Identifying high-order genetics associations with non-additive (i.e. epistatic) effects in population-based studies of common human diseases is a computational challenge. Multifactor dimensionality reduction (MDR) is a machine learning method that was designed specifically for this problem. The goal of the present study was to apply MDR to mining high-order epistatic interactions in a population-based genetic study of tuberculosis (TB).The study used a previously published data set consisting of 19 candidate single-nucleotide polymorphisms (SNPs) in 321 pulmonary TB cases and 347 healthy controls from Guniea-Bissau in Africa. The ReliefF algorithm was applied first to generate a smaller set of the five most informative SNPs. MDR with 10-fold cross-validation was then applied to look at all possible combinations of two, three, four and five SNPs. The MDR model with the best testing accuracy (TA) consisted of SNPs rs2305619, rs187084, and rs11465421 (TA = 0.588) in PTX3, TLR9 and DC-Sign, respectively. A general 1000-fold permutation test of the null hypothesis of no association confirmed the statistical significance of the model (p = 0.008). An additional 1000-fold permutation test designed specifically to test the linear null hypothesis that the association effects are only additive confirmed the presence of non-additive (i.e. nonlinear) or epistatic effects (p = 0.013). An independent information-gain measure corroborated these results with a third-order epistatic interaction that was stronger than any lower-order associations.We have identified statistically significant evidence for a three-way epistatic interaction that is associated with susceptibility to TB. This interaction is stronger than any previously described one-way or two-way associations. This study highlights the importance of using machine learning methods that are designed to embrace, rather than ignore, the complexity of common diseases such as TB. We recommend future studies of the genetics of TB take into account the possibility that high-order epistatic interactions might play an important role in disease susceptibility. Understanding the genetic architecture of common human diseases such as tuberculosis (TB) remains one of the greatest challenges in biomedical research. The goal of the present study was to approach the genetic analysis of TB susceptibility with the assumption that the underlying genetic architecture is complex.Specifically, we used a machine learning method called multifactor dimensionality reduction (MDR) that was designed specifically for detecting and characterizing non-additive gene-gene interactions (i.e. epistasis) The MDR method was designed as a machine learning alternative to parametric statistical methods such as logistic regression 5As with any machine learning method, there is always the concern of overfitting that can lead to false-positives. To avoid this problem here, we implemented MDR in a cross-validation framework that assesses the predictive ability of the models The data set used in this study was originally analyzed by Olessen et al. We first applied the ReliefF algorithm to filter the 19 SNPs to a total of five. Here, we used 100 nearest neighbors. The goal for the ReliefF analysis was to retain only those SNPs that provide the greatest signal. This reduces the total number of models that need to be explored.We then applied MDR to five filtered SNPs. We combinatorially evaluated all two-way to five-way models. Balanced accuracy in the context of 10-fold cross-validation was used to assess model quality. An overall best model was selected that had the maximum accuracy in the testing data (i.e. testing accuracy or TA). We also recorded the cross-validation consistency or CVC. This provides a summary of the number of cross-validation intervals in which a particular model was found. Higher numbers indicate more robust results. Statistical significance was assessed using 1000-fold permutation testing. Here, the data are randomized 1000 times to create 1000 datasets consistent with the null hypothesis. The complete MDR analysis is repeated in each permutated dataset and a best model selected just as in the real data. This procedure generates an empirical estimate of the null distribution of testing accuracies and corrects for multiple testing because the same number of models are evaluated in all permutated and real data. We performed two tests. First, we tested the general null hypothesis of no association by randomizing case–control labels. Second, we tested the linear null hypothesis that the only genetic effects are additive according the genotype randomization methods of Greene et al. In addition to the MDR analysis, we performed an independent assessment of non-additivity using entropy-based measures of information gain ReliefF filtering returned the following five SNPs (corresponding genes shown in parentheses): rs187084 (TLR9), rs4986790 (TLR4), rs11465421 (DC-SIGN), rs2305619 (PTX3), rs1840680 (PTX3), and rs2287886 (DC-SIGN). A summary of the MDR results for these five SNPs is shown in Table 1. None of the SNPs were found to have statistically significant main effects after correction for multiple testing. Additionally, no statistically significant pairwise models were reported. The overall best model consisted of SNPs rs2305619, rs187084, and rs1145421. These three SNPs had a training accuracy of 0.6115 and a testing accuracy of 0.5878. The cross-validation consistency of this model was 10/10. The distribution of cases and controls for each of the three-locus genotype combinations in the best MDR model can be seen in Figure Permutation testing confirmed the statistical significance of the model suggesting it is unlikely to see a mode this good in null data (p = 0.008). Additional permutation testing revealed that the non-additive effects in the model were also statistically significant (p = 0.013). Taken together, these results suggest a role for high-order non-additive epistatic effects.Figure Few studies consider the role of epistasis in disease susceptibility. Even fewer consider the possibility that multiple genetic variants might have synergistic effects beyond main effects or pairwise effects. We have demonstrated how the ReliefF and MDR machine learning algorithms can be employed in conjunction with cross-validation and permutation testing to move beyond the detection of low-order genetic effects. We have applied these approaches to the genetic analysis of TB susceptibility and have demonstrated a statistically significant three-way epistatic interaction exhibiting non-additivity that is not predicted by the one-way and two-way effects. These results were confirmed using an independent analysis approach based on information theory. An important question is whether this three-locus epistatic effect has biological and clinical implications. The biological connection is not difficult given these genes were pre-selected as good immunological candidates for TB http://epistasis.org.All methods are freely available as open-source software from the authors. More information can be found at MDR: Multifactor dimensionality reduction; SNP: Single-nucleotide polymorphism; TB: TuberculosisThe authors declare no competing interests.RC performed the data analysis and drafted the manuscript. TH imputed missing data, performed information gain measurements and critiqued manuscript drafting. CW, GS and SW provided and summarized the data, assisted with results interpretation and assisted with the writing. JM conceived of the study, provided administrative direction, assisted with results interpretation, assisted with the writing, and secured financial support for the study. All authors read and approved the final manuscript.


