Simulation is a critical part of method development and assessment. With the increasing sophistication of multi-trait and multi-locus genetic analysis techniques, it is important that the community has flexible simulation tools to challenge and explore the properties of these methods.PhenotypeSimulator, a comprehensive phenotype simulation scheme that can model multiple traits with multiple underlying genetic loci as well as complex covariate and observational noise structure. This package has been designed to work with many common genetic tools both for input and output. We describe the underlying components of this simulation tool and illustrate its use on an example dataset.We have developed PhenotypeSimulator is available as a well documented R/CRAN package and the code is available on github: https://github.com/HannahVMeyer/PhenotypeSimulator.Bioinformatics online. The relationship between genotype and phenotype has been a topic for over a 100 years of biological research. There are a multitude of phenotypes for each organism, defined by the observations and measurements one can make on individuals, and these phenotypes can be related to each other in complex ways. Furthermore, the link between genotype and phenotype is equally complex, with many phenotypes being influenced by more than one genetic locus (polygenic effects) and one locus influencing many phenotypes (pleiotropic effects). Finally, a multitude of environmental and measurement effects influence phenotypes. Statistical genetics continues to develop novel ways to analyse genotype to phenotype relationships; models range from simple linear models with genetic variant effects on a single trait to complex linear mixed models (LMMs) with additional genetic and non-genetic random effect components on multiple traits. All models account for observational noise and, usually, known environmental covariates . With thMany simulation packages put a strong focus on the genotype simulation allowing for the simulation of different evolutionary selection processes via forward-time  and coalPhenotypeSimulator, an R/CRAN package for the flexible simulation of phenotypes with different genetic and non-genetic variance components. PhenotypeSimulator is a framework focusing on the simulation of phenotypes, with a particular emphasis on complexity of both multiple phenotypes and multiple genetic loci, which is not provided by other multi-phenotype simulation software  and it can generate output suitable as input for a number of standard genetic association tools such as PLINK  genetic variant effects In S random SNPs for N samples are drawn from the (simulated) genotypes. From the S random SNPs, a proportion PhenotypeSimulator: Bshared is the matrix product of the two vectors sb and pb are drawn from two normal distributions, where sb and S SNPs are simulated to have an independent effect across a specified number of traits Bμ and Bσ as specified by the user (same as for shared effect). Subsequently, Bind at these traits set to zero. The independent genetic variant effect is the matrix product of Bind. Genetic variant effects: For the genetic variant effects, ribution  across tK non-genetic covariates γ being shared across all traits yielding the shared covariates matrix K non-genetic covariates are independent and can be either normal, uniform, binomial or categorical. The distribution and respective parameters are chosen by the user. The effect size matrices Non-genetic covariate effects: The non-genetic covariate effects are based on U is the N × N genetic relationship matrix K, either estimated from the genotypes of the simulated samples as m is the mean value of the diagonal elements of N × N sample covariance K and trait covariance C is a multivariate normal distribution . A detailed derivation of U described by a multivariate normal distribution is effectively modelled as the product of three matrices, representing the sample covariance (B), a normally distributed variable (Z) and the trait covariance (A). Different designs of A will allow for the simulation of shared and independent genetic random effects. For the independent effect, Aind is a diagonal matrix with normally distributed entries: Ashared of the shared effect is simulated as a matrix of column rank one, with normally distributed entries in column one and zeros elsewhere: Infinitesimal genetic effects: The basis of the infinitesimal genetic effect C can be supplied by the user. In addition, as a simple approximation for spatially correlated phenotypes  will have the highest specified correlation r, traits with d = 2 have a correlation of r2, up to traits with Correlated non-genetic effects: Correlated non-genetic effects are simulated as a multivariate normal distribution with a covariance matrix described by a defined trait-by-trait correlation. Any correlation structure between the phenotypes can be simulated with this effect component, as the desired correlation matrix Ashared is simulated as a matrix of row rank one, with normally distributed entries in row one and zeros elsewhere: A of the independent component is a diagonal matrix with normally distributed entries: Observational noise: The observational noise effects PhenotypeSimulator requires at least one phenotype component to simulate the phenotypes. Components can be combined as specified by the user and the correlation they introduce in the trait structure can be controlled by the specified levels of independent and shared effects . If desired, a simple phenotype structure following a model as cast, for instance, in the multivariate normal model by PhenotypeSimulator enables the specification of the amount of variance that each component should contribute to the total phenotypic variance. Every component is thereby scaled by a factor a such that its average column variance x of the total variance:Y is expressed as the sum of the scaled genetic variant effects, the non-genetic covariates, the correlated non-genetic effects and observational noise effects:The analysis code and parameters of this case study, from the data simulation to the genome-wide association study, can be found in the PhenotypeSimulator, using the simulated genotypes as basis for the SNP and infinitesimal genetic effects. A total of three phenotypes for 1000 samples with the ten SNP genetic effects shared across all traits (randomly sampled from the simulated genotypes), four non-genetic covariates, an infinitesimal genetic, a correlated noise and an observational noise effect were simulated. For the genetic variant effects, only shared effects across traits were simulated. For the remainder of the phenotype component, 80% of their variance was simulated to be shared across all traits while the remaining proportion of variance remained independent. The total genetic variance was set to 40%, leaving 60% of variance explained by the noise terms.Genotypes (8 073 414 genetic variants) for 1000 individuals were simulated via Hapgen2 . PhenotyP-values of the single-trait GWAS were adjusted by the number of test conducted (Bonferroni adjustment for three tests).The simulated genotypes, phenotypes, kinship and covariates were used in GWAS. Two different types of GWAS were conducted (i) a multi-trait association study, jointly mapping all three traits and (ii) single-trait association studies, where each trait was individually tested for association with the genotypes. Single-trait GWAS was run for all three traits. All GWAS were conducted with GEMMA (version 0.96) . In bothPhenotypeSimulator works by:Simulating or importing genotypes , age  or country of origin , correlated non-genetic effects and observational noise. Correlated non-genetic effects can be used to simulate a phenotype component with a defined level of correlation between traits. For instance, such effects can reflect correlation structure decreasing in phenotypes with ordered or spatial components, e.g. in imaging data. Observational noise captures any non-specified effects that arise due to, e.g. experimental measurement error. PhenotypeSimulator can also be used with a combined non-genetic covariance model, similar to more standard LMMs . We simulated genotype data for 1000 individuals via a re-sampling-based approach  to real covariates. Third, the different components can be independently extracted and scaled, for example having the ‘true’ variance components and covariance matrices from the simulation readily available for comparison to inference schemes. Finally, we have developed PhenotypeSimulator as a flexible component in the standard genetics pipeline, with the ability to both read genetic formats from well used tools and output phenotypes compatible with many tools. This allows easy large-scale deployment for comprehensive simulation across many parameter settings. The underlying model for PhenotypeSimulator corresponds to the common place LMM framework. As such, it is limited in its use for benchmarking between methods, where LMMs methods are likely to perform best. However, the need for an underlying model is true for any simulation package. We have extensively documented PhenotypeSimulator for ease of use, providing vignettes for sample genotype simulation with the supported genotype simulation tools (PhenotypeSimulator (https://github.com/HannahVMeyer/PhenotypeSimulator) and we welcome other additions to this tool. For example, although we currently model polygenic and pleiotropic effects, we have not yet modelled epistatic effects and would enthusiastically accept extensions in this area.Supplementary DataClick here for additional data file.


How variants with different frequencies contribute to trait variation is a central question in genetics. We use a unique model system to disentangle the contributions of common and rare variants to quantitative traits. We generated ~14,000 progeny from crosses among 16 diverse yeast strains and identified thousands of quantitative trait loci (QTLs) for 38 traits. We combined our results with sequencing data for 1011 yeast isolates to show that rare variants make a disproportionate contribution to trait variation. Evolutionary analyses revealed that this contribution is driven by rare variants that arose recently, and that negative selection has shaped the relationship between variant frequency and effect size. We leveraged the structure of the crosses to resolve hundreds of QTLs to single genes. These results refine our understanding of trait variation at the population level and suggest that studies of rare variants are a fertile ground for discovery of genetic effects. A detailed understanding of the sources of heritable variation is a central goal of modern genetics. Genome-wide association studies (GWAS) in humans  have impEmpirical results have been consistent with the theoretical expectation that rare variants should have larger effect sizes, or, equivalently, that variants implicated in trait variation should be shifted to lower frequencies relative to all variants. An increased burden of ultra-rare protein-truncating variants has been observed in human diseases , and mulRecent studies employed indirect variance partitioning approaches to uncover appreciable contributions of lower frequency variants to heritability of complex traits in humans, including prostate cancer susceptibility , height Here, we report a comprehensive study in yeast designed to overcome these limitations. We built a mapping population consisting of approximately one thousand progeny from each of 16 biparental crosses. In this mapping