Formica exsecta ants has allowed phenotypic variation in chemical profiles to be quantified across a natural population of 83 colonies. We investigated if this variation was correlated or not with intrinsic (genetic relatedness), extrinsic , or social (queen number) factors. (Z)-9-Alkenes and n-alkanes showed different patterns of variance: island (location) explained only 0.2 % of the variation in (Z)-9-alkenes, but 21–29 % in n-alkanes, whereas colony of origin explained 96 % and 45–49 % of the variation in (Z)-9-alkenes and n-alkanes, respectively. By contrast, within-colony variance of (Z)-9-alkenes was 4 %, and 23–34 % in n-alkanes, supporting the function of the former as recognition cues. (Z)-9-Alkene and n-alkane profiles were correlated with the genetic distance between colonies. Only n-alkane profiles diverged with increasing spatial distance. Sampling year explained a small (5 %), but significant, amount of the variation in the (Z)-9-alkenes, but there was no consistent directional trend. Polygynous colonies and populous monogynous colonies were dominated by a rich C23:1 profile. We found no associations between worker size, mound exposure, or humidity, although effect sizes for the latter two factors were considerable. The results support the conjecture that genetic factors are the most likely source of between-colony variation in cuticular hydrocarbons.Phenotypic variation arises from interactions between genotype and environment, although how variation is produced and then maintained remains unclear. The discovery of the nest-mate recognition system in The online version of this article (doi:10.1007/s10886-013-0366-0) contains supplementary material, which is available to authorized users. Disentangling the various genetic and environmental factors that contribute to phenotype variability in out-bred natural populations is a major challenge (Peaston and Whitelaw It is well established that cuticular hydrocarbon (CHC) production in insects is under genetic control  that presumably arise from monogynous colonies through adoption of daughter queens. The chemical profile of this species has been extensively studied across Europe  and three (Z)-9-alkenes , with a fourth  of each series always present in lower quantities -9-alkenes have been shown to act as nest-mate recognition cues -9-alkene and n-alkane profiles across the 83 colonies, and to search for a series of intrinsic and extrinsic factors that might contribute to the observed pattern of profile variation. For intrinsic factors, we included 72 colonies, and investigated whether genetic and chemical distances were correlated. For extrinsic factors, we studied temperature and humidity, since these can affect the CHC profile of ants  and an array of invertebrates  not associated with nest mate recognition.After the elucidation, based on 10 colonies, of the recognition system of  Skinner . TherefoF. exsecta colonies were marked the first time they were found with a unique number, and their position recorded using GPS (Garmin eTrex). All colonies had been genotyped at ten DNA microsatellite loci , Rovholmar (5-ha), and Furuskär (30-ha), all adjacent to the Tvärminne Zoological station, on the Hanko peninsula in Southern Finland .Although und Fig. . We measZ)-9-alkene profiles found in the populations. Each logger was placed 5 cm below the mound surface, and logged temperature every hour. This was also carried out from 16th May to 1st September 2010 and again from 20th April to 15th June 2011. These data were used to calculate the average mound temperature over each study period and over the three study years for each colony. During both 2009 and 2010, nine loggers also recorded the relative humidity every hour in nest mounds. Again, the average relative humidity was calculated for each mound, separately for the 2 years, and overall.To quantify variation in mound temperature, we placed temperature loggers (Thermochron iButtons), from August 6th to September 2nd 2009, into the mounds of ten colonies that covered the entire range of  using high temperature GC/MS methods  connected to an Agilent 5975 MSD (quadropole) mass spectrometer . The GC was equipped with a ZB-5HT column , and the oven temperature programmed from 50 to 110 °C at 40 °C.minZ)-9-alkene or n-alkane calculated using the total amount of (Z)-9-alkenes or n-alkanes, respectively. Five (Z)-9-alkenes (C23:1–C31:1) and five n-alkanes (C23–C31) were identified, but in both cases the C31 compounds were present only in trace amounts in <50 % of individuals. These C31 compounds were omitted from all analyses. In addition to the three dominant compounds each of (Z)-9-alkanes and n-alkenes included in earlier studies, a fourth one (either C29:1 or C29) of each was present in low amounts in all samples, and was included in the analyses. Three percent of samples had low ion counts (<1E+7) and were discarded, as low concentrations can distort the profile. The (Z)-9-alkene or n-alkane colony profile was determined from the ten workers collected in 2008, and from five workers collected in 2010, for each colony.The peak area of each hydrocarbon was integrated manually from the total ion chromatogram, and then the proportion of each (Z)-9-alkene and n-alkane profile stability in the subset of colonies that were sampled in both study years (N = 33), we examined the variance components (REML) among colonies and between years within colonies. We followed this up with a linear regression on mean colony factor scores in the two study years and examined both the association between profiles between years, and the intercept for trends in the direction of change. These analyses were carried out in Statistica 10. Throughout, all analyses were carried out separately for (Z)-9-alkenes and n-alkanes.Peak areas were log normalized using the Aitchison transformation (Aitchison ST), using the program Fstat 2.9.3.2 (Goudet Z)-9-alkenes and n-alkanes], and spatial and genetic distance between every pair of colonies were tested using a Mantel test -9-alkene or n-alkane profile. In addition, we used partial correlations to test for effects of temperature and humidity in a subset of colonies. Colony size, head width, and shading were standardized to improve normality of residuals, which was verified by examining residual plots as described in Zuur et al. (P > 0.15), sequentially, to achieve the minimal model with only significant terms (P < 0.05). Each dropped term was retested by adding it back into the final model, in order to verify that the (non-) significance of the term was not contingent on the order in which it was removed from the model. These statistical analyses were conducted in GenStat 12.2.0.3717, VSN International Ltd.We used general linear models (GLM) to test for environmental (mound exposure) and colony-specific  effects on colony chemical profile, as represented by the mean of the factor scores of the -9-alkene  (data not shown) chemotypes, both across the entire population and on each island. The first factor (PCA) explained 80 % of the total variation in the four (Z)-9-alkenes, but only 59 % of the total variation of the four n-alkanes. The loadings for the first factor (PCA) for C23:1 and C25:1 were negative , whereas those for C27:1 and C29:1 were positive . For the (Z)-9-alkenes, between-colony variation explained 96 % , between-island variation explained 0.2 % , and within-colony variation (error variance) explained only 4 %, of the total variation along the first factor. Individual compounds all produced the same outcome , between-island variation explained 21 % of the variation , and within-colony variance (error) explained 34 % of the variation; the last mentioned was considerably higher than that for the (Z)-9-alkenes. Again, individual compounds produced largely similar outcomes, except that C27 produced no among-island differences (Supplementary Table The distribution and range of colony-specific profiles of the 83 colonies sampled in 2008 indicated a wide range of (Z)-9-alkenes and n-alkanes chemical distances increased with increasing genetic distance . For (Z)-9-alkenes, spatial distance did not correlate with chemical distance , but for n-alkanes, the chemical distance increased with spatial distance . No correlations were found between spatial and genetic distance for either type of compound .Chemical, spatial and genetic data were available for 72 colonies across the three islands. Both (Z)-9-alkenes and n-alkanes. Colony of origin explained 91 % of the total variation in the (Z)-9-alkene factor scores , and year of sampling also explained a significant, although small, proportion (5 %) of the variation within each colony . Individual compounds gave the same pattern , but no significance for the intercept .Analysis of the variance components for colonies sampled both in 2008 and 2010 revealed a year effect for both . Colony of origin only explained 20 % and 19 % of the total variation . All four compounds, individually, also gave a very similar pattern -9-alkenes, we found no association between colony-specific n-alkane factor scores between years . As for the (Z)-9-alkenes, the intercept was not significant . The same pattern applied for each compound individually -9-alkene profile , with polygynous colonies showing a preponderance of shorter-chain compounds; i.e., they had a C23:1-rich profile. Given that colony size also had an effect on the chemical profile , this effect was partly due to differences in colony size between the two social types. Thus, when combining the information from the factor scores for each compound and colony type/size, shorter-chain compounds dominated in polygynous colonies, as well as more populous monogynous colonies, whereas longer-chain compounds dominated in less populous monogynous colonies. In the case of n-alkanes, we entered island as a main effect in the model, as the earlier analysis indicated differences among islands for both factors. Factor 1 scores also decreased with increasing within-colony relatedness  explained a borderline significant amount of variation in the . Mound exposure ranged from completely exposed (<1 % cover) to largely shaded . This indicated that most mounds were relatively exposed, which is typical for this species. Larger colonies were more shaded , but there was no effect of shading on worker size . We found no association among worker size, mound exposure, nor any of the other tested variables or their interactions, and the (Z)-9-alkene factor scores , which suggests that colonies had different microclimates. Like temperature . Average temperature and humidity were not correlated , and neither was correlated with colony exposure . Neither colony temperature nor humidity correlated with the (Z)-9-alkenes , 16.4–22.8 °C in summer (2010) and 18.1–21.7 °C in autumn (2009). The average temperature of colonies was highly correlated among study years -9-alkenes, between-colony variation accounted for 96 % of the total variation, and within-colony variation accounted for only 4 %. By contrast, for n-alkanes, between-colony differences explained 45 % of the variation and within-colony variance (error) 34 %. Moreover, for a given colony, the (Z)-9-alkene profile was consistent, whereas the n-alkane profile was more variable among years. This supports an earlier interpretation that the (Z)-9-alkene profile conveys information on colony identity -9-alkenes, provides an anti-desiccation function.As expected, chemotypic variation among colonies was very high, both across the entire population and on each island. For (Z)-9-alkenes and significant segregation for n-alkanes, yet we found correlations between genetic and chemical distance for both groups of compounds, such that chemical distance increased with genetic distance. This suggests a genetic influence on the CHC profile, as demonstrated earlier in a smaller data set -9-alkene profiles, although the change was non-directional. The findings that 91 % of this variation was explained by colony of origin, and that the between-year relationship was highly significant, again supports the role of (Z)-9-alkenes as recognition cues -9-alkenes, as would be expected if their primary role is protecting ants from the environment  explained a small (5 %), but significant, proportion of variation in colony-specific . This is in agreement with earlier findings from four polygynous populations, containing a total of 37 colonies, chemotyped across Europe; these all had C23:1-rich and C27:1-poor profiles -9-alkene profile, and an interaction between social type and colony size, such that more populous colonies had more C23:1-rich profiles. Given that polygynous colonies of this species are more populous than monogynous ones -9-alkene profile, and also among colony size, colony age, and worker size, we found no association between worker size and (Z)-9-alkene profile. This most likely is due to the fact that although polygynous colonies are larger, they have relatively smaller workers. We found, however, a small change in the colony-specific profile between 2008 and 2010 for the (Z)-9-alkenes. Apart from environmental differences between the two sampling periods, only age and size of the colonies might have changed. As colony age had no effect on either (Z)-9-alkene or n-alkane profiles, a change in colony size seems likely.Although there was an association between colony size and (Z)-9-alkenes in all nine F. exsecta colonies under study, thereby maintaining the chemical differences among the nine colonies. This change was transitory, as by the autumn of 2010 colony profiles had returned to their pre-summer positions -9-alkenes responded to environmental factors, but often in different ways, indicating that their production is controlled by different genetic pathways. In particular, n-alkane profiles showed patterns of variation that corresponded to both population structuring and spatial distance, at scales much greater than those previously found between colonies. This would help explain why there is a large difference between within-colony and between-colony variation in (Z)-9-alkenes, but not for n-alkanes, and supports the primary role of (Z)-9-alkenes as recognition cues and that of n-alkanes, and other cuticular lipids, as anti-desiccants.In summary, the conjecture that genetic factors are the most likely source of between-colony variation in CHCs is supported by our study. Both ESM 1(DOC 194 kb)Below is the link to the electronic supplementary material.