Testing whether genetic information could inform the selection of the best drug for patients with depression, Rudolf Uher and colleagues searched for genetic variants that could predict clinically meaningful responses to two major groups of antidepressants. It has been suggested that outcomes of antidepressant treatment for major depressive disorder could be significantly improved if treatment choice is informed by genetic data. This study aims to test the hypothesis that common genetic variants can predict response to antidepressants in a clinically meaningful way.p<5×10−8). No biological pathways were significantly overrepresented in the results. No significant associations (genome-wide significance p<5×10−8) were detected in a meta-analysis of NEWMEDS and another large sample (STAR*D), with 2,897 individuals in total. Polygenic scoring found no convergence among multiple associations in NEWMEDS and STAR*D.The NEWMEDS consortium, an academia–industry partnership, assembled a database of over 2,000 European-ancestry individuals with major depressive disorder, prospectively measured treatment outcomes with serotonin reuptake inhibiting or noradrenaline reuptake inhibiting antidepressants and available genetic samples from five studies . After quality control, a dataset of 1,790 individuals with high-quality genome-wide genotyping provided adequate power to test the hypotheses that antidepressant response or a clinically significant differential response to the two classes of antidepressants could be predicted from a single common genetic polymorphism. None of the more than half million genetic markers significantly predicted response to antidepressants overall, serotonin reuptake inhibitors, or noradrenaline reuptake inhibitors, or differential response to the two types of antidepressants . Prescription of an antidepressant is often the first step in treating the disease. However, less than half of patients get well taking the first antidepressant prescribed. Those who don't respond to the first drug need to, together with their doctors, try multiple courses of treatment to find the right drug and the right dose for them. For some patients none of the existing drugs work well.To see whether genetic information could help improve the choice of antidepressant, researchers from universities and the pharmaceutical industry joined forces in this large study. They examined two ways to use genetic information to improve the treatment of depression. First, they searched all genes for common genetic variants that could predict which patients would not respond to the two major groups of antidepressants . They hoped that this would help with the development of new drugs that could help these patients. Second, they looked for common genetic variants in all genes that could identify patients who responded to one of the two major groups of antidepressants. Such predictors would make it possible to know which drug to prescribe for which patient.The researchers selected 1,790 patients with severe depression who had participated in one of several research studies; 1,222 of the patients had been treated with an SRI, the remaining 568 with an NRI, and it was recorded how well the drugs worked for each patient. The researchers also had a detailed picture of the genetic make-up of each patient, with information for over half a million genetic variants. They then looked for an association between genetic variants and responses to drugs.They found not a single genetic variant that could predict clearly whether a person would respond to antidepressants in general, to one of the two main groups (SRIs and NRIs), or much better to one than the other. They also didn't find any combination of variants in groups of genes that work together that could predict responses. Combining their data with those from another large study did not yield any robust predictors either.This study was large enough that it should have been possible to find common genetic variants that by themselves could predict a clinically meaningful response to SRIs and/or NRIs, had such variants existed. The fact that the study failed to find such variants suggests that such variants do not exist. It is still possible, however, that variants that are less common could predict response, or that combinations of variants could. To find those, if they do exist, even larger studies will need to be done.http://dx.doi.org/10.1371/journal.pmed.1001326Please access these websites via the online version of this summary at personalized medicineThe National Institute of General Medical Sciences at the US National Institutes of Health has a fact sheet on major depressive disorderPubMed Health at the US National Library of Medicine has a page on major depressive disorder and pharmacogenetics, the study of how genetic variation affects response to certain drugs (note that Wikipedia is a free online encyclopedia that anyone can edit)Wikipedia has pages on depressionThe UK National Health Service has comprehensive information pages on  Major depressive disorder (MDD) is a disabling illness, affecting a high proportion of individuals at some point in their life Identification of genetic determinants of antidepressant response has the potential to improve the treatment of MDD in two important ways. First, genetic and molecular predictors of poor treatment outcome with available antidepressants can provide targets for the development of novel therapeutic agents that may be effective for the type of depression that is resistant to current treatments. Second, for many individuals with MDD, delay in reaching recovery is avoidable, since they have the potential to respond to one of the currently available treatments. If a predictor of differential outcome with alternative treatments is identified, a clinician could use it to select the antidepressant that is most likely to alleviate depression in a given individual. For both applications, the clinical implications are predicated on the effect size of the prediction. A consensus criterion has been set for what size of difference in depressive symptoms is clinically meaningful: a panel of experts and service users has concluded that a difference in outcome equal or greater than three points on the Hamilton Rating Scale for Depression is noticeable to the patients and their relatives and can be considered as clinically significant The first aim is to identify common genetic polymorphisms that predict unfavourable outcome of treatment with currently available antidepressants. Addressing this issue in the large combined NEWMEDS sample will substantially expand on the evidence from the first genome-wide studies on outcomes for single-drug treatment The second aim is to obtain predictors of differential outcomes of treatment with antidepressants with different modes of action in the largest comparative pharmacogenetic study to date. Specifically, we aim to identify common genetic variants that differentially predict outcome of treatment with antidepressants that act primarily through the inhibition of serotonin reuptake (serotonin reuptake inhibitors [SRIs]) or act primarily through the inhibition of norepinephrine reuptake . For the first time, to our knowledge, these two aims will be pursued in a sample that is large enough to provide sufficient power to ensure interpretable results.http://www.newmeds-europe.com) n = 868; GENPOD, a randomized controlled trial of two active antidepressants, n = 601; and GODS, a treatment cohort of severe depression, n = 131) n = 355, and GlaxoSmithKline, n = 191) were combined to obtain a sample of 2,146 adult individuals  or Illumina Human660W-Quad BeadChips , which have identical tag SNP coverage. More specifically, 727 samples from the GENDEP study were genotyped at the Centre National de Génotypage  using the Illumina Human610-Quad BeadChip and were subjects of previous reports Samples were genotyped on Illumina Human610-Quad BeadChips (p<1×10−3) by genotyping centre were excluded. Overall, 520,978 (99.0%) of the 526,424 genotyped SNPs passed all stages of quality control and were included in pharmacogenetic analyses. Hardy–Weinberg equilibrium was tested, but was not used as an exclusion criterion for markers, since departures from Hardy–Weinberg equilibrium are expected in a case-only study Quality control was implemented in PLINK n = 22), abnormal heterozygosity (n = 16), cryptic relatedness up to third-degree relatives by identity by descent (n = 20), genotyping completeness less than 97% (n = 9), and non-European ethnicity admixture detected as outliers in iterative EIGENSTRAT analyses of a linkage-disequilibrium-pruned dataset (n = 35). One additional individual was excluded because of invalid phenotypic information, leaving 1,790 (94.6%) of the 1,893 genotyped individuals for the pharmacogenetic analyses.Individuals were excluded for ambiguous sex (genotypic sex different from phenotypic sex) , is independent of depression rating scale used, and is clinically relevant since it closely reflects clinician's impression of improvement Response to antidepressants involves changes in depressive symptoms over a number of weeks and is more accurately captured by continuous than by dichotomous variables Studies included in NEWMEDS used several outcome measures. The Montgomery–Åsberg Depression Rating Scale n = 1,222) and NRIs (n = 568). A fourth analysis, of primary interest to our second aim, searched the genome for common variants that differentially predict response to SRIs and NRIs. To avoid confounding by covariation between antidepressant drug and genetic background due to different studies contributing unequal numbers of individuals to each antidepressant group, we tested this hypothesis as a drug-by-genotype interaction in a sample restricted to individuals that were randomly allocated to treatment with either an SRI or an NRI (n = 949), thus ensuring full comparability of the two drug groups on measured and unmeasured confounders. In all analyses, the influence of genetic population structure was controlled by the inclusion of the four significant principal components from the final iteration of the EIGENSTRAT analysis of linkage-disequilibrium-pruned genetic data. We defined genome-wide statistical significance at the generally accepted threshold p<5×10−8Data analysis was carried out according to a protocol specified prior to data acquisition . Joint ap<5×10−6 are reported in Associations reaching a less stringent threshold of R2 = 0.8) to estimate power for detecting effects of genotyped and ungenotyped variants. The quality-controlled sample provided a power well above 80% to detect a clinically significant effect at the genome-wide significance level for three of the four analyses . The meta-analysis of NEWMEDS and STAR*D samples had an adequate power to detect even an effect that was half of what would be considered clinically significant. Details of the power analysis can be found in Our aim was to determine whether any common genetic variant predicts a clinically significant difference in the outcome of treatment with antidepressants, taking a difference of at least three points in the reduction of depression symptom severity on HRSD-17 as the benchmark for clinical significance Enrichment of genome-wide association signal in genes that belong to known biological pathways was tested using ALIGATOR A meta-analysis was undertaken between NEWMEDS and data subsequently obtained from the first level of the STAR*D (Sequenced Treatment Alternatives to Relieve Depression) trial, when all participants with MDD were treated with citalopram (an SRI), in the hope of finding genome-wide significant associations. For further information about the STAR*D sample, genotyping, and quality control procedures see To maximize the overlap between the two samples and genome coverage, both NEWMEDS and STAR*D were imputed to include over 1.4 million markers using BEAGLE 3.3 While both our main analysis in NEWMEDS and the meta-analysis with STAR*D had sufficient power to detect clinically significant genetic associations, there could also exist an underlying weak signal from across the genome that could offer insight into the mechanism of antidepressant response. The methodology of polygene scoring allows for the detection of such weakly distributed signal p-values, with no inflation of the test statistic  in their effects on the adjusted percentage change in depression severity among the 949 individuals randomly allocated to SRI or NRI antidepressant. The quantile–quantile plot showed a uniform distribution of For all four analyses, a meta-analysis of results from contributing studies also gave negative results  than expected by chance. None of the four analyses  showed a significant excess in the number of enriched pathways, and no single pathway was significantly enriched after correcting for multiple testing. Full results are given in n = 2,329) found no genome-wide significant results. For more information see A meta-analysis tested percentage improvement in 2,897 individuals from NEWMEDS and STAR*D using over 1.1 million genotyped and imputed SNPs and found no genome-wide significant results. A meta-analysis restricted to SRI-treated individuals , there was no significant prediction across the 13 progressive p-value thresholds. In a sample restricted to SRI-treated individuals , there was no significant prediction from any of the 13 progressive p-value thresholds either. Further information about the results can be found in Polygenic scores were calculated to test the combined effect of multiple weak associations across the genome. Scores were created using NEWMEDS and used to predict outcomes in STAR*D. In the analysis that included all individuals  results from whole genome analyses in NEWMEDS, pathway analysis, meta-analysis between NEWMEDS and STAR*D, polygenic score, study-level meta-analysis between samples in NEWMEDS, reporting of results for previously identified candidate genes for antidepressant response, and imputation results from NEWMEDS.(PDF)Click here for additional data file.Text S2Study protocol.(PDF)Click here for additional data file.


