Our empirical results demonstrate that phantom epistasis can be a very serious problem in GWAS studies . Some studies have sought to avoid this problem by only testing interactions between SNPs with R-sq. <0.1. We show that this threshold is not appropriate and demonstrate that the magnitude of the problem is even greater with large sample size, intermediate allele frequencies, and when the causal locus explains a large amount of phenotypic variance. We conclude that caution must be exercised when interpreting GWAS results derived from very large data sets showing strong evidence in support of epistatic interactions between markers.The genetic architecture of complex human traits and diseases is affected by large number of possibly interacting genes, but detecting epistatic interactions can be challenging. In the last decade, several studies have alluded to problems that linkage disequilibrium can create when testing for epistatic interactions between DNA markers. However, these problems have not been formalized nor have their consequences been quantified in a precise manner. Here we use a conceptually simple three locus model involving a causal locus and two markers to show that imperfect LD can generate the illusion of epistasis, even when the underlying genetic architecture is purely additive. We describe necessary conditions for such “ Genome-wide-association (GWA) studies address part of this challenge by testing for the association between phenotype (or a disease indicator) with genotype, one locus at a time. In the last decade, many GWA studies were conducted; these studies have reported thousands of SNPs (single nucleotide polymorphism) associated to complex traits and diseases . Under those conditions, evidence supporting the existence of a non-null interaction between markers does not necessarily provide definite evidence of epistasis at causal loci. Specifically, when the SNPs used in association analyses are in imperfect LD with the alleles at causal loci, linear regression on SNPs may lead to unaccounted variance, or missing heritability  and of the (multilocus) LD involving the two markers and the QTL genotypes. In the population, given the centered genotype codes, the regression coefficients entering in the right-hand-side of [2] areb) and of pair-wise (1st order) LD but also of higher order LD, e.g., joint disequilibrium at three loci, D-coefficients for two and three loci linkage disequilibrium; see section 1 of the Supplementary Methods for further details).We begin by considering a simple model with three biallelic loci. One of them, denoted as In the population, the interaction effect first necessary conditiona  is that the QTL must be in LD with at least one of the SNPs. If the QTL is in LE with the two markers, then second necessary condition for phantom epistasis to emerge is imperfect LD between the QTL and the marker pair. This guarantees that some fraction of the QTL variance is not captured by linear regression on the two marker genotypes. Furthermore, if the left-out QTL signal is not orthogonal to the interaction contrast On the other extreme, if there is perfect LD between the QTL and the marker pair third necessary condition for phantom epistasis to emerge is that the three loci must be jointly in LD.Consider now an intermediate case where one of the markers  model becomes first, imperfect LD between Second, phantom epistasis requires mutual LD at the three loci. If one of the markers  that explained either 0.5 or 1% of the phenotypic variance. The position of the QTL genotype In a We analyzed the simulated phenotypes using an instrumental model such as the one in [2] extended with inclusion of an intercept and the top 5 SNP-derived PCs to avoid confounding due to any substructure that may be present (see section 3 of Supplementary Methods for details). The null hypothesis -package .Since the power to detect a non-null interaction effect depends on sample size we analyzed data using a sample sizes of n = 10K, 50K, 100K and 250K .To assess the potential impact of long-range LD, in a new analysis setting we maintained the QTL-proximal-marker pair .To consider the problem of phantom epistasis in multi-locus models we Second, we simulated data using a model that contains three marker-QTL pairs: nd pair in the middle point (based on base-pair distance). The empirical model used to test for interaction was as that in expression [2] with http://www.ukbiobank.ac.uk/register-apply/. The Institutional Review Board (IRB) of Michigan State University has approved this research with the IRB number 15-745. Supplemental material available at Figshare: https://doi.org/10.25387/g3.7848233.The genotypes used in the simulation were from the UK Biobank. Data were acquired under project identification number 15326. The data are available for all bonafide researchers and can be obtained by applying at We begin presenting results from our main simulation scenario which involves a single-locus with two SNPs, one proximal  rejection rates were maximum for intermediate allele frequencies and decreased with extreme allele frequencies. This is likely a consequence of the fact that intermediate allele frequencies confer higher power to the test.Finally, SNPs in different chromosomes are provided in Table S1. In all cases, the rejection rates were very close to 0.05 suggesting that phantom epistasis between SNPs on different chromosomes, if it exists, it occurs at a rate that does not induce an inflation of rejection rates above the significance level.The results from the model with infinitesimal effect. The empirical rejection rates were almost identical to those obtained, for the same sample size, with the single-QTL model  increased, the estimated rejection rates approached the nominal rejection rate. Specifically, when the distance between the 1st and the 2nd pair is of 2Mb or larger the three pairs become independent and phantom epistasis vanishes.The results from a scenario involving et al.; however, in each case, using sequence data, a single third variant could explain all the apparent epistasis. This happened even after removal of all pairs of SNPs with There is a substantial amount of literature reporting the presence of epistasis affecting complex traits but results, when scrutinized, have been controversial. Sometimes the controversy spawns from the suspicion that epistatic interactions may be capturing additive signals that were missed by the baseline additive model used to test interactions. For instance, simultaneous but imperfect mutual LD between the three loci (the QTL and the two markers involved in the interaction). This conceptually simple three loci model can be extended to more complex settings  without affecting the underlying source of the principle: if additive QTL variance is imperfectly captured by linear regression on markers and the unexplained variation is not orthogonal to interaction contrasts, then phantom epistasis emerges.However, the problem of why and under what conditions additive effects may generate “epistatic signals” has not be formalized. In this work, we considered a simple three locus model to reveal conditions that lead to phantom epistasis. We show that phantom epistasis emerges in the presence of e.g., We stress that simultaneous LD between the triplet Several authors  can lead to large numbers of false discoveries especially when sample size is large. However, our simulations also show that near independence between the two SNPs , a condition that in the data set used in this study was achieved at distances of 1.5Mb-2Mb or longer, was enough in the scenarios tested to guarantee rejection rates very close to the significance level.Testing interactions among weakly correlated SNPs only  generates clear signs of phantom epistasis. However, rejection rates are not highly elevated over the significance level when sample size was smaller (n = 10k) because at that R-sq. the size of the interaction effect is small and therefore the power to detect such small interaction effect with small sample size is low. Big Data are a blessing for genomic analysis of complex traits; however, in some cases, large sample size can make an inferential problem even more problematic.If phantom epistasis exists  showed, as one would expect, higher rejection rates than the one observed when the QTL explained a small fraction of the phenotypic variance  may lead to more serious apparent epistasis.The presence of e.g., e.g., Several studies have reported results highlighting the importance of ‘local’ epistatic interactions . Therefore, with the size of samples used in standard GWA studies, lack of normality of the error term should not be a cause for inflated rejection rates.Based on an earlier version of this manuscript Dr. P. Visscher  commented that under imperfect LD the distribution of the error terms of the empirical model is not normal. Indeed, because the QTL genotype has three levels, under imperfect LD the distribution of the error terms would be a mixture of three normal distributions with different means. This could certainly explain the inflation of rejection rates in small samples because the conditions for the test statistic to follow a A second possible cause for inflated rejection rate of the null hypothesis can be underestimation of the error variance of the empirical model. However, it can be shown that the estimator of the error variance of the empirical model used in the simulations is unbiased with respect to the marginal distribution of the data. Therefore, phantom epistasis cannot be attributed to underestimation of the error variance.e.g., Quantitative genetics studies properties of complex traits using regression analysis. In the field a careful distinction is made between observable and causal features of complex traits. For instance, it is well established that the linear regression of a phenotype on allele content yields estimates of the average effect of allele substitution and that both truly additive as well as dominance and epistatic effects can contribute to allele substitution effects. Furthermore, theoretical and empirical research has demonstrated that highly non-linear systems can generate signals that can often be explained almost completely with a linear model . For thiThe recognition that phantom epistasis may be an important phenomenon does not negate the relevance of gene-gene interactions at the causal level. It simply stresses the difficulties that one faces when trying to learn about causal features of a system using observational data and inputs (markers) which are proxies for the underlying variants that may have causal effects on traits.In this work, we have stressed that imperfect LD can limit the possibility to learn about causal effects. However, linear and non-linear genomic regressions can be very powerful predictive machines, and it is well established that the model that is best for inferences is not necessarily the best predictive tool. Phantom epistasis creates inferential problems but also opens opportunities for improving prediction models. Indeed, by capturing signals that are missed by an additive model, non-linear models using interactions between markers may increase the amount of genetic variance captured and improve prediction accuracy. This may explain, for instance why some non-linear models such as kernel regressions have shown better predictive performance than additive models, especially in breeding populations with long-span LD and low marker density (