Next generation sequencing platforms and high-throughput genotyping assays have remarkably expedited the pace of development of genomic tools and resources for several crops. Complementing the technological developments, conceptual shifts have also been witnessed in designing experimental populations. Availability of second generation mapping populations encompassing multiple alleles, multiple traits, and extensive recombination events is radically changing the phenomenon of classical QTL mapping. Additionally, the rising molecular breeding approaches like marker assisted recurrent selection (MARS) that are able to harness several QTLs are of particular importance in obtaining a “designed” genotype carrying the most desirable combinations of favourable alleles. Furthermore, rapid generation of genome-wide marker data coupled with easy access to precise and accurate phenotypic screens enable large-scale exploitation of LD not only to discover novel QTLs via whole genome association scans but also to practise genomic estimated breeding value (GEBV)-based selection of genotypes. Given refinements being experienced in analytical methods and software tools, the multiparent populations will be the resource of choice to undertake genome wide association studies (GWAS), multiparent MARS, and genomic selection (GS). With this, it is envisioned that these high-throughput and high-power molecular breeding methods would greatly assist in exploiting the enormous potential underlying breeding by design approach to facilitate accelerated crop improvement. IntUnlike regular breeding programmes, the major objective of phenotyping in GS is to predict GEBVs rather than selection of genotypes , 107. PrBy its nature, GS focuses on genetic improvement of QTs rather than understanding their genetic basis , 115. Inin silico and Peleman and van der Voort [Ideotypes or ideal plant types are known to plant breeder, since 1968 when Donald  defined er Voort  describein silico designing of a superior genotype through combining desirable loci (https://www.integratedbreeding.net/ib-tools/breeding-decision). The concept of breeding by design includes (i) locating genes/QTLs associated with important traits (ii) exploring the allelic variation at these loci and the estimation of phenotypic effects of these allelic variants (iii) choosing desirable recombinants by targeting marker/haplotype-defined genomic fragments , 118. ReAvailability of highly saturated genetic maps and populations like ILs has facilitated fine mapping of various QTLs . FurtherOnce genetic loci influencing the expression of the trait have been mapped precisely, allelic variants at all these loci can be mined along with their relative contribution to complex traits, and highly resolved marker haplotypes could be recovered for several agriculturally important traits . With thMoreover, precise phenotyping or phenomics is one of the major bottlenecks in capitalizing the full potential of breeding by design concept . TherefoRapidly decreasing genotyping and sequencing costs are dramatically changing the scenario of genomics-assisted breeding. For instance, a shift has been seen from biparental to multiparental populations, and, with the help of various NGS-based sequencing platforms, a detailed genetic analysis of these complex mapping resources would likely to be feasible. Moreover, extensive recombination and multiallelic nature of these lines make them an excellent platform for practising multiparent MARS and GS. More importantly, the development of such public resources like MAGIC and NAM would strengthen the community-based research approach . Additionally, by virtue of eliminating need for any prior QTL information, MARS and GS schemes would save time, money, and energy that is required for finding significant gene-trait relationships. Still, realization of immense potential of all these approaches would greatly rely on throughput, precision, and cost effectiveness of phenotyping techniques. Though, precise phenotyping has always been a potent limiting factor in genetic analysis of QTs, efforts are underway to meet the growing demands for accurate and HTP screening against various biotic/abiotic stresses. It is envisaged that parallel developments in the next-generation phenotyping systems would help in making GS a practical reality in case of plant species as well. Therefore, rising molecular breeding methods like MARS or GS would enable harnessing unexplored genetic variation to a greater extent, thereby facilitating speedy development of superior cultivars.


Here, most pair-wise interactions in the network are replicated in an independent eight-generation advanced intercross line (AIL). The original report showed an important contribution of capacitating epistasis to growth, meaning that the genotype at a hub in the network releases the effects of one or several peripheral loci. After fine-mapping of the loci in the AIL, we show that these interactions were persistent over time. The replication of five of six originally reported epistatic loci, as well as the capacitating epistasis, provides strong empirical evidence that the originally observed epistasis is of biological importance and is a contributor in the genetic architecture of this population. The stability of genetic interaction mechanisms over time indicates a non-transient role of epistasis on phenotypic change. Third-order epistasis was for the first time examined in this study and was shown to make an important contribution to growth, which suggests that the genetic architecture of growth is more complex than can be explained by two-locus interactions only. Our results illustrate the importance of designing studies that facilitate exploration of epistasis in populations for obtaining a comprehensive understanding of the genetics underlying a complex trait.Dissection of the genetic architecture of complex traits persists as a major challenge in biology; despite considerable efforts, much remains unclear including the role and importance of genetic interactions. This study provides empirical evidence for a strong and persistent contribution of both second- and third-order epistatic interactions to long-term selection response for body weight in two divergently selected chicken lines. We earlier reported a network of interacting loci with large effects on body weight in an F This study provides evidence for a strong and persistent contribution of epistatic interactions to the selection response in two chicken lines subjected to 50 generations of divergent selection for 8-week body weight. We show that the genetic architecture of the trait involves genetic interactions of both second- and third-order and that, together, they explain a large portion of the phenotypic divergence between the lines. By replicating a radial epistatic network found in an independent intercross from the same founder individuals, we show that the type of genetic interactions affecting this complex trait is persistent over time. In addition to replicating pair-wise interactions, the size of the pedigree also facilitated evaluation of third-order interactions, which allowed us to further describe the complex genetic mechanisms underlying growth phenotype in chicken. Moreover, a new approach for measuring and detecting capacitating epistasis was proposed. By showing the importance of third-order epistasis in this system, we reinforce the importance of taking it into account when designing experiments aimed at elucidating the genetic architecture of complex traits. The regulation of most biological traits is complex and results from the action and interaction of multiple genes and environmental factors. Phenotypic variability within populations resulting from polymorphisms in the genes regulating these traits is the key to evolutionary change of the phenotypes over time, resulting from natural or artificial selection (selective breeding), as well as differences in responses of individuals to e.g. environmental challenges leading to disease. Identifying key polymorphisms and how they contribute to trait expression, i.e. dissection of the genetic architecture of the trait, is therefore of considerable interest in fields such as evolution, agriculture and medicine. The availability of affordable, large-scale assays of genome-wide genetic variation has facilitated a large number of studies to elucidate the genetic regulation of complex traits. The focus of studies has generally been to identify the effect of individual polymorphisms on trait expression, and in this way several individual genes and polymorphisms making large contributions to trait expression have been identified 2 cross between the selected lines In genomics, gene interaction networks have been evidenced in numerous biological systems using e.g. expression profiling 2 population et alGrowth9, was shown to contain two independent QTL, which were then designated Growth9.1 and Growth9.2.To replicate and study the QTL inferred in the original population, an eight-generation advanced intercross line (AIL) was bred from the founder individuals of the original FHere, we used the large AIL pedigree to study whether the original finding of strong epistatic interactions in QTL network replicated in this independent dataset and to explore the network further by extending the analyses to also include three-locus interactions. By replicating, fine mapping and extending the QTL-network in this independent population, we show that the epistasis can be stable across generations, i.e. the estimates of the QTL interactions are similar, and that interactions higher than second order are important in the genetic architecture of the selected trait. The implications of the replication of epistatic interactions across generations and novel insights that can be gained from also studying three-locus interactions are discussed. Suggestions are also given concerning designs of future studies to elucidate the role of epistasis in the genetic architecture of complex traits. A new method for performing genome wide scans for third order interactions is also introduced.When a locus acts as a capacitor, its genotype modifies the genetic effects of other loci to be either smaller or larger. For third order epistasis, capacitation can be studied by examining the genotype-phenotype map for triplets of loci, and comparing differences between the “planes” or “slices” of the three dimensional map. Each plane is a two-locus genotype-phenotype map and the effect of the third locus is observed as the distance between the planes for the other two loci . Let us pR) the capacitating epistatic effect of each locus in a given triplet can be quantified. Calculating this type of measure is computationally efficient compared to regression-based methods, which opens new possibilities for developing more refined strategies for identifying gene-gene interactions. However, scaling and significance testing is not straightforward, as the range of the ratio is strongly affected by the magnitude of the smallest variance. Screening for an effect of loci on the variance rather than the mean appears to have a large potential for identification of interacting loci and the computational efficiency should make exhaustive scans of large data sets feasible in spite of the high dimensionality.By measuring the ratio between the plane with the highest variance and the plane with the lowest variance  also present in the AIL and ii) displayed the same type of capacitating epistasis as in the F2 population.From Growth9 QTL was shown in Growth9.1) in the remainder of this report. The genotypes at the markers that displayed the strongest interactions in each chromosome segment  as well as epistatic  interactions was fitted for all pairs of markers in the nine segments as in  segment  were useGrowth9 at the center Growth9) released the effects of the three radial loci  and second, that high-line alleles at the radial loci released the effects of the central locus. Consequently, the total effect of the network could be released (or suppressed) by introduction of high-weight (or low-weight for suppression) alleles either at the central locus or at the radial loci. Here, we tested whether this radial network architecture and capacitating reciprocal interaction could be replicated, and potentially also extended, in the AIL pedigree.Strong epistasis was previously reported in a radial QTL network with Growth9 as in the original study Growth9 high-line (HH) and low-line (LL) homozygote backgrounds and reciprocally the additive effects of Growth9 in the HH- and LL-backgrounds for the radial loci.To evaluate the contribution of capacitating epistasis to body-weight, one needs to estimate the contribution of the loci in a fully capacitated network as well as in a fully suppressed network. Assuming that the main capacitation occurs in the radial network topology around Growth9 for five  of the eight QTL. They differed either by being significantly higher in the HH genetic background and/or by being significant in one of the genetic backgrounds and non-significant effect in the other  were part of the original epistatic QTL network detected in Growth9 . The decrease in effect is thus much larger (33%) when compared against the parental line difference than when compared to the available variation in the analyzed pedigree (13%). This is a result of the small