GBLUP is a mixed model approach where GEBV are obtained using a relationship matrix calculated from the SNP genotypes. The remaining methods are regression-based approaches where the SNP effects are first estimated and, then GEBV are calculated given the individuals' genotypes.Five main methods, commonly applied in genomic selection, were used to estimate the GEBV on the 15The differences between the regression-based methods are in their prior distributions for the SNP effects. The prior distribution for LASSO is a Laplace distribution, for Bayes A is a scaled Student-t distribution, and the Bayes B type methods have a Spike and Slab prior where only a proportion (π) of SNP has an effect, following a given distribution. In this study, two different distributions were considered for the Bayes B type methods: (i) normal and (ii) scaled Student-t. They are referred here as the BBn and BBt methods, respectively. These prior distributions are defined by one or more parameters controlling their scale/rate (λ), shape (df) or proportion of SNP with effect (π). LASSO requires one (λ); two for Bayes A  and Bayes Bn ; and three for Bayes Bt . In this study, all parameters were estimated from the data. An extra scenario for Bayes A and BBt was included where df was not estimated but fixed to 4 (suffixed _4df). The implementation of GBLUP was done using ASREML, the heritability was also estimated from the data. All other methods were implemented using a MCMC approach.All Bayes A and B methods showed accuracy (correlation between True and Estimated BV) as high as 0.94 except for BA_4df (r = 0.91). Compared to the traditional BLUP using pedigree information, these methods improved the accuracy between 50 and 55%. GBLUP and LASSO were less accurate (0.81 and 0.85 respectively) and the improvements were 34 and 40% compared to BLUP.Results of all methods were consistent and the accuracies for GEBV ranged between 0.81 and 0.94. When all parameters were estimated the results were similar for the Bayes A and Bayes B methods. Results showed that Bayes A was more sensitive to the changes in the shape parameter, and the parameter changes led to change in the accuracy of GEBV. However BBt was more robust to the change in this parameter. This may be explained by the fact that BBt estimates one extra parameter and it can buffer against a non-proper shape parameter. With the availability of cost-effective SNP chips, genomic selection is currently been applied in agricultural species, using different statistical approaches. SNP information can be used to estimate breeding values by using (i) a mixed model or (ii) a regression-based approach. For the first approach, the SNP genotypes are used to estimate the relationship matrix among individuals, which later is used in a BLUP analysis (GBLUP) to estimate genomic breeding values (GEBV). For the second approach, the effect of individual SNPs can be estimated using multiple regression, and then GEBV for each individual are calculated as the sum of the SNP effects given their genotypes. Estimated SNP effects may also be of value to be used as a criterion for QTL mapping. Examples of methods based on this approach include Bayes A, Bayes B  and LASSThe aim of this study was to compare the GEBV using different methods of genomic selection on the common dataset from the 2011 QTLMAS workshop. For the different methods, the values for the parameters regulating the prior distribution of the SNP effect were also estimated from the data.th QTLMAS workshop. It consisted of 3220 individuals, all were genotyped for about 10000 SNP on five chromosomes of equal length (1 Morgan each). The pedigree included 20 half-sib and 200 full-sib families, each including 15 offspring. Eight QTLs were simulated to affect the quantitative trait, with the largest one on chromosome 1, 2 linked QTLs on chromosomes 2 and 3, 1 imprinting one on chromosome 4, and 2 epistatic QTLs on chromosome 5. Heritability of the trait was 0.3 and two third (n = 2000) of the offspring were phenotyped.The dataset used here was the one provided by the organisers of the 15For the GBLUP approach, breeding values are assumed to be a random effect and included in a mixed model as the following:g is the vector of random total genetic effect assumed to be normally distributed as N, with G being the realised relationship matrix calculated from SNP information [2g the variance of g. The GBLUP was implemented using ASREML [2g was first estimated from the data and later used to calculate the GEBV.where ormation , and σ2gg ASREML , in a twThe model for all these methods is the following:zi is the vector of genotypes at SNP i; βi indicates the allelic substitution effect for SNP i.where, n is total number of SNP, The difference between the regression-based methods lays on the assumption of the prior distributions for the SNP effects. For instance, the prior distribution for LASSO  is a Lap2SNP were estimated from data using flat priors. For each analysis, a MCMC chain was run and the first 10000 cycles were discarded as burn-in period. Following this, 10000 realisations were collected, each separated by 20 cycles between consecutive realisations . The posterior mean was used as the estimate for each parameter of interest. For the case of Bayes A and B where df was estimated, the chain was 5 times longer.These prior distributions for SNP effects are described by one or more parameters which includes scale/rate (λ), shape (df) and/or proportion of SNP with effect (π). The prior distribution assumed with LASSO is defined by one parameter (λ); two for Bayes A  and Bayes Bn ; and three for Bayes Bt . In this study, all parameters were estimated from the data (suffixed _edf). An extra scenario for Bayes A and Bayes Bt was included where df was not estimated but fixed to 4 (suffixed _4df). The models were implemented under a Bayesian framework using Gibbs sampling. Bounded flat priors (between 0.5 and 9) were used for the estimation of df. The parameters π and σFor this estimation, an approximation based on the infinitesimal model theory was used :r is the accuracy of estimates. The explained additive genetic variance (σ2g ) was obtained using the above equations, for regression-based methods and the corresponding heritability was reported.where PEV is the Prediction Error Variance, and Additionally to the GEBV, the regression-based methods also estimate the effects for each individual SNP used in the analysis. We compared these results with association and linkage analysis results, in order to assess its potential use as a criterion for QTL mapping.Half-sib analysis (HS-QTL) was performed as described by Haley et al. , and impAssociation analysis was performed using the GRAMMAR approach , which cr=0.999). LASSO and GBLUP had similar results (r=0.991) and slightly less correlated with the other methods.Generally speaking, the GEBV with the different methods were consistent among themselves with the correlation between GEBV ranging from 0.898 to 1  with BA_4df having a slightly lower accuracy (r = 0.91) representing an improvement between 50 and 55% compared to traditional BLUP. The accuracy of GBLUP and LASSO were 0.81 and 0.85, an improvement over BLUP of 34 and 40%, respectively. Heritability (simulated h2 =0.30) estimated by all methods were very similar (~0.29), except for GBLUP (h2=0.27).The accuracy of the methods, expressed as correlation between TBV and EBV, are shown in Table Previous studies reported in the literature, have shown a superiority of Bayes B method over Bayes A (e.g. ). The reThe dataset simulated includes 5 simple additive QTLs , one imprinted QTL (chromosome 4) and 2 QTLs with epistasis effect (on chromosome 5).Figure Good consistency was observed for the results of all applied methods. For this specific dataset, the accuracy of Bayes A and B type of methods were better than those of GBLUP and LASSO. When all parameters of the prior distribution were estimated with the data, the results of Bayes A and Bayes B were the same. Fixing the shape parameter with Bayes A have a slight decrease in the accuracy but little effect on Bayes B. These results are consistent with previous studies reporting a superiority of Bayes B over Bayes A when the parameters of the prior distribution are assumed known.The authors declare that they have no competing interests.JN carried out the analyses and drafted the manuscript; RPW implemented the methods, all authors contributed to the design of the study and the final text of the manuscript.Correlation between GEBV estimated by different methods.Click here for filePosterior distribution of the shape parameter, df, for BA_edf and BBt_edf.Click here for file