The importance of expression quantitative trait locus (eQTL) has been emphasized in understanding the genetic basis of cellular activities and complex phenotypes. Mixed models can be employed to effectively identify eQTLs by explaining polygenic effects. In these mixed models, the polygenic effects are considered as random variables, and their variability is explained by the polygenic variance component. The polygenic and residual variance components are first estimated, and then eQTL effects are estimated depending on the variance component estimates within the frequentist mixed model framework. The Bayesian approach to the mixed model-based genome-wide eQTL analysis can also be applied to estimate the parameters that exhibit various benefits. Bayesian inferences on unknown parameters are based on their marginal posterior distributions, and the marginalization of the joint posterior distribution is a challenging task. This problem can be solved by employing a numerical algorithm of integrals called Gibbs sampling as a Markov chain Monte Carlo. This article reviews the mixed model-based Bayesian eQTL analysis by Gibbs sampling. Theoretical and practical issues of Bayesian inference are discussed using a concise description of Bayesian modeling and the corresponding Gibbs sampling. The strengths of Bayesian inference are also discussed. Posterior probability distribution in the Bayesian inference reflects uncertainty in unknown parameters. This factor is useful in the context of eQTL analysis where a sample size is too small to apply the frequentist approach. Bayesian inference based on the posterior that reflects prior knowledge, will be increasingly preferred with the accumulation of eQTL data. Extensive use of the mixed model-based Bayesian eQTL analysis will accelerate understanding of eQTLs exhibiting various regulatory functions. Identification of expression quantitative trait loci (eQTLs) is of great interest to geneticists studying the underlying genetic mechanisms of cellular activities and complex phenotypes. A genome-wide eQTL analysis makes it possible to determine a profile of regulatory signals for a single gene at a time. Recent technological developments have accelerated data production for genome-wide eQTL analysis. Research efforts have been made to obtain RNA-seq data to examine the profiles of eQTLs for all expressed genes in a single cell. For example, the Geuvadis consortium produced RNA-seq data using lymphoblastoid cell lines derived from 462 individuals participating in the 1,000 Genome Project  of gene expression levels; n is the number of the gene expression levels; β is the vector (nl × 1) of fixed effects such as sex, age, and candidate nucleotide variant effects; nl is the number of the fixed effects; X is the design matrix (n × nl) for the fixed effects; g is the vector (n × 1) of random polygenic effects; ε is the vector (n × 1) of random residuals. To identify eQTL, β includes the minor allele effect of the candidate single nucleotide variant, and the corresponding column of X includes elements of 0, 1, and 2 as the number of minor alleles under the assumption of an additive genetic model with a biallelic single nucleotide variant. The random variables g and ε in the analytical model have the following normal distributions:where I is the identity matrix (n × n); A is the genomic similarity matrix (n × n) with elements of pairwise genomic similarity coefficients based on genotypes of single nucleotide variants. The genomic similarity coefficient (ajk) between individuals j and k can be calculated as follows  of minor alleles for the single nucleotide variant i of the individuals j and k; fi is the frequency of the minor allele.where Unlike fixed model analyses, the mixed model analyses for genome-wide eQTL mapping additionally includes random polygenic effects and the corresponding variance component, as shown above. Marginal posterior distribution is required for each unknown parameter in the Bayesian inference. Marginalization can be attained by using an MCMC-based numerical integration as mentioned above. This review presents a Gibbs sampler as an MCMC for mixed model-based Bayesian eQTL analysis.The conditional density function of all parameters given gene expression levels is defined based on Bayes' theorem as follows:f indicates function. Since the denominator f(y) is not a function of the parameters, the conditional density function is proportional to the numerator, i.e.,where g, which depends on the hyperparameter of The left-hand side is called posterior, and this is proportional to the product of the likelihood corresponding to A) is dropped in the formula to avoid confusion with parameters, i.e., Note that conditioning on the known genomic similarity matrix (f(β) is assumed to have uniform distribution. The Second, Thus, the joint posterior density is presented as follows:g and κε are scale parameters of the scaled inverse chi-square distributions for g and ωε are shape parameters (degrees of freedom) of the distributions.where κFull-conditional posterior density for each parameter is derived from the joint posterior density. Removing independent components of the parameter from the density function helps to determine the kernel of the full-conditional posterior density. As a result, full conditional density of a scalar solution of fixed and random effects exhibits the following Normal distribution:Cs = r is equivalent to where coefficient matrix yy] Lee, .The full conditional density of the polygenic variance component shows the following scaled inverse chi-square distribution:where Sample individual fixed and random effects consecutively from the full conditional density of described by Equation (1).ε = y − Xβ − g).Calculate residuals .Calculate quadratics for residuals.Sample the residual variance component from the full conditional density as described in Equation (3).The Gibbs sampler requires intensive iterative sampling from the consecutively updated full conditional posterior distributions. Prior to the intensive iteration, arbitrary initial values are set for parameters. Each round of iteration in the Gibbs sampling, for example, consists of the following consecutive steps:mth sample after the burn-in period functions to reduce lag correlation among samples produced by the Markov chain and thus avoids sample size inflation. The m is termed the “thinning interval” for the Gibbs chain.Burn-in periods and thinning intervals are determined to collect samples for posterior distributions of parameters. Samples generated until the Gibbs chain approaches a stationary distribution are all discarded as a burn-in period. Saving only every g) of the prior distribution for the variance component. This avoids the improper prior, and the resulting posterior distribution largely reflects the likelihood in practice.A key advantage of the Bayesian approach is that it applies prior knowledge to statistical inference. When prior knowledge on the parameters is unavailable in a Bayesian approach, uninformative or flat prior is intuitively considered. Such an application should be used with caution, as it may lead to a theoretically improper prior  by using either the Gauss-Seidel iteration  and the best linear unbiased predictor (BLUP), respectively. Sample-based estimates of polygenic and residual variance components, instead of unknown variance components, are used at every round of the Gibbs chain. Conversely, the frequentist approach first to estimates the variance components and then estimates the fixed and random effects, based on the variance component estimates. This produces a problem of non-BLUE and non-BLUP conditions by violating the assumption of known variance components required for BLUE and BLUP Lee, . FurtherUncertainty in the unknown polygenic and residual variance components is reflected in the Bayesian analysis, by treating the unknown parameters as random variables. The Bayesian analysis results in a probability distribution  for each parameter. This enables us to make straightforward inferences concerning the parameters. For example, specific credible intervals for every parameter can be directly obtained using the samples generated from the posterior distribution by the Gibbs sampler. This credible interval is interpreted as a range within which a parameter value falls, with a specific probability. This is intuitively more acceptable than the confidence interval, with which frequentists interpret the confidence level as the proportion of the confidence intervals that contain the true value of parameter when confidence intervals are repeatedly estimated from independent sample statistics. Of course, confidence intervals are not repeatedly estimated in reality. As uncertainty is also reflected by the probability distribution, the Bayesian analysis does not require large samples. Given this, the resulting posterior allows for the calculation of probability of the true parameter  although the posterior might show the dispersed distribution with a large variance. Conversely, a large amount of data is necessary as the core assumption for the frequentist approach .cis-eQTL) and/or candidate eQTL analysis. Furthermore, only a representative variant within each linkage disequilibrium block can be considered for identifying eQTLs. Second, reduction in computational burden can be achieved by employing efficient algorithms. For example, use of Hamiltonian Monte Carlo can reduce the number of iterations, by decreasing autocorrelation between successive samples, as explained above. Third, parallel computation is important to reduce computation time. Analyses by individual candidate genes or by their groups can be carried out simultaneously. This also helps reduce computing time in solving a gene- or eQTL-specific problem. Lastly, computation time is reduced by high performance computing facilities. In particular, cloud computing provides efficient techniques for intensive parallel computing (Hamdaqa and Tahvildari, Some strategies might be useful to reduce computation time. First, computational burden is reduced by limiting the amount of analyses. After a preliminary study, only a limited number of genes and/or loci can be subsequently examined by the Bayesian analysis. For example, Bayesian inference might be applied to a genome-wide eQTL analysis, with the candidate genes identified by transcriptome-wide association analysis, or to regional (e.g., This review is provided for geneticists to understand the various backgrounds of mixed model-based Bayesian eQTL mapping. This may aid geneticists to overcome their skepticism of the Bayesian approach. As small or even negligible differences are often observed in practice between estimates resulting from the Bayesian approach and the frequentist approach, geneticists tend to possess a neutral point of view concerning these approaches, and they are reluctant to employ the Bayesian method simply because of its difficulty in theory and computation. As explained in this review, the advantages of the Bayesian approach are considerable and can be applied to the mixed model-based eQTL analysis. In particular, the inference on probability distribution of parameters in the Bayesian approach, provides a major advantage by reflecting uncertainty in unknown parameters. In comparison, the frequentist approach requires a large number of samples to estimate the true parameter as a critical assumption. Sample size for genome-wide eQTL analysis is not usually large, particularly in comparison to those of genome-wide association analyses of complex phenotypes. The prior is becoming important, as systems genetics improves in conjunction with a dramatic increase of eQTL data in the near future. The Bayesian approach will considerably aid researchers to examine eQTLs and understand their regulatory functions by characterizing eQTLs using various techniques.The author confirms being the sole contributor of this work and has approved it for publication.The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


We identify 43 tissue‐specific gene associations with Dupuytren's risk, including one in a novel risk region. We also estimate the genome‐wide genetic correlation between Dupuytren's disease and 45 complex traits and find significant genetic correlations between Dupuytren's disease and body mass index (BMI), type II diabetes, triglycerides, and high‐density lipoprotein (HDL), suggesting a shared genetic etiology between these traits. We further examine local genetic correlation to identify 8 and 3 novel regions significantly correlated with BMI and HDL respectively. Our results are consistent with previous epidemiological findings showing that lower BMI increases risk for Dupuytren's disease. These 12 novel risk regions provide new insight into the biological mechanisms of Dupuytren's disease and serve as a starting point for functional validation.Dupuytren's disease is a common inherited tissue‐specific fibrotic disorder, characterized by progressive and irreversible fibroblastic proliferation affecting the palmar fascia of the hand. Although genome‐wide association study (GWAS) have identified 24 genomic regions associated with Dupuytrens risk, the biological mechanisms driving signal at these regions remain elusive. We identify potential biological mechanisms for Dupuytren's disease by integrating the most recent, largest GWAS  with eQTLs (47 tissue panels from five consortia, total  This resulted in 24 independent risk regions.We used PLINK , the Metabolic Syndrome in Men study , the Young Finns Study , the CommonMind Consortium , and the Netherlands Twin Registry  reference panels  as a function of the vector of GWAS summary Z‐scores at a given cis‐region (ZGWAS) and the weights vector (wGE) learned from one of the 47 gene expression panels aforementioned. Specifically, the strength of association between predicted expression of a gene in tissue and DD is defined aswGE′ is the transpose weights vector and V is the reference panel LD  is obtained using a two‐tailed test under N. This process was repeated for each reference tissue panel and gene, resulting in 98,147 tissue‐specific gene models involving 15,189 genes (Table S1). We assessed significance with the Bonferroni‐corrected threshold at PTWAS≤0.0598,147.FUSION estimates the strength of association between predicted expression of a gene and DD (2.3rˆg) between DD and another trait as significant if the associated p‐value from cross‐trait LDSC passed the Bonferroni‐corrected threshold of PT1,T2≤0.0545.We estimate the genome‐wide genetic correlation between DD and 45 complex traits to identify shared genetic risk for DD with other complex traits. To this end, we used cross‐trait LDSC  between two traits at a given region was defined as significant if the associated p‐value from ρ‐HESS passed the Bonferroni‐corrected threshold of Pregion≤0.051,702.To understand the genome‐wide correlation from cross‐trait LDSC at a local level we use ρ‐HESS  and the local genetic correlation for all trait 2 specific regions are summed ; these summed values are a good representation of true genetic correlation at trait 1 specific regions or trait 2 specific regions. Confidence intervals are determined by 1.96 times jackknife standard error on each side; significance is determined if the confidence intervals do not overlap. If trait 1 correlation is significantly nonzero while trait 2 correlation is near zero, then this is consistent with a model that trait 1 causally influences trait 2. The intuition behind this test is that if trait 1 causally influences trait 2 then trait 1 specific regions would have a strong genetic correlation with trait 2 but trait 2 specific regions would not have a strong genetic correlation with trait 1. To avoid spurious claims, we only do this test if there are more than 10 regions harboring GWAS significant SNPs for each trait. Thus, we can leverage the difference in correlations for a trait‐specific signal at these regions to see if the correlations are consistent with a suggestive causal model  annotations, each of which represents a set of genes that are specifically expressed in a single tissue or cell type  as well as in 5115 study‐defined cell types  using single cell RNA‐seq data from 28 studies .We also used the web application FUMA , associated with DD (see section 2). Briefly, TWAS identifies candidate risk genes for DD by integrating results from GWAS and reference panels of gene expression measurements from eQTL studies to associate cis‐regulated expression with DD, while accounting for LD. We used tissue reference panels from GTEx . This region has been previously investigated because of its strong association signal (Odds Ratio 1.93 and PGWAS = 7.2 × 10−41) with DD  and (2) that the TSS of the TWAS‐gene is not within 0.5 Mb of the previously known 24 risk regions. With these constraints, we identified one novel risk region for DD , was significantly associated with DD risk at this region . There were 12 tissue panels that expression for TMEM106A was modeled from (Table S3).To identify possible novel risk regions from TWAS associations, we aimed to see if any tissue‐specific gene models were independent of established GWAS associations. After grouping association signal into 1 Mb regions, we found 13 regions with only significant GWAS SNP(s), 1 region with only significant TWAS model(s), and 11 regions with both significant GWAS SNP(s) and TWAS model(s). Here we define a region identified through TWAS to be novel if (1) the strongest DD associated SNP in the gene's region is not genome‐wide significant  and  that the0−8) and  that the3.3We obtained an SNP‐heritability estimate of 0.67 (SE = 0.08), using LDSC : body mass index (BMI), rˆg=−0.196; high density lipoprotein (HDL), rˆg=0.133; triglycerides (TG), rˆg=−0.139; and type II diabetes (T2D), rˆg=−0.182 ; differences may have resulted from using metabochip array  between DD and BMI, three regions between DD and HDL, and no regions between DD and TG or between DD and T2D .Having found evidence for BMI, HDL, TG, and T2D sharing genetic factors with DD at a genome‐wide scale, we next aimed to locate possible shared genomic regions. We did this by running ρ‐HESS ; this is most likely because of the relatively reduced sample size in the DD GWAS study. Nonetheless, there is evidence of a putative causal relationship with BMI affecting TG , the effect was strongest in cell transformed fibroblasts (Table S7). We then assessed whether the GWAS gene set was enriched in any of the differentially expressed gene (DEG) sets for tissues. The upregulated DEG sets for tibial artery and aorta tissues both demonstrated significant  overlap with the GWAS gene set (Table S8). We also performed a gene property analysis using cell type specific expression data for 5115 study‐defined cell types from 28 scRNA‐seq studies , stromal cells and muscle cells were among the top five results (Table S9). As a final analysis, we averaged the χ2‐statistic (TWASZ2) for the 43 significant TWAS models within each tissue to determine which tissue had the most enrichment of TWAS signal. We found adipose subcutaneous tissue was most enriched among the 23 tissues with significant TWAS models . Because of the lack of consistency between methods and lack of statistical significance in many methods, we are lead to believe that likely the relevant tissue or cell type is not represented in current datasets.Finally, we aimed to identify relevant tissues or cell types for DD. First, we used S‐LDSC  is relatively close to estimates of heritability from twin studies (0.8). We also note that the strong concentration of DD GWAS signal in a handful of genomic regions is more consistent with an oligogenic architecture than a polygenic one, suggesting that further functional studies could be particularly fruitful as compared to more polygenic traits and diseases. We also identify a negative genetic correlation between DD and BMI, supporting a previous epidemiological study that observationally showed a negative correlation between the traits (Hacquebord et al., Additionally, we note a few caveats in our results. First, though the sample size of 8,557 for the DD GWAS is the largest yet, it is possible that additional GWAS regions remain undiscovered due to the limit in power and this also would further reduce power to fully detect associations and relationships with other traits. Second, while the patterns of genetic correlation between BMI and DD as well as TG and DD are somewhat consistent with causal relationships, true causality between these traits cannot be determined without functional experimentation. Third, we emphasize that TWAS may not detect the true mechanism of disease if the gene expression is not mediated through genetics or if disease‐relevant tissue is not well‐represented in available gene expression reference panels. This may be further illustrated by the fact we were unable to identify a specific tissue or cell type to prioritize for further study in DD. This could also be due to the small sample size of the DD GWAS, the cell‐type specificity of enhancer elements, or again the publication bias away from musculoskeletal connective tissues, leading to a gap in the available datasets.EPDR1 may contribute to the pathogenesis of DD; further work should be dedicated to functionally validate and understand this gene in connection with DD, as it may represent an attractive therapeutic target. Second, there is strong evidence for a relationship between BMI/TG and DD‐elucidating the mechanism may lead to interesting observations with implications for the treatment of both traits. Third, additional GWAS, with larger sample sizes and in additional populations, will uncover more of the contribution of genetic variation to DD. And fourth, given the putative oligogenic architecture of DD, and that our tissue and cell type analyses lacked consistent results, it might also be rewarding to generate more functional‐omics data, such as reference gene expression panels or chromatin accessibility data in the palmar fascia tissue. These resources would offer valuable insight into the underlying mechanisms of DD and opportunity to explore therapeutic avenues.Future work should be taken in multiple directions. First, we provide additional evidence that The authors declare that there are no conflict of interests.https://www.omim.org/OMIM: https://www.cog‐genomics.org/plink2/PLINK: http://gusevlab.org/projects/fusion/FUSION: https://gtexportal.org/home/GTEx Portal: https://data.broadinstitute.org/alkesgroup/LDSCORE/LD scores and annotations: https://data.broadinstitute.org/mpg/depict/depict_download/tissue_expression/DEPICT: http://fuma.ctglab.nl/FUMA: The data that support the findings of this study are available from the corresponding author upon reasonable request.Supporting informationClick here for additional data file.Supporting informationClick here for additional data file.