population, even variants that are rare in the yeast population and occur in only a single parental strain are present in approximately 1000 progeny, resulting in high power to detect them. We mapped thousands of QTLs that account for most of the heritable variation in 38 quantitative traits and measured the QTL effect sizes. We then decoupled variant frequency from effect size by measuring the population allele frequencies of QTL lead variants detected in our panel in a separate large catalog of sequenced yeast isolates . AnalysiS. cerevisiae strains that capture much of the known genetic diversity of this species. Specifically, they contain both alleles at 82% of biallelic SNPs and small indels observed at minor allele frequency >5% in a collection of 1011 S. cerevisiae strains  in this collection, we designated variants as rare (MAF <0.01) or common (MAF >0.01). By this definition, 27.8% of biallelic variants in our study were rare. For each trait, we computed the relative fraction of variance explained by these two categories of variants in the segregant panel  . Across ectively .In a complementary analysis, we investigated the relationship between the allele frequency of the lead variant at each QTL and the corresponding QTL effect size. Although the lead variant is not necessarily causal, in our study it is likely to be of similar frequency as the causal variant, and a simulation analysis showed that this approach largely preserves the relationship between frequency and effect size . Most QTS. cerevisiae—S. paradoxus—allowed us to distinguish rare variants by their ancestral state. Variants that share the major allele with S. paradoxus are more likely to have arisen in the S. cerevisiae population recently than those that share the minor allele with S. paradoxus. We classified low-frequency variants as recent or ancient according to whether their major or minor allele was shared with S. paradoxus, respectively. Recently arising deleterious alleles have had less time to be purged by negative selection, and therefore recent variants are expected to have stronger effects on gene function, and hence manifest as QTLs with larger effects. Consistent with this expectation, we observed that recent variants were 1.8 times more likely than ancient variants to have an effect size greater than 0.1 SD units (Fisher’s exact test p=9e-5) (The existence of a close sister species of  p=9e-5) . We furtAn understanding of trait variation at the level of molecular mechanisms requires narrowing QTLs to the underlying causal genes. Such fine-mapping is a challenge because genetic linkage causes variants across an extended region to show mapping signals of similar strength. Statistical fine-mapping aims to address this challenge by estimating the probability that each variant within a QTL region is causal based on the precise pattern of genotype-phenotype correlations . Our croIRA1, IRA2, BCY1, CYR1, and RAS1; 0.19 expected, q = 0.0002). Additional genes in the RAS/cAMP signaling pathway were also identified as causal, including GPR1, which is involved in glucose sensing, SRV2, which binds adenylate cyclase, and RHO3, which encodes a RAS-like GTPase. In yeast, the RAS/cAMP pathway regulates cell cycle progression, metabolism, and stress resistance , metal ion transport , and positive regulation of nitrogen compound biosynthesis  . Strikinsistance . VariatiS. cerevisiae population and show that S288c is not exceptional from the standpoint of genetic variation and quantitative traits. We believe that the findings that the majority of the genetic variance of most traits is additive, and that there is little additive ‘missing heritability’ in studies with sufficiently large sample sizes, will apply broadly beyond yeast.We previously used a cross between lab (BY) and vineyard (RM) strains of yeast to show that the majority of heritable phenotypic differences arise from additive genetic effects, and we were able to detect, at genome-wide significance, specific loci that together account for the majority of quantitative trait variation . It has S. cerevisiae and have appreciable phenotypic effects on growth, and therefore provide a comprehensive starting point for more fine-grained analyses of the genetic contribution to quantitative trait variation. We were able to localize approximately 8% of the QTLs to single genes based on genetic mapping information alone. Interestingly, these genes cluster in specific functional categories and pathways, suggesting that different strains of S. cerevisiae may have evolved different strategies for nutrient sensing and response as a function of specializing in particular environmental niches (We discovered over 4500 quantitative trait loci (QTLs) that influence yeast growth in a wide variety of conditions. These loci likely capture the majority of common variants that segregate in l niches . In addil niches , and forl niches .By combining our results with deep population sequencing in yeast , we werehttps://github.com/joshsbloom/yeast-16-parents (https://github.com/elifesciences-publications/yeast-16-parents). Additional links to generated data are also provided in the github repository. The version numbers of R packages used are listed in this repository. Sequencing data for parents and segregants is available in the Sequenced Read Archive (SRA) under the Bioproject ID PRJNA549760.Unless otherwise specified, all computational analyses were performed in R (v3.4.4). Analysis code and processing scripts are available at https://github.com/theboocock/long_read_cnv (https://github.com/elifesciences-publications/long_read_cnv). Parental genotypes were obtained by deep (>100X) paired-end sequencing of the 16 parental strains. A VCF file containing SNPs and small indels was generated for the parents using bwa (v0.7.1)  to alignhttp://dunham.gs.washington.edu/sporulationdissection.htm) and tetrad dissection using the MSM 400 dissection microscope (Singer Instrument Company Ltd.). Four-spore tetrads were retained. For BYxRM, one segregant was randomly chosen per tetrad (https://openwetware.org/wiki/McClean:Random_Spore_Prep), modified to exclude the use of glass beads for spore separation. Cells were plated on selective media, grown for two days, and colony fluorescence was visualized. Green fluorescent colonies and red fluorescent colonies corresponding to MATa and MATα haploid progeny were picked to deep-well 96-well plates and then split into frozen stocks.Segregants for the BY-RM cross and YPS163-YJM145 cross were obtained by sporulation of the hybrid diploid parents for 5–7 days in SPO++ sporulation medium (r tetrad . For ther tetrad . Then thYeast were grown in 1 ml of yeast peptone dextrose in 2 ml deep-well 96-well plates (Thermo Scientific). Plates were sealed with Breathe-Easy gas-permeable membranes (Sigma-Aldrich). Yeasts were grown without shaking for 2 days in a 30°C incubator. Cell walls were digested with Zymolase, and DNA was extracted using either the 96-well DNeasy Blood and Tissue kits (Qiagen) for the BY-RM and YPS163-YJM145 segregants, or 96-well E-Z 96 Tissue DNA kit, following the bacterial protocol (Omega) for all other segregants. DNA concentrations were determined using the Quant-iT dsDNA High-Sensitivity DNA quantification kit (Invitrogen) and the Bio-Tek Synergy two-plate reader. DNA was diluted to 0.22 ng per μl using a Biomek FX liquid handing robot (Beckamn Coulter). For each segregant, 5 μl of 0.22 ng per μl of DNA was added to 4 μl of 5X Nextera HWM buffer (Illumina), 6 μl of water and 5 μl of 1/35 diluted Nextera enzyme. The transposition reaction was performed for 5 min at 55°C. Directly after the tagmentation reaction and without additional sample purification, Illumina sequencing adaptors and custom indices were added by PCR. 10 μl of tagmented DNA was combined with 0.5 μl each of 10 μM index primers   and aligSegregants were arrayed to 384-well liquid plates in duplicate with different plate positions across the duplicates. Segregants were grown in YPD for approximately 48 hr without shaking and then pinned to agar plates using a BM-5 colony arraying robot (S and P Robotics). Plates were incubated for 48 hr and end-point growth was quantified by automated plate imaging using the colony arraying robot. Colony radii were calculated using functions in the EBImage R package , and end2, where r is the Pearson correlation coefficient between segregant genotypes at the marker and segregant phenotypes. 10,000 permutations of phenotype to strain assignment were performed and this statistic was calculated across the genome for each of the permutations. For each of the permutations, the maximum statistic was recorded to generate an empirical null distribution of the maximum statistic , and the entire procedure was repeated (including permutations) with the previously identified marker(s) included as regression covariates. A ‘FowardStop’, FDR-controlling statistic  as covariates in a multiple regression model, and scanned each marker on the chromosome on which the QTL peak being re-localized was detected to identify the marker that maximized the likelihood of the multiple regression model. The marker that maximized the likelihood of the multiple regression model was retained as the new, re-localized, QTL peak position.The amount of additive variance explained by detected QTLs was estimated using cross-validation. For the within-cross analysis, segregants were randomly split into 10 sets. Each set of segregants was left out of the procedure one at a time (held-out set). The within-cross QTL mapping procedure was performed for all the other sets (training set). For the QTL markers detected in this training set and with effects estimated in the training set, the amount of variance explained by the joint model of the set of significant QTL markers was estimated in the held out set. For the joint analysis described below, we performed a similar procedure, splitting the segregants within each cross into 10 sets, leaving one of the sets from each cross out (held-out set) identifying QTL jointly across the other sets (training set) and estimating their effects in each cross (training set) and then estimating the variance explained in the held-out set.y = a+e, where y contains the segregant phenotype values and is standardized to have mean 0 and variance 1. Here, a are the additive genetic effects and the residual error is denoted as e. The distributions of these effects are assumed to be multivariate normal with mean zero and variance-covariance as follows:To estimate the fraction of phenotypic variance attributable to additive genetic effects for each cross and trait we fit the model A is the additive relatedness matrix, the fraction of genome shared between pairs of segregants and was calculated as M is the n x m matrix of standardized marker genotypes, n is the number of segregants and m is the number of markers.Here, We also fit an expanded model to estimate the relative contribution of additive vs non-additive (pairwise epistatic) effects. For the pairwise epistatic component, we believe that the assumption that all pairs of loci contribute to trait variation with effect sizes drawn from a single normal distribution is violated when one or a few QTL-QTL interactions with large effects are present, resulting in a downward bias. We previously showed  that locy is a vector of length L that contains phenotypes for n segregants including replicate measurements such that L = n x [number of replicates]. β is a vector of estimated fixed effect coefficients. X