Previous genome-wide scans of positive natural selection in humans have identified a number of non-neutrally evolving genes that play important roles in skin pigmentation, metabolism, or immune function. Recent studies have also shown that a genome-wide pattern of local adaptation can be detected by identifying correlations between patterns of allele frequencies and environmental variables. Despite these observations, the degree to which natural selection is primarily driven by adaptation to local environments, and the role of pathogens or other ecological factors as selective agents, is still under debate. To address this issue, we correlated the spatial allele frequency distribution of a large sample of SNPs from 55 distinct human populations to a set of environmental factors that describe local geographical features such as climate, diet regimes, and pathogen loads. In concordance with previous studies, we detected a significant enrichment of genic SNPs, and particularly non-synonymous SNPs associated with local adaptation. Furthermore, we show that the diversity of the local pathogenic environment is the predominant driver of local adaptation, and that climate, at least as measured here, only plays a relatively minor role. While background demography by far makes the strongest contribution in explaining the genetic variance among populations, we detected about 100 genes which show an unexpectedly strong correlation between allele frequencies and pathogenic environment, after correcting for demography. Conversely, for diet regimes and climatic conditions, no genes show a similar correlation between the environmental factor and allele frequencies. This result is validated using low-coverage sequencing data for multiple populations. Among the loci targeted by pathogen-driven selection, we found an enrichment of genes associated to autoimmune diseases, such as celiac disease, type 1 diabetes, and multiples sclerosis, which lends credence to the hypothesis that some susceptibility alleles for autoimmune diseases may be maintained in human population due to past selective processes. Adaptation to local environments is one of the most important factors shaping human genetic variation among different geographically distributed populations. Here we develop a statistical framework aimed at identifying signals of genetic adaptation. We correlate the spatial distribution of allele frequencies of a large sample of SNPs, genotyped in more than 50 populations distributed worldwide, to a set of environmental factors, describing local geographical features such as climate conditions, diet regimes, and pathogens load. Our results show an excess of putative functional variants for high levels of population differentiation, measured by the degree to which genetic variation correlates with a set of environmental variables. We demonstrate that selection on pathogens is the primary driver of local adaptation and affects the distribution of genetic variation at a large number of genes. Among the selected genes, we also identify an excess of genes associated with autoimmune diseases, such as celiac disease, type 1 diabetes, and multiples sclerosis. Anatomically modern humans appeared in East Africa about 200 k years ago, spread out from sub-Saharan Africa approximately 100 k years ago, and subsequently colonized the rest of the world in a series of migratory events Recent evidence suggests that the observed phenotypic diversity among human population groups may to some extent be a product of local adaptive processes  the median value for the re-sampled distribution of the enrichment statistic (see p<0.05).We examined the relative abundance of genic versus intergenic SNPs in the upper tail of the distribution of stic see  was equaSTF) or recombination rates (and therefore linkage disequilibrium) between genic and non-genic SNPs, by directly comparing non-genic and genic SNPs with similar minor allele frequency (MAF), STF and recombination rates. We observed an enrichment of genic SNPs for the highest bins of prediction accuracy in almost every classes of equal MAF, STF, or recombination rate in which we divided our sample of SNPs . There was a similar enrichment of non-synonymous vs. synonymous SNPs for high values of Q2 , but this value was not significantly different from 1, possibly due to the small number of SNPs and linkage between non-synonymous and synonymous SNPs.We also observed an even stronger excess of non-synonymous vs. non-genic SNPs at increasing values of prediction accuracy . The med2Q for each of the three variables   . Genic e2Q bin is 0.974).Temperature and precipitation rate ranges have been shown to influence the biological diversity and distribution of pathogen species Our next goal was to identify the relative fraction of loci for which population genetic variation is significantly correlated with specific environmental factors, and to use these results to further elucidate the role played by different environmental variables in shaping human variation.An unusually high correlation between allele frequencies and environmental variables may help identify loci involved in local human adaptation. However, these correlations are strongly affected by the non-independence of allele frequencies between closely related populations I(R2), a measure of the relative importance of each environmental variable in explaining the distribution of allele frequencies for a particular gene (see I(R2), with some values as high as 15%  within each environmental category, we still more frequently observed high values for pathogens and subsistence factors than for climate, using either temperature or precipitation rate mean levels or range levels (I(R2) values.Other environmental variables, or other quantifications of the environment, could potentially provide different results. These analyses may not have captured the main factors affecting fitness when quantifying the environment. Nevertheless, when testing each variable individually and assigning the maximum e levels . We usedp-values, which assesses the strength of the evidence against a model in which the environmental variables do not affect allele frequencies, we observed a strikingly larger number of loci with allele frequencies significantly associated with the pathogen distance matrix (I(R2) value when considering the pathogen distance matrix  while no genes were detected when considering the subsistence distance matrix or the climate distance matrix, using either temperature or precipitation rate mean levels or range levels. Again, when testing each variable individually, we observed a larger number of genes significantly correlated  with at least one pathogen variable (229), rather than one subsistence (10) or one climate variable (9).Examining the distribution of e matrix . Indeed,p-values lower than 1e-5). More importantly, among 2120 genes having at least one SNP correlated with pathogens using Bayenv, 419 are highly correlated using our method  and this overlap is significantly greater than expected by chance .We also applied the Bayenv software see  to our dp-values of 3.62e-05 and 3.27e-06, respectively), while no difference is observed when comparing subsistence and climate variables . This suggest that the discrepancy between the results using our method and the results using Bayenv is caused by the larger number of tests carried out for subsistence and climate factors in the Bayenv analysis  and such extreme values were more common for pathogens factors than for subsistence or climate predictors  with the pathogen distance matrix (109), while only 0 and 11 genes were detected when considering the subsistence distance matrix or the climate distance matrix, respectively. Among the 109 genes correlated with pathogens using sequencing data, 53 exhibited a previous p-value, computed using genotype data, lower than 0.05 and this overlap was statistically significant . The latter result suggests that, despite the different number of populations and the difference in the genetic data analyzed, the results are qualitative concordant suggesting that a correlation between ascertainment bias and pathogen reporting cannot explain our results.A correlation between the strength of ascertainment bias and a bias in pathogen reporting may potentially affect our results and lead to an inflation in the importance of pathogen-driven selection. To investigate this possibility, we validated our finding using low-coverage new-generation sequencing data from 1000 Genomes Project edictors . AssessiI(R2) for the model with all pathogen species (I(R2)FULL) to the ones missing one of the pathogen groups I(Rw/o VIRUS) it is possible to evaluate the impact of the missing pathogen group on the relationship between genetic variation and pathogen diversity. The reduction in I(R2) when not considering a particular pathogen group provides a measure of the relative impact of this particular group in explaining local adaptation. QQ plots showing the difference between including all pathogens and dropping one of them are illustrated in I(R2) (I(R2), presumably because the matrix then is more strongly dominated by the helminth distances.It is possible that different groups of pathogens have differed in their impact on human local adaptation. To test this hypothesis, we recomputed the partial Mantel correlations for each gene using different environmental matrices relating to different aspects of pathogen diversity by removing one pathogen group  in the calculation of the environmental distances. By comparing the distribution of n I(R2) . ConversThe above results demonstrate that pathogens diversity is a major factor in human adaptation to local environments. We further examined the genes whose genetic variation is correlated with the pathogen diversity matrix using analysis of Gene Ontology (GO), by testing whether certain ontology terms are enriched for SNPs correlated with pathogen diversity.By investigating statistically enriched terms in our set of pathogen-associated SNPs, we found an over representation of shared GO terms relating to regulation of immune system, defense and inflammatory response . In addiWe further interrogated the KEGG PATHWAY database, focusing our attention on hierarchical categories related to the immune system or immune diseases. We identified 3 KEGG pathways showing a significantly higher than expected number of pathogen-associated genes as determined by a bootstrap procedure . Two of www.genome.gov).It has previously been argued that SNPs associated with susceptibility to complex diseases, or other important phenotypic traits, are more likely to be targets of natural selection than random genes 10 of the I(R2) p-values in a set of 770 genes containing at least one significant SNP from a GWAS study. Genes were divided into three categories depending on whether the SNPs were associated with an autoimmune disorder, another disease, or a quantitative trait. We use the p-values as more appropriate measures of the strength of the evidence rather than the I(R2) themselves. Genes associated with autoimmune diseases show a clear increase in the proportion of genes with low I(R2) p-values , ulcerative colitis (susceptibility), multiple sclerosis , and type 1 diabetes (susceptibility) , as the In recent years, great efforts have been made to assess the role played by natural selection during human evolution Here we developed a statistical framework for identifying signals of adaptation to local environments. We