CYBRD1 that associated with disease in individuals of English, but not Scottish, ancestry. The association replicated in two additional, independently-collected data sets. Our method can be used to detect associations between genetic variants and disease that have been obscured by population genetic heterogeneity. It can be readily extended to the identification of genetic interactions on other covariates such as measured environmental exposures. We envisage our methodology being of particular interest to researchers with existing GWAS data, as ancestry groups can be easily defined and thus tested for interactions.Genome-wide association study (GWAS) data on a disease are increasingly available from multiple related populations. In this scenario, meta-analyses can improve power to detect homogeneous genetic associations, but if there exist ancestry-specific effects, via interactions on genetic background or with a causal effect that co-varies with genetic background, then these will typically be obscured. To address this issue, we have developed a robust statistical method for detecting susceptibility gene-ancestry interactions in multi-cohort GWAS based on closely-related populations. We use the leading principal components of the empirical genotype matrix to cluster individuals into “ancestry groups” and then look for evidence of heterogeneous genetic associations with disease or other trait across these clusters. Robustness is improved when there are multiple cohorts, as the signal from true gene-ancestry interactions can then be distinguished from gene-collection artefacts by comparing the observed interaction effect sizes in collection groups relative to ancestry groups. When applied to colorectal cancer, we identified a missense polymorphism in iron-absorption gene  Genome-wide association studies have had a marked impact on our understanding of the contribution of common variants to common disease To circumvent these problems, we have developed a robust statistical test for gene-ancestry interactions that makes use of observed and measured relatedness between closely-related populations. The method re-assigns individuals to new ancestry groups by clustering in the space defined by the leading principal components of the empirical genotype matrix Since intra-study effect heterogeneity can obscure true associations between polymorphisms and disease, a potential benefit of our approach is the un-masking of true associations that are specific to ancestral groups or stronger in one group than another. Although intra-study gene-gene interactions or gene-pathway interactions have previously been analysed Materials and methods section. In brief, the analysis pipeline consists of an initial step where two or more GWAS have been identified on the same disease or trait of interest across closely related populations. SNPs are then identified which appear to show an interaction on ancestry; by first clustering the combined set of individuals into ancestry groups and then statistically testing for evidence of an ancestry group interaction term of association with the trait. SNPs identified as putative interaction markers are then tested for strength of association for an interaction on the original cohort groups. For true ancestry-interactions the effect size should increase when clustering on ancestry rather than cohort label. Markers are then filtered to take forward only those showing largest difference. Markers for which the statistical evidence of an interaction is overwhelming, or ones showing milder evidence but with additional functional or biological relevance linking the marker to the trait, are taken forward to a Replication stage. In the replication stage it is valid to only genotype the marker(s) of interest in individuals sampled from the original population groups. In this situation you are not abel to assign such replication individuals to ancestry groups, but the population label can be used as a noise proxy without bias, but with some loss in power. Below, we present our results for a GWAS of colorectal cancer.The method is summarised in The discovery stage involves steps 1 to 5 in Materials and methods). In Phase 1, only the first two principal components (PCs) provided a significant measure of separation between the two groups collected from England and Scotland  after filtering out SNPs in regions of long-range linkage disequilibrium Scotland  and we uScotland . ClusterScotland .Materials and methods).We then looked for single marker-ancestry interactions genome-wide by fitting the heterogeneous logistic model of association  and comparing the fit of this model to that of the null model with the same genetic association across all clusters . Since the first principal genetic component used to characterise ancestry was disease-associated, we included this together with gender as main effect adjustment covariates in both the heterogeneous and null models. To compare the model fits, we used the BIC which adjusts the model fit for complexity. We calculated the difference in BIC statistics between the null-BIC and heterogeneous-BIC models and used this difference as a test statistic . We retained markers above the 1% D-statistic significance threshold . After imposing this filter, 4,445 out of 485,757 markers remained, consistent with the number  expected by chance.We also performed an analogous scan for single marker-collection