent that gives an estimate of the relatedness of individuals. The genomic matrix, in contrast, uses high-density marker information and thus, can identify genes that are identical by state and may be shared through common ancestor not recorded in the pedigree . Hence, it provides a more accurate measure for the relationship between individuals. It also enables better differentiation among closely related individuals since it captures Mendelian sampling with greater precision. Thus, the use of a marker based relationship matrix in the unified approach greatly helps to improve the accuracy of estimated breeding values for low heritability traits and/or negatively correlated traits, e.g. traits with negatively correlated maternal and direct effects.