correlated the spatial allele frequency distribution of a large sample of SNPs, genotyped in more than 50 populations distributed worldwide, to a set of environmental factors, describing local geographical features such as climate conditions, diet regimes (measured as subsistence strategies) and pathogen loads.STF or other statistics) are enriched for genic SNPs 2Q I of the variance in allele frequencies among populations can be explained by non-adaptive processes. Nonetheless, we were able to identify a non-negligible contribution of selection. Several loci showed large values (>15%) in the improvement of explained variance 2)II.Genes with a statistically significant Furthermore, we validated our results using low-coverage sequencing data for a smaller set of SNPs and populations, ruling out the possibility that ascertainment bias coupled with a bias in reporting pathogen diversity may lead to the observed prevalence of pathogen-driven selection. We should add that other factors could affect local adaptation than the factors examined here. The quantitative measures used here may not be the ones that correlate most closely with the components of the environment that affect fitness. Other measures of local climate or subsistence, that include variables not examined here might show a stronger effect on local adaptation. However, among the quantitative measures of environmental factors explored here, it is clear that pathogen load has been the most important factor shaping human genetic diversity.It is perhaps not surprising that selection related to pathogens appears to be the most dominating driver of local adaptation, given the number of studies reporting pathogen related selection in humans, including selection on proteins used by pathogens to infect cells  on human genes has been stronger than the one due to viral, protozoa or bacterial agents . PerhapsWe identified signatures of pathogen-mediated selection in 103 distinct human genes. Overall, genes highly correlated with pathogen diversity show a significant enrichment of immunity related functions, according to Gene Ontology analysis . Again twww.immport.org). These genes encode signaling molecules involved in the inflammatory response, such as IL6, LRRC19, and PON2, cell surface proteins participating in immune functions, such as ADAM17, ITGAL, and LAG3, and signal transducers of the innate and adaptive immune response such as MYD88 . In addition to ADAM17, we have identified 9 other genes with high I(R2) values when using pathogen diversity as covariate that also participate in the Toll-like receptor signaling pathway I. Thus, the parasite is likely to have exerted a strong selective pressure during human evolutionary history.The second signaling pathway enriched with 13 genes targeted by pathogen-driven selection genes is Leishmaniasis . LeishmaDendritic cells (DC), sentinels of the immune system, detect Leishmania in vivo. It has been shown that MyD88-dependent receptors are implicated in the direct recognition of Leishmania by DC Genes related to immunity and inflammation regulation are known to be common targets of natural selection Indeed, our data indicate that SNPs with allele frequencies that correlate highly with pathogen variables are enriched for GWAS SNPs associated with autoimmune diseases . Specifip-values, respectively). Most likely, our criterion for selecting extreme genes is more conservative than the one used by Hancock and colleagues. However, when applying their approach to our data set, we retrieved a significant overlap of genes correlated with different environmental factors  transmitted in a given geographic location is a good estimate of the pathogen-driven selective pressure for populations living in that area More accurate worldwide epidemiological data, as well as more detailed description of diet regimes for human population, are required to obtain a clearer picture of the effect of genetic adaptation to pathogen load or subsistence strategies, especially when comparing with adaptation to climate.However, any inadequacies of the statistics we use to measure pathogenic environment will lead us to underestimate the role of the pathogenic environment in human local adaptation. Perhaps pathogen related selection plays an even stronger role in human evolution than what has been evidenced in this study and in previous studies.We investigated the spatial distribution of allele frequencies using genotype data for 55 distinct human populations, comprising more than 1,500 individuals, by joining data from the Human Genome Diversity Panel (HGDP-CEPH) A total of more than 500k SNPs were analyzed after removing those not covered in both panels and those located on sex chromosomes . We usedhttp://genome.ucsc.edu). In case of multiple isoforms, the longest transcript was used. A total of 225,502 and 216,151 polymorphisms were classified as genic and intergenic, respectively. A total of 14,804 genes containing at least one genotyped SNP was retrieved.Two categories of SNPs were considered: genic and intergenic. SNPs were defined as genic if they were located in transcribed regions or were no further than 500 bp upstream transcription start sites. SNPs were defined as intergenic if they were located in a region larger than 100 kbp containing no annotated gene, according to USCS Genome Browser database of gene predictions based on data from RefSeq, Genbank, CCDS and UniProt (http://www.1000genomes.org/). Low-coverage SNP genotypes for each one of the nearly 1,5 K analyzed genes located on chromosome 1 were organized in a MySQL database. Populations from countries not included in the HGDP-CEPH panel were excluded. A total of 727 unrelated individuals belonging to 9 distinct populations located in 8 different countries were analyzed. A set of programs was developed to retrieve genotypes from the database and to analyze them according to selected populations. These programs were developed in C++ using the GeCo++ Data from the 1000 Genomes Project We defined a set of environmental variables for each country from which SNP data were available. Previous studies examining signatures of adaptation to local climates, selected specific variables to represent the physiological effects of different climates on humans http://www.esrl.noaa.gov/psd/data/reanalysis/reanalysis.shtml) by averaging annual values across the last 50 years. Subsistence strategy data were collected from Murdock's Ethnographic Atlas (1967): for each population we retrieved the percentage of activity spent in each of the examined subsistence activities. For three populations we could not assess an unambiguous set of subsistence values. The number of different pathogen species (pathogen richness) was retrieved from the Gideon database (http://www.gideononline.com/), as in references We obtained climatic data from the NCEP/NCAR Reanalysis Project database  multiple regression We applied a Projection to Latent Structures (F) of dimensions 55x1 and environmental predictors matrix (M) of 55x14 dimensions. F describes minor allele frequency at each population for the examined SNP, whereas M describes all the 14 environmental variables for each population. For each regression we computed the cross-validated prediction accuracy (2Q), estimated by a leave-one-out procedure, as:PRESS is the Predictive Residual Sum of Squares calculated from the models obtained on the reduced data of the leave-one-out procedure, and SS is the Sum of Squares of F corrected for the mean. Formally, PRESS is the sum of squares of the differences between observed and predicted responses:SS is computed as:N is the number of observations (55 populations in our case), thi population and PLS regressions and model parameters estimation).For each SNP we assessed the relationship between population allele frequencies matrix  overlapping blocks  and drawing n/b blocks. Block sizes were set to 40 and 100 contiguous SNPs corresponding to segments of approx. 200 k bp and 500 k bp on average, respectively. Bins with less than 100 SNPs were merged with the immediately lower bin. The results were qualitatively similar using 40 and 100 SNPs, and only the results for 40 SNPs are discussed in the main text. The results for 100 SNPs are also provided in We divided the distribution of STF, a measure of population genetic difference, was estimated as previously proposed http://genome.ucsc.edu). For each retrieved gene we computed population genetic distances, as proposed by Reynolds and colleagues Nearly 15,000 genes containing at least one genotyped SNP were retrieved, according to UCSC Genome Browser database (Y) and the distance matrix for environmental variables (X) via partial Mantel correlations X and Y correspond to a population. Y contains locus specific population genetic distance values and X contains environmental distances. Partial Mantel correlations are a non-parametric statistical procedure for quantifying association between two distance matrices, while controlling for the effect of a third distance matrix. The latter independent distance matrix, Z, is here the overall population genetic distance among populations For each gene we assessed the relationship between the locus-specific population genetic distances matrix (I(R2), and used this as a measure of the relative importance of each environmental variable in explained the distribution of allele frequencies for a particular gene.Our procedure, therefore, accounts for the non-independence of populations and controls, at least in part, for the correlations caused by standard neutral demographic processes . For eacI(R2) is calculated as:R2 is the explained variance of the model, estimated as:YZr is the correlation coefficient between Y and Z, while XY/Zr is the partial correlation coefficient between X and Y given Z defined as:XYr is the correlation coefficient between X and Y while XZr is the correlation coefficient between X and Z.Y) and recalculating our statistic for the permuted data. Rows were permuted only within the same stratus (continent). P-values are then calculated as the fraction of