interactions by using the original collection groups in place of ancestry, “Path B” in hreshold , estimatIn our special case we also have discovery data on a second Phase. We then made use of the Phase 2 data in our discovery stage by performing the same heterogeneity analysis , but no disease association for those in the Scottish ancestry group. Although, statistically, the evidence for heterogeneity and an English ancestry-specific disease association was mild and, indeed, we would expect exactly one marker to pass through the filters by chance, we proceeded with replication given the functional context of rs10455. rs10455 is located within the last exon of an iron-regulated gene, cytochrome B reductase 1, that is expressed in the intestine and plays a key role in dietary iron absorption (Genome Browser refSeq NM 001127383).We grouped Phase 2 individuals into ancestry clusters using the ng label . We thenTo ascertain independent evidence for the rs10455 association, we undertook a targeted replication stage in which we sought additional CRC case-control cohorts from equivalent (English and/or Scottish) populations. We identified a small Phase 3 multi-ethnic cohort  of 631 cases and 731 controls. We did not have access to genome-wide genotype data and hence ancestry clustering could not be performed. However, as stated above, in the Replication step this is not prohibitive as the population label can be used as a noisy proxy for ancestry without biasing the result, albeit for a loss in power see  and S6.Testing Phase 3 for variation in association signal for rs10455, using logistic regression, showed additional mild, but consistent evidence of a protective effect in England-collected individuals  and no evidence of association in the Scotland-collected Phase 3 individuals . Our power calculations  suggesteGiven the support for rs10455 in Phase 3, we undertook a further analysis and sought additional replication in a larger independent cohort of 7,395 cases and 4,202 controls collected in England , at the ancestry . In a meCYBRD1 in iron absorption is of particular interest given that many studies have investigated the link between dietary iron intake and the risk of colorectal cancer. Although the relationship is not fully understood, increased dietary iron intake correlates with increased risk of colorectal tumours in several populations CYBRD1 appears to bind quercetin which has been posited as a chemopreventive agent for colorectal cancer CYBRD1 SNP rs884409 .We have described a new method to detect interaction effects of specific genotypes on genetic background. It can be used to detect associations between genetic variants and disease that have been masked by population genetic heterogeneity. Our method can be extended easily to look for interactions on other covariates such as treatment or measured environmental exposures. We envisage our method being of particular interest to researchers with existing GWAS data sets, as the ancestry exposure variable can be easily defined and thus tested for interactions. Here we discuss particular issues that may arise in applying the method  to otherIf only a single collection is available, the method can be applied by clustering on ancestry and investigating evidence by inspection of large In cases where there is near-complete confounding of collection and ancestry, our method can still be used to detect evidence of heterogeneity, but lacks the ability to distinguish whether the source is artifactual or the result of a disease risk factor correlating with ancestry. In such cases, evidence of heterogeneity would be assessed as for the Single Collection case using CYBRD1 here. For targeted replication where the ancestry  cannot be used directly, power calculations can be performed to show what level of evidence would be expected given a range of plausible switch/error rates, thereby guiding the sample sizes expected to be necessary. Details of power calculations are provided in the supplementary methods and implementation is included in the available R code.In selecting candidates for targeted replication, we suggest that both statistical evidence and functional context are considered. In our case, the statistical evidence for rs10455 was consistent but mild and indeed the marker may have been missed by a conventional GWAS analysis even within an English ancestry group. However, true interactions acting through say environmental effects covarying with ancestry may well lead to identified markers more closely related to disease mechanisms and hence located in or nearby genes with function previously implicated in disease processes, as was the case for It is important to note that statistical evidence of interaction of a polymorphism with an exposure need not reflect a direct biological interaction. Such evidence is also consistent for an interaction with an unobserved environmental exposure correlated with ancestry. For example, diet might correlate more strongly with ancestry than with residential location. Markers showing evidence of collection, but not ancestry, heterogeneity might also be of interest and could reflect any differences in the way the data was ascertained. This might result from technical artefacts or other sources of heterogeneity, such as those introduced by different ascertainment criteria.Heterogeneity in ethnic origins or sample collection is usually regarded as a problem