A. thaliana. We found that allometric relationships between traits constrain phenotypic variation in a nonlinear and similar manner in hybrids and accessions. These allometric relationships behave predictably, explaining up to 75% of heterosis amplitude, while genetic distance among parents at best explains 7%. Thus, our findings are consistent with Wright’s model of physiological dominance and suggest that the emergence of heterosis on plant performance is an intrinsic property of nonlinear relationships between traits. Furthermore, our study highlights the potential of a geometric approach of phenotypic relationships for predicting heterosis of major components of crop productivity and yield.Heterosis describes the phenotypic superiority of hybrids over their parents in traits related to agronomic performance and fitness. Understanding and predicting nonadditive inheritance such as heterosis is crucial for evolutionary biology as well as for plant and animal breeding. However, the physiological bases of heterosis remain debated. Moreover, empirical data in various species have shown that diverse genetic and molecular mechanisms are likely to explain heterosis, making it difficult to predict its emergence and amplitude from parental genotypes alone. In this study, we examined a model of physiological dominance initially proposed by Sewall Wright to explain the nonadditive inheritance of traits like metabolic fluxes at the cellular level. We evaluated Wright’s model for two fitness-related traits at the whole-plant level, growth rate and fruit number, using 450 hybrids derived from crosses among natural accessions of  The phenotypic superiority of hybrids — “hybrid vigour” or heterosis — is often considered to be a biological mystery. Rooted on the mathematical modelling of trait variation, however, this study demonstrates that it can be explained simply with the non-linearity of phenotypic relationships. Arabidopsis thaliana. Rooted in the mathematical modelling of phenotypic relationships, our study demonstrates that heterosis can be explained simply with the nonlinearity of trait variation. Our model notably predicts the amplitude of heterosis of two performance traits: growth rate and fruit production. We expect that our model can help to understand the physiology of nonadditive inheritance in different species and that it will open new avenues in both theoretical and applied biology.Hybrids often grow faster and produce more offspring than their parents. This phenomenon, called hybrid vigour or heterosis, has been extensively exploited in agriculture. Even though several hypotheses have been proposed to explain the genetic basis of hybrid superiority, there is still no unifying model able to accurately predict the extent and amplitude of heterosis. Here, we tested a model based on physiological constraints to explain the emergence of heterosis in the model plant  If the inheritance of phenotypic traits was additive, progenies would always exhibit intermediate trait values compared to their respective parents. Genetic nonadditivity is, however, a common result of intraspecific crosses. It has been exploited for decades in agronomy –5, althoAa) contributes to the superiority of the hybrid compared to both homozygotes (AA or aa). Pseudo-overdominance corresponds to cases in which dominant, favourable alleles are in linkage with recessive, unfavourable alleles so that the heterozygous combinations appear to behave as overdominant loci. These different mechanisms are not mutually exclusive, and they can all operate at the same time in a given species, which can explain some of the contradictory results observed in different studies. The picture is further complicated by the contributions of epistasis , f[M], We focused on two traits with important evolutionary and agronomic outcomes: growth rate and fruit number. As predicted by the MST ,58, thesllometry ,60,88, gWe first compared what fraction of heterosis can be explained by genetic and phenotypic distances between inbred parents. For all hybrids, we quantified heterosis as the observed phenotypic deviation relative to mid-parent heterosis (MPH) value and best parental heterosis (BPH) value. Pairwise genetic distances were calculated either with all SNPs in the genome or with SNPs in the 1% top-genes associated with the corresponding trait . For ther2 = 0.05, r2 = 0.09, P < 0.001; r2 < 0.10). Even when combined in a multivariate model, genetic and phenotypic distances together explained less than 10% of heterosis of growth rate and fruit number  and to the predicted best-parent value (NLDevBP)—with the observed MPH and BPH .The high fraction of negative heterosis observed in our study for plant biomass is consistent with previous findings in thaliana ,71, alththaliana ,73. It cthaliana , for insthaliana . Autoimmthaliana . Moreovethaliana , we did A. thaliana populations pointed to a positive but weak correlation between heterosis and parental genetic distance for growth rate but no such correlation for fruit number. This suggests that a genetic approach alone may not be sufficient to accurately predict heterosis. By contrast, our results indicate that phenotypic nonlinearity determines the emergence of heterosis. We have shown that even if vegetative dry mass exhibited important deviation from additivity, it could still be used to predict heterosis of growth rate and fruit number based on parental allometric relationships. Our model notably predicts that strong heterosis of biomass  is always associated with strong heterosis of growth rate. However, strong heterosis of biomass can be associated with negative heterosis of fruit number because fruit number is linked to biomass with a hump-shaped curve. For instance, consider a case in which two parents are to the right of the fitness peak: it is expected that BPH of biomass results in fewer fruits than for either parent. As observed in yeast )From a theoretical point of view, the predominance of outcrossing and the maintenance of recessive alleles among organisms have been suggested to be directly linked to nonadditive inheritance and superior performance of hybrids . Wright’A. thaliana, which highlights the power of a geometric approach of trait–trait relationships for predicting heterosis related to two major components of plant productivity and yield. It opens promising avenues for cultivated species with a perspective of targeting optimal crosses based on allometric relationships in parental lines. However, several differences between crops and A. thaliana might hamper the prediction of heterosis based on allometric relationships. For instance, the genetic architecture of metabolism and performance-related traits could differ in crops compared to A. thaliana. Strong selection for high-yielding lines in crops may have reduced genetic variability in modern varieties and may have modified to a certain degree the relationship between genetic and phenotypic distance. Deleterious recessive alleles may have been purged in cultivated species as a result of domestication and human selection. Unfortunately, most plant species that have been evaluated for inbreeding depression and heterosis are cultivated species, and we lack a proper comparison of wild and cultivated species regarding these processes. In addition, traits other than biomass  could be relevant for prediction of hybrid performance in crops, especially in field conditions. For instance, plant height might be more related to grain yield than biomass, as suggested by the quadratic relationship between these traits in wheat ..M (mg). P = 0.03). We thus corrected trait values in Exp 2 with the following equation: agecorrected at reproduction = −37 + 1.8 × ageobserved at reproduction.To correct for potential biases between the two experiments performed, 16 accessions phenotyped in Exp 1 were also included in Exp 2. Among all traits measured, only plant age at reproduction exhibited a significant difference between the two experiments (t test (ɑ = 0.05) as well as to the worst and best parent values using a one-sided t test (ɑ = 0.05). To determine the significance of heterosis categories , P values were adjusted for multiple testing by a Bonferroni correction.First, hybrid phenotypic classes were categorized by comparing trait distribution in hybrids to mean and best (or worst) parental values. Trait distributions for hybrids were obtained from a bootstrap approach with 1,000 permutations. Each F1 trait distribution was compared to the mean parental value using a two-sided Y, i.e., growth rate and fruit number:Secondly, two metrics commonly used in the literature to quantify heterosis  were calMPH, the deviation of observed hybrid value scaled to observed mean parental value:BPH, the deviation of observed hybrid value scaled to observed best parental value:nls function in R [g[M] in y = axebx−) and inverse polynomial function. The inverse polynomial equation . We then predicted mean parental value of growth rate as MPpred = (g[M1] + g[M2])/2 and best parental value as BPpred = max. Finally, we predicted the phenotypic nonlinearity asWe used the allometric equations fitted on the accessions to predict the phenotype of the hybrids from vegetative dry mass the nonlinear deviation of predicted hybrid value scaled to predicted mean parental value :NLDevMPand the nonlinear deviation of predicted hybrid value scaled to predicted best parental value :NLDevBPMP and NLDevBP were calculated for growth rate, and we performed similarly for estimating the nonlinearity of fruit number (Both NLDevt number .http://1001genomes.org/) ), we fitted a mixed model (lmer function in R) as Y = Genotype + residuals, in which Y is trait value and Genotype is used as random factor. Statistical analyses were conducted in R v3.2.3 [10 scale Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S1 Fig10-transformation of trait values in the 451 accessions (red dots and line) and 447 hybrids (blue dots and line). Slopes after log10-transformation represent the scaling exponent without transformation. SMA, standard major axis.Slopes measured from SMA regressions after log(TIF)Click here for additional data file.S2 Fig−1) predicted by phenotypic nonlinearity (brown dots) and genetic additivity  and compared to observed hybrid value (n = 447). (B) Hybrid fruit number predicted by phenotypic nonlinearity (brown dots) and genetic additivity  and compared to observed hybrid value (n = 449). r2 are Pearson’s coefficients of correlation (***P < 0.001). Dashed line represents 1:1 line. NS, nonsignificant.(A) Hybrid growth rate (mg/d(TIF)Click here for additional data file.S3 Fign = 447). (B) Relationship between hybrid growth rate and BPH of growth rate (n = 447). (C) Relationship between hybrid growth rate and MPH of growth rate (n = 449). (D) Relationship between hybrid growth rate and BPH of growth rate (n = 449). r2 are Pearson’s coefficients of correlation. BPH, best-parent heterosis; MPH, mid-parent heterosis.(A) Relationship between hybrid growth rate and MPH of growth rate ((TIF)Click here for additional data file.S4 Fig(A) Seed production experiment performed in 2013 at MPI-Tübingen (Germany). After manual crossing or self-fertilization, mother flowers were isolated in small paper bags until fruit ripening. Seeds for accessions and hybrids used in this study came from the same mother plants. (B) RAPA growth chamber at MPI-Tübingen with trays of accessions phenotyped during Exp 1 in 2014. MPI-Tübingen, Max Planck Institute for Developmental Biology in Tübingen; RAPA, Raspberry Pi Automated Plant Analysis.(TIF)Click here for additional data file.


The associations between higher intelligence test scores from early life and later good health, fewer illnesses, and longer life are recent discoveries. Researchers are mapping the extent of these associations and trying to understanding them. Part of the intelligence-health association has genetic origins. Recent advances in molecular genetic technology and statistical analyses have revealed that: intelligence and many health outcomes are highly polygenic; and that modest but widespread genetic correlations exist between intelligence and health, illness and mortality. Causal accounts of intelligence-health associations are still poorly understood. The contribution of education and socio-economic status — both of which are partly genetic in origin — to the intelligence-health associations are being explored. Current Opinion in Psychology 2019, 27:6–12GeneticsThis review comes from a themed issue on Brian B Boutwell and Michael A WhiteEdited by Issue and the EditorialFor a complete overview see the Available online 23rd July 2018https://doi.org/10.1016/j.copsyc.2018.07.005http://creativecommons.org/licenses/by/4.0/).2352-250X/© 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license  is associated with an increased risk of developing Alzheimer’s disease. Limitations of the candidate gene method include the fact that most candidate gene findings are not replicated (APOE e4 possession is an exception to this), and that it is difficult to choose a candidate genetic variant from the millions that are known. Third, genetic linkage analysis was used to track genetic markers in families where specific phenotypes were common, to identify regions of the genome that segregate with the phenotype. The main limitations of this method are that large families are required and it identifies relatively large regions of the genome, rather than specific genetic variants or genes.Before the mid-2000s, genetic studies were done by three main methods. First, pedigree-based  studies of relatives’ phenotypic associations were used to estimate the heritability of phenotypes, and genetic correlations among them. Limitations of pedigree methods include the fact that several assumptions must be made in doing the modelling, and that one does not learn about the specific genes involved. Second, candidate gene studies tested hypotheses concerning whether certain genetic variants were associated with phenotypic differences. For example, the possession of the e4 allele of the gene for Apolipoprotein E (Box 11. Genome-wide association study (GWAS)P-value of <5 × 10−8 is usually considered genome-wide significant. As GWASs do not analyse every variant in the genome they do not usually identify causative variants, but rather indicate regions of the genome that are implicated in a particular phenotype. If the same regions of the genome are identified in GWASs of multiple phenotypes this may indicate that the phenotypes share genetic aetiology.GWAS is used to identify genetic variants associated with phenotypes. For diseases, large numbers of cases and controls are genotyped using testing arrays, most commonly from the companies Illumina or Affymetrix. The arrays contain up to 1 million genetic variants spread throughout the genome. For quantitative traits, large numbers of individuals on whom the trait is measured are genotyped. Using reference datasets, for example, Hap Map, 1000 Genomes and the haplotype reference consortium (HRC), several million genetic variants are then imputed to give greater genomic coverage and to harmonize datasets genotyped using different genetic testing arrays, containing different variants. Logistic (for case control) or linear (for quantitative traits) regressions are then performed between each genetic variant and the phenotype. As millions of regressions are performed for each phenotype a -genomic-relatedness-based restricted maximum-likelihood single component (GREML)2. Genome-wide complex trait analysis (GCTA)GREML  is used 3. Bivariate GCTABivariate GCTA  is an ex4. Linkage disequilibrium (LD) regressionLD regression ,31 is a 5. Polygenic scores (PGS)PGS analysis uses summary GWAS data for a given phenotype to test whether polygenic liability to that phenotype is associated with the same or different phenotype measured in an independent sample. It allows the amount of variance in one phenotype attributed to the polygenic score for the same or a second phenotype to be calculated. A PGS for a particular phenotype can be calculated for each individual in a sample, by summing the known effect size of each individual SNP (obtained from a GWAS of that phenotype) multiplied by the number of reference alleles present for that SNP in a particular individual. PGSs can be calculated using PRSice . For exa6. Mendelian Randomization (MR)The methods described above will indicate whether or not two phenotypes share genetic aetiology, but do not reveal the direction of causation. Once shared genetic aetiology between two phenotypes is established, MR methods can be used to investigate whether one phenotype directly influences the other phenotype, or whether genetic variants independently affect both phenotypes. Bi-directional MR allows each phenotype to be used as the exposure or the outcome in turn, potentially providing support for the direction of effect. In MR, genetic variants (often variants that are genome-wide significantly associated with the relevant phenotype) are used as instrumental variables (IV) for the exposure. Unlike the exposure itself, these genetic variants should be largely independent of confounding factors and reverse causation. The IV is used to estimate if the exposure causally influences the outcome. There are three basic assumptions of MR: Firstly, the genetic variants are associated with the exposure; secondly, the genetic variants are only associated with the outcome of interest via their effect on the exposure; and finally, the genetic variants are independent of confounders of both the exposure and the outcome. Biological pleiotropy, whereby a genetic variant independently influences multiple traits, may violate the second assumption. The more SNPs that make up the IV the more likely that biological pleiotropy will be present. Methods have now been developed that test and correct for biological pleiotropy . Two-samAlt-text: Box 1This changed with the advent and rise of genome-wide association studies (GWASs)  See Box. Sample The typical finding — there are exceptions — in health and cognitive GWASs is that many genetic variants of small effect contribute to phenotypic variation. In 2017, a survey of the first ten years of GWASs’ discoveries enumerated the SNPs that were associated with, for example, Crohn’s disease, diabetes, blood lipid levels, heart function, height, bone density, red blood cell traits, metabolic traits, blood platelets, breast cancer, rheumatoid arthritis, blood metabolites, menarche, Alzheimer disease, kidney function, lung function, and education . Often, In 2011 the first apparently-decently-sized GWAS of intelligence appeared (N approximately 3500), and found no significant SNPs . By the Three things are clear. First, higher intelligence in early life is a significant predictor of better health behaviours, fewer and later illnesses, and longer life. Second, many of the relevant health and illness outcomes, as well as health behaviours, have many SNPs associated with them, and have a detectable level of common-SNP-based heritability. Third: the same goes, genetically, for intelligence. Relatively new methods — bivariate extension of GREML run on GCTA , and LD The list of significant molecular genetic correlations between intelligence and physical health variables is now long •,25••,32As described above, genetic correlations have been identified between intelligence and many diseases, and physical health traits; moreover, polygenic scores for diseases and health traits predict intelligence. However, it is not clear if these findings are due to: (1) genetic variants influencing health traits/diseases, and then those health traits/diseases influencing intelligence; (2) genetic variants influencing intelligence, and then intelligence influencing health traits/diseases; or (3) genetic variants influencing general bodily system integrity  that infUsing a bi-directional two-sample MR approach we identified no causal association between intelligence or educational attainment (a proxy measure of intelligence), and the physical health traits of body mass index (BMI), systolic blood pressure, height, coronary artery disease and type 2 diabetes , using dAnother part of understanding the genetic contribution to intelligence-health correlations concerns other predictors of health inequalities, and intelligence’s correlations with them. Intelligence, we saw earlier, is related to education and socio-economic status (SES), and those were known to be related to health inequalities before intelligence was known to have health associations. Although education and SES are principally thought of as social-environmental variables, both have been found to be partly heritable, by both twin-based and molecular genetic studies, both have high genetic correlations with intelligence, Mendelian Randomisation results show bidirectional genetic effects between intelligence and education, and both have genetic correlations with health outcomes ,43,44,45Intelligence has predictive power for many health outcomes. Part of that association is genetic. The genes involved, and the causal pathways of the associations are being explored.IJD and SEH are supported by the University of Edinburgh Centre for Cognitive Ageing and Cognitive Epidemiology which is funded by the UK Medical Research Council and Biotechnology and Biological Sciences Research Council (Grant no. MR/K026992/1). WDH is supported by Age UK (Disconnected Mind programme).Nothing declared.• of special interest•• of outstanding interestPapers of particular interest, published within the period of review, have been highlighted as:


The logistic mixed model (LMM) is well-suited for the genome-wide association study (GWAS) of binary agronomic traits because it can include fixed and random effects that account for spurious associations. The recent implementation of a computationally efficient model fitting and testing approach now makes it practical to use the LMM to search for markers associated with such binary traits on a genome-wide scale. Therefore, the purpose of this work was to assess the applicability of the LMM for GWAS in crop diversity panels. We dichotomized three publicly available quantitative traits in a maize diversity panel and two quantitative traits in a sorghum diversity panel, and them performed a GWAS using both the LMM and the unified mixed linear model (MLM) on these dichotomized traits. Our results suggest that the LMM is capable of identifying statistically significant marker-trait associations in the same genomic regions highlighted in previous studies, and this ability is consistent across both diversity panels. We also show how subpopulation structure in the maize diversity panel can underscore the LMM’s superior control for spurious associations compared to the unified MLM. These results suggest that the LMM is a viable model to use for the GWAS of binary traits in crop diversity panels and we therefore encourage its broader implementation in the agronomic research community. The genome-wide association study (GWAS) is one of the most widely used quantitative genetics analyses in agronomy due to its potential to unlock the genomic sources of phenotypic variation . Used asThe unified mixed linear model , which An extensive amount of research has been conducted for quantitative trait locus (QTL) analysis of binary traits in biparental crosses and related experimental populations. Many of these approaches assume that there is an unobserved continuous trait  that underlies the binary trait; individuals with liability values that exceed an unknown threshold have a value of “1” (instead of “0”) for the binary trait . The likImportant strides in the development of statistical approaches to analyze binary traits and to account for spurious associations have also been made outside the realm of QTL analyses. For example a considerable amount of work has been done in human case-control studies , which The purpose of this study was to compare the performance of the LMM to the unified MLM when analyzing binary traits in real crop diversity panels. To achieve this, we dichotomized three quantitative traits in a maize diversity panel and two quantitative traits in a sorghum diversity panel, and then conducted a GWAS on these dichotomized traits using both the LMM and the unified MLM. We also simulated an additional two binary traits using the maize data set to explore how well the LMM and unified MLM control the type I error rate in the presence of subpopulation structure. The objectives of this work were to i.) assess whether or not the LMM is capable of identifying the same peak marker-trait associations as those reported in the analysis of the original quantitative traits, and ii.) use agronomic data to determine if the LMM is capable of superior control of spurious associations for binary traits where the observed proportion of “1’s” differ across subpopulations, as was originally demonstrated using human case-control and simulated data in . We wereth percentile were given a value of “1”, while the remaining lines were given a value of “0”. The second dichotomization was conducted in a similar manner, except that all lines with trait values greater than the 75th percentile were given a value of “1” and the remaining lines were given a value of “0”. Given that the observed proportion of “0’s” and “1’s” in a binary trait could theoretically range from , these two dichotomizations were essential for determining whether or not any advantages in the performance of the LMM for binary trait were specific to a particular observed ratio of “0’s” and “1’s”. All genotypic, phenotypic, and R scripts used in this work are available at: https://figshare.com/articles/Shenstone_et_al_2018_zip/7212902.We used publicly available phenotypic and genotypic data from two crop diversity panels to conduct our analyses. One of these diversity panels consists of maize lines, while the other consists of sorghum lines. To assess the performance of the LMM for binary traits where there were roughly an equal number of observed “0’s” and “1’s”, as well as for binary traits where there was an unequal number of “0’s” and “1’s”, we dichotomized  each of five studied quantitative traits twice. First, for a given quantitative trait, all lines with trait values greater than the 50α-tocopherol grain content, was measured in the subset of 252 lines originally published in  distribution would suggest inadequate control of type I errors.To further explore the influence of unequal proportion of “1’s” of a binary trait among these two subpopulations on the empirical null distribution of th percentile of each trait. For each of these five dichotomized traits, we then used marker data in the respective maize and sorghum diversity panels to conduct a GWAS using two statistical models, specifically the LMM and the unified MLM. For each trait, the performance of each model was evaluated by assessing how well they controlled for spurious associations and how many statistically significant marker-trait associations that they identified. Both the LMM and the unified MLM appeared to adequately control for spurious associations when commonly used diagnostic approaches were implemented (α-tocopherol in maize and plant height in sorghum), either an equal or greater number of statistically significant associations were identified by the LMM. These significantly associated SNPs identified using both models colocalized to the same genomic regions harboring the most significant marker-trait associations in the published GWAS results of the original quantitative traits reported in , th percenth percentile. Similar to when these traits were dichotomized using the 50th percentile, the LMM and the unified MLM appeared to sufficiently control for spurious associations  compared to non-tropical lines (0.18), which results in a larger variance for this trait in the tropical subpopulation  and non-tropical (π = 0.05) subpopulations, while the other was simulated to have an equal proportion of “1’s” (π = 0.5) in both subpopulations. Consequently, the former binary trait had substantially different variances in the two subpopulations, while the latter had equal variances regardless of subpopulation Click here for additional data file.S1 FigThe X-axis is the principal component number and the Y-axis is the amount of variance explained. This plot suggests that the first three principal components adequately explain the variation among the genome-wide markers.(TIFF)Click here for additional data file.S2 FigThe X-axis is the principal component number and the Y-axis is the amount of variance explained. This plot suggests that the first three principal components adequately explain the variation among the genome-wide markers.(TIFF)Click here for additional data file.S3 FigP-values from either the unified mixed linear model  or the logistic mixed model . Quantile quantile (QQ)-plots depicting the observed (Y-axis) and expected (X-axis) −log(10) P-values are inserted into each Manhattan plot.The specific trait and species of each plot is indicated in the row labels. The X-axis of each graph is physical position of either the B73_RefGen v2 position of the maize genome (for first three rows) or the Btx623 v2.1 position of the sorghum genome (for the bottom two rows), and the Y-axis shows the −log(10) (TIFF)Click here for additional data file.S4 FigP-values) of SNPs from the logistic mixed model (Y-axis) against those from the unified mixed linear model (X-axis) for the genome-wide association study conducted for α-tocopherol levels in maize grain in the Goodman diversity panel dichotomized at the 50th percentile. Both sets of -log10 are from testing H0: no association between the tested SNP and the phenotype.Plot of -log10((TIFF)Click here for additional data file.S5 FigP-values) of SNPs from the logistic mixed model (Y-axis) against those from the unified mixed linear model (X-axis) for the genome-wide association study conducted for zeaxanthin levels in maize grain in the Goodman diversity panel dichotomized at the 50th percentile. Both sets of -log10 are from testing H0: no association between the tested SNP and the phenotype.Plot of -log10((TIFF)Click here for additional data file.S6 FigP-values) of SNPs from the logistic mixed model (Y-axis) against those from the unified mixed linear model (X-axis) for the genome-wide association study conducted for maize ear height in the Goodman diversity panel dichotomized at the 50th percentile. Both sets of -log10 are from testing H0: no association between the tested SNP and the phenotype.Plot of -log10((TIFF)Click here for additional data file.S7 FigP-values) of SNPs from the logistic mixed model (Y-axis) against those from the unified mixed linear model (X-axis) for the genome-wide association study conducted for sorghum plant height in the US sorghum association panel dichotomized at the 50th percentile. Both sets of -log10 are from testing H0: no association between the tested SNP and the phenotype.Plot of -log10((TIFF)Click here for additional data file.S8 FigP-values) of SNPs from the logistic mixed model (Y-axis) against those from the unified mixed linear model (X-axis) for the genome-wide association study conducted for sorghum branch length in the US sorghum association panel dichotomized at the 50th percentile. Both sets of -log10 are from testing H0: no association between the tested SNP and the phenotype.Plot of -log10((TIFF)Click here for additional data file.S9 FigP-values from either the unified mixed linear model  or the logistic mixed model . Quantile quantile (QQ)-plots depicting the observed (Y-axis) and expected (X-axis) −log(10) P-values are inserted into each Manhattan plot.The specific trait and species of each plot is indicated in the row labels. The X-axis of each graph is physical position of either the B73_RefGen v2 position of the maize genome (for first three rows) or the Btx623 v2.1 position of the sorghum genome (for the bottom two rows), and the Y-axis shows the −log(10) (TIFF)Click here for additional data file.S10 FigP-values) of SNPs from the logistic mixed model (Y-axis) against those from the unified mixed linear model (X-axis) for the genome-wide association study conducted for α-tocopherol levels in maize grain in the Goodman diversity panel dichotomized at the 75th percentile. Both sets of -log10 are from testing H0: no association between the tested SNP and the phenotype.Plot of -log10((TIFF)Click here for additional data file.S11 FigP-values) of SNPs from the logistic mixed model (Y-axis) against those from the unified mixed linear model (X-axis) for the genome-wide association study conducted for zeaxanthin levels in maize grain in the Goodman diversity panel dichotomized at the 75th percentile. Both sets of -log10 are from testing H0: no association between the tested SNP and the phenotype.Plot of -log10((TIFF)Click here for additional data file.S12 FigP-values) of SNPs from the logistic mixed model (Y-axis) against those from the unified mixed linear model (X-axis) for the genome-wide association study conducted for maize ear height in the Goodman diversity panel dichotomized at the 75th percentile. Both sets of -log10 are from testing H0: no association between the tested SNP and the phenotype.Plot of -log10((TIFF)Click here for additional data file.S13 FigP-values) of SNPs from the logistic mixed model (Y-axis) against those from the unified mixed linear model (X-axis) for the genome-wide association study conducted for sorghum plant height in the US sorghum association panel dichotomized at the 75th percentile. Both sets of -log10 are from testing H0: no association between the tested SNP and the phenotype.Plot of -log10((TIFF)Click here for additional data file.S14 FigP-values) of SNPs from the logistic mixed model (Y-axis) against those from the unified mixed linear model (X-axis) for the genome-wide association study conducted for sorghum branch length in the US sorghum association panel dichotomized at the 75th percentile. Both sets of -log10 are from testing H0: no association between the tested SNP and the phenotype.Plot of -log10((TIFF)Click here for additional data file.S15 FigP-values) of SNPs from the logistic mixed model (Y-axis) against those from the unified mixed linear model (X-axis) for the genome-wide association study conducted for binary trait Y simulated in the Goodman maize diversity panel where P{Y = 1} = 0.5 in the non-tropical subpopulation and P{Y = 1} = 0.05 in the non-tropical subpopulation. Both sets of -log10 are from testing H0: no association between the tested SNP and the phenotype.Plot of -log10((TIFF)Click here for additional data file.S16 FigP-values) of SNPs from the logistic mixed model (Y-axis) against those from the unified mixed linear model (X-axis) for the genome-wide association study conducted for binary trait Y simulated in the Goodman maize diversity panel where the P{Y = 1} = 0.5 regardless of the subpopulation. Both sets of -log10 are from testing H0: no association between the tested SNP and the phenotype.Plot of -log10((TIFF)Click here for additional data file.


HERC2) with all three skin pigmentation traits, but also variants associated solely with certain pigmentation traits, namely rs6058017 and rs4911414 (ASIP) with skin sensitivity to sun and tanning abilities, rs12203592 (IRF4) with freckling and rs4778241 and rs4778138 (OCA2) with skin color and tanning. Finally, we assessed significant differences in allele frequencies in comparison with CEU data and our study provides a starting point for the development of prediction models for homogeneous populations with less internal differentiation than in the global predictive testing.Predicting phenotypes from DNA has recently become extensively studied field in forensic research and is referred to as Forensic DNA Phenotyping. Systems based on single nucleotide polymorphisms for accurate prediction of iris, hair and skin color in global population, independent of bio-geographical ancestry, have recently been introduced. Here, we analyzed 14 SNPs for distinct skin pigmentation traits in a homogeneous cohort of 222 Polish subjects. We compared three different algorithms: General Linear Model based on logistic regression, Random Forest and Neural Network in 18 developed prediction models. We demonstrate Random Forest to be the most accurate algorithm for 3- and 4-category estimations . Binomial Logistic Regression was the best approach in 2-category estimations . Our study confirms the association of rs12913832 (The online version of this article (10.1007/s00439-019-02012-w) contains supplementary material, which is available to authorized users. DNA phenotyping is recently one of the most relevant study areas in the forensic field. Predictions of human externally visible characteristics (EVCs) are possible through genotyping of single nucleotide polymorphisms (SNPs). Most of the EVCs, e.g., human pigmentation or hair and facial morphology, are complex polygenic and multifactorial traits, yet they are highly heritable and can be classified into easily described categories  were recruited for our study in 2016. Oral swabs [FloqSwabs hDNA Free (COPAN)] were collected and genomic DNA was extracted using ExtractMe DNA Swab & Semen Kit (Blirt S.A.) according to the manufacturer’s instruction.A total of 222  unrelated individuals from Poland, aged 20–63   gene, (b) rs1800407, (c) rs7495174, (d) rs4778241 and (e) rs4778138 in the oculocutaneous albinism II (OCA2) gene, (f) rs12896399 in solute carrier family 24, member 4 (SLC24A4) gene, (g) rs16891982 in solute carrier family 45, member 2 (SLC45A2) gene, (h) rs12203592 in interferon regulatory factor 4 (IRF4) gene, (i) rs1393350 in tyrosinase (TYR) gene, (j) rs731236 in vitamin D receptor (VDR) gene, (k) rs6058017, (l) rs1015362 and (m) rs4911414 in Agouti signaling protein (ASIP) gene, (n) rs1805007 in melanocortin 1 receptor (MC1R) gene. We chose the SNPs based on their documented association with pigmentation traits within Europe and not the ones that have been reported as an Ancestry Informative Markers (AIM) that correlated more with an ethnic descent rather than with a visible trait, e.g., rs1426654 in SLC24A5  and they were genotyped according to Walsh et al. . This was followed by the multiplex sbe reaction using 1 μl cleaned product, 1 μl SNaPshot reaction mix (Applied Biosystems) and a desired concentration of sbe primers in a total volume of 5 μl. Thermocycling conditions were: 96 °C for 2 min, 25 cycles of 96 °C for 10 s, 50 °C for 5 s, 60 °C for 30 s. The SNaPshot reaction product was cleaned using rSAP and SmartCut buffer (New England Biolabs). Finally, all products were run on an ABI 3130 Genetic Analyzer (Applied Biosystems) with POP-7 on a 36 cm capillary length array and run parameters were optimized to increase sensitivity, i.e. the injection voltage of 2.5 kV for 10 s and run time of 600 s at 60 °C. GeneMapper v4.0 (Applied Biosystems) was used for allele calling.14 autosomal SNPs affecting the general pigmentation were chosen for genotyping in our study. They were: (a) rs12913832 in h et al. . To ensuh et al. . The proV test where the result varied from 0 (corresponding to no association between the variables) to 1 (corresponding to complete association). All analyses were made using the R language v3.5.0 and RStudio IDE v1.1.383.Haploview v4.2 was used to assess the linkage disequilibrium (LD) values for tested SNPs as well as to estimate whether the distribution of genotypes in the training group was consistent with Hardy–Weinberg equilibrium (HWE). The frequencies of alleles and genotypes for subjects, for phenotypes and for comparison with 1000 Genomes data of European Americans   is performed in hidden layers of NN. For categorical variables, the model requires one neuron per each category level. Both RF and NN were defined by the sensitivity, total number of correct calls and LogLoss values, with percentage number of single SNP importance in each model. In addition, H2O package translated our input categorical data using one-hot encoding method  methods), Dplyr v0.78 (implementation of the method used in data manipulation) and Readr v1.3.1 (support for the import of *.xls/xlsx files to R session).Prediction modeling was performed on 150 individuals of the training group using machine learning (ML) approach. We compared three different algorithms: general linear model (GLM), random forest (RF) and neural network (NN). To avoid false-positive results and over-fitting of the model, all ML algorithms, analogically to the study group, used two data sets, namely training (to train the developed model) and testing . Each algorithm uses a different approach, which is vividly shown in Fig. p = 0.0498), rs4778138 (p = 0.0337), rs731236 (p = 0.0097), rs12203592 (p = 0.0056), rs12896399 (p = 0.0010), rs1805007 (p = 0.0018) (data not shown). One SNP, rs7495174, turned out to have a heterozygote status in all training individuals and for that reason, it was excluded from further analyses. When genotype and allele frequencies were considered, we found significant difference between males and females for two OCA2 variants, rs4778241 and rs4778138. The OR values and corresponding p values for 13 SNPs calculated for males and females in the training group can be found in Supplementary Table 2. When we analyzed the association of allele and genotype frequencies with the phenotype, we found significant results for 8 SNPs  for both binomial and multinomial estimations. All OR and corresponding p values with allele and genotype distribution in distinct phenotypes of skin pigmentation traits analyzed in this study can be found in Supplementary Table 3.The frequencies of phenotypic traits are shown in Table R2 > 0.8  and did not contribute any [valuable] information gain from the model.In total, 18 prediction models were developed, namely 6 separate models for binomial and multinomial estimations for each algorithm tested. To specify the best-fitting model, we conducted a grid search over distinct hyperparameters that were specific to each algorithm. They were: for RF—number of trees, maximum depth of trees, minimal rows of features in each tree, sample rate and column sample rate per tree, and for NN—activation function, number of hidden layers as well as neurons in each layer, number of epochs , regularization level and model scoring interval. MLR was iterated over regularization of alpha parameter and that approach was supported by the a priori knowledge about the distribution family, i.e., multinomial for MLR, and the type of data, which in this case reduced the number of tested hyperparameters. The ultimate hyperparameters’ values that were applied to prediction modeling were different for each model and detailed summary of the results is shown in Supplementary Table 4. The parameters of prediction are shown in Table Three types of prediction models were applied and compared for best performance. The highest value of total correct calls for most predictions tested on both a 3- and 4-category levels was obtained with Random Forest and, slightly lower, with Neural Network, while GLM turned out to give the lowest predictive values. The latter produced 100% predictive values; however, it was due to the fact that all query phenotypes were classified as one phenotype in test prediction. On the other hand, GLM gave the best prediction values on a 2-category level, while RF and NN gave lower values, comparable with each other (Table n = 3) in test predictions. Nevertheless, the significantly predictive variants were rs12913832 for all three pigmentation traits, accompanied with rs16891982 for skin color and tanning, rs1015362 and rs4911414 for tanning and rs4911414 and rs12203592 for freckling  for tanning and rs12203592 (14.3%) followed by rs1015362, rs12896399, rs4911414 and rs731236 (above 9% each) for freckling . 90% of subjects with severe sunburns and 66.7% of those with initial sunburns had rs12913832-CC. The association was milder for the freckling phenotype; however, the results were still significant. Our results are similar to those of other authors who demonstrated rs12913832 as one of the strongest and directly associated with melanin production in skin  within the intron 1 of SLC24A, rs731236 in VDR, rs1805007 in MC1R, rs16891982 in SLC45A2, rs1393350 in TYR. In the literature the minor rs12896399-T variant was associated with blue eyes, paler skin and poor tanning ability  between our study and the CEU of 1000Genomes study which were all in favor of presumable darker skin pigmentation traits among our study participants than in individuals of general European consent. We also observed different genotype distribution between males and females for two SNP markers used in this study for skin pigmentation traits predictions. Characteristics for each SNP, PCR and sbe primers with concentration are included 1 (XLSX 15 kb)a wild homozygote/allele as first; b number of individuals with a genotype/allele  2 (XLSX 16 kb)The frequency of alleles and genotypes in 13 differentiated SNPs genotyped in this study with the respective training sets of 150 individuals, using the Fisher’s exact test. The frequency of alleles and genotypes in 13 differentiated SNPs genotyped in this study for 150 training individuals calculated for distinct phenotypes using the Fisher’s exact test. ¹ wild homozygote/allele as first 3 (XLSX 39 kb)Hyperparameters tested in grid search analysis for GLM, RF and NN algorithms prior to developing the prediction models 4 (XLSX 11 kb)Below is the link to the electronic supplementary material.


Choristoneura fumiferana Clem.) cause major recurrent damage in boreal conifers such as white spruce (Picea glauca [Moench] Voss) and large losses of forest biomass in North America. Although defensive phenolic compounds have recently been linked to chemical resistance against SBW, their genetic basis remains poorly understood in forest trees, especially in conifers. Here, we used diverse association genetics approaches to discover genes and their variants that may control the accumulation of acetophenones, and dissect the genetic architecture of these defence compounds against SBW in white spruce mature trees.Outbreaks of spruce budworm  from 2312 genes genotyped in a population of 211 unrelated individuals, genetic association analyses identified 35 SNPs in 33 different genes that were significantly associated with the defence traits by using single-locus, multi-locus and multi-trait approaches. The multi-locus approach was particularly effective at detecting SNP–trait associations that explained a large fraction of the phenotypic variance (from 20 to 43%). Significant genes were regulatory including the NAC transcription factor, or they were involved in carbohydrate metabolism, falling into the binding, catalytic or transporter activity functional classes. Most of them were highly expressed in foliage. Weak positive phenotypic correlations were observed between defence and growth traits, indicating little or no evidence of defence-growth trade-offs.This study provides new insights on the genetic architecture of tree defence traits, contributing to our understanding of the physiology of resistance mechanisms to biotic factors and providing a basis for the genetic improvement of the constitutive defence of white spruce against SBW.The online version of this article (10.1186/s12870-018-1434-y) contains supplementary material, which is available to authorized users. Trees use a battery of constitutive and inducible defence strategies to limit the damage of herbivory from insects over their long life span , 2. ConsChoristoneura fumiferana Clemens (Lepidoptera: Tortricidae) is one of the most destructive native insect pests in coniferous and mixed forests of North America, particularly in the East [3/ha of wood [Abies balsamea [L.] Mill.), white spruce (Picea glauca [Moench] Voss), red spruce (P. rubens Sarg.) and black spruce (P. mariana [Mill.] BSP) [The spruce budworm (SBW) the East –15. In tthe East . The outthe East  and caus of wood  dependin of wood . SBW larl.] BSP) –20. DespQuantitative genetics studies of chemical defence compounds such as monoterpenes in conifers have reported considerable intraspecific variation at the phenotypic level and relatively high estimates of heritability, which indicates the strong genetic control underlying these traits , 21–23. Pgβglu-1 gene [In white spruce trees, constitutive chemical defence against SBW has been linked to the accumulation of piceol and pungenol, which belong to a class of phenolic compounds known as acetophenones , 29. Conu-1 gene , sib andu-1 gene . In contu-1 gene . These fEucalyptus [Pinus [Association genetics approaches are often used to dissect complex traits in forest trees including wood quality –34 and dcalyptus  and Pinus [Pinus , 6. Howes [Pinus . Alternas [Pinus  and mults [Pinus .The high constitutive levels of acetophenones reported for white spruce  also raiPgβglu-1 expression but it accounted for less than half of the variation [Pgβglu-1 expression as quantitative defence traits. (2) to examine potential trade-offs between acetophenone defences and growth given that phenolic compounds such as picein accumulate to very high concentrations in the foliage of some trees but not in others.This study pursued two major objectives: (1) to identify genes and SNPs associated with variation in acetophenone concentrations. To date, the level of acetophenone aglycons has been explained in part by ariation . MoreovePgβglu-1gene, which is responsible for their release, and the acetophenone glucoside picein. These traits were first described in [The four defence traits assessed in this study were the acetophenones piceol and pungenol, the expression levels of the ribed in  and in [ribed in . Samplinribed in . In a seribed in  were usePicea glauca) trees, each from a distinct open-pollinated family and representing 42 geographic origins (provenances), were sampled in a provenance-progeny test established by the Canadian Forest Service in the field with three-year old trees in 1979 at the site of Mastigouche, Québec, Canada  (described in [Foliage of 211 unrelated 38-year-old mature white spruce (ribed in ). Only cThe sampling was non-destructive and the trees were part of an experimental plantation established for research on land of the government of Québec. A collaborative research agreement between the organizations as part of the Arborea II project gave permission for the sampling, which followed guidelines of the institutions involved in the research and in force in Québec (Canada).Pgβglu-1 gene  were obtained using an Infinium iSelect genotyping chip  and were previously described . In the ar e.g. –52; 2) e; 2 eArabar  overar e.g. –57; 4) c; 4 cArabar  ar (e.g. . The genar (e.g. .Simulations were used to assess the effectiveness of the multi-locus mixed model (MLMM) and single-locus mixed model (SLMM) in detecting associations under different genetic architectures of the complex traits in the present population. Simulated phenotypic data sets were generated by simulating genetic effects based on real genotype data (4767 SNPs) drawn from this study using the R-package BGLR . A theorrntransform function in the GenABEL R Library [Data for the four investigated defence traits were normalized using the rank-based inverse normal transformation, implemented as the  Library  in orderP < 2 × 10− 4 , which is roughly equivalent to a Bonferonni correction [The single-locus mixed model (SLMM) implemented in TASSEL v5.2.1  as descrrrection , 66, to The modified version of multi-locus mixed model (MLMM), as developed by  where PCprcomp function implemented in R [Pgβglu-1 transcripts on one hand, and growth traits on the other hand by examining the biplot graphics. Third, association analyses were performed between SNPs and all of the growth and defence traits by using permissive statistical test conditions , stem diameter at breast height in cm (DBH), and growth ring width averaged from pith to bark in cm (RW) as reported previously in . First, ted in R  to graph testing ) in ordePgβglu-1 transcript levels though the distribution was skewed toward high levels   terms associated to these functionally annotated genes. We found that the genes belonged essentially to three molecular functions: binding , catalytic activity  and transporter activity . The catalytic activity category harboured the largest number of genes and involved several different enzymatic functions.None of the genes were annotated as encoding enzymes of the shikimic or general phenylpropanoid pathways that are responsible for the synthesis of phenolic compounds used in the formation of acetophenones, despite the fact that most of the corresponding genes were represented on the SNP array , suggesting a genetic architecture involving a moderate number of genes. It has been shown that traits involved in resistance to biotic stress may favour fixation of large-effect QTLs, and these QTLs are more common than predicted by the infinitesimal model of genetic adaptation [Robertson  proposedaptation . This inaptation , and witaptation , eucalypaptation , 82, andaptation , 84.We also observed that a large proportion of the phenotypic variation for acetophenone metabolites remained unexplained in the present association genetics study . This waPgUGT5b) [Pgβglu-1) [We observed that acetophenones and their glucoside conjugates reach high levels of accumulation. For instance, picein accumulated to 62.4 mg/g on a dry weight basis on average and reached much higher levels in some trees. The larvae of SBW feed primarily on newly formed foliage of spruce and fir trees in late Spring and early Summer , 39 and PgUGT5b)  and deglgβglu-1) . The higgβglu-1) . In the In this study, glutamine synthetase (GS) was associated with piceol and its glycosylated form picein with the MTMM approach. In conifers, GS has been shown to be responsible for the re-assimilation of ammonium provided by the deamination of phenylalanine, the precursor for phenylpropanoid biosynthesis, in the reaction catalysed by the enzyme phenylalanine ammonia-lyase (PAL) , 89. ThiConifers produce diverse phenolic compounds that are involved in chemical defence against natural enemies . The acePgβglu-1 expression. GAE1 was associated with picein by the SLMM and MLMM approaches and both picein and pungenol by the MTMM approach; GAE4 was only associated with Pgβglu-1 transcript levels. Glycosylation consists of the attachment of a sugar moiety to phenolic compounds and is important to enhance their stability and solubility and reduce their toxicity [In this study, two UDP-D-Glucuronate 4-epimerases (GAEs) (GAE1 and GAE4) were significantly associated with acetophenones and toxicity . Glycosytoxicity . UDP-glutoxicity . UDP-D-Gtoxicity . One othPgβglu-1 gene transcripts on one hand, and the oxidative stress related genes on the other hand, is unknown. But such a link is suggested by indications that piceol is cytotoxic for plant cells [Several of the genes identified here by association testing were potentially involved in detoxifying systems to protect cells from oxidative damage. The physiological link between acetophenones or the level of nt cells  in additnt cells  and fungnt cells .2O2) concentration in cells by catalysing its conversion to water using ascorbate as an electron donor [2O2 concentration in Arabidopsis thaliana is known to trigger DNA damage [SMR4, SMR5, and SMR7 (belonging to the SIAMESE/SIAMESE-RELATED class), which are transcriptionally activated by DNA damage [The genes identified here by association genetics testing included an ascorbate peroxidase (APX) enzyme, which controls the hydrogen peroxide  [PCBER1 may protect against oxidative damage by chemically reducing phenylpropanoid dimers in poplar xylem. Another gene associated with Pgβglu-1 transcripts encoded a glutathione S-transferases (GST), which is involved in detoxification in plants [One of the genes significantly associated with (PCBER1) , which h(PCBER1) , 108. Ni(PCBER1)  showed tn plants . In popln plants .We considered both the phenotypic correlations between traits and the list of genes significantly associated with the various traits analysed, and found little evidence for trade-offs between defence traits against SBW and growth in white spruce. These results suggest that the cost of constitutive production of piceol and pungenol as secondary metabolites does not affect primary metabolism needed to sustain growth, which is consistent with previous results in other forest trees. Similar findings were reported in a previous investigation on white spruce resistance to SBW based on the analysis of full-sib families and clonal lines where low and non-significant genetic correlations were observed between defence and growth traits . In DougPopulus tremuloides) [Among the three acetophenones studied here, the glycosylated acetophenone picein was the most abundant, and by far, as it made up 6% of the total needle dry mass on average. High foliar concentrations of phenolic compounds were also observed in other tree species and were correlated with resistance to herbivores. For instance, condensed tannins represented over 10% of the dry mass in birch leaves , 113 anduloides) . Picein uloides) , 116.The present study represents a first step in understanding and dissecting the genetic architecture of defence traits against SBW in white spruce. We explored three different association genetics testing approaches and, taking advantage of the genomic resources developed for white spruce, we detected 33 genes carrying SNPs significantly involved in the observed variation for defence traits. Our results indicate that the multi-locus association genetic approach is more powerful than the single-locus approach for identifying candidate genes implicated in the constitutive defence against SBW. We further showed that these traits are likely to be under the mixed control of minor and major genes with no significant trade-offs with growth traits. The present results should open up new opportunities for functional studies to determine the molecular roles of these genes in influencing SBW resistance. In addition, these genes and a more complete determination of their polymorphisms should allow to develop molecular tools to help identify and breed trees that are more resistant to SBW, which have been lacking to date. These tools may thus represent a means to shorten the long periods of time that tree breeders need to assess defence against SBW in the field.Additional file 1:Figure S1. Heatmap of tissue-specific expression pattern of candidate genes involved in phenylpropanoid pathway used in this study and their functional annotations. Expression data are from the PiceaGenExpress database [database . Columns