permuted values that are greater than the observed value of the statistic. This imposes the need for a large number of permutations when estimating small p-values which is computationally expensive and unfeasible for some problems. To reduce computational time we computed approximate p-values using a previously proposed asymptotic method p-values were computed by approximating the right tail of the distribution of permuted statistics by a Generalized Pareto distribution. Parameters of the Pareto distribution are fitted using either the asymptotic maximum likelihood method or a ‘combined method’ previously proposed P-values were corrected for multiple testing using a procedure which controls the false discovery rate under dependence assumptions Statistical significance was assessed by permuting rows (populations) for the dependent matrix  analyses were performed with GONOME www.genome.jp/kegg) in the following hierarchical categories: Immune system, Immune system diseases, Neurodegenerative diseases, Infectious diseases. Enriched pathways were retrieved as having a significantly higher than expected number of associated genes using 10,000 bootstrap samples. For GO analyses we considered pathogen-associated genes to be those having an uncorrected I(R2) p-value lower than 5e-3 in order to increase the number of analyzed loci and thus statistical power.Analyses of functional pathways were investigated querying the KEGG database (www.genome.gov), updated on December 1st, 2010.Genome-wide association studies (GWAS) data were retrieved from A Catalog of Published Genome-Wide Association Studies Figure S1th confidence interval computed with 1,000 bootstrap resamplings on overlapping blocks of 100 contiguous SNPs.Enrichment of genic  or non-synonymous  vs. intergenic SNPs  for different values of prediction accuracy. Peach region denotes 90(EPS)Click here for additional data file.Figure S2UPGMA (Unweighted Pair Group Method with Arithmetic Mean) clustering of populations according to the overall population genetic distance matrix. Each node of the dendogram represents a distinct population and is labeled regarding its continental origin .(JPG)Click here for additional data file.Figure S3Frequencies of genes displaying different values of improvement of explained variance with three distinct models, comprising only pathogen diversity, subsistence strategies and climate conditions , separately (A); and when testing each variable separately and taking the maximum value for each environmental category (B).(EPS)Click here for additional data file.Figure S4Frequencies of genes on chromosome 1 displaying different values of improvement of explained variance with three distinct models, comprising only pathogen diversity, subsistence strategies and climate conditions, using low-coverage new-generation sequencing data from 1000 Genomes Project.(EPS)Click here for additional data file.Table S1List of sampled populations with specification of their country, continental group and number of genotyped individuals.(XLS)Click here for additional data file.Table S2Chromosomal location for the entire set of analyzed SNPs.(XLS)Click here for additional data file.Table S3Environmental variables for each population. Values were averaged for each country.(XLS)Click here for additional data file.Table S4STF or recombination rate.Enrichment of genic SNPs for different classes of similar Minor Allele Frequencies (MAF), (PDF)Click here for additional data file.Table S52)I(R) values and their p-values for the whole set of genes.Improvement of explained variance (termed (XLS)Click here for additional data file.Table S6Genes having at least one significantly associated SNP with Bayenv software (ranked Bayes factor >0.995) for one variable for each environmental class.(XLS)Click here for additional data file.Table S7Gene ontology analysis results (Function and Component domains) for SNPs mapping on genes which correlate with pathogen diversity.(PDF)Click here for additional data file.Table S8Annotation of genes correlated with pathogen diversity.(XLS)Click here for additional data file.


Motivation: Genotype imputation methods are used to enhance the resolution of genome-wide association studies, and thus increase the detection rate for genetic signals. Although most studies report all univariate summary statistics, many of them limit the access to subject-level genotypes. Because such an access is required by all genotype imputation methods, it is helpful to develop methods that impute summary statistics without going through the interim step of imputing genotypes. Even when subject-level genotypes are available, due to the substantial computational cost of the typical genotype imputation, there is a need for faster imputation methods.Results: Direct Imputation of summary STatistics (DIST) imputes the summary statistics of untyped variants without first imputing their subject-level genotypes. This is achieved by (i) using the conditional expectation formula for multivariate normal variates and (ii) using the correlation structure from a relevant reference population. When compared with genotype imputation methods, DIST (i) requires only a fraction of their computational resources, (ii) has comparable imputation accuracy for independent subjects and (iii) is readily applicable to the imputation of association statistics coming from large pedigree data. Thus, the proposed application is useful for a fast imputation of summary results for (i) studies of unrelated subjects, which (a) do not provide subject-level genotypes or (b) have a large size and (ii) family association studies.Availability and implementation: Pre-compiled executables built under commonly used operating systems are publicly available at http://code.google.com/p/dist/.Contact:dlee4@vcu.eduSupplementary information:Supplementary data are available at Bioinformatics online. Genome-wide association studies (GWASs) have been successful in detecting associations between genetic variants and complex diseases .Most commonly used genotype imputation tools, e.g. IMPUTE2  and BEAGTo directly impute summary statistics while (i) substantially reducing the computational burden and (ii) retaining imputation accuracy, we propose Direct Imputation of summary STatistics (DIST). DIST avoids the imputation of subject-level genotypes by directly applying, to unmeasured SNP statistics, the classical conditional expectation formula for multivariate normal variates.Supplementary Material). To reduce computation time, DIST is implemented in C++, which ensures that it can be easily used under Linux, Windows, MacOS etc. DIST takes as input a file containing the  GWAS/meta-analysis summary statistics . It provides a command line interface with various options for specifying the number of measured SNPs to be contained in (i) the prediction window and (ii) each side region of the extended window, and so forth (Supplementary Table S1).DIST imputes the statistics at the unmeasured SNPs in a prediction window as a function of (i) the statistics at measured SNPs in a larger window, henceforth denoted as extended window, and (ii) the correlation matrix of both measured and unmeasured statistics, as estimated from a relevant reference dataset. Similar to BLIMP , DIST usSection 2 in Supplementary Material). Imputations used Europeans in 1KG as the reference sample and were performed on a single Linux machine (Intel Xeon 2.67 GHz processor and 64 GB of RAM).We compare the performance of DIST with the performance of typical HMM and MM methods. Given the speed and accuracy of SHAPEIT phasing . The pheZ-scores in the above 50 simulations, as measured by the squared correlation coefficient (r2) between imputed and true Z-scores, is high for DIST (0.98) and IMPUTE2 (0.99) and moderately high for PLINK (0.92) (The average accuracy of imputed K (0.92) . The avewww.uk10k.org) as the reference panel .To impute untyped statistics, DIST requires only the joint correlation matrix for the statistics at typed and untyped SNPs. Because this matrix does not depend on the relationship between subjects in the study, unlike genotype imputation methods, DIST can be readily used to impute statistics for family association studies. We illustrate this advantage by applying the method to a proprietary Irish alcohol dependence study sample consisting of 1755 controls and 710 cases from 431 Irish families. The subjects were genotyped using Affymetrix 6.0 SNP array, and the association statistics were computed using MQLS . To impuP-values but (i) do not have access to subject-level genotypes, (ii) do not want to go through the laborious process of imputing subject-level genotypes or (iii) have association statistics coming from (large) pedigree data. Unlike genotype imputation methods, as the available reference panels are increasing in size, DIST can avoid incurring large increases in running time/memory by storing the local correlation structures into pre-computed tables.DIST is a novel tool for direct imputation of summary statistics at untyped SNPs. When compared with genotype imputation methods, DIST (i) does not need access to subject-level genotypes, (ii) provides comparable imputation accuracy while substantially shortening the running time and (iii) can be readily applied to family association statistics. Consequently, DIST is useful for investigators who need fast and fairly accurate access to imputation-based When compared with genotype imputation methods, DIST uses a smaller imputation window and requires that study and reference populations to be well matched. Thus, when access to subject-level genotypic data is available, genotype imputation methods are likely to outperform DIST (i) for regions with long-range linkage disequilibrium, e.g. major histocompatibility complex locus, and (ii) when the study and the reference populations are not well matched. Consequently, whenever possible/appropriate, we recommend to follow-up DIST signals using a genotype imputation method.Funding: Virginia Commonwealth University start-up fund (to S.A.B.)Conflict of Interest: none declared.