in GWAS owing to the type I and II errors that it can introduce into the analysis. We have shown, however, that heterogeneity between related populations can be used to a researchers's advantage when there is interaction between genotype and ethnicity, or a factor that co-varies with ethnicity. For such variants, our method potentially provides a way of identifying disease SNPs with relatively small effects that can be assessed further in appropriate validation sample sets without GWAS data or in other ways, such as functional evaluation. Such considerations apply to our putative colorectal cancer SNP rs10455 which demonstrated the potential of our technique for identifying interactions and hence predisposition genes.Our clustering step makes discrete allocations of samples to clusters. It would be interesting to take into account the uncertainty in cluster membership within the association model, perhaps using a probabilistic clustering model, see for example The ethics board was the “Southampton and South-West Hampshire Research Ethics Committee (A)MREC/06\Q1702\99”. The collection of blood samples and clinico-pathological information from patients and controls was undertaken with written informed consent and ethical review board approval in accordance with the tenets of the Declaration of Helsinki.The discovery set of colorectal cancer cases and controls was derived from two distinct and independent collections, one based in Scotland only, and the other from across the UK, but predominantly from England. For convenience, we have analysed the Scottish collected Phase 1 in parallel with the UK collected Phase 1, and done the same for Phases 2.Phase 1 samples  to summarize observed relatedness of individuals. We selected markers for the PCA by first removing SNPs in regions of long-range linkage disequilibrium The collection exposure is a one dimensional factor variable. It is fixed and defined according to design of the study/studies.We clustered individuals (in phase 1 and phase 2) in the space defined by the first two principal genetic components using the k-means algorithm The collection clustering is defined by the collection factor variable and hence no clustering algorithm is required. Individuals of the same collection are clustered together with the number of clusters equal to the number of collection groups in the data. In our example there are two clusters, one containing individuals collected in Scotland and the other containing individuals collected predominantly in England.clustvarsel. Other model-based clustering algorithms might be more appropriate for defining an ancestry clustering, particularly if the clusters are not of equal volume and shape as was the case with our example. We also note that the number of collection clusters need not be the same as the number of ancestry clusters; for example, there may be a single collection comprising multiple ancestry groups. Since the BIC is used for comparing models in our definition of the T- and D-Statistics , the number of clusters is automatically accounted for by our statistics. If the number of clusters is the same for both ancestry and collection groupings, it allows comparisons to be made easily and the switch rate from collection to ancestry can be determined, but this is not essential for the method to be effective.In our analysis the number of principal components selected for defining the ancestry clustering was guided by differences observed between our collections. More generally, and if there is only a single cohort, this can be done by model-based variable selection such as the techniques implemented in R package To detect evidence of heterogeneous associations we fitted a mixture model for genetic association with phenotype. If multiple clusterings of the individuals in the space defining relatedness (or any other known source of heterogeneity) are considered then a mixture model is defined for each clustering (i.e. one for the Collection clustering and one for the Ancestry Clustering). For the general case, we letThe The function The cluster specific intercept terms To quantify evidence for the heterogeneous association we define the T-statistic by taking the difference in BIC statistics computed for the heterogeneous model and the null model of association thus accounting for model complexity.To specify the null model, we note the null hypothesis is one of no interaction heterogeneity at the genetic marker. If this is true, there are two possible scenarios;There is no genetic association with phenotype for any of the individuals at the marker.There is a homogeneous genetic association with phenotype across all individuals at the marker.In both of these instances it could also be there are different background prevalences of the disease and/or differences in allele frequency or linkage disequilibrium within different clusters of individuals (independently of genotype). It is important to allow for this in the specification of the null model to prevent within cluster main effects from dominating differences observed in the multi-cluster interaction model fit. Consequently the null model for the We compute the BIC statistic for the null model and use The test statistic (referred to as the T statistic) we use to assess evidence of heterogeneity is the difference in BIC for the heterogeneous and null models. If we are assessing the fit of a heterogeneous model with