is a matrix of fixed effects . Z is an L x n incidence matrix that maps L total measures to n total segregants. In order, the random effect terms correspond to the effects of detected QTL, effects from the whole genome, epistatic interactions between detected QTL, epistatic interactions between additive QTL and the genome, epistatic interactions between all pairs of markers across the genome, and residual repeatability, following very similar methods and syntax as described previously :The distributions of these effects are assumed to be multivariate normal with mean zero and variance-covariance as follows:y is a vector of length 13,950 that contains phenotypes for segregants concatenated across the different crosses. β is a vector of estimated fixed effects of each cross. X is an incidence matrix mapping segregants to crosses. Here, the two relatedness matrices Amaf<1% and Amaf>=1% were calculated separately for all markers with MAF<1% and MAF>=1% respectively in the larger panel of 1,011 yeast isolates. Per marker, the genotype values were scaled to have mean 0 and variance 1, for each of the segregants from crosses in which that marker segregates. Markers that are fixed within a cross were excluded from the subsequent calculation of genetic covariance. The rationale for excluding data for variants not segregating in a given cross is that all such variants are completely confounded with each other and with any other effects specific to that cross. Thus, their effects are more appropriately captured by including a fixed effect for each cross within the analysis. Then, with M being the n segregants by m markers matrix corresponding to the standardized genotypes for that subset of markers, we calculated the relatedness matrix as a Gower’s centered matrix . Bins were chosen to contain approximately equal numbers of variants. We also fit the seven allele-frequency bins model using only variants that were private to each parent (variants that only segregate in a pair of crosses). In this last model, the allele-frequency of variants used for the analysis are all approximately the same across the panel. Therefore, this last model does not make the assumption that the variance of variants effects is inversely proportional to their frequencies in the mapping panel .The procedure for fitting these models was the same as described above in the section ‘within-cross variance component analysis’.cy = CQ+L+sca where cy is the vector of trait values for a given trait and cross, Q is a matrix of QTL genotypes at peak markers from the within-cross mapping described above, with FDR < 5% that are not located on the chromosome of interest, C is a vector of estimated QTL effects from the section ‘within-cross QTL mapping’, La is the additive genetic variance from all chromosomes excluding the chromosome of interest. La comes from the REML-based BLUP estimate of the effect all other chromosomes, including the fixed effects of detected QTL on the other. The goal of this step was to obtain the residual trait values cs that can be used to scan for QTLs on a chromosome of interest and corrects for mapped genetic sources of variation that do not arise from the chromosome of interest  was recorded. This statistic was calculated for each marker on the chromosome. 1000 permutations of phenotype to strain assignment were performed, but these permutations were performed with phenotype values within each cross  and this statistic was calculated across the genome for each of the permutations. For each of the permutations, the maximum statistic was recorded to generate an empirical null distribution of the maximum statistic , and the entire procedure was repeated (including permutations) with the previously identified marker(s) included as regression covariates. A ‘FowardStop’, FDR-controlling statistic  from this procedure were then used for effect size estimation. For each trait and cross, the phenotypes are scaled to have mean 0 and variance 1, and effect sizes within each cross are estimated using multiple regression for the peak markers that segregate within that cross. The betas in this analysis correspond to the differences in the means between the two QTL alleles . For peak markers that segregate in multiple crosses, the average betas over the different crosses are shown in We implemented the probabilistic identification of causal snps (PICS) procedure, a Bayesian approach to estimate the probability that a variant is causal. A very thorough description of the method, including details about the logic and implementation, is present in Next, we identified overlapping QTL. Overlapping QTL were defined as the QTL coming from neighboring crosses that shared a parent, have 1.5 LOD drop confidence intervals that overlap, and have QTL effect directions that are consistent between the neighboring crosses. For these overlapping QTL, we calculated the product of the causality probabilities (described above) for each variant shared between the two crosses (and segregating in both crosses) and then normalized these probabilities so that they sum to 1. To calculate the probability that a gene was causal, we summed these probabilities for all variants that fell within each gene. Here, a gene was defined as all variants that fell within the defined open-reading frame as well as variants that fell halfway between the start and stop of the adjacent open-reading frames. We calculated a FDR by sorting the observed posterior probabilities of causality per gene from highest to lowest, calculating a posterior error probability as one minus the posterior probability of causality, and calculating the cumulative mean of these probabilities .We note that the causal gene statistic is an estimate of the posterior probability that a gene is causal assuming that one causal variant in the defined window is responsible for generating a signal in two crosses that share a parent strain, that we estimate the effects of causal variants in both crosses without error, and that genotypes are called without error.We tested for GO enrichments using the R package topGO , using t In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.Acceptance summary:The authors show that rare and recent variants contribute proportionally more than common ones to trait variation in budding yeast. They combine a powerful quantitative genetics approach with extensive trait phenotyping and population genomics data to illustrate how natural selection may be keeping mutations with large effects from reaching high frequency. The expected negative correlation between effect size and frequency has been studied theoretically, but much less so at the experimental level because of the complex type of data needed. The study has broad significance, from population genetics, to quantitative genetics and evolution of complex traits.Decision letter after peer review:eLife. Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Naama Barkai as the Senior Editor. The reviewers have opted to remain anonymous.Thank you for submitting your article "Rare variants contribute disproportionately to quantitative trait variation in yeast" for consideration by The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.Summary:eLife is a generalist journal, the manuscript would appeal to a larger audience with these changes. Your manuscript is currently very short so this would be feasible by the addition of a few short sections in the current structure of the manuscript. You will see that one specific comment relates to the novelty of the work with respect to previous studies. This means that the novelty may not be obvious as presented. It would therefore also be important to emphasize this aspect in a revised version.Your manuscript addresses an important question in genetics and evolutionary biology: what are the relative contributions of genetic variants to phenotypic variation and do these contributions correlate with the frequency of these variants within a species? The reviewers agree that this is an important question that has rarely been comprehensively addressed. They therefore find the work of interest and the findings to be important for the field, in addition to appreciating the quality of the writing and of the presentation. However, they identify some aspects that would need to be reconsidered or better presented and interpreted (details below). In addition, your paper could be strengthened if it was extended to include a more detailed Introduction on why these questions are important for the non-specialists. You could also include more discussions on the implications of your findings, including the implications for biology and evolution in general and for yeast in particular. Since Essential revisions:1) There are two analyses, within cross and joint analysis. I have to go back and forth between Results and Materials and methods to figure out exactly what is done. It would be nice to make clear when discussing the results from which one they are derived.2) Because the segregants are haploid, there is only the A x A interaction. The majority of variance generated by A x A in fact goes into the additive variance, hence the non-additive variance is small. The authors did not make a big deal out of the fact that non-additive variance is only 1/6 of additive variance, but I feel it's important to stress that large additive variance is expected given the population design. In addition, when estimating the variance attributable additive variance and epistatic variance, the authors broke the non-additive variance into three components, AQTL x A, AQTL x AQTL, and A x A. I wonder if this is necessary because there was no mention of the differences between these three components. A single component A x A could be fitted.3) The two-component mixed model analysis has some caveats. There is correlation between rare and common variants, i.e., the variance components are not orthogonal. This makes any claim about the relative importance of rare versus common less reliable. For example, for the Cadmium chloride trait , the 7-component model seems to disagree with the 2-component model, with MAF < 0.01 explaining much less in the 7-component model than in the 2-component model in A. I think comparing the 2-component and one component model could suffer from the same problem. Perhaps a more appropriate (but still not perfect) analysis is to fit single component model first and then fit two component models, do it in two sequential orders , and look at how the cumulative variance increase. This will tell you which MAF class is more important or can explain more variance. I think in this case, one-component model is more informative than the 2-component model.4) In Figure 3, the relationship between effects and MAF or DAF is a major result. Although many other papers have reported similar results, I think this paper  has the most appropriate design, i.e., the discovery panel is independent of where MAF is estimated. Given its central role in this paper, it probably deserves a bit more clarity. A few questions came to mind when reading this part of the paper. In what analysis is the effect size estimated, single crosses or joint? Could you briefly explain how the effect sizes are estimated in the Results section? If effects estimated from joint analysis, the t-statistic used a factor (n-2) to normalize the degree of freedom, which is smaller for rare variants. This would lead to Beavis effect. I believe the authors used a cross validation strategy to estimate effects, but it's not very