There is increasing empirical evidence that whole-genome prediction (WGP) is a powerful tool for predicting line and hybrid performance in maize. However, there is a lack of knowledge about the sensitivity of WGP models towards the genetic architecture of the trait. Whereas previous studies exclusively focused on highly polygenic traits, important agronomic traits such as disease resistances, nutrifunctional or climate adaptational traits have a genetic architecture which is either much less complex or unknown. For such cases, information about model robustness and guidelines for model selection are lacking. Here, we compared five WGP models with different assumptions about the distribution of the underlying genetic effects. As contrasting model traits, we chose three highly polygenic agronomic traits and three metabolites each with a major QTL explaining 22 to 30% of the genetic variance in a panel of 289 diverse maize inbred lines genotyped with 56,110 SNPs.We found the five WGP models to be remarkable robust towards trait architecture with the largest differences in prediction accuracies ranging between 0.05 and 0.14 for the same trait, most likely as the result of the high level of linkage disequilibrium prevailing in elite maize germplasm. Whereas RR-BLUP performed best for the agronomic traits, it was inferior to LASSO or elastic net for the three metabolites. We found the approach of genome partitioning of genetic variance, first applied in human genetics, as useful in guiding the breeder which model to choose, if prior knowledge of the trait architecture is lacking.e.g. for novel traits which only recently received attention in breeding, we suggest to inspect the distribution of the genetic variance explained by each chromosome for guiding model selection in WGP.Our results suggest that in diverse germplasm of elite maize inbred lines with a high level of LD, WGP models differ only slightly in their accuracies, irrespective of the number and effects of QTL found in previous linkage or association mapping studies. However, small gains in prediction accuracies can be achieved if the WGP model is selected according to the genetic architecture of the trait. If the trait architecture is unknown  Whole-genome prediction (WGP) is expected to reshape plant breeding fundametally in the near future -3. Whereβ-carotene [e.g. for rust [In maize, several economically important traits are genetically less complex with few quantitative trait loci (QTL) explaining a large proportion of the genetic variance. Examples include pest and disease resistances or nutrifunctional compounds such as bioavailable minerals  or β-carcarotene . In addifor rust , Giberelfor rust ,15 or tofor rust ,17.et al.[et al.[et al.[For such traits, the assumption of normally distributed SNP effects underlying ridge regression, the most commonly applied WGP model, is severely violated. Heslot et al. found fol.[et al. simulatel.[et al. found alCattle differs greatly in its population structure and LD level from elite maize germplasm, which has faced severe genetic bottlenecks during domestication and the creation of genetically distinct heterotic pools to maximize exploitation of heterosis in hybrid breeding ,22. HencTo fill this apparent gap of knowledge, we investigated WGP in a diverse collection of 289 maize inbred lines with traits which largely vary in their genetic architecture. To let the genetic basis differ as much as possible, we chose three highly polgygenic agronomic traits and three metabolites, each one controlled by a different major QTL explaining about 22% to 30% of genetic variance. With this empirical set-up, we asked the following questions: ● To what extent do distinct WGP models differ in their prediction accuracies for a diversity panel of maize inbred lines if the genetic architecture of the trait changes dramatically?● Are there guidelines for plants concerning the choice of the most promising WGP model?The genetic material consisted of 289 maize inbred lines which were previously described in great detail -25. The r2=0.1 at approximately 500 kb with a mean LD between adjacent SNPs of 0.34 [The population was genotyped with the Illumina SNP chip MaizeSNP50 containing 56,110 SNPs . Quality of 0.34 .α-lattice design with two replications and were planted in 2-row plots. Plots were thinned to a final plant density of 100,000 plants/ha. The common check genotypes were used to adjust for potential differences in the soil fertility among trials in each environment.The population was phenotyped in six environments  in Germany . Brieflyr|≤0.10) and only weakly (|r|≤0.28) correlated with agronomic traits (Table Leaf samples were collected in one location 33 d after sowing and processed using an established GC-MS method . GenotypDry matter yield of whole-plant biomass (t/ha) and plant height (m) were measured per field plot of the inbred lines. Lignin content was measured as acid detergent lignin (ADL) in the harvested plant material of the inbred lines using calibrated near-infrared spectroscopy (NIRS). The NIRS calibration model was built using phenotypic data from 20 inbred lines, 32 testcrosses and 3 hybrids grown in the same environments as the population of inbred lines analyzed in this study . HeritabTo further characterize the genetic architectures of the investigated traits irrespective of the significance thresholds for SNP-trait associations, we compared how the ten chromosomes contributed to the total genetic variance. Later on, we will use these results as a guideline for model selection based on trait architecture.et al.[We adopted the approach of Yang et al. to simuly is a vector with n trait values, 1is a vector of 1’s, Qis a matrix of size n×10 containing the first 10 principal components calculated from SNP data with β containing the corresponding regression coefficients, S is an incidence matrix allocating components of yto components of gc, which is a vector of length n with random genotypic effects attributable to chromosome c with Zc is a matrix of size n×pcwith standardized levels of SNP alleles on chromosome c. Vector e contains normally distributed residuals with c was then estimated as where Gcwere often found to be singular, we used the algorithm of Higham [Variance components were estimated by restricted maximum likelihood (REML) using ASReml-R 3 . Since mf Higham  implemenf Higham , to apprWe investigated five WGP models that have been recently advocated in the literature for this purpose ,32-34.All based upon the classical regression set-up y is a vector with n trait values, μ is the overall mean, 1 is a vector with 1’s, Z is the n×p matrix of standardized values of SNP alleles, u is a vector with SNP effects, and e is a vector of residuals with where p≫nproblem in WGP by minimizing the residual sum of squares (RSS=(y−1μ−Zu)T(y−1μ−Zu)) by bounding the Euclidean (L2) norm of u to a constraint: Ridge regression (RR) tackles the s (RSS=y−μ−ZuT(y−1λRRis a regularization parameter which controls the amount of shrinkage. It can be estimated as u as random effects with u[The Lagrangian multiplier LUP) of u,36.For computational convenience, RR-BLUP can be transformed to a mathematically equivalent model g being a vector of random genotype effects with var(g) = G=ZZT/p. The solution vector of SNP effects can then be obtained as G is an inner-product kernel which allows to perform all computations in the space of n genotypes instead of p SNPs, a shortcut which is well established in the field of kernel-based machine learning [with R=ZTG−1g^. Here, Glearning .L1 penalty to tackle the p≫nproblem [As an alternative to ridge regression, it was suggested to use an nproblem . This esnproblem ,40,41. TL1) norm of u to a constraint: i.e., it is not possible to transform the LASSO estimator into an equivalent kernel regression problem in the space of n genotypes [which bounds the Manhattan L norm of enotypes . Hence, enotypes .The LASSO penalty is known to be somewhat indifferent to the choice among a set of strong but correlated variables. The RR penalty, on the other side, tends to shrink the coefficients of correlated variables toward each other . The elaα=0) and the LASSO penalty (α=1) [α and λEN, which yielded the lowest mean squared error in the training population.and is a weighted mixture between the RR penalty (ty (α=1) . While tty (α=1) . We agaiG with a kernel matrix K. The motivation behind RKHS regression lies in the ability to effectively perform non-linear regression in a higher-dimensional feature space so it might capture non-additive genetic effects, if present. Here, we used a Gaussian kernel on genetic distances with ij is the modified Rogers’ genetic distance  between genotype i and j, and θ is a smoothing parameter which controls the rate of decay of Kij with increasing genetic distance. The optimum value for θwas chosen from a sequence from 0.1 to 100 at which the maximum likelihood was obtained.The theory of RKHS regression is rooted in the field of kernel-based machine-learning  and has t-distributed with a point-mass at zero [th post burn-in iteration were stored. For computational convenience, we reduced the number of markers to 5,000 SNPs for which we did not observe any decline in prediction accuracy up to the numerical precision reported in this study.As a Bayesian approach, we used a modified version of BayesB, which has a prior assumption that the SNP effects are  at zero . Followi at zero , we modey) and predicted (g) and was calculated by h is the square root of the heritability on a line-mean basis for the agronomic traits. For metabolites, the square root of the estimated repeatability was used.A five-fold cross-validation scheme was applied and repeated 20 times. In each repetition, the dataset was divided into 5 disjoint subsets of genotypes whereas one subset served as the validation set and the other four subsets served as the training population to estimate the model parameters for predicting the left-out genotypes in the validation set. In each of the five rounds, the Pearson correlation between the observed and predicted phenotypic values was calculated. The procedure was repeated twenty times to yield 100 cross-validation runs. The predictive ability was then calculated as the Pearson correlation .For the agronomic traits, the total genetic variance was largely uniformly distributed over all chromosomes. Using the same GWA model as for the metabolites , we founP<0.10) for lignin content  and dry matter yield . The grey area in Figure r=0.98,P=0.003) with the explained genetic variance of the individual SNPs found by GWA mapping  can be gained if the WGP model is selected according to the genetic architecture underlying the trait.et al.[Arabidopsis thaliana, maize, and wheat. For the metabolites, however, our results differ from those obtained from Clark et al.[Recently, Heslot et al. reportedrk et al., who invrk et al.. Althougr2=0.1 at ≈ 500 kb), accuracies are quite similar irrespective whether the effect of large QTL are precisely captured  or spread over a larger region (as in the case of RR-BLUP and RKHS). Since our population was highly diverse for elite maize germplasm in Europe, it is unlikely that breeders are confronted with lower levels of LD unless they work with highly exotic germplasm for which LD has been reported to decline within 5-10 kb [One major reason of the minor differences in prediction accuracies among the different models lies in the high level of LD found in elite breeding germplasm of maize. Our results suggest that with this level of LD  non-additive, epistatic genetic effects are not present, (ii) these are so small that they are negligible in WGP for the investigated traits, or (iii) RKHS regression is unable to capture them. In either case, for prediction purposes RKHS does not seem to yield any advancements over RR-BLUP for situations comparable to our germplasm and traits. Dominance, as another source of non-additive genetic, effects cannot be present in the inbred lines investigated in this study. For predicting heterozygeous Fcuracies .Although BayesB reached for 5 of the 6 traits a higher prediction accuracy than the worst model, we cannot recommend it because of the excessively larger computation time and the negliable differences in prediction accuracies compared with RR-BLUP in case of the metabolites as the result of probably only sampling error.L2 penalty (RR-BLUP), the L1penalty (LASSO) or a mixture of both penalties (elastic net) performed better in the case of the metabolites with a strong convex curve curvature  different WGP models differ only slightly in their prediction accuracies, irrespective of the number and effects of QTL found in association analysis, (ii) small gains in prediction accuracies can be obtained if the WGP model is selected according to the genetic architecture of the trait, (iii) genome partitioning of genetic variance offers a straightforward approach for model selection if the genetic architecture is unknown. The question of which WGP model to choose is therefore not expected to hamper implementation of WGP in maize breeding.The authors declare that they have no competing interests.CR analyzed the data and wrote the manuscript. AEM supervised the research. FT wrote the C code for implementing BayesB. All authors read and approved the final manuscript.


Eucalyptus trees (family Myrtaceae) are well-known for their high foliar content of several classes of secondary metabolites and these have a strong effect on the feeding patterns of several species of marsupials and at least some insects. Best known are the essential oils, which is mostly a mixture of terpenoids, but there are also significant concentrations of flavonoid and formylated phloroglucinol compounds. There is extensive quantitative and qualitative variation within and between species of Myrtaceae in these chemical groups and all appear to be under strong genetic control with heritabilities (2H) between 0.3 and 0.9. As well as being important ecologically, the terpenes in particular are valued as industrial and medicinal products and Australia supports a strong essential oil industry focused on Eucalyptus and Melaleuca foliar oils.Eucalyptus grandis genome provides the opportunity to discover the genetic makeup of the biosynthetic pathways for secondary metabolites. We present data from pathways leading into the biosynthesis of terpenes, flavonoids and lignins. The homology of genes and gene families were investigated and compared to a variety of other species including poplar (Populus trichocarpa), grape (Vitis vinifera) and apple . For example, terpene synthases  has 120 members in the genome of Eucalyptus grandis, compared to 44 and 99 in poplar and grape, respectively  studies that investigated variability in secondary metabolites and wood properties in eucalypts. This approach allowed the discovery of candidate genes for a large number of QTL.The Eucalyptus globulus, investigating 200 SNPs and roughly 40 traits ranging from terpenoids to terpene-adducts to flavonoids and to tannin-related traits. We discovered several significant trait associations between allelic variants in the chloroplastic MEP pathway and monoterpenes and between the cytosolic MVA pathway and sesquiterpenes, as well as one allelic variant in a prenyl pyrophosphate synthase that associates with the ratio of monoterpenes to sesquiterpenes. Loci with significant associations were mapped to the Eucalyptus grandis genome and compared to published QTL datasets that investigated similar traits. These results represent the first species wide analysis of the molecular basis of quantitative variation in secondary metabolites in any tree.Understanding the genetic basis of variations in quantitative traits provides insights into ecosystem function and at the same time may help breeders in the essential oil industry. We have characterized trait associations with polymorphisms from The publicly available genome sequence of Eucalyptus grandis is a great resource that can be applied to a variety of questions including the genetic make-up of gene families for biosynthesis of plant secondary metabolites, genome organization of these genes and evolution of traits such as resistance to herbivores or the ability to re-sprout after fire. Combining studies of association genetics, QTL studies together with the genome sequence helps to shed light on the underlying control mechanisms of phenotypic variation.