In our analysis we refer to the We have developed a statistical framework to compare two different exposure spaces (Ancestry and Collection in our work). More generally, we use More generally, the exposure spaces There is no theoretical distribution for the D-Statistic, so we simulated null data sets (i.e. genotypes not associated with phenotype) to estimate the properties and quantiles of this distribution. Note that null distributions can differ between data sets according to the number of individuals in the data set, the number of clusters, and the contribution of adjustment variables to the model fit. The null hypothesis includes two scenarios. Firstly, no genetic association with phenotype for any individuals, and secondly, a homogeneous (non-zero) genetic association for all individuals. Since our method is designed to be used with GWA data, we assume that the vast majority of markers will fall into the first category. Consequently we estimate the distribution of test statistics under the null hypothesis assuming there is no genetic association with phenotype for any individuals. GWA case-control data sets are ascertained retrospectively, so we use a retrospective simulation technique i.e. simulating genotypes conditional on phenotype. The phenotype remains fixed (at the observed phenotype) for all simulations and the adjustment variables are also fixed and included in all interaction and null models. Since we assume there is no association of genotype with phenotype, under the assumption of Hardy-Weinberg equilibrium, the simulation of genotypes depends on the MAF. We investigated a range of allele frequencies from 0.05 to 0.5 by intervals of 0.05 and noted that the distribution of D-statistics were independent of MAF. Consequently to define a significance threshold for D-statistics we used the 99th centile of the statistics after pooling the 10A 99% one sided threshold for D-statistics is used to select markers enriched for ancestry heterogeneity rather than collection heterogeneity (i.e. exposure A relative to exposure B). To define a threshold to select markers enriched for collection heterogeneity (exposure B) the 1% centile could be chosen.anc). If multiple phases of data are available for these markers then these markers can be checked for consistency across phases.To identify candidate (interaction/heterogeneous) phenotype associated markers we suggest selecting markers whose D-statistics exceed the significance and then rank on the basis of the T statistic  used to perform the original analysis can be collected  and further more, that individuals in the replication phase lie in the same region of exposure space as the original data. Replication can also be undertaken even if the primary (ancestry) exposure and thus clustering cannot be computed directly provided a variable highly correlated with the primary exposure can be collected. The power to detect the interaction will be poorer (depending on the strength of the correlation between the proxy and the primary exposure) but power calculations can be undertaken to show the expected power.In our example, in the replication phases 3 and 4 ancestry information was not available but we used geographical collection location as a proxy for it. We performed power calculations to show what we might expect to see given the expected error in using geographical collection location rather than ancestry. Details of our power calculations are documented in the Figure S1PCA Plot. First principal component versus second principal component in Phase 2: Individuals in Phase 2 plotted in the space defined by the first two principal components computed from the genotype matrix. Individuals are coloured by their collection group and case-control status indicated by the plotting symbol.(TIFF)Click here for additional data file.Figure S2PCA Projection. Projection of Phase 1 genotypes onto Eigen vectors  in Phase 2: Separation of the English and Scottish collected samples indicate the components were representative of ancestry rather than a collection artefact.(TIFF)Click here for additional data file.Figure S3D-statistics. The distribution of the D-Statistics computed for Phase 1. The 1% significance threshold is indicated by the red dashed line.(TIFF)Click here for additional data file.Table S1Cohorts details and genotype data collected at each phase.(PDF)Click here for additional data file.Table S2Composition of the ancestral clusters for phase 1 individuals stratified by collection source and disease status.(PDF)Click here for additional data file.Table S3Composition of the ancestral clusters for phase 2 individuals stratified by collection source and disease status.(PDF)Click here for additional data file.Table S4Summary of Evidence for CRC Association at rs10455 in English Collected/Ancestral Cohorts.(PDF)Click here for additional data file.Table S5Estimated power and p-values to detect an association at rs10455 in Phase 3 without principal component information as the switch rate varies.(PDF)Click here for additional data file.Table S6Estimated power and p-values to detect an association at rs10455 in Phase 4 without principal component information as the switch rate varies.(PDF)Click here for additional data file.Text S1Description of Power Calculations for Replication Phases 3 and 4.(PDF)Click here for additional data file.Text S2Web Resources.(PDF)Click here for additional data file.