clear by reading the Materials and methods. Can you also plot 2pqa^2 versus MAF? Even if a is large, the variance contributed by rare variants could be small.5) The main conclusion of the manuscript is that rare variants significantly contribute to genetic variance. In my view, this conclusion is biased as these rare causal variants are being analysed in genetic backgrounds in which they are no longer rare; actually, these variants are biallelic. Several studies have shown that a rare variant of MKT1(89A) is a significant contributor to phenotypic variation whenever it is present in segregating populations. However, MKT1(89A) allele hardly identified when one of the parents is not S288c, the strain which harbours this allele. So, the extension that if the rare variant has a significant effect in a sub-population, then its effect size would be similar in a large heterogeneous population is false. Furthermore, the authors conclude that in their larger 16 strain segregant populations, a representative distribution of 1000 strain collection, most of the variants have additive effects. This the authors claim is revalidation of their other previous studies , where they identified that most of the causal variants between BYxRM had additive effects. However, in their subsequent paper  and another paper  showed that variance mapping in BYxRM segregants helped to account for genetic interactions and showed how non-additive interactions also contribute significantly to phenotypic variation. Therefore, I find that just doing a few more strains and larger no. of segregants per cross does not make this manuscript a significant advance over the previous studies. One can argue that taking into account all causal variants identified till date , one can identify what frequency of rare variants have been identified, e.g. a typical example being MKT1(89A) allele as causal, even though their effect size will not be identified using this strategy. Peltier et al., 2019, show that 284 rare QTNs variants have been identified till date and these functional variants being private to a subpopulation, possibly due to their adaptive role to a specific environment. Moreover, this conclusion can be made without these extensive experimental crosses. Essential revisions:1) There are two analyses, within cross and joint analysis. I have to go back and forth between Results and Materials and methods to figure out exactly what is done. It would be nice to make clear when discussing the results from which one they are derived.We apologize for any confusion resulting from our presentation of these analyses. We have made a clarification to the text to emphasize that, except for the one paragraph comparing the two analyses beginning with “We complemented the joint analysis with QTL mapping within each cross…”), the text focuses entirely on results from the joint analysis.2) Because the segregants are haploid, there is only the A x A interaction. The majority of variance generated by A x A in fact goes into the additive variance, hence the non-additive variance is small. The authors did not make a big deal out of the fact that non-additive variance is only 1/6 of additive variance, but I feel it’s important to stress that large additive variance is expected given the population design. In addition, when estimating the variance attributable additive variance and epistatic variance, the authors broke the non-additive variance into three components, AQTL x A, AQTL x AQTL, and A x A. I wonder if this is necessary because there was no mention of the differences between these three components. A single component A x A could be fitted.Our estimates of additive variance per trait and cross are not exceptional when compared with those obtained from approaches that have used pedigree or marker-based measures of relatedness for numerous traits in plants, livestock, other model organisms, and humans . We note that our population of line cross progeny is actually expected to give a higher estimate of epistatic variance when compared to outbred populations: as e.g. Mackay et al., 2014, PMID 24296533 Figure 2 shows, estimates of epistatic variance are maximized as allele frequencies of the interacting loci approach 0.5 (as in our line crosses here). As the reviewer notes, another potential non-additive component, dominance variance, is not accessible in our experiment design which uses haploids, but study designs that can estimate dominance variance have not detected a large contribution .We are grateful to the reviewer for pointing out an omission in the Materials and methods section of our manuscript regarding an explanation of why we modeled the epistatic variance with three components. First, as the reviewer suggests, we have added results from a model with a single A x A component to Supplementary file 2. In 3) The two-component mixed model analysis has some caveats. There is correlation between rare and common variants, i.e., the variance components are not orthogonal. This makes any claim about the relative importance of rare versus common less reliable. For example, for the Cadmium chloride trait , the 7-component model seems to disagree with the 2-component model, with MAF < 0.01 explaining much less in the 7-component model than in the 2-component model in A. I think comparing the 2-component and one component model could suffer from the same problem. Perhaps a more appropriate (but still not perfect) analysis is to fit single component model first and then fit two component models, do it in two sequential orders , and look at how the cumulative variance increase. This will tell you which MAF class is more important or can explain more variance. I think in this case, one-component model is more informative than the 2-component model.We agree with the reviewer that genetic linkage creates a correlation between rare and common variants in genetic mapping studies. The variance component analysis performed here is based on approaches that are the standard in the field, and that have been extensively used in studies of human datasets that seek to address similar fundamental questions about the contribution of variants at different allele frequencies in a population . How the robustness of estimators obtained from these procedures is affected by the presence of genetic linkage, assumptions about the distributions of causal variant effect sizes, and the relationship between effect size and allele frequency is an active area of research.  The reviewer is proposing a new forward stepwise variance component analysis which to our knowledge has not been reported before in the literature and which poses its own issues of implementation and interpretation that are beyond the scope of our paper. We agree that this is an interesting idea, and we hope that by making our dataset available, we can stimulate the development of this and other new methods.PCA1, and that the patterns of segregation in different crosses are consistent with allelic heterogeneity at this locus. Contributions of QTLs with large effects are often poorly modeled with whole-genome variance component approaches, and we believe that this accounts for the discrepancy noted by the reviewer.With regard to the comparison between the estimates of the contribution of rare alleles from the two-component allele frequency model  and the 7-component model , one can see that for nearly all traits, the estimate of variance explained is very similar, with the exception of cadmium chloride pointed out by the reviewer. We note that cadmium chloride is exceptional among the traits, with nearly all the additive heritability explained by a single locus near the gene We further note that the known limitations of variance component analyses were a primary motivation for our study, and that in subsequent sections we also analyzed our dataset using fixed effects models based on detected QTLs. Our study design is highly-powered to detect QTL effects that jointly account for most of the heritable variance, enabling these analyses for the first time. As we show in Figure 3B, Figure 3C, Figure 3—figure supplement 2, and Figure 3—figure supplement 5, the fixed effects models lead to conclusions similar to those obtained from the variance component models.4) In Figure 3, the relationship between effects and MAF or DAF is a major result. Although many other papers have reported similar results, I think this paper  has the most appropriate design, i.e., the discovery panel is independent of where MAF is estimated. Given its central role in this paper, it probably deserves a bit more clarity. A few questions came to mind when reading this part of the paper. In what analysis is the effect size estimated, single crosses or joint? Could you briefly explain how the effect sizes are estimated in the Results section? If effects estimated from joint analysis, the t-statistic used a factor (n-2) to normalize the degree of freedom, which is smaller for rare variants. This would lead to Beavis effect. I believe the authors used a cross validation strategy to estimate effects, but it’s not very clear by reading the Materials and methods. Can you also plot 2pqa^2 versus MAF? Even if a is large, the variance contributed by rare variants could be small.We appreciate the reviewer’s positive comments regarding our study design, which decouples allele frequencies in the population from allele frequencies in the mapping panel, thereby allowing us to obtain estimates of effect sizes of rare variants without the typical complications one encounters in GWAS designs regarding sample size and confounding. We welcome the opportunity to clarify the details here, in the revised main text, and in the Materials and methods. Briefly, QTL peak markers are detected in the joint analysis for each trait. Then, for each trait and cross, the phenotypes are scaled to have mean 0 and variance 1, and effect sizes within each cross are estimated using multiple regression for the peak markers that segregate within that cross. The betas in this analysis correspond to the differences in the means between the two QTL alleles. For peak markers that segregate in multiple crosses, the average betas over the different crosses are shown in Figure 3. This is now described in greater detail in the Materials and methods subsection “Effect size estimation for joint QTL mapping”.The reviewer correctly points out that because we perform model selection and parameter estimation on the same data set, parameter estimates may be upwardly biased (this is known as the Beavis effect). We note that we carried out simulation analyses  which indicated that while some estimate inflation is present, it does not qualitatively alter the results in Figure 3. To further address the reviewer’s concern, we have now calculated unbiased estimates of effect sizes by training a model on 9/10 of the data and estimating parameters on the 1/10 of the data held out from the training procedure. The results are shown in a new supplementary figure  and are very similar to Figure 3, but estimates are noisier due to the smaller sample size available for unbiased estimation in this procedure. This is now described in the aforementioned Materials and methods subsection.We believe that it is important to proceed carefully when reporting and interpreting the relationships between allelic effect sizes, variance explained, and allele frequencies for individual QTL effects. We have modified our Introduction to give additional background as to the relevant issues. Figure 3—figure supplement 5 shows the cumulative fraction of variance explained in our mapping panel for each trait by the detected QTLs. In this calculation of variance explained, we used the allele frequency of the QTL peak marker in our mapping population. Were we to instead calculate variance explained in the larger panel of yeast isolates  using the allele frequencies of variants in that panel, but effect sizes estimated in our mapping population, the variance contributed by rare variants would necessarily be small because the study design severely undersamples variants that are rare and ultra-rare in this larger population . We are concerned that presenting such results would be actively misleading and confusing. We believe that the results from the variance components analysis and those shown in Figure 3—figure supplement 5 would be recapitulated in the larger yeast population if we could detect and estimate the effects of all the variants present in that population, rather than the small fraction that segregates in our crosses.5) The main conclusion of the manuscript is that rare variants significantly contribute to genetic variance. In my view, this conclusion is biased as these rare causal variants are being analysed in genetic backgrounds in which they are no longer rare; actually, these variants are biallelic. Several studies have shown that a rare variant of MKT1(89A) is a significant contributor to phenotypic variation whenever it is present in segregating populations. However, MKT1(89A) allele hardly identified when one of the parents is not S288c, the strain which harbours this allele. So, the extension that if the rare variant has a significant effect in a sub-population, its effect size would be similar in a large heterogeneous population is false. Furthermore, the authors conclude that in their larger 16 strain segregant populations, a representative distribution of 1000 strain collection, most of the variants have additive effects. This the authors claim is revalidation of their other previous studies , where they identified that most of the causal variants between BYxRM had additive effects. However, in their subsequent paper  and another paper  showed that variance mapping in BYxRM segregants helped to account for genetic interactions and showed how non-additive interactions also contribute significantly to phenotypic variation. Therefore, I find that just doing a few more strains and larger no. of segregants per cross does not make this manuscript a significant advance over the previous studies. One can argue that taking into account all causal variants identified to date , one can identify what frequency of rare variants have been identified, e.g. a typical example being MKT1(89A) allele as causal, even though their effect size will not be identified using this strategy. Peltier et al., 2019, show that 284 rare QTNs variants have been identified to date and these functional variants being private to a subpopulation, possibly due to their adaptive role to a specific environment. Moreover, this conclusion can be made without these extensive experimental crosses.The summary and the previous reviewer comment underscore the novel contributions of our paper, including the ability to address the empirical contribution of rare variants to trait variation in a more comprehensive manner than has previously been possible, and the decoupling of allele frequency from variant discovery. We have taken the opportunity, as requested in the summary, to significantly expand the Introduction to make these and other key points clearer to the non-specialist. We agree that theoretical approaches in evolutionary, population and quantitative trait genetics have been applied to predict the relative contributions of common and rare variants to trait variation under different sets of assumptions; indeed, we cite many relevant papers in our manuscript. We also agree that there is value in aggregating information from individual case reports in the literature – we cited Fay, 2013 in our manuscript, and we noted that the large set of candidate QTGs systematically identified in our study is enriched for QTGs reported in that study. The variants reported in Fay, 2013 represent a sparse sampling of variant effects in yeast, and were by necessity based on studies with small sample sizes, which biased this set of variants in favor of large effects. The review by Peltier et al., 2019 (published after the submission of our manuscript) is similarly based on genes and variants previously reported in the literature. We have added a citation to this paper. We believe that our systematic, comprehensive, empirical approach provides much more general insights into the relative contributions of variants of different frequencies.


Dental caries and periodontitis account for a vast burden of morbidity and healthcare spending, yet their genetic basis remains largely uncharacterized. Here, we identify self-reported dental disease proxies which have similar underlying genetic contributions to clinical disease measures and then combine these in a genome-wide association study meta-analysis, identifying 47 novel and conditionally-independent risk loci for dental caries. We show that the heritability of dental caries is enriched for conserved genomic regions and partially overlapping with a range of complex traits including smoking, education, personality traits and metabolic measures. Using cardio-metabolic traits as an example in Mendelian randomization analysis, we estimate causal relationships and provide evidence suggesting that the processes contributing to dental caries may have undesirable downstream effects on health. Dental caries and periodontitis are among the most common medical conditions. Here, the authors report a GWAS for measures of oral health that reveals 47 risk loci for caries, find genetic correlation with 31 other complex traits and use Mendelian randomization analyses to explore potential causal relationships. Characterising the aetiology of these diseases is a priority as they confer major health2 and financial burden, with the global cost of dental diseases exceeding 540 billion US dollars in 20153. Part of this story is the genetic contribution to oral health outcomes and the heritability of dental caries and periodontitis have been reported to be as high as 50%5. However, the nature of this contribution remains poorly characterised despite the promise that increased understanding of genetic factors can bring with respect to aetiology dissection and theoretically, clinical managementThe 2016 Global Burden of Diseases, Injuries and Risk Factors Study7, specific presentations of disease and the presence or absence of disease in paediatric populations9. To date, few reliable genetic-association signals have been found, and this is likely to reflect different measurement approaches used, complex genetic architecture10 of dental caries or limited statistical power to detect associations. GWAS for periodontitis have investigated measures, including the presence or absence of disease11, quantitative measures of periodontal status12, severe presentations of disease13, molecular and microbial intermediaries of disease14 and composite phenotypes such as GWAS for principal components which aim to capture multiple facets of periodontal health15. These studies have not yielded consistent evidence of specific genetic contributions to periodontitis9.Genome-wide association studies (GWAS) for dental caries have investigated measures, including overall caries experience16. The presence of less well defined but informative phenotypes has enabled successful association signal discoveries for several complex traits, yielding important biological insights17. In order to achieve further understanding of genetic contributions to caries and periodontitis, a shift in analysis scale—afforded by a similar approach to measurement—is required.Currently, there is a trade-off between phenotypic refinement and obtaining valid phenotype data in sufficiently large cohorts to allow statistical power for genome-wide analyses. Given the logistical and economic challenges in obtaining detailed phenotypes in large populations, studies have focused on clinical outcomes indicating the presence or absence of manifest disease. Recent studies of other complex traits have taken a different approach and circumvented the limited availability of refined clinical phenotypes by taking advantage of extremely large, population-based, cohorts with both genetic data and less-refined proxy phenotypes. The UK Biobank (UKB), for example, includes information from approximately half a million participants18, which is a unique collection of epidemiological cohorts with detailed information on clinical endpoints of dental diseases; and UKB, which contains less-refined self-reported oral health data at a larger scale. In isolation, the biological meaning and relevance of the approximate measures in UKB would not be clear, but anchored against and unified with the more detailed clinical information in GLIDE, this combination of complementary resources provides a unique opportunity for genetic association discovery and application.Here, we synthesise evidence from two sources; the Gene-Lifestyle Interactions in Dental Endpoints (GLIDE) consortiumUsing this combination of resources, we identify 47 novel risk loci for dental caries and show that the heritability of dental caries is partially shared with a range of complex traits. Applied analysis using Mendelian randomisation suggests that dental caries has undesirable downstream effects on health. Together, these findings improve our understanding of the potential causes and consequences of an important complex disease.19  were undertaken within the GLIDE consortium, using clinical measures of dental diseases and imputed genotype data, accounting for age-specific, sex-specific and other study-specific covariates. The primary traits were measures of caries experience  and the sum of Decayed and Filled tooth Surfaces per available tooth Surface (DFSS)), number of teeth (Nteeth) and a dichotomous classification of periodontal health or disease Table . All metn = 461,031 for all traits; see the Methods section)In parallel, genetic contributions to self-reported measures of oral health were characterised in UK Biobank (UKB). Participants were asked to report whether they had bleeding gums, painful gums, dentures, loose teeth, toothache or mouth ulcers as part of a baseline study questionnaire. GWAS for each trait was performed within individuals of European ancestry, accounting for age, sex and relatedness using a linear mixed model (2LDSR) was estimated using univariate linkage-disequilibrium score regression (LDSR)20 (Methods). In GLIDE, the highest and lowest heritability estimates were reported for Nteeth  and periodontitis , respectively; while in UKB the highest and lowest heritability estimates were for dentures  and toothache , respectively -based heritability  were estimated using bivariate LDSR21 with an unconstrained intercept term to allow for sample overlap. For clinical measures within GLIDE, there were strong genetic correlations (Rg > 0.4 or Rg < −0.4) between DMFS and DFSS, DMFS and Nteeth and DFSS and Nteeth  . For periodontitis, the highest Rg value was seen for loose teeth (Rg~1); however, this was imprecisely estimated due to the low heritability of periodontitis .To guide interpretation of dental disease traits and identify those with similar genetic contributions, genetic correlations  and dentures ; the other combining periodontitis  and loose teeth . These analyses included ~8.9 million SNPs and insertion/deletions (INDELS) present in both GLIDE and UKB. There was evidence of a polygenic contribution to phenotype in both combined analyses with reasonable inflation given the nature of the traits and anticipated genetic architecture .Exploiting this shared heritability for gene discovery, single-variant association statistics from GLIDE and UKB were combined using a z-score genome-wide meta-analysis weighted by effective sample size. There were two principal analyses; one combining DMFS (P < 5 × 10−8) in the unconditional results and following a stepwise selection procedure  change in DMFS residuals, odds ratio [OR] for having dentures = 0.85 ). rs121908120 is a missense variant within WNT10A which results in a phenylalanine to isoleucine substitution and is predicted to have deleterious consequences in multiple WNT10A transcripts using the ExAC browser22. In a population of 28,691 adults aged 30–75 years who represent the Northern Swedish adult population with access to dental care, the estimated effect of the A allele corresponded to 2.1  fewer decayed, filled or missing tooth surfaces (Methods).The largest estimated per-allele effect of any variant in the combined analysis was observed for rs121908120, a low-frequency variant ), with an estimated effect corresponding to 1.2  additional decayed, missing or filled tooth surfaces per T allele. The lead variant lies within an uncharacterised protein-coding region, C5orf66, however, putative gene mapping using reference expression quantitative trait locus (eQTL) and chromatin interaction data implemented in FUMA23 highlighted 25 potential genes at this locus  to make comparison with published studies, 46/47 variants or proxies  were available in the PhenoScanner database, and 26 of these (57%) have previously reported association with one or more non-dental diseases or health traits, termed ‘overlaps’ in this description. Traits seen repeatedly in this overlap analysis include adiposity traits (11/26 overlaps), height (9/26 overlaps) and bone mineral density (3/26 overlaps). A summary is shown in Supplementary Table The remaining 45 genetic risk loci in the DMFS/dentures combined analysis include some investigated in candidate gene studies for dental caries, such as the Human Leucocyte Antigen (HLA) regionSIGLEC5, which was recently reported as a risk locus for aggressive periodontitis13 . Effect estimates in GLIDE and UKB were consistent at this lead locus, and there was also evidence for consistency in effect estimates at conditionally independent single variants passing an arbitrary threshold for suggestive association . In the DMFS/dentures, meta-analysis aggregate results were available for 15,522 transcripts. Of these, varying expression levels at 221 transcripts were predicted to influence the phenotype, including multiple HLA-region transcripts. Outside the HLA region, the strongest evidence was seen for CA12, located in the region of single-variant association signal at 15q22, (P = 2.8 × 10−17 in Z-test). CA12 encodes a member of the carbonic anhydrase family of zinc enzymes which catalyse the hydration of carbon dioxide to form bicarbonate and hydrogen ions to regulate pH. This family has several functions relevant to dental caries, including tooth formation, where multiple carbonic anhydrases are produced by maturation-stage ameloblasts27, salivary buffering, where defects in CA12 lead to poor salivary function and xerostomia28; and regulation of tooth biofilm microbiota, where CA6 may affect colonisation by the cariogenic microorganism Streptococcus mutans29. In the region of the lead single-variant signal in 5q31, the S-TissueXcan approach prioritised PITX1 as the most relevant transcript (P = 2.9 × 10−12). PITX1 encodes a developmentally expressed transcription factor with roles in skeletal and mandibular growth and tooth development, and deletion of the Pitx1 locus in animal models results in abnormal mandibular tooth morphology30. The results are given in Supplementary Data In an exploratory hypothesis-generating investigation, summary statistics from the two primary combined analyses and eQTL data were integrated using the S-PrediXcanSIGLEC5 was predicted to associate with increasing odds of periodontitis/loose teeth (P = 8.7 × 10−07). Full results are given in Supplementary Data In the periodontitis/loose teeth analysis, the same 15,222 transcripts were tested, but here only a single transcript was associated with the phenotype after correction for multiple testing. Increasing transcription of 31, which tests whether loci housing dental disease-associated single variants are over-represented in predefined sets of functionally related genes. For the DMFS/dentures analysis, there was no evidence for enrichment in gene sets passing an acceptable false discovery rate (Supplementary Data 23 using a hypergeometric test to test whether the transcripts prioritised by S-TissueXcan were over-represented in curated gene sets defined in the Molecular Signatures Database (MSigDB C2). No enrichment beyond chance was observed after correction for multiple testing for DMFS/dentures loci, and there were insufficient loci to perform this analysis for periodontitis/loose teeth.Gene set enrichment was assessed using DEPICT32 or in regions surrounding genes with tissue-specific expression patterns33. In the DMFS/dentures combined analysis, there was evidence for enrichment in 38/85 functional annotations including annotations providing evidence for evolutionary conservation. Treating Genomic Evolutionary Rate Profiling (GERP) scores as a continuous annotation, DMFS/dentures association signal was enriched in genomic regions under evolutionary constraint (P = 1.5 × 10−28 in Z-test for enrichment), while the 1.9% of variants annotated as highly conserved from primates to humans accounted for 30% of the heritability of DMFS/dentures  using HLA haplotype dosage as the exposure and ‘Dentures’ as the outcome. Ten haplotypes were associated with dentures, including haplotypes of HLA class I and class II. The strongest evidence for association was observed for DQB1_201, a common haplotype encoding the DQ-beta 1 chain of the HLA class II complex , P = 8.9 × 10−13 in χ2 test) . For the periodontitis/loose teeth analysis, effect estimates at the lead variant were obtained from a meta-analysis of independent studies within GLIDE of East Asian ancestry . There was no strong evidence for association at rs12461706 in this population , where the A allele is common (EAF = 0.96) compared with the European ancestry population.The composition of the samples in GLIDE affords an opportunity to assess heterogeneity across strata of ancestry or clinical status. To explore whether lead variants identified the DMFS/dentures combined analysis had effects driven by periodontal tooth loss, genetic effect sizes were estimated in individuals with or without periodontitis and contrasted (GLIDE only). There was little evidence for different effect sizes between groups  between oral disease traits and all available traits with genome-wide association data, excluding any GWAS results obtained solely in UKB (Methods). For DMFS/dentures combined analysis, positive genetic correlations were seen for smoking traits, for example ever vs. never smoked , adiposity traits, such as body mass index  and smoking-related diseases, such as lung cancer  and coronary artery disease . Negative genetic correlations were seen for longevity  and complex traits reflecting socio-demographics and cognition, in particular educational attainment   Fig. . For the40 approach for primary analysis. Treating DMFS/dentures as an exposure, a one standard deviation greater burden of dental disease  was nominally associated (P < 0.05) with greater waist-to-hip ratio  , higher plasma triglyceride levels ), increased odds of type 2 diabetes ) and increased odds of all stroke ). Of these findings, only waist-to-hip ratio and triglycerides survived a Bonferroni correction for multiple testing. The primary results are given in Table The genetic correlations between dental diseases and metabolic traits and cardiac outcomes suggest shared genetic contributions to the same biological underpinnings, but also can be due to pathway effects where dental diseases are a risk factor for health outcomes. To explore this, we undertook bidirectional two-sample Mendelian randomisation (MR) to estimate causal relationships between DMFS/dentures and a subset of traits reflecting metabolic and cardiovascular health, using the Generalized Summary Mendelian Randomisation (GSMR)) CI: 0.0, 0.13, hSensitivity analysis used alternative estimation tools to explore whether these findings were robust under different modelling assumptions  and fasting blood glucose were nominally associated with greater burden of dental disease, but only body mass index survived correction for multiple testing  for 1 KgM−2 greater BMI, with consistent effect estimates in sensitivity analysis  for 1 KgMThis investigation used detailed clinical measures in combination with genetically validated proxy phenotypes to investigate the two major dental diseases, caries and periodontitis.PITX1, CA12 and in the HLA region in addition to uncommon variation with large effects in WNT10A. Combined analysis of periodontitis and loose teeth (a late symptom of advanced periodontitis) confirmed association at a previously reported locus, SIGLEC5. Integration of GWAS results with external sources of expression data prioritised 221 gene transcripts which may be involved in the pathogenesis of dental caries, while integration with functional annotation data showed that heritability of dental caries was enriched in conserved genomic regions, with a fold-enrichment value similar to other complex traits with serious health consequences32. Cross-trait comparisons showed overlap in the genetic determinants of dental diseases and complex non-oral health traits at both a single-variant level and genome-wide level. Finally, using a Mendelian randomisation analysis framework, there was evidence suggesting that biological processes leading to dental caries may have downstream effects on general health.Combined analysis of DMFS and dentures identified 47 novel risk loci, including common variation near 41, but here we extend this approach to the selection of disease proxies where the prior expectation is less clear. This workflow may be adaptable to other complex diseases where it is difficult to obtain detailed phenotypic information in large collections.This investigation used an empirical approach informed by shared heritability to select dental disease proxy measures with similar biological meaning to detailed clinical measures. This approach has similarities to a recent investigation which used genetic correlation for post hoc confirmation of a prior expectation that family history of Alzheimer’s disease is a satisfactory proxy of clinical diagnosisWNT10A, the locus harbouring the variant with the largest associated effect in the DMFS/dentures analysis, encodes a member of the WNT/β-catenin family of signalling proteins which have documented roles in inducing and regulating tooth formation in animal models44 in addition to their widely known functions in embryological patterning and oncogenesis. In humans, WNT10A mutations have been reported to cause isolated defects in tooth number45 and quality46 and to regulate the cusp architecture and other morphological characteristics of teeth47. Genes encoding other proteins in the WNT signalling cascade (but not WNT10A) were identified as candidates in an early GWAS for dental caries with some sample overlap with this study6. Other examples with plausible biological relevance, including HLA, CA12 and PITX1, are flagged in the results.At a single-variant level, the associated loci in this study may provide insight into the biological processes that are relevant to dental diseases. As an example, These genetic associations improve disease understanding and may provide a foundation for innovative approaches to risk assessment, outcome prediction, disease management or treatment. The availability of genetic proxies for dental diseases in large data sets also unlocks previously unavailable approaches, such as two-sample MR to infer potential consequences of dental diseases. As an illustrative example, the MR analysis included in this work provides some support for the hypothesis that dental diseases proxied by the DMFS/dentures may be an upstream risk factor for metabolic disturbance and cardiovascular disease events and prioritises specific relationships for additional investigation. This analysis also provides a broader demonstration of the utility of these data for generating and testing research hypotheses.48. This might be due to heterogeneity introduced by the different approaches to disease classification, different patterns of periodontal treatment and varying distributions of age in the GLIDE cohorts or gene–environment interactions not accounted for in the study design. Here, DMFS/dentures is described as a measure of dental caries. This measure might capture some variation in periodontal status, as periodontitis is a major cause of tooth loss49. Conversely, we note that the SIGLEC5 periodontitis risk locus is not a main finding for DMFS/dentures and that there is little evidence for heterogeneity in DMFS effect sizes between periodontal cases and controls, supporting the idea that the two primary meta-analyses capture distinct dental diseases.The dental traits examined in this study appeared moderately heritable, except for periodontitis where the quantifiable heritable signal was much lower than estimates reported in the literatureThe combination of genetically similar but non-identical pairs of phenotypes creates challenges in harmonising effect sizes, which we addressed using standardised regression coefficients, allowing valid comparison of the relative magnitude of genetic or causal effect estimates and valid inference about the probability of a non-zero effect. Indicative estimates on a tooth surface scale are also provided, however, these rely on assumptions about the variance in DMFS scores in any given population and should be interpreted with caution.50, they are limited by the quality and availability of the external data, for example the data on odontoblast or ameloblast tissue are not available in GTEx. Cross-trait comparisons of dental diseases with other traits at single-variant level are only possible when GWAS results are available for any given trait, and well-powered investigations are likely to report more associations than small studies. Together, this means that the list of observed overlaps between dental diseases and other traits will be biased towards well-investigated traits and outcomes.GWAS results were explored in follow-up analyses using approaches which exploit external sources of information, including gene expression data. While these approaches maximise value from GWAS and improve statistical power to identify relevant genes51 or confounded if both the exposure and outcome are influenced by a latent shared trait with genetic determinants52. The different approaches to detect and account for horizontal pleiotropy used in this study yielded similar causal effect estimates; however, lack of precision in these estimates may have masked important differences or evidence for horizontal pleiotropy which will only emerge in future experiments with greater statistical power. Finally, the non-specific-nature of the DMFS/dentures phenotype may capture a range of latent treats upstream of clinically manifest disease and tooth loss due to periodontitis, meaning that the downstream effects of DMFS/dentures might involve a wide range of potential mechanisms or mediators.Causal effect estimates in MR experiments may be biased by unaddressed horizontal pleiotropyIn summary, this study leveraged self-reported dental disease proxies and clinical disease measures in meta-analysis to identify novel risk loci for dental caries. Characterising the functional biology at these loci may provide insight to improve diagnosis or guide the development of new therapeutic approaches targeting the most prevalent global disease. At a single-variant and whole-genome level, the heritability of dental caries partially overlaps with other complex traits and diseases, arguing against the notion that dental diseases can be diagnosed, managed or researched in isolation. Finally, the results of MR analysis support the idea that population-level interventions to reduce the burden of dental diseases may have benefits for population health more generally.Each contributing study obtained informed consent from all study participants. This study complied with all relevant ethical regulations, including the Declaration of Helsinki, and ethical approval for data collection and analysis was obtained by each study from local boards as described in Supplementary Data The contributing studies were 1) Atherosclerosis Risk in Communities (ARIC); 2) The Center for Oral Health in Appalachia cohort 1 (COHRA1), which is part of the GENEVA caries consortium; (3) the Dental Registry and DNA Repository of the University of Pittsburgh School of Dental Medicine, (DRDR), also part of the GENEVA caries consortium; (4) the Hispanic Community Health Study/Study of Latinos (HCHS/SOL); (5) the Malmö Diet and Cancer Study (MDC); 6) the Northern Finland Birth Cohort 1966 (NFBC 1966); (7) the Study of Health in Pomerania (SHIP), (8) the Study of Health in Pomerania Trend (SHIP Trend); (9) TWINGENE, which is a genotyped epidemiological study recruited from the Swedish Twin Registry (TWINGENE); (10) the Women’s Genome Health Study (WGHS); (11) Biobank Japan (BBJ) and (12) Tokyo Medical and Dental University Aggressive Periodontitis Study (TMDUAGP). A detailed description of each study is included in . In one study (HCHS/SOL), participants were recruited from Hispanic and Latino communities in the USA, who self-reported ancestry from six broad groups . To undertake analyses within this highly admixed population, a bespoke modelling approach was undertaken. Multi-dimensional clustering was used to generate genetic analysis groups containing participants of similar ancestry. These group allocations were then used as covariates in a linear mixed model  alongside the first five genetic principal components, study center and log-transformed sampling weightsFor periodontitis only, there were two studies with participants of East Asian ancestry , totalling 17,287 participants. For periodontitis, separate meta-analyses were performed for studies of European ancestry and studies of East Asian ancestry.Dental records used to calculate DMFS, DFSS and Nteeth were either obtained by a trained assessor as part of the study protocol, or from index linkage to records completed by a dental professional in primary care (MDC and TWINGENE). The examination protocols used by each study are described in Supplementary Data Nteeth was obtained by counting the number of remaining natural permanent teeth . This was derived from records of clinical dental examination for all studies apart from WGHS, where participants were asked to self-report this information. Participants were asked whether they had lost any teeth and, if so, asked to specify the number of teeth lost.54 were used. In COHRA1, participants were classified as cases if two or more sextants had probing depth of at least 5.5 mm, or if participants reported ever having ‘gum surgery'. In TwinGene and MDC, participants were classified as cases if at least two tooth surfaces had probing depth of 5 mm or deeper, or at least four tooth surfaces had probing depth of 4 mm or deeper. In BBJ, participants were classified as cases or controls based on clinical diagnosis by physicians at participating hospitals, with data retrieved from diagnosis codes in hospital registers. In TMDUAGP, the participants were classified as cases based on the classification developed at the 1999 international workshop for a classification of periodontal disease and conditions55. In WGHS, the participants reported if they had periodontal disease or not. The question stems were ‘Since you started the trial (around 3 years ago)/In the past year, were you newly diagnosed with/have you had any of the following', with ‘Periodontal disease' as one possible response. Participants who selected this response were asked to provide the month and year of diagnosis. Participants with no teeth were excluded from scoring the primary oral health traits in GLIDE.For periodontal status, participants were classified as having (cases) or not having (reference) clinical symptoms of periodontitis, using definitions applied by each participating cohort. In ARIC, SHIP, SHIP-Trend and HCHS/SOL, criteria published by the Centers for Disease Control and Prevention/American Academy of Periodontology (CDC/AAP)56 (1000 Genomes project (1kGp) phase 1 version 3 (March 2012) release for all studies apart from COHRA, which used the 1000 Genomes project phase 1 version 2 release).Genotyping was performed using commercially available arrays , derived variables were created to account for major covariates. Raw phenotype counts were regressed on age, age squared, genetic principal components and other study-specific covariates as described in Supplementary Data 57. Variants were excluded if they had low imputation quality , departed from Hardy–Weinberg equilibrium (PHWE < 10−6 in the entire sample for continuous traits or in controls for periodontitis), or had per-file minor allele count <6. Directly genotyped SNPs with poor call rate (<95%) were also excluded. Association statistics within each study were corrected using genomic control inflation factor (max λGC = 1.07).In addition to study-specific measures, central QC of the association result files was performed using EasyQC software and a previously published protocol19.Fixed effect inverse-variance weighted meta-analyses were performed using METAL software58. The HCHS/SOL study contains participants of Latino/Hispanic ancestry. To assess for ancestry-related heterogeneity, meta-analyses in GLIDE were repeated, excluding HCHS/SOL, and tests for heterogeneity were performed between these results and results from HCHS/SOL for the lead SNPs, again using EasyStrata.For lead associated variants, DMFS effect sizes were compared between periodontitis cases and controls in stratified meta-analysis. Tests for difference in effect size were performed using the CALCPDIFF function of EasyStrataWhere available, genotype data for chromosome X were analysed. Haploid allele calls for male participants were coded as 0 or 2. Genotypes for female participants were coded as 0, 1 or 2 under the additive genetic model. Summary statistics from the participating studies were combined using fixed effects, inverse-variance weighted meta-analyses following the same workflow described for autosomal results.16.UK Biobank is a population-based health research resource consisting of ~500,000 people, aged between 40 and 69 years, who were recruited between the years 2006 and 2010 from densely populated regions of England, Scotland and Wales16. Single-variant analysis used the 2018 (v3) imputed data release including imputation to both Haplotype Reference Consortium and UK10K/1000 genomes combined panel. Additional QC of the imputed data was performed at the University of Bristol. Participant-level QC involved restricting analysis to participants of European ancestry  as well as standard exclusions for mismatch between reported and genetic sex, possible sex chromosome aneuploidy, outliers in heterozygosity and missing rates. An additional two participants were removed as they were apparently related to a very large number of participants at 3rd degree or closer; otherwise related participants passing all other quality control were included in single-variant analysis59. For HLA haplotype analysis, imputation of classical HLA haplotypes was performed using the HLA*IMP:02 algorithm with a multi-population reference panel16 and analysis was restricted to unrelated participants who self-identified as ‘White British’ and were located within the largest cluster in k-means analysis.Participants in UKB were genotyped using the UK BiLEVE and UK Biobank axiom array '. The possible answers included ‘Dentures', ‘Bleeding gums', ‘Painful gums', ‘Loose teeth', ‘Toothache' or ‘Ulcers'. Participants who selected one of these answers were coded as cases for each respective analysis. Participants who did not select this answer were coded as reference. GWAS included the following number of cases; dentures: 60. Age, age squared, sex and genotyping array were included as covariates in association testing. BOLT-LMM association statistics on a linear scale were transformed to log odds ratios and their corresponding 95% confidence intervals on the liability scale using a Taylor transformation expansion series as detailed in a full description of the GWAS pipeline which has been published online61. The association statistics were corrected using the estimated intercept term from univariate LDSR20  prior to meta-analysis with GLIDE.GWAS were performed using a linear mixed model (LMM) implemented in BOLT-LMM (v2.3)20 was used to estimate heritability attributable to common genetic variants (h2LDSR). Scripts are available at (https://github.com/bulik/ldsc). Pre-computed reference LD scores and weights derived from 1000 Genomes European ancestry data were downloaded from . In GLIDE, summary statistics from the primary meta-analysis for each trait were used. A subset of high-confidence SNPs  were used to minimise bias related to imputation accuracy. Summary statistics for each phenotype were first re-formatted with the munge_sumstats.py python script and then heritability was estimated using the–h2 option of ldsc.py.Univariate LDSRg) for all pairs of traits between GLIDE and UKB were estimated using the–rg option of ldsc.py script (https://github.com/bulik/ldsc), and files were prepared using the same criteria described above. To estimate Rg with a range of publicly available GWAS summary statistics, the prepared files for dental traits were uploaded to the LD hub39 resource (ldsc.broadinstitute.org) using all available traits with genome-wide data available on 9th January 2019, apart from those obtained solely in UKB. The logical maximum and minimum values of Rg are +1 and −1, however, the mathematical derivation used by LDSC can occasionally create values >+1 or <−1, which should be interpreted as values lying near +1 or −1, respectively.Genome-wide genetic correlations . Segmented LDSR using tissue-specific annotations was performed using the –h2-cts flag and multi-tissue gene expression files derived using 1000 Genome phase 3 data (April 2018 release).19. The contributions of GLIDE and UKB were weighted by sample size for continuous traits (DMFS) and by effective sample size for binary traits . The effective sample size was estimated from the number of cases and number of controls using the formula recommended by METAL’s authors19.Combined two-way meta-analysis of association results between GLIDE and UKB was performed using the fixed effects z-score method implemented in METALP < 5 × 10−8. Within any given genomic locus, the lead SNP was defined as the variant with the lowest association P-value within a+/− 500-kb distance, using EasyStrata58. To test for conditional independence of lead variants, a stepwise selection procedure was performed using approximate conditional analysis62, implemented using the cojo-slct function of GCTA (version 1.91.4)63. Loci were only considered functionally independent if at least one variant reaching genome-wide significance was selected in that risk locus during this procedure. For the HLA region (chr6: 25–35 Mb), the broad association signal and complex LD structure prevented testing for conditional independence between variants, so only a single lead variant was reported for this region. Where more than one conditionally independent variant was selected within a single-risk locus, the lead variant was presented in Table Genome-wide significance was set at To understand the relative size of genetic effects for variants in the Z-score combined analysis, beta coefficients and corresponding standard errors were derived using a transformation described in Supplementary Note Standardised regression coefficients in combined analysis were transformed to provide indicative effect estimates in a clinically interpretable scale of affected tooth surfaces or log odds of disease. The transformation is described in Supplementary Note P < 1 × 10−5) in the combined analysis were used to test for correlation in effect sizes.Directional consistency of effects for lead in combined meta-analysis of GLIDE and UKB data was assessed by counting the number of directionally consistent SNPs between the GLIDE and UKB data sets. Correlation in effect sizes was assessed by calculating Pearson correlation coefficient weighted by inverse variance (1/SE) in the GLIDE meta-analysis. For periodontitis/loose teeth, there was only a single risk locus, therefore independent suggestively-associated single variants (http://www.phenoscanner.medschl.cam.ac.uk/phenoscanner), an online curated database of publicly available GWAS summary statistics results. The results were retrieved for variants identified in combined analyses and their proxies . If variants had previously been associated with a non-dental disease trait (P < 5 × 10−8 in GWAS), then details of the traits, association test statistics and publication references were retrieved.Cross-trait analysis of single variants was performed using PhenoScanner , was used to test whether associated loci are preferentially located within predefined functionally similar gene sets, assessed against a null expectation informed by GWAS results for randomly distributed phenotypes. Associated loci were defined at (P < 5 × 10−8) in combined analysis. Reconstituted gene sets, tissue expression matrix and gene annotation files were downloaded from the DEPICT repository (data.broadinstitute.org/mgp/depict/documentation).DEPICT23. Associated genes were defined as those passing Bonferroni correction in S-TissueXcan analysis. Pathways and gene sets were taken from the Molecular Signatures Database (MSigDB C2), and all protein-coding genes in the FUMA database were used as background. Enrichment P-values were corrected for multiple testing using Bonferroni correction.A hypergeometric test for gene set enrichment was performed using FUMA25 web pipeline (https://cloud.hakyimlab.org/). Gene-level mediating effects of expression levels using were estimated using the summary GWAS association results and pre-fitted elastic net prediction models of gene expression levels in the 48 GTEx tissues26, which are available online (http://predictdb.org/). Following this, multi-tissue results were aggregated using the S-TissueXcan64 pipeline and post-processing pipeline (both hosted at (https://cloud.hakyimlab.org/). A Bonferroni correction was applied to account for the number of gene transcripts tested.Summary results from the combined meta-analyses were uploaded to the S-PrediXcan23. eQTL mapping included data on cis-eQTLs (up to 1MB between SNP and gene) from all available tissues in GTEx v6 and v7. Chromatin interaction mapping included 21 tissues with HiC data and enhancer/promoter regions defined in Roadmap 111 epigenomes. By default, sites 250 bp upstream to and 500 bp downstream from transcription factor start sites were considered promoter region windows.Associated single variants were mapped to candidate genes using the ‘SNP2GENE’ function in the online functional annotation tool FUMA40 (GSMR), implemented in GCTA (v1.92.0). Compared with other summary-statistic based estimators, GSMR is reported to have greater statistical power because GSMR uses genome-wide data to account for sampling variance in SNP-exposure and SNP-outcome estimates40.Primary analysis was performed using Generalized Summary Mendelian Randomisation65; for waist-to-hip ratio adjusted for BMI; GIANT consortium66, for coronary artery disease CARDIOGRAM plus C4D meta-analysis67; for stroke the MEGASTROKE consortium68; for type 2 diabetes, the DIAGRAM consortium69; for fasting glucose the ENGAGE consortium70; for HDL cholesterol, LDL cholesterol and triglycerides, the GLGC data sets were used71.Genome-wide summary statistics for seven metabolic traits and two cardiovascular outcomes were selected as follows: BMI; meta-analysis of GIANT with UK BiobankP < 5 × 10−8) after LD clumping using reference data from the cohorts arm of the UK10K project (https://www.uk10k.org/data.html) to produce index SNPs  were included as potential instrumental variables. No attempt was made to manually screen variants for possible undesirable pleiotropic effects, with filtering instead performed as part of the HEIDI-outlier procedure.To achieve adequate variance explained and therefore statistical power, multiple SNPs were included as instrumental variables for all traits. All variants associated with dental disease or metabolic traits  estimated from a non-outlying genetic instrumental variable, and tests whether other single nucleotide polymorphisms (SNPs) have values of βxy compatible with this estimate, on the assumption that pleiotropic variants will have outlying values40. Following default criteria, potentially outlying variants with (P < 0.01 for pleiotropy) were removed and βxy was estimated from the remaining instruments.HEIDI-outlier filtering, is an extension of the heterogeneity in dependent instruments methodIn the primary analysis, variants in the HLA region (chr6: 25–35 Mb) were removed for estimation of casual effects of DMFS/dentures, except for a single-lead variant. For estimation of causal effects of other traits on DMFS/dentures, full genome-wide data were used.Methods used for sensitivity analysis are described in Supplementary Note Further information on research design is available in the Peer Review FileSupplementary InformationDescription of Additional Supplementary FilesSupplementary Dataset 1Supplementary Dataset 2Supplementary Dataset 3Supplementary Dataset 4Supplementary Dataset 5Supplementary Dataset 6Supplementary Dataset 7Supplementary Dataset 8Supplementary Dataset 9Supplementary Dataset 10Supplementary Dataset 11Supplementary Dataset 12Supplementary Dataset 13Supplementary Dataset 14Supplementary Dataset 15Reporting Summary