absolute size, and thus variation, of the F8 generation, which constitutes a large part of the pedigree; the standard deviation of the F8 generation is 127 g, compared to 187 g in the original F2 cross.In the AIL, the additive effects differed in HH and LL backgrounds at he other . Four of Growth9  and explckground . A re-anGrowth2, Growth4, Growth6 and Growth12 were screened using individuals that were high-line homozygous for Growth9 (HH-Growth9 strata) and then screened again using individuals that were low-line homozygous for Growth9 (LL-Growth9 strata), and so on until all segments had been screened for all data. The results of these scans are shown as bootstrap-averages in The regions that displayed capacitating epistasis in the single marker analysis described above were subjected to further analysis to evaluate the robustness of the pair-wise interactions in the radial epistatic network. For this analysis, one-dimensional QTL scans were performed in all the HH- and LL- stratified data sets described in the Growth2, Growth4, Growth6 and Growth12), only the HH stratum (except a single maker in the Growt6 LL stratum) showed a QTL signal above the significance threshold across the Growth9 region (including both 9.1 and 9.2)  . Growth4Growth2, Growth4, Growth6, and Growth12); that is, the individuals were assigned to one of five groups depending on whether they were HWS homozygous for 0, 1, 2, 3 or 4 of the radial loci. From these five groups, individuals that were HWS or LWS homozygous at Growth9 were separated to obtain in total 10 genotype-classes for which sex and generation corrected phenotypic means were calculated. The results, presented in Growth2, Growth4, Growth6, Growth9 and Growth12 gave the highest and lowest phenotype values, respectively; ii) Only in the Growth9 HH homozygous genotypic background did the predicted phenotype increase with the addition of HWS alleles at the radial loci.To examine the effects of higher order interactions, we estimated a partial, model-free, genotype-phenotype map using the observed phenotypic mean for each genotype. Here, the phenotypic means were calculated for a subset of genotype classes to which the studied individuals were assigned. Individuals were classified based on the number of HH genotypes they carried in the four non-transgressive radial loci  framwork Growth9, which can be detected in a QTL scan for marginal effects, is caused by an individual genetic effect of Growth9 in combination with capacitation by beneficial alleles at the four radial loci. The same holds for the marginal additive effects of Growth2, Growth4 and Growth12, which also supports the original observation from The results from the predicted multi-locus GP-map is thus in agreement with the results from analyses of the stratified data in that LWS homozygosity at Growth2, Growth4, Growth6, Growth9 and Growth12) and the QTL Growth1. Growth1 was included because it had a strong individual marginal effect, displayed suggestive interactions in the exhaustive 2D-scan  affecting growth nor how inter-dependent the genetic effects of these loci were in determining growth. Therefore, in our genetic analyses we first sought to detect loci determining the trait and then estimate their effects by calculating phenotypic means for k-locus genotypes (k> = 1). Although technically the upper bound is k = n, very high order effects are not likely for mechanistic reasons and difficult to detect due to the rarity of the individual genotypes for high n. When k<n, the phenotypic means will be an average across the genotypes of all the remaining (n-k) loci that affect the trait. If there are no interactions between the k primary loci and the remaining (n-k) loci, these analyses will provide estimates of genetic effects that sum to the total genetic effects on the trait. If there are interactions, however, they will not. To explore how results are affected by taking averages over different subsets of loci, we estimated the phenotypic means for the detected QTL using k = 1, k = 2 and k = 3 . Growth4, Growth9 and Growth12). The effect of considering multi-locus genotypes for phenotypic predictions is shown by the increase of explained variation with higher values of k.If a complex trait determined by a, c: Growth1-Growth6-Growth12; b, d: Growth4-Growth9-Growth12). In the Growth4-Growth9-Growth12 triplet, the difference in weight between the genotype with the highest phenotypic value (HH-HH-HH) and that with the lowest (HH-LL-LL) is 207 g. This number nearly doubles the expectation from the summation of the individual effects of the loci  genetic variation, which has earlier been implicated as a source of Selection Induced Genetic Variation (SIGV) The cryptic genetic variation that this epistatic mechanism can hide in a population also has implications for estimation of the heritability in that population, because the marginal genetic (additive) effects of individual loci in a network involving capacitating epistasis will be highly dependent on the allele-frequencies at the other loci in the network. This is clearly illustrated by the network studied here, where the sum of the marginal genetic effects is much higher in a HWS genetic background (i.e. a capacitated network), than in a LWS genetic background (i.e. a suppressed network). The genetic potential Replication and cloning of complex trait loci becomes more of challenge for loci in capacitation networks. As the effects of the loci are context dependent, it is not possible to use traditional approaches to identify single, main loci and then replicate and clone these independently using standard methods. Instead, it becomes necessary to first identify the interacting loci, which in most cases is difficult due to the costs and work involved in generating sufficiently large datasets, and then to thoroughly identify the dependencies between the interacting loci. Only once that is done, is it possible to develop an appropriate strategy for simultaneous replication and cloning of the key loci. Due to the complexities and the cost involved, we can expect that the ability to identify and clone causative mutations using top-down approaches will impede progress in identifying new loci for multifactorial disorders where capacitation is important.PR measure suggested here, or variations thereof.The potential impact of capacitating genetic interactions in evolution is considerable. The existence of key loci that suppress and release cryptic variation in response to selective forces will allow populations to either stably maintain a robust phenotype while adapted to an environment , or facilitate a rapid phenotypic change in response to changing environments by releasing the selectable genetic variation by capacitating the genetic network through the master regulator loci. It will therefore be of great interest to in a directed way search for capacitating epistasis in evolutionary studies using the Using a large multigenerational pedigree we are able to demonstrate replication of a multi-locus QTL interaction network in vertebrates. Our results show that the type of interactions detected in the original population replicate to a considerable extent, both regarding the loci included as well as their combined effects. Due to the large population size we were also able to include analyses of higher order interactions that show that the primary interaction mechanism, genetic capacitation, is a main feature of the network that involves not only pairs but also triplets of loci. Based on these results we introduce the idea that high order epistasis can be studied by examining the variance differences between genotypes in multi-dimensional genotype-phenotype maps.This study provides further evidence for the importance of genetic interactions in determining complex phenotypes and indicates that the value of epistatic analyses in studies aiming at genetic dissection of the architecture of complex traits.An eight generation Advanced intercross line (AIL) was produced from two selected lines of chickens obtained by bi-directional, single trait selection for bodyweight at 56 days of age (referred to as the High Weight Selected “HWS” and Low Weight Selected “LWS” lines). The lines originate from a common base population, consisting of crosses of seven partially inbred lines of White Plymouth Rock chickens 0, at all autosomal loci was calculated as 0.146 and 0.156 in the high and low lines, respectively 1 progeny, 10 HWS males were mated with 22 LWS females and 8 LWS males were mated to 19 HWS females). About 100 individuals were produced in generations F2, F4, F5, F6 and F7 and 300 and 400 individuals in generation F3 and F8 respectively. The F8 generation has undergone the most number of recombination events and should therefore give the best resolution, which is why it is also the largest. The f3 generations was increased in number in order to provide power to detect variation that might be lost deeper in the pedigree.Individuals from generation 40 of the HWS and LWS lines were used as founders for the AIL. The sex-averaged 56-day body weight at this generation was 1522 g (SE: ±36 g) for the HWS line and 181 g (SE: ±5 g) for the LWS line. The observed mean heterozygosity, H2 generation n = 1529) were genotyped for the set of 384 markers using the GoldenGate assay  at the SNP technology platform in Uppsala (Sweden).Nine chromosome regions with significant or suggestive QTL for body weight in the FTo study the effects of the radial network we used the stratification based QTL interaction analysis employed in Growth1, Growth2, Growth4, Growth6, Growth9 and Growth12), yielding a total of 12 subsets. The sizes of the strata varied between 229 and 377 individuals. These stratified datasets were then used for the interaction analyses.We generated a series of stratified datasets, i.e. subsets of the data that contained only the individual most likely to be homozygous at a conditioning locus. Two strata for each conditioning locus (one stratum with the LL homozygotes and one with the HH homozygotes) was produced using the genotypic contrasts at the marker position in each selected chromosomal segment that had the strongest indication of epistasis in the two-dimensional QTL scan. We stratified using six conditioning loci  map was constructed using the “transformation” operation in NOIA Loci defined as epistatic in the two-dimensional scan were included in a joint network analysis as follows: initially, all marginal and two-way interactions for epistatic loci in the network were estimated jointly using the NOIA framework In addition, phenotypic means of genotype classes were estimated directly using a discretized version of the data set. Genotypes of each individual were discretized at the marker positions based on the genotype contrast value. The contrasts ranged from −1 to 1, with 0.4/−0.4 used as thresholds for assigning a HH, HL, or LL genotype to a marker. These thresholds are conservative , to reduce the number of falsely assigned homozygotes because they are most critical to the outcome. However, because most individuals had accurately estimated genotype probabilities, i. e. contrast values close to −1, 0 or 1, the choice of cut off has little effect on the outcome. We also used the discretized data in a second order interaction model-based NOIA-approach, and constructed a partial GP map directly from the phenotypic means of individuals with given genotypes. The observed means of the genotype classes were then compared to the expected ones from the NOIA model. Differences between these values are an indication of the effect of higher order interactions.Discretized data were used to study three-way interactions. For a set of triplets of loci, the phenotypic mean (again corrected for sex and generation) for each three-locus genotype was calculated. Thus, for each triplet of loci, means were calculated for 27 classes of individuals, each corresponding to a three-locus genotype. Since each genotype was scored separately, any type of interaction was detected from the pattern of these values. For detection of capacitating epistasis, the 27 means were grouped into three “planes,” where each plane consists of the nine genotypes that shared a single genotype of the potentially capacitating locus . Then, the variance within each plane was calculated together with the ratio between the planes with highest and lowest variance. This ratio measures the capacitating effect of the conditioning locus.Figure S1Complete 2D scan. The profile of an exhaustive 2D QTL scan over all markers in the data set.(PDF)Click here for additional data file.Figure S2Growth9.1. The phenotypic values were predicted using the NOIA model framework. The values are plotted as a function of the degree of HWS and LWS homozygosity at its interacting loci Growth2, Growth4, Growth6 and Growth12. The error bars represent s.e.m.Parametric genotype-phenotype maps in HWS and LWS genetic background at (TIFF)Click here for additional data file.Figure S3pR-values for all possible loci combinations. Panel a shows all values, in decreasing order, from all possible combinations within the six loci set. . Panel b shows a histogram of these values.Distribution of (TIFF)Click here for additional data file.Text S1Prediction of multi-locus network effects using a parametric genotype-phenotype map.(DOC)Click here for additional data file.


In quantitative trait mapping and genomic prediction, Bayesian variable selection methods have gained popularity in conjunction with the increase in marker data and computational resources. Whereas shrinkage-inducing methods are common tools in genomic prediction, rigorous decision making in mapping studies using such models is not well established and the robustness of posterior results is subject to misspecified assumptions because of weak biological prior evidence.a posteriori point estimation. The performance of the method is evaluated by using two publicly available data examples: the simulated QTLMAS XII data set and a real data set from a population of pigs.Here, we evaluate the impact of prior specifications in a shrinkage-based Bayesian variable selection method which is based on a mixture of uniform priors applied to genetic marker effects that we presented in a previous study. Unlike most other shrinkage approaches, the use of a mixture of uniform priors provides a coherent framework for inference based on Bayes factors. To evaluate the robustness of genetic association under varying prior specifications, Bayes factors are compared as signals of positive marker association, whereas genomic estimated breeding values are considered for genomic selection. The impact of specific prior specifications is reduced by calculation of combined estimates from multiple specifications. A Gibbs sampler is used to perform Markov chain Monte Carlo estimation (MCMC) and a generalized expectation-maximization algorithm as a faster alternative for maximum Combined estimates of Bayes factors were very successful in identifying quantitative trait loci, and the ranking of Bayes factors was fairly stable among markers with positive signals of association under varying prior assumptions, but their magnitudes varied considerably. Genomic estimated breeding values using the mixture of uniform priors compared well to other approaches for both data sets and loss of accuracy with the generalized expectation-maximization algorithm was small as compared to that with MCMC.Since no error-free method to specify priors is available for complex biological phenomena, exploring a wide variety of prior specifications and combining results provides some solution to this problem. For this purpose, the mixture of uniform priors approach is especially suitable, because it comprises a wide and flexible family of distributions and computationally intensive estimation can be carried out in a reasonable amount of time. Genetic association studies, quantitative trait loci (QTL) mapping and genomic prediction rely on increasingly dense DNA information such as single nucleotide polymorphisms (SNP). The increasing abundance of marker data amplifies one of the essential statistical problems in such studies: the number of potential explanatory variables represented by single markers is often larger than the number of observations in the sample studied, and some regularization is required to ensure the identifiability of the marker effects. Suitable statistical models can accomplish this regularization by variable (i.e. marker) selection, shrinkage of marker effects towards zero or a combination of these two strategies -4.Many variable selection and shrinkage techniques based on Bayesian modelling and Markov chain Monte Carlo (MCMC) algorithms have been proposed for genetic association studies, QTL mapping and genomic prediction see ,6). They. They6])a posteriori estimation , and compared it to other methods in the context of QTL detection . Compareion (see ).Bayesian shrinkage methods are common tools in genomic prediction, but rigorous decision making in the context of QTL detection via such models is not well established . Here, wa posteriori (MAP) point estimation  or in , with the effect size limit set to l>b. If the three hyper-parameters p0, b and l are appropriately chosen, this density has a narrow peak around zero and is flat on the rest of its support. Thus, this density is a step function, resembling a spike and a slab [(|βm|), the posterior probability of the hypothesis can be expressed as P(Sm=1|data). To obtain the Bayes factor for the two competing hypotheses H1: Sm=1 against H0: Sm=0, the posterior odds is divided by its prior odds [As in our previous study, we calculated the Bayes factor for the hypothesis that the absolute value of the marker effect exceeds a certain threshold value to assess the strength of the association between the phenotype and a single marker henotype . In the ior odds ,33:P(Sm=1)=1−p0 is readily available from the prior specification of βm in MU.where the prior probability m), as a slight modification to the categories presented by Jeffreys [Kass and Raftery  have sugJeffreys : evidencβm is generally problematic in shrinkage approaches, whereas the prior specification of MU entails a justification for a specific threshold in MU. Unless indicator variables are integrated into the likelihood of the model , most sg. as in , where tβm, another conceptual problem may arise in shrinkage approaches in which improper priors for the effect sizes are used, such as the model proposed in [P(Sm=1|data) and consequently the posterior odds may exist also for improper priors, the prior odds is not available for the complementary hypotheses b<|βm| vs. |βm|≤b, because the integral over the prior distribution corresponding to the former hypothesis does not exist.Besides the choice of a threshold for posed in  as a modposed in ; althougWe assessed the sensitivity of single analyses by comparing results under varying prior specifications, and for MCMC additionally under identical prior specifications to detect convergence or mixing problems. In addition, we combined Bayes factor information from different analyses to increase the robustness in detecting association signals.i isWe also evaluated the predictive abilities of our model by comparison of genomic estimated breeding values (GEBV) either with the true breeding values (TBV), as available in simulated data sets, or with the phenotype measurements directly, as available in real data sets. The GEBV for individual βm in the case of MCMC or the MAP point estimate in the case of the GEM algorithm, and (xim) is the vector of genotype codes for the individual. For cross-validation of our results, we employed the faster GEM algorithm. Also here, we compared estimates from single prior specifications with combined estimates from multiple ones. A more detailed description of these procedures is given in the following sections.where This simulated data set was originally distributed as a part of the 12th European workshop on QTL mapping and marker assisted selection (QTLMAS XII) held in Uppsala, Sweden, on 15–16 May 2008. Detailed information on the publicly available data  has beenP-values of less than 0.05 after Bonferroni correction in a multiple linear regression including all genotypes of true QTLs. The whole data set available for QTL detection consists of 4665 individuals from a pedigree of consecutive generations. We excluded the 165 individuals of the first generation from our analysis, because they do not form full-sib families of size 10 like the 4500 individuals in the subsequent generations. The founders of each generation were 15 males and 150 females. In the first generation, all individuals were used as parents, whereas in the second and third generation, they were randomly sampled. Each male parent was mated to 10 females, each producing 10 full-sib offspring. Thus, the pedigree actually has a full-sib and half-sib structure. However, we did not take into account the familial resemblance between half-sibs or between parents and offspring from consecutive generations in our statistical model.The simulation of the phenotype involved a total of 50 bi-allelic QTLs with additive effects. Crooks et al.  classifiuk) for full-sib families and extended the regression in Equation (1) toFor simplicity, we merely considered polygenic family effects =2.10, the prior variance of the common intercept α to c=106, and the shape and rate parameters  were all set to 0.01 in the inverse-gamma distributions used as priors of the variance components σ2 [see Additional file s and rate parameter r, its mean has the value s>1, and its variance has the value s>2. Thus, the mean and variance do not exist for our choice of shape and rate parameters because of a heavy right tail. However, the mode exists, with a value of r and s decreasing towards 0, the inverse-gamma distribution approaches the noninformative scale-invariant, but improper prior with density ∝1/σ2.We ran MCMC simulations for four different sets of prior specifications , as well as in a previous study [To assess the predictive abilities of our model, we first calculated GEBV for the validation individuals, using the posterior means of the effect sizes, us study . FurtherWe evaluated these GEBV for single prior specifications and their averages across the four prior specifications considered. As in , we asseuk, from the model. Instead of using the original phenotype and genotype information, we standardized the phenotype and the genotype codes at each SNP to have a sample mean of 0 and a variance of 1 in the training set. The GEBV were then estimated as above and translated back to the original scale. The GEM algorithm for one prior specification required 3 to 14 seconds and 19 to 125 iterations to converge on the same computer as mentioned above (with a 3 GHz processor and 2 GB memory). Convergence was declared when the sum of deviations between current and updated parameter values was smaller than (M+2)×10−7, where M+2=5896 is the number of parameters in the model.We also obtained GEBV from the GEM algorithm and assessed their predictive ability as just described. Again for simplicity, we excluded the family effects, As TBV are only available in simulated data sets, we also applied a cross-validation (CV) approach as a method to assess predictive ability of the model in real data sets. Here, we used only the 4500 individuals in the three training generations. Specifically, we used two different 10-fold CV strategies: (I) we randomized the data into 10 distinct validation sets, each holding 45 full-sib families, i.e. all members of a family belonged to the same validation set; (II) each of the 10 full-sibs of a family was randomly assigned to a different validation set. To predict GEBV for the individuals of a single validation set, the other nine sets were combined to form the training set. We divided the correlation between GEBV and phenotype by the square root of heritability h=0.30 to conveTo test the predictive ability of our method in real data, we analysed a pig data set made available by Pig Improvement Company (a Genus company) to the scientific community . Here, wA total of 52 843 SNP were contained in the genotype data made public. The original genotype codes were 0, 1, and 2 for the three SNP genotypes, respectively, and for missing genotypes (< 1%), a non-integer between 0 and 2 had been imputed =2.10). We defined a summary statistic for the number of QTL based on the marker-specific indicator variables by Y) was used as an approximation of the phenotypic variance, ignoring the relatedness between the individuals studied. Here, the variance component We begin with an overview of the posterior estimation for the model parameters, with the exception of marker-specific parameters and compare results obtained from the eight MCMC chains A-H. Table ter 7 in ).b=0.01 (chains A vs. B and E vs. F) than when it was set to b=0.001 (chains C vs. D and G vs. H). Thus, at least for these parameters, the prior specification b=0.001 yielded more robust results.For the common intercept, somewhat higher deviations of the posterior results were observed between chains with identical prior specifications when the border value of the effect sizes was set to σ2. The point estimates for the between-family variance σ2. This indicates that the polygenic effects, uk, absorbed rather little phenotypic variation in the simultaneous analysis of all chromosomes, which is consistent with the results reported by Lund et al. [b=0.001, i.e. in chains C, D, G and H, since b=0.01. Here, we should note that the true heritability of the trait for the full pedigree data is 0.30 [All chains produced virtually identical estimates for the residual variance d et al. . Since td et al. ). Althou is 0.30 , which cNQ for the number of QTL were, as expected, higher for the chains with p0=0.99, i.e. with a smaller prior probability of marker exclusion. Here we note that the prior mean of NQ is M·(1−p0). Thus for p0=0.99, the posterior mean values between 24 and 33 were lower than the prior mean of 60. In contrast, the prior mean of NQ was 6 for p0=0.999, but the posterior means were larger with values ranging from 14 to 22. In this sense, the intuition that the prior specifications with p0=0.999 are more conservative is confirmed. We also observed that the chains with b=0.01 produced lower posterior means of NQ for fixed p0. This result is intuitive also, since marker indicators are expected to reach the value 1 more easily, when the interval  is shortened.Estimates of the summary statistic M=5894 markers: for each marker, we calculated the Bayes factor for the hypothesis Sm=1  in each of the eight MCMC chains A-H. Next, we ranked the Bayes factors within each chain and calculated a marker-specific mean rank across chains as a measure to summarize information from the eight chains. This was done to increase the robustness in assessing the strength of evidence by making the results less dependent on the specific choices of the hyper-parameters in single MCMC chains.Two of our main goals were (1) to assess how well MU identifies true QTL in this data set and (2) to evaluate the risk of false positive QTL detection when applying the Bayes factor as the measure of the evidence in favour of marker association. In Table 2, the 20 markers with the strongest signals in our analysis are listed. Here, we used the following criterion to rank the strengths of association from all m)averaged across chains as a consensus measure of evidence, the minimal and maximal means across the chains, and the absolute values of the effect sizes (|βQ|) for the true major QTL as reported in [Epost(βm), from our analysis, because the minima and maxima from the eight MCMC chains could have opposite signs – although this did not happen for the 20 markers reported. Finally, the posterior means of the percentage of phenotypic variance explained are given in Table m is the minor allele frequency of marker m, Y) is as defined above. Note that Epost(%PVE) are estimates for single markers and simply summing them up does not yield an estimate for the entire proportion of variance explained by markers, as covariances due to LD between markers are missed in this sum. However, the proportion of variance accounted for by the regression on markers is captured in our estimates For each of these 20 markers, their position in the genome, minor allele frequency and distance to the closest true major QTL are given in Table orted in . Here wePVE=2MAFm−MAFmEposTwelve of the 15 major true QTL were located within 5 cM from the markers reported in Table Three true major QTL, namely M5, M10 and M11, are absent from Table In the list of the 20 markers with the strongest signals in our analysis, two markers were more than 5 cM from a major true QTL and would have been considered false positives in : one of m) across the chains when multiple chains are considered. Sixteen of the markers shown in Table Up to now, we have considered an arbitrary number, namely 20, of markers showing the strongest signals of association across different MCMC chains. In many empirical studies, a decision making tool is used to classify markers into two groups: markers with ”significant” and ”non-significant” QTL signals. For this purpose, one can apply a threshold of, say, 10 to the average of 2 ln, with a correlation of 0.99, and the weakest agreement between chains C and D (p0=0.999 and b=0.001), with a correlation equal to 0.84. For chains with different prior specifications, the correlation coefficient obtained its lowest value, 0.67, between chains C and E, which differ in both p0 and b.To quantify the robustness among the eight MCMC chains, we calculated pairwise Spearman’s rank correlation coefficients We also report the ratios of the 2 × log-transformed Bayes factors averaged across the 20 markers for pairs of chains in the lower left triangle of Table The comparison of GEBV and TBV in the three validation generations showed accuracies between 0.79 and 0.90 for MCMC-based and GEM-based estimation under the four prior specifications considered (see Table rI and rII from 0.91 to 0.96) than those reported above for the three validation generations. This result supports the expectation that accuracy of GEBV declines for genetically more distant individuals. We did not observe clear differences in the results between the two cross-validation approaches, although keeping the individuals from an entire family together in the same validation set (approach I) increases the genetic distance between training and prediction sets more than assigning individuals from the same family to different validation sets (approach II).The accuracies obtained by cross-validation within the first three generations via GEM were higher (bI and bII), from values below 1 for single prior specifications to values above 1 for the combined estimates.Also for cross-validation, averaging GEBV across prior specifications improved accuracy, when compared to single prior specifications. However, averaging increased estimates of bias  and (4) do not restrict a priori heritability to the range from 0 to 1. For the non-standardized genotype codes used in MCMC estimation, the four prior specifications as ordered in Table h2-values of 7.9, 7.7, 0.86 and 0.78, respectively. For the standardized genotype codes used in GEM estimation, the corresponding h2-values are 20.0, 19.7, 2.2 and 2.0, respectively. Thus, impossible values for heritability, i.e. with values above 1, were implicitly assumed in most of the prior specifications. However, reasonable estimates of accuracy were obtained in all cases and the a priori heritabilities varied far more in magnitude than estimates of accuracy.Finally, we used Equations (3) and 4) to calculate values of  to calcup0 from 0.9 to 0.9999 and b from 0.0001 to 0.036, the best accuracy, with a value of 0.631, was obtained with p0=0.9999 and b=0.008 for the set of 10 000 random SNP (RAND10K). For this combination of p0 and b, the accuracy for the 10 000 SNP filtered by SIS (SIS10K) was only slightly lower, with a value of 0.623. The highest value reported in [b<0.008 yielded lower accuracies, despite the fact that they corresponded to more realistic, i.e. lower, values of heritability, which was 0.62 for this trait.For the tested combinations of orted in  was 0.63b and, for SIS10K and RAND10K, deteriorated with b approaching 0 and b>0.015. In contrast, both RAND1K and SIS1K exhibited the best accuracies for b>0.015, showing horizontally asymptotic-like behaviour for increasing values of b. The accuracies were quite similar for RAND10K and SIS10K, except for b ranging between 0.015 and 0.03, where SIS10K yielded higher accuracies. In all cases, RAND1K had lower accuracies than SIS1K. As mentioned above, the higher accuracies for SIS may be, at least partially, due to the over-estimation induced during pre-selection by SIS.As shown in Figure p0, the accuracy showed very similar behaviour when b was varied. For both RAND10K and SIS10K, accuracies were best for b ranging between 0.005 and 0.012 and deteriorated when b tended towards 0 and also for increasing values of b. In contrast, both RAND1K and SIS1K exhibited the best accuracies for b>0.015, showing horizontally asymptotic-like behaviour for increasing values of b. In all cases, RAND1K had lower accuracies than SIS1K.For all values of b between 0.002 and 0.008 and deteriorated down to 0.2 for increasing values of b. For RAND1K and SIS1K, the bias was more stable with respect to b, with the exception of a considerable bias upward for p0=0.9999 and b between 0.006 and 0.015.For both RAND10K and SIS10K, the least biased estimates, i.e. with regression coefficients closest to 1, were obtained for p0,b), as well as the combined estimates obtained from averaging GEBV across the prior specifications. In contrast to the observations made in the analysis of the QTLMAS XII data, averaging GEBV did not consistently improve the accuracies of single prior specifications. Whereas the best single estimate for SIS10K was 0.62 and the estimate combined across all 16 prior specifications was also 0.62, at least one single estimate in each of the three other SNP sets was slightly superior to the corresponding estimate combined from 16 prior specifications.Tables In this article, we successfully applied MU, a shrinkage-based Bayesian variable selection that we had previously presented in , to the We have compared our results regarding QTL detection and false positive signals to findings from previous studies of the QTLMAS XII data. Overall, our analyses by MU ranked well among the association and mapping methods that were summarized by Crooks et al. . Only ona priori, such as scattering of QTL signals over several markers. Several authors have suggested procedures to improve model performance in such settings: for example removing part of the data to reduce the collinearity  in genome-wide dense marker data may cause problems in multi-locus models that assume mutual independence of predictors ty (e.g. ). This gP-values, the systematic differences in magnitude, that we observed between the Bayes factors from different MCMC chains, demonstrate the problems and limitations of the categories suggested by Jeffreys [The rather strong positive correlations among Bayes factors with QTL signals observed in several MCMC chains suggest an appreciable robustness of the results with regard to QTL detection under varying prior assumptions. Besides its advantages  oJeffreys  and KassJeffreys . SpecifiObviously, an exhaustive sensitivity analysis under varying prior assumptions is necessary in shrinkage-based or other Bayesian variable selection approaches in general. However, we argue that MU provides some solution to the open problem of selecting relevant variables in Bayesian shrinkage approaches (see ), becausFor the purpose of genomic prediction, MU was competitive with other studies in the estimation of GEBV for both data sets. For the simulated QTLMAS XII data set, it is noteworthy that we considered only four prior specifications in our analysis and did not attempt an exhaustive coverage of the hyper-parameter space. For this data set, our main focus was to compare MCMC and GEM estimations. Although point estimation via the GEM algorithm produced accuracies of GEBV that were inferior to accuracies from point estimation by MCMC for the single prior specifications, accuracy for GEM estimation was improved by combining GEBV across prior specifications to almost the same level as MCMC results.b in MU and that the sensitivity increased with the number of markers. Unfortunately, comparison of the sensitivity with other Bayesian genomic prediction approaches was hampered, because accuracies from an extensive search across varying prior specifications in other approaches are not documented for this data set.In the analysis of the real data set, we explored a larger part of the hyper-parameter space and considered a dense grid of hyper-parameter values. Thus, we were able to assess accuracies of GEBV and differences more comprehensively than for the QTLMAS XII data set. Our results showed that the estimated accuracies were very sensitive to the choice of the hyper-parameter In very poorly stated problems with many more SNP than individuals, as in the real data set, it may be beneficial to decrease the number of SNP to reduce this disparity prior to variable selection ,51. ThisPre-selection of SNP surely remains an issue for future research and SIS cannot be the final solution, since some drawbacks of SIS remain unresolved. Because SIS exploits only marginal correlations between markers and the phenotype, and LD between markers is ignored, this approach is associated with a risk that too many SNP in the proximity of a QTL, that carry essentially identical information, are pre-selected. In contrast, SNP with a low marginal correlation but still in LD with a QTL have no chance of entering the set of pre-selected SNP. Methods that simultaneously exploit the connection between SNP and the phenotype and the LD structure between markers could be more appropriate.Three approaches are available for choosing hyper-parameters. First, cross-validation can be employed to detect the optimal prior configuration with respect to the assessment of prediction for some specific set of individuals. This approach is probably the most suitable and most widely used approach for prediction purposes in experimental studies.Second, prior expectation about the heritability and limiting assumptions about the genetic architecture of the trait yield a criterion to calibrate hyper-parameters via the prior variance of additive genetic effect sizes. In this study, we derived such a criterion for MU and tested its performance in the analysis of the real data. However, the results do not support the idea that values of hyper-parameters corresponding to realistic heritabilities according to this criterion positively affect prediction accuracy.As a third alternative to choose hyper-parameters, expert knowledge may be available on the size of hyper-parameters. However, these three approaches are not free of error in practical situations and, therefore, doubt will remain for any specific prior choice. Combining results from varying prior specifications using ”poor man’s” model averaging, as was done here, may provide some solution, as a wider choice of hyper-parameters can be integrated into ”consensus” estimates. For this purpose, an approach like MU is especially suitable, because it comprises a wide and flexible family of prior distributions.a posteriori estimation algorithms such as EM, GEM or variational Bayes algorithms . We havs e.g., ,25). Thi. Thia poThe authors declare that they have no competing interests.All authors were involved in the conception and the design of the study. TK derived the fully conditional distributions for the Gibbs sampler and the GEM algorithm of MU, implemented the C modules, performed the data analysis and drafted the manuscript. All authors participated in the interpretation of results. EL and MJS critically revised the manuscript. All authors read and approved the final manuscript.Complete model specifications and fully conditional distributions. Complete distributional specification of the likelihood and of the priors in MU, derivation of the fully conditional distributions for the Gibbs sampler and their expected values for GEM.Click here for fileC code for the Gibbs sampler. The C implementation of the Gibbs sampler.Click here for fileC code for the GEM algorithm. The C implementation of the generalized expectation-maximization algorithm (GEM).Click here for file


The incorporation of genomic coefficients into the numerator relationship matrix allows estimation of breeding values using all phenotypic, pedigree and genomic information simultaneously. In such a single-step procedure, genomic and pedigree-based relationships have to be compatible. As there are many options to create genomic relationships, there is a question of which is optimal and what the effects of deviations from optimality are.G05), equal to the average minor allele frequency (GMF), or equal to observed frequencies (GOF). A genomic matrix considering random ascertainment of allele frequencies was also used (GOF*). A normalized matrix (GN) was obtained to have average diagonal coefficients equal to 1. The genomic matrices were combined with the numerator relationship matrix creating H matrices.Data of litter size  for 338,346 sows were analyzed. Illumina PorcineSNP60 BeadChip genotypes were available for 1,989. Analyses were carried out with the complete data set and with a subset of genotyped animals and three generations pedigree . A single-trait animal model was used to estimate variance components and breeding values. Genomic relationship matrices were constructed using allele frequencies equal to 0.5  were: 0.79 using G05, 0.79 using GMF, 0.78 using GOF, 0.79 using GOF*, and 0.78 using GN. Accuracies calculated by inversion increased with all genomic matrices. The accuracies of genomic-assisted EBV were inflated in all cases except when GN was used.In Parameter estimates may be biased if the genomic relationship coefficients are in a different scale than pedigree-based coefficients. A reasonable scaling may be obtained by using observed allele frequencies and re-scaling the genomic relationship matrix to obtain average diagonal elements of 1. G) can be calculated by different methods [Traditional genetic evaluation of livestock combines only phenotypic data and probabilities that genes are identical by descent using the pedigree information. Genetic markers for many loci across the genome can be used to measure genetic similarity and may be more precise than pedigree information . Genomic methods ,2.A) and G into a single matrix (H). A BLUP evaluation using H called single-step genomic evaluation has been successfully applied in dairy cattle [H, no further modifications in the standard mixed model equations used in animal breeding have been needed [As an entire population is unlikely to be genotyped in livestock species, Legarra et al.  and Miszy cattle . Besidesn needed .H includes the expression G - A, which is the difference between genomic and pedigree-based relationships. If G is inflated, deflated or in some other way incompatible with A, the weighting of the pedigree and genomic information will be incorrect. Various G used in a genetic evaluation by Aguilar et al. [G may be much larger than those using A [G can lead to different accuracies of EBV [G relative to A.The formula for r et al.  have res using A . Differes of EBV . These dG on EBV and estimates of variance components. The second objective was to develop a strategy to create an optimal G that is easy to create and yields reasonably accurate EBV and estimates of the additive variance.The first objective of this study was to apply different genomic matrices to analyses of litter size in a swine population and evaluate the impact of those Data of litter size  for 338,346 sows, of which 1,919 were genotyped using the Illumina PorcineSNP60 BeadChip, were analyzed. Genotypes of their 70 sires were also available. Genotyped females were crosses of two pure lines derived from the same breeds, and they were born in a two-year span. After quality control procedures, 44,298 markers remained and were used to estimate genomic relationship coefficients. In the quality control analysis, SNP were excluded if: the minor allele frequency was smaller than 0.05, the marker mapped to the sex chromosomes, the chi-square statistics for Hardy-Weinberg equilibrium from males and females differed by more than 0.1, or more than 20% of animals had missing genotypes. Phenotypes were collected in genetic nucleus (pure lines) and commercial herds (line crosses) and the parental lines were included as fixed effects in the model to account for differences in the genetic backgrounds. All analyses were carried out with the complete data set and with a subset containing only genotyped females and three generations of pedigree . Records were analyzed using an animal model. Fixed effects included parity order, age at farrowing (linear covariable), number of services, mating type , contemporary group, sow line and sire line . Contemporary groups were defined by season, year and farrowing farm. The numerator relationship matrix was obtained with pedigree information on 382,988 animals. Prediction error variances (PEV) were obtained by inversion of the coefficients matrix of the mixed model equations.A-1) was replaced by H-1 that combines the pedigree and genomic information [In the animal model, the inverse of the numerator relationship matrix  and n rows , and P is a matrix containing the frequency of the second allele (pj), expressed as 2pj. Mij was 0 if the genotype of individual i for SNP j was homozygous 11, was 1 if heterozygous, or 2 if the genotype was homozygous 22. Frequencies should be those from the unselected base population, but this information was not available. Instead the frequencies used were: 0.5 for all markers (G05), the average minor allele frequency (GMF), and the observed allele frequency of each SNP (GOF). The last option assured that the average off-diagonal element was close to 0. For GMF only, the second allele was the one with smaller frequency.where (GOF*) was obtained by modification of the denominator as in Gianola et al. [A different matrix with observed frequencies a et al. :0 and q0 are expectations of allele frequencies following a Beta distribution with hyperparameters α and β. The values for the hyperparameters were the same as observed in the genotyped animals. A normalized matrix was obtained to have average diagonal coefficients equal to 1:where pGN by the sum of (1 + F) across genotyped animals, where F are individual inbreeding coefficients derived from pedigree. Different from the numerator relationship matrix, values on the diagonal of GN can be smaller than 1. An average diagonal of 1 can also be obtained by multiplying (4) by a constant. A similar relationship matrix with sample variance of 1 was used by Kang et al. [The denominator should assure compatibility with A when either the average inbreeding is low or the number of generations low. Higher levels of inbreeding in the genotyped population can be accommodated by substituting "n" in the denominator of g et al. .G was calculated as G = wGr + (1 - w)A22, where w = 0.95 and Gr is a genomic matrix before weighting. Tests showed that the value of w was not critical. Aguilar et al. [The genomic matrix is positive semidefinite but it can be singular if the number of loci is limited or two individuals have identical genotypes across all markers. It will be singular if the number of markers is smaller than the number of individuals genotyped. To avoid potential problems with inversion, a1) and non-genotyped animals (a2) is:The joint distribution of breeding values of genotyped  using the EM algorithm [The additive variance is on average the same for the entire population, and coefficients of lgorithm .A22 or G) are in Table G05 and GMF, the same allele frequency was used for all markers, and the average of both diagonal and off-diagonal elements was greater than the coefficients in A22. The average minor allele frequency was 0.26. The distribution of frequencies of the second allele was nearly flat  and average off-diagonal elements equal to zero. For all genomic matrices, diagonal coefficients had greater variance than the pedigree-based coefficients. Off-diagonal genomic coefficients had a greater variance only for GOF and GN. Greater variance was expected between the elements of G than A because genomic relationships reflect the actual fraction of genes shared whereas pedigree-based coefficients are predictions. Predictions have smaller variance than the variable predicted when the prediction error is not zero.Statistics of pedigree-based and genomic relationship coefficients for genotyped animals , allows the same expectation of variance for breeding values of genotyped and non-genotyped animals. Assuming that a genomic relationship matrix standardized such as GN produces realistic estimates of additive variance, the use of genomic information resulted in smaller standard errors (0.30) than only pedigree information (0.44).Estimates of variance components obtained with the full data set are in Table a et al.  have demG. Table GN, 456 animals among the 597 would also be selected using A. For other genomic matrices, the number of animals selected in common with GN was: 567 for G05, 568 for GMF, 593 for GOF, and 554 for GOF*.Estimates of breeding values for genotyped animals were on average similar regardless the choice of G05 or GN were similar. When applied to dairy data, Aguilar et al. [G with allele frequencies equal to 0.5 than with either current or estimated base allele frequencies. When the allele frequency is p, the relative contribution to the diagonal of G is (2p)2 for the first homozygote, (1-2p)2 for a heterozygote, and (2-2p)2 for the second homozygote. With p = 0.5, these contributions are 1, 0, and 1, respectively. When the allele frequencies are assumed different from 0.5, these contributions are different for each homozygote. For example, contributions with p = 0.2 would be 0.16 for the first homozygote, 0.36 for the heterozygote, and 2.56 for the second homozygote. Consequently, rare alleles contribute more to the variance than common alleles. It would be interesting to compare the results with a normalized matrix from G05 by multiplying and deducting a constant as in VanRaden [G might be helpful if this does not create a negative eigenvalue.Correlations between pedigree-based EBV and EBV obtained using either ozygote, -2p2 for Statistics on computed breeding values with various relationship matrices are in Table GN, the accuracies using non-normalized G were inflated. VanRaden et al. [Estimates of accuracy obtained using PEV with different genomic matrices are in Table n et al.  have preG. Using the genotyped population as base, A would have to be re-scaled according to G but allele frequencies in the base population would not have to be estimated.Pedigrees may include many generations into the history of the population but must end eventually. In standard genetic evaluations, founder animals are the earliest generation recorded and the assumption is that they do not share genes from older ancestors. Relationship and inbreeding coefficients from later generations are estimated as deviations from the founders' relatedness. Genomic analysis typically reveals that founder animals actually share genes identical by descent, which shift relationship and inbreeding coefficients up or down. Genomic and pedigree-based matrices should be compatible in scale to be integrated. Ideally, genomic relationships should be estimated using the allele frequencies from the unselected base population. This information can be rarely extracted from historical data and approximations must to be used. Errors in the allele frequency estimates may result in biased relationships and consequently biased GEBVs, especially for young animals . Yang etGN had greater variance than the corresponding elements of A22. The variance was greater because individuals equally related in the pedigree have more or less alleles in common than expected. Genomic analysis achieved higher accuracies probably because genomic information improved prediction of the Mendelian sampling terms. More differentiation within families and reduction of co-selection of sibs are expected with genomic-assisted selection because Mendelian sampling can be better estimated. As a result, inbreeding across generations is expected to increase more slowly than it would increase with standard evaluations [Coefficients of luations .We considered only phenotypes of crossbred animals. The performance of crossbred animals is considered a different trait than the performance of purebred animals in routine evaluations of this population. Using a multitrait model, one can predict EBV for elite animals as parents at the nucleus and commercial level simultaneously. However, only additive inheritance is considered in this model and differences in allele frequencies between pure lines are ignored. Cantet and Fernando  have shoG when a greater part of the pedigree was genotyped. An entire genotyped population is rarely found in livestock species, and pedigree and genomic information have to be combined. Estimates of relationships are always relative to an arbitrary base population in which the average relationship is zero. Genomic and pedigree-based relationships must be relative to the same base to be combined in the H matrix. We chose to use the animals with unknown parents in A as the base, and we modified G accordingly. Because there were no changes in the genetic base, the same additive variance is expected when including the genomics coefficients. A practical solution to avoid inflation of the additive variance is to re-scale G to obtain average diagonal elements equal to 1, when off-diagonal elements are already on average zero. In the data set analyzed, average off-diagonal elements equal to zero were obtained using the observed allele frequencies.Estimates of additive variance were sensitive to the choices of Several studies have indicated accuracy gains with the inclusion of genomic information in genetic evaluations via marker regression or identical-by-descent matrices ,17,18. HG are similar to those in A. Adding the genomic information to A results in lower standard errors of additive variance estimates. Accuracies of EBV with the pedigree-genomic matrix are a function not only of the average of diagonal and off-diagonal elements of G, but also of the difference between these averages. The accuracy estimates may be inflated with non-normalized G. Matrix compatibility can be obtained by using observed allele frequencies and re-scaling the genomic relationship matrix to obtain average diagonal elements equal to 1. If allele frequencies in the base population are different from 0.5, rare alleles contribute more to the genetic resemblance between individuals than common alleles.Estimates of the additive genetic variance with pedigree or joint pedigree-genomic relationships are similar when the differences between the average diagonal and the average off-diagonal elements in The authors declare that they have no competing interests.SF performed data edition, statistical analysis and drafted the manuscript. IA developed scripts for genomic computations and helped in statistical analysis. IM provided core software, mentored statistical analysis and made substantial contributions for the results interpretation. All authors have been involved in drafting the manuscript, revising it critically and approved the final version.


Expression traits can vary quantitatively between individuals and have a complex inheritance. Identification of the genetics underlying transcript variation can help in the understanding of phenotypic variation due to genetic factors regulating transcript abundance and shed light into divergence patterns. So far, only a limited number of studies have addressed this subject in Arabidopsis, with contrasting results due to dissimilar statistical power. Here, we present the transcriptome architecture in leaf tissue of two RIL sets obtained from a connected-cross design involving 3 commonly used accessions. We also present the transcriptome architecture observed in developing seeds of a third independent cross.cis-acting), compared to distant loci (acting necessarily indirectly or in trans). Distant eQTLs hotspots were essentially not conserved between crosses, but instead, cross-specific. Accounting for confounding factors using a probabilistic approach (VBQTL) increased the mapping resolution and the number of significant associations. Moreover, using local eQTLs obtained from this approach, we detected evidence for a directional allelic effect in genes with related function, where significantly more eQTLs than expected by chance were up-regulated from one of the accessions. Primary experimental data, analysis parameters, eQTL results and visualisation of LOD score curves presented here are stored and accessible through the QTLstore service database http://qtlstore.versailles.inra.fr/.The utilisation of the novel R/eqtl package  allowed us to map 4,290 and 6,534 eQTLs in the Cvi-0 × Col-0 and Bur-0 × Col-0 recombinant populations respectively. In agreement with previous studies, we observed a larger phenotypic variance explained by eQTLs in linkage with the controlled gene (potentially Our results demonstrate the extensive diversity and moderately conserved eQTL landscape between crosses and validate the utilisation of expression traits to explore for candidates behind phenotypic variation among accessions. Furthermore, this stresses the need for a wider spectrum of diversity to fully understand expression trait variation within a species. Arabidopsis thaliana showed that at least 46% of the genes in the genome are differentially expressed between a pair of accessions [Arabidopsis thaliana [Saccharomyces cerevisiae [Caenorhabditis elegans [Most traits vary quantitatively between individuals and are significantly influenced by genetic variation and its interaction with the environment. In general, transcript abundance of a gene can be considered as a quantitative trait since it differs between individuals with respect to genetic factors ,2. The ucessions ,3 and uncessions  or variacessions ... Previthaliana -12, Saccrevisiae ,14, and  elegans . No less elegans . For inscis- and/or trans-regulatory changes. Cis- acting regulations represent polymorphisms in physical linkage to the gene, affecting the transcription in an allele-specific manner. Consequently, cis-eQTLs are usually detected as local-eQTLs, being mapped in the vicinity of the gene; whereas trans-acting regulations act distantly in a non allele-specific way and can be located anywhere in the genome, most likely detected as distant-eQTL [cis and trans effects should be directly assessed by allele-specific expression assays [trans-acting loci, where few modifiers regulate the expression of hundreds of genes [C. elegans revealed an opposite pattern, with an over-representation of local-eQTLs compared to distant regulators [A. thaliana. Using microarray technology in recombinant inbred lines (RILs) from a cross between accessions Bayreuth (Bay) and Shahdara (Sha), more than 36,000 eQTLs were described using whole rosettes [er) and Cape Verde Island (Cvi) accessions as RIL progenitors, detected 9 times less eQTLs than those mapped in the Bay x Sha population [Transcript level differences can originate from ant-eQTL ,11,17. An assays . In yeasof genes . Contrasgulators . Only fepulation . DiscrepSaccharomyces species exhibiting polygenic directional divergence in cis-regulatory variants [Mus musculus [The identification of thousands of local eQTLs allows testing for marks of concerted evolution in transcript abundance from genes with related function . Severalvariants . Similarmusculus . Thus famusculus .A. thaliana and signatures of selection between genes with related function, we performed eQTL mapping in two well-established recombinant populations. The analysis was essentially based on a connected-cross design between three accessions [In order to identify genomic regions underlying transcript variation in cessions : the refeQTL analyses were performed in three displays: two on young rosette transcripts in Cvi-0 × Col-0 (hereafter 'CviCol') and Bur-0 × Col-0 (hereafter 'BurCol') RIL sets, and one on developing seed transcripts in Bay-0 × Shahdara (hereafter 'BaySha') RIL set. We will henceforth focus on and compare the results obtained for rosette samples, while the BaySha data is briefly presented as Additional file A. thaliana accessions, we utilised the CATMA array technology [P < 5 × 10-2; Additional file Transcript abundance can be treated as a highly heritable phenotype affected by natural genetic diversity . In ordechnology , which hchnology ), includP < 2.2 × 10-16). In the CviCol set we found a higher average explained variance (13.3% vs. 10.2% in BurCol) with proportionally more eQTLs having larger effects . We identified 4,290 significant eQTLs at a FDR of 5%  from the CviCol dataset . Moreover, compared to distant eQTLs, local eQTLs explained a significantly higher fraction of the phenotypic variance per trait . We also compared the distribution of local eQTLs along the genome between crosses. For this, we divided the genome into 1Mb windows (bin) and estimated the fraction of transcripts with local eQTLs on every bin per chromosome. A spearman test detected a significant correlation between both distributions (P < 0.01), suggesting major structural genomic aspects. We determined whether dense eQTL regions were enriched for SNP polymorphisms or were gene-dense regions. A genome-wide regression analysis did not detect a significant correlation between the number of SNPs and eQTLs within intervals for CviCol, however a marginally significant association was found for BurCol . In contrast, an expected significant correlation was found with gene density in both cases . Furthermore, we compared the top 11 bins  in both sets and detected 4 overlapping intervals with high eQTL density between crosses  on chromosome 1 and cell-adhesion (P < 1.3 × 10-5) on chromosome 2 . In the CviCol population, a total of 17 bins contained more than the 34 distant eQTL peaks expected by chance, and up to 170 peaks were found within the strongest hotspot . From the 41 hotspots detected in total, only three were collinear between sets, suggesting little conservation in the major determinants of distant eQTLs across the genome. None of the hotspots co-localised with any of the major-effect developmental QTLs known to segregate in A. thaliana , except in BurCol where a marginally significant hotspot was found on chromosome 5 (bin #93), which contains FLC. Although 62 traits with a distant eQTL mapping to this region were observed, only 2 have been shown to interact with FLC [We found little overlap between hotspots in the two populations  compared with standard approaches [Variation in transcript abundance can also be influenced by non-genetic factors, such as experimental noise and hidden factors ,25: greeproaches . Hence, proaches . We testproaches ,27.We focused the utilisation of this approach on the CviCol population. Linkage analysis detected a total of 8,156 eQTLs , association mapping, or the combination of both, will help elucidating and validating transcript abundance divergence with a greater resolution within We used 158 RILs from the core-population of the Cvi-0 × Col-0 set and 156 RILs from the core-population of the Bur-0 × Col-0 set , along wA. thaliana [Transcript abundance estimates were carried out using the bicolour CATMA microarrays version 5, containing 34,529 spots  allowing, among others, to uniquely interrogate 26,166 nuclear genes  in thaliana ,35. For thaliana .t-test. A trimmed variance is calculated from spots which do not display extreme variance [P-values were adjusted by the Bonferroni method, which controls the Family Wise Error Rate in order to keep a strong control of the false positives in a multiple-comparison context. We considered probes as being differentially expressed after Bonferroni correction using a P < 0.05. For the eQTL analysis, normalised intensity per probe × RIL has been calculated from the normalised log-ratio by sharing the correction value between both samples [For each array, the raw data comprised the logarithm of the median feature pixel intensity at wavelengths 635 nm (red) and 532 nm (green) and no background was subtracted. An array-by-array normalisation was performed to remove systematic biases. First, spots considered as badly formed features were excluded. Then a global intensity-dependent normalisation using the loess procedure was performed to correct the dye bias . Finallyvariance . The raw samples . To be shttp://www.ncbi.nlm.nih.gov/geo/, accession no. GSE28791 and at CATdb  according to the 'Minimum Information About a Microarray Experiment' standards.Microarray data was deposited at Gene Expression Omnibus http://cran.r-project.org/web/packages/eqtl/, which exploits functions from R/qtl [trans- (distant) and cis-acting  eQTL , projecting and plotting the QTL estimated location relative to the gene location and summarising eQTL data at the genome scale with various generic plots and tabular files. R/eqtl is a free and open-source multi-platform package developed under the statistical language R, and is available under the GPLv3 license. R/qtl and its extension R/eqtl are hosted and can be downloaded from the Comprehensive R Archive Network (CRAN) at http://cran.r-project.org.eQTL mapping was performed utilising the normalised microarray data using our R package R/eqtl om R/qtl . R/eqtl minus Col . We also estimated the proportion of the phenotypic variation explained by the segregation of each individual eQTL or significant eQTL × eQTL interaction (R2) by analysis of variance. QTLs were defined using a LOD significance threshold computed by permuting the phenotypes while maintaining the genotype across the RIL set [P-value from each randomly chosen trait and estimated the corresponding q-value [P-values for transcriptome-wide FDR 5% (P = 6 × 10-3 in CviCol and P = 9 × 10-3 in Burcol) and 1% (P = 1 × 10-3 in CviCol and BurCol) were also used as significance threshold.Interval Mapping (IM) and Composite Interval Mapping (CIM) were performed on each cross for all of the 32,300 non-technical and non-repetitive probes on the CATMA array, as implemented in the R/eqtl package. The Cvi × Col and Bur × Col RIL populations have been previously genotyped for 90 and 87 markers, respectively . For eac RIL set  and a 1. RIL set . In orde RIL set . To corr q-value . P-valuehttp://qtlstore.versailles.inra.fr/ and is composed of an extensive SQL database and a web interface, which are available under the GPLv2 license. The SQL database is convenient for all kinds of QTL experiments and analysis, by being able to store all the experiments primary data separately from all subsequent analyses results. It typically stores and interrogates QTL parameters such as location, significance, effect and type, among others.All results are recorded in QTLstore, a comprehensive web service which allows to store, manage, explore and cross QTL experiment results from the single-trait scan to genome-wide expression QTL experiments. QTLstore is hosted at trans-hotspots. For local eQTLs, we performed a regression analysis against SNP  and gene densities as described in [P < 2 × 10-5 after Bonferroni correction.Local and distant eQTLs were classified in 1Mb bins as in . Bins coP < 1 × 10-2, FDR 5%). We tested for 5, 10, 20 and 30 factors and chose the model with the highest number of additional linkages (FDR 5%). Next, potential directional selection was tested as previously described with modifications [P < 8 × 10-4 after Bonferroni) considering the number of genes within each category at the whole-genome level. Within the selected functional categories, we focused the subsequent analysis on GO categories containing more than 20 genes. For each category we tested departure from the 1.6:1 ratio (Col:Cvi) using a hypergeometric test.We applied the VBQTL  approach as previously described  on the dThe authors declare that they have no competing interests.OL, CC, JPR, LL, SeB and BD designed the study. JY, CC, SeB, BD, SaB and SE handled plant culture for RNA. JY, SE, SaB and MLMM performed the array experiments and initial data analyses. HK, JY, FAC, MLMM and OL developped R/eqtl and analysed the statistical data. HK and YS developped databases and web tools. FAC and OL wrote the manuscript, while JY, HK, MLMM, LL, SeB, BD, JPR and CC corrected the manuscript. All authors read and approved the final manuscript.eQTL mapping in the Bay × Sha recombinant population [pulation .Click here for fileTable S1. Set of differentially expressed genes between parental accessions Cvi, Bur and Col. Expression differences are reported in log2.Click here for fileFigure S1. Venn diagram depicting the overlap between genes with differential expression in parental accessions pairs (Cvi vs. Col and Bur vs. Col). Figure S2. Histograms of the explained phenotypic variance  for the eQTLs in the a.CviCol and b. BurCol populations. Figure S3. Number of eQTLs per trait. Figure S4. Venn diagram depicting the overlap between probes with local eQTLs in the CviCol and BurCol populations. Figure S5. Histogram of the number of probes with a significant eQTL for different numbers of hidden factors tested with VBQTL in CviCol. Figure S6. Genetic landscape for transcript accumulation variation in BaySha. Figure S7. Histogram of the explained phenotypic variance (R2) for the eQTLs in the BaySha population. Figure S8. Number of eQTLs per trait in BaySha. Figure S9. Distribution of distant-eQTLs along the genome in BaySha.Click here for fileTable S2. List of eQTLs detected in each cross. Abbreviations: eQTL Chr = chromosome localisation of eQTL, type = eQTL tentative classification , peak.bp = physical position of the LOD peak, inf.pb = inferior limit, sup.pb = superior limit of supporting physical interval, Add = additive effect , Rsq = variance explained, Rpf = significance.Click here for fileTable S3. Number of -eQTLs per 1 Mb interval. a. local, b. distant.Click here for fileTable S4. Overrepresented GO terms within the BurCol distant-hotspots.Click here for fileTable S5. List of eQTLs detected by VBQTL in CviCol. See Additional file 4: Table S2 for column headings.Click here for file