The biological justification for the choice of the genetic mode in genetic association studies (GAS) is seldom available. Then, the mode of inheritance is approximated by investigating a number of non-orthogonal genetic contrasts making the interpretation of results difficult.h), which is a function of two orthogonal contrasts (the co-dominant and additive). Non-dominance exists when the co-dominant contrast is non-significant and, hence, the risk effect of heterozygotes lies in the middle of the risk of the two homozygotes. Otherwise, dominance (including over- and under-dominance) is present and the direction of dominance depends on the value of h.We propose to define the mode of inheritance by the significance of the deviance of the co-dominant contrast and the degree of dominance . In addition, power for detecting significance of h when the study conforms to HWE rule increases with the degree of dominance and to some extent is related to the mutant allele frequency.Simulations show that The introduction of the degree of dominance provides useful insights into the mode of inheritance in GAS. In otTesting the significance of the genotype effect is thus equivalent to simultaneously testing the significance of the additive and co-dominant contrasts based on the respective deviances or z-tests.h of the mutant allele mt. In the extreme case where there is non-dominance , the heterozygote wtmt "lies" exactly in the middle of the two homozygotes, with mtmt having the maximum susceptibility of being diseased and wtwt having the least  irrespectively of the significant level of We define here for a GAS showing a significant statistical association  the model of disease inheritance according to the degree of dominance t Figure . The devmtmt), or under-dominance (the heterozygote has least risk for the disease than the homozygote wtwt) , over-dominance (the heterozygote has a greater risk of disease than the homozygote ) Figure . Therefocoθ) determines the direction of dominance, and the value of ln(coθ) relative to the absolute value of ln(aθ) the magnitude of dominance deviation h, which can take any value from negative infinity to positive infinity  the sign of ln , or vs. Ha: h < -1 (under-dominance) is equivalent to test:The statistical test to asses the significance of over- or under-dominance -that is, to test the null hypothesis Hαθ) > 0,i)H0: k = ln(co θ× αθ) = 0 vs. H1: k = ln(co θ× αθ) > 0 (over-dominance) or H1: k = ln(co θ× αθ) < 0 (under-dominance) when ln(αθ) < 0.ii) z- test where the variance of k is approximately π) is arising from the variance of a half-normal distribution .Assume 10,000 individuals at h against parameter H assuming s = 0.2 and 0.5. For very low allele frequencies (0.05 ≤ q1 ≤ 0.40) there is little chance of detecting recessiveness of allele mt  because, in general, h ≥ -0.2; whereas for relatively high allele frequencies (q1 = 0.40), h-index can estimate more efficiently H. In any case, h-index tends to perform better when the selection coefficient increases (i.e. the risk of disease is higher in homozygous mutants).Figure h ≤ 1.0 (0.1 ≥ h ≥ -1.0) in case-control studies. Genotype frequencies ni2 for the cases in (1) were randomly generated with the restriction mt bounded by 0.09 ≤ qcases ≤ 0.11, 0.09 ≤ qcases ≤ 0.21, or 0.39 ≤ qcases ≤ 0.41. Genotype frequencies in the controls were generated assuming HWE (P ≥ 0.05) with the restriction qcontrols ≤ qcases. Power to detect dominance was assessed as  as a function of h for the co-dominant and the additive contrasts. Statistical significance of the additive model was (with a few exceptions) only found when under- or over-dominance were absent.Also important is that in a significant proportion of studies (25%) our method detects under- (12%) or over-dominance (13%). Figure h, which is based on the ratio of the odds ratio of the co-dominant contrast divided by the absolute value of the odds ratio of the additive contrast. Numerical results suggest that the h index captures the essence of what should be understood by genetic model or mode of inheritance. A meticulous analysis has been performed to check performance against an a priori model where we already know that a mutant allele is associated to a disease and also the degree of dominance of this allele. Simulations also show that the degree of dominance h is affected by deviations from HWE, although the bias is more serious when there is population stratification. In these cases the findings should be interpreted carefully, and adjustments for departures from HWE might be applied [h when the study conforms HWE rule increases with the degree of dominance and to some extent is related to the mutant allele frequency.Herein, we have proposed to identify the mode of inheritance in a continuous scale using the degree of dominance  applied ,10. Furth and, also important, in the range of over- or under-dominance the additive contrast is non-significant. In general, candidate-gene studies have a tendency to lack power for detecting dominance arising from weak genetic contributions of common variants; though, large genome-wide association studies have been undertaken recently and an effort to create consortia for data sharing is initiated [h. Nevertheless, the power to detect the significance of the co-dominant contrast and/or the additive contrast is the same with the power to detect a significance association between the genotype distribution and the disease using a logistic regression with explanatory variable the genotype with three levels. The proposed index may be applied to both types of GAS (candidate-gene studies and GWAS) in the same way (of course the recording of the genotype distribution is a necessary condition). However, in testing the significance of the orthogonal contrasts for an individual variant of a GWAS a multiplicity adjustment should be considered.The empirical study we carried out showed the degree of dominance may sufficiently indicate the mode of inheritance. Any degree of dominance exists when the co-dominant contrast is significant irrespectively to the additive contrast. The co-dominant and additive contrasts show a reverse pattern in nitiated ,22. An uG) for analyzing and meta-analyzing GAS. ORG is a single statistic that summarizes the magnitude and significance of the association without considering the hash of possible contrasts, and provides a straightforward interpretation of the results in GAS. The ORG utilizes the complete genotype distribution and provides an estimate of the magnitude of the association, given that the mutational load and the phenotype  are treated as a graded exposure (case-control or disease progression). Specifically, ORG express the probability of a subject being diseased relative to probability of being free of disease, given that the diseased subject has a higher mutational load than the non-diseased. ORG with values greater than one suggests that disease is proportional to increased genetic exposure and inversely proportional for values less than one. Thus, the application of ORG may overcome the shortcomings of multiple model testing or erroneous model specification and provides an alternative and robust way for genetic association testing.In order to avoid the obstacle of the multiple genetic contrasts, Zintzaras  proposedRegarding meta-analysis, model-free approaches have been proposed to estimate the genetic model ,23. Howeh, which is the ratio of the two orthogonal contrasts, may provide useful insights into the mode of disease inheritance.The introduction of the degree of dominance The authors declare that they have no competing interests.Both authors contributed equally to this paper and they read and approved the final manuscript.The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1471-2288/11/171/prepub


This is the first published report examining the combined effect of diet and genotype on body iron content using a classical twin study design. The aim of this study was to determine the relative contribution of genetic and environmental factors in determining iron status. The population was comprised of 200 BMI- and age-matched pairs of MZ and DZ healthy twins, characterised for habitual diet and 15 iron-related candidate genetic markers. Variance components analysis demonstrated that the heritability of serum ferritin (SF) and soluble transferrin receptor was 44% and 54% respectively. Measured single nucleotide polymorphisms explained 5% and selected dietary factors 6% of the variance in iron status; there was a negative association between calcium intake and body iron (p = 0.02) and SF (p = 0.04). HFELevels of iron in the body are tightly regulated through changes in the efficiency of absorption to ensure sufficient iron is available for vital functions but at the same time to avoid the accumulation of excessive iron. It is well established that genetics plays a significant role in iron overload, the most common example being hereditary hemochromatosis which, in spite of its low penetrance, is attributable to mutations in the hemochromatosis gene, A sample of 100 MZ and 100 DZ female healthy twin pairs was selected from a group of around 3,500 twins enlisted in the TwinsUK registry. The key inclusion criteria were data on body mass index (BMI), dietary intake and genotype, together with a serum blood sample. The sample size was chosen to provide power of 90% and type-I error rate of 0.05 Dietary information was collected from a validated 131-item food frequency questionnaire (FFQ), previously developed for the European Prospective Investigation into Cancer and Nutrition Study Blood samples were collected at approximately the same time as the FFQ and other questionnaires and stored at −80°C. As part of other on-going research, some of the samples had been analysed for C-reactive protein, (data shown in http://www.micronutrientgenomics.org/index.php/Iron). The list was filtered to include only SNPs with a minor allele frequency (MAF) >5%. The pairwise linkage disequilibrium was examined and where r2>0.2, the SNP with the greater MAF was retained. A total of 15 iron- related SNPs were included in the analysis.Single nucleotide polymorphisms (SNPs) selected for this analysis were from genes known to be involved in iron metabolism , where g2σ and e2σ are the variances of the polygenic and environmental effects and I is the identity matrix. The trait heritability was estimated from g2σ/(g2σ+e2σ) in Model 1. The significance of individual covariates was assessed by examining the change in model likelihood after the covariates were omitted.SOLAR models the covariance among phenotype values (Ω) using the kinship coefficient matrix (Φ)  and iβ (isnp) in Models 2 and 3 respectively.To account for multiple testing, the Benjamini-Hochberg adjustment was applied to p values using the p.adjust function in R, assuming a 10% false discovery rate. The proportional contribution of measured nutritional factors and measured SNPs to overall variance was estimated from the variance of Phenotypic data for the twins and the SF and TfR concentrations are shown in The heritability of iron status (Model 1) was calculated to be 46 % for SF, 54 % for sTfR, and 44 % for body iron.The overall contribution of the selected dietary factors to variance in iron status was 6% (Model 2). There was a negative association between calcium intake and body iron (p = 0.004) and SF (p = 0.008) which remained significant (p = 0.02 and 0.04 respectively) after taking multiple testing into account.CYBRD1, rs9366637 HFE, rs4434553 TFR2) (The contribution of the 15 SNPs examined to variance in iron status was 5% (Model 3). Three were significant for one or more measures of iron status (rs960748 53 TFR2)  althoughet alThis is the first published report examining the combined effect of diet and genotype on body iron content using a classical twin study design. The results demonstrate that there is a substantial genetic contribution to iron status, which agrees with Whitfield CYBRD1, rs9366637 HFE, rs4434553 TFR2) are worthy of further investigation. These genes have also emerged in other studies. In a multi-ethnic population of iron-deficient and normal iron status adults SNPs in the TR and HFE genes were identified that were associated with at least one iron phenotypic measure TF) gene and the HFE C282Y mutation, but the proportion of phenotypic variance in SF and other measures of iron status could not be explained by SNPs other than C282Y et alHFE and TMPRSS6 genes and the PCSK7 locus. The involvement of these genes suggests that they might have a role in screening for susceptibility to iron deficiency. However, a substantial proportion of genetic variation remains unexplained, justifying the pursuit of more detailed genetic analysis in large scale genome wide studies.Our study provides evidence to support a contribution for genes known to be involved in iron metabolism. In particular, three (rs960748 Among the potential environmental factors influencing iron status, this study identified calcium as being negatively associated with iron status, which agrees with its reported inhibitory effect on iron absorption in single meal studies, for example, Minihane & Fairweather-Tait et alet alWhitfield The results of our study quantify heritability of iron status using the most appropriate measures of body iron. With the classical twin study design we have been able to gain a unique insight into the effect of environmental factors and genotype on iron status, and demonstrated that they make an approximately equal contribution.


Although variations in allele frequencies at common SNPs have been extensively studied in different populations, little is known about the stratification of rare variants and its impact on association tests. In this paper, we used Affymetrix 500K genotype data from the WTCCC to investigate if variants in three different frequency categories  show different stratification patterns in the UK population. We found that these patterns are indeed different. The top principal component extracted from the rare variant category shows poor correlations with any principal component or combination of principal components from the low frequency or common variant categories. These results could suggest that a suitable solution to avoid false positive association due to population stratification would involve adjusting for the respective PCs when testing for variants in different allele frequency categories. However, we found this was not the case both on type 2 diabetes data and on simulated data. Indeed, adjusting rare variant association tests on PCs derived from rare variants does no better to correct for population stratification than adjusting on PCs derived from more common variants. Mixed models perform slightly better for low frequency variants than PC based adjustments but less well for the rarest variants. These results call for the need of new methodological developments specifically devoted to address rare variant stratification issues in association tests. Population stratification is an important cause of false positive results in case-control association studies. Indeed, if the sampled population includes subgroups with different allele frequencies at some markers and different disease prevalences, there is a risk of detecting false positive associations between these stratified markers and the disease. This often occurs when the individuals are sampled from different ethnic groups. The most famous example in the literature is the association between a Gm haplotype and type 2 diabetes explained by Pima-Papago ancestry However, most of the studies on population stratification have focused on common genetic variants, namely SNPs with a minor allele frequency (MAF) above 5% because of the “common disease-common variant hypothesis” Our aim is to assess population stratification based on rare variants using the population-based control data from the WTCCC1 study and to examine how this stratification can impact the results of association tests, using the example of type 2 diabetes. We take advantage here of the high content in rare variants of the Affymetrix 500K SNP-chip used in the WTCCC1 study. This chip contains about 55,000 variants with MAF below 0.05 in Europeans, whereas the Illumina 317k chip contained approximately 9,000.http://www.ebi.ac.uk/ega/home) are considered: the two control datasets  and the type 2 diabetes (T2D) case dataset . These samples originate from 12 UK regions . In part−9). Most of−9). Interes−9). These p−9).2) between PCs. PCs computed from the rare variant set are poorly correlated to the PCs computed from the common or low frequency sets and this, even if we consider jointly several PCs extracted from these different sets and look if one PC from one set is captured by several PCs from another set (2 = 0.02). To rule out the possibility that this could be due to stochastic variations given the low number of SNPs used to perform the PCA , we extracted from the 54,599 pruned common SNPS, four disjoint subsets of 11,848 SNPs and measured their correlations . This is less true for PC2 from rare variants that shows a correlation with PC2 from common variants of 0.28, similar to the level of correlation observed on the disjoint subsets of common SNPs. PCs computed using the low frequency variant set show R2 correlation values of about 60% with the top 10 PCs from both the rare and common variants sets, showing that their stratification pattern is relatively well captured by the PCA performed on either set of variants.The distributions of the principal component (PC) scores for individuals from the different UK regions overlap considerably. No difference in these scores is found when comparing the two control datasets, ruling out concerns of batch effects between them (data not shown). However, significant differences are observed between the different regions for the top PC computed on the 3 MAF sets . To invether set . This iselations . We founAlthough the top PCs of the PCA performed on the different pruned MAF sets appear to be strongly correlated to region of origin  test that accounts well for the bias introduced by stratifying on the 2 regions shows λGC values closer to one on the different sets of variants even if these λGC values still remain slightly inflated for the low frequency variants (λGC = 1.023) and more strongly inflated for the rare variants (1.802 for the entire set and 1.103 for the one with MAF >0.005). When the tests are adjusted on the PCs, λGC values are decreased compared to the unadjusted tests and tend towards those observed for the CMH test. When adjustment is performed on 10 PCs, the λGC values are slightly smaller than those of the CMH and this might indicate some over-adjustment. No major differences are seen whether the adjustment is performed with PCs computed using the pruned MAF sets corresponding to the tested variant or not. Moreover, the mixed model implemented in EMMAX provides good results for the common category but leads to inflation factors very similar to the uncorrected test for low frequency and rare variants and thus slightly worse than the PC-based corrections. In the more realistic scenario where association with type 2 diabetes is tested, we also observe that the λGC values of PC adjusted tests are very similar when PCs are computed on variants with the same allele frequencies as the ones tested or on variants with different frequencies  and compared to control individuals more often sampled in region R11. The genomic control lambda values λtegories . When thquencies . Focusinquencies .With the development of next-generation sequencing technologies, investigators will soon be able to study the impact of rare variants on complex traits. Indeed, when performing a principal component analysis on the different sets of variants determined based on their MAF, we found that the top PCs are poorly correlated. This result is in discrepancy with the one reported by Heath et al. Since the top PC values calculated on the different sets of markers are all significantly different between the 12 UK regions, except for PC1 from rare variants, one could wonder whether it would be efficient to use principal component analysis to cluster individuals and then perform stratified analyses to test for association. Such a strategy for association testing where individuals are first clustered using the genetic information and then stratified association tests are performed was first proposed by Pritchard et al. Results on type 2 diabetes also tell us that it is not easy to adjust for stratification in rare variant association tests. Since the PCs computed on common and rare variants were poorly correlated, one would have expected to see an improvement when adjusting on PCs computed from rare variants as compared to PCs computed from common variants. This was not the case however even when the level of stratification was strong as in the extreme stratification scenario that we simulated. Interestingly, mixed models did also no better than simple PC-based corrections for rare variants. Since these models have been shown to better adjust for stratification of common variants, especially in the presence of remote relatedness between individuals, one could have expected an improvement for rare variants. Indeed, remote relatedness might be a concern when studying rare variants since carriers of a same rare allele are likely to be more related than random individuals. Recently, Mathieson and McVean A major concern in our study is the fact that the rare variants we considered here might not be very representative of rare variants that would be discovered through resequencing studies. Indeed, to be included in the SNP-chip, these variants need to have been observed on other samples than the one investigated here and we are therefore not investigating the lower tail allele frequency spectrum. The number of rare variants investigated is also much reduced as compared to what will be found in resequencing studies and the investigation of population stratification based on such a small number of variants might not be very reliable. We could also not exclude the possibility that genotyping errors could have obscured regional membership assignment especially for the rare variants that are more prone to genotyping errors than more common ones. The current dataset was not ideal to answer the question raised and our observations will thus need to be confirmed on other more appropriate datasets. With the increasing availability of sequence data, it will soon be possible to perform a study similar to ours using rare variants discovered through direct resequencing. Nevertheless, we believe it is important to evaluate rare variant stratification at this stage and using the available empirical data to guide researchers in the planning of their future studies using next-generation sequencing technologies.−8). Finally, only the SNPs retained in all three samples were kept, giving a total of 319,276 SNPs post-QC. No specific QC was performed on the individuals as the 4,862 individuals considered here were the ones selected in the WTCCC1 study after QC.Stringent quality control (QC) was performed in several steps. First, each dataset was treated separately and only SNPs with an rs number and genotypes with a calling probability >0.99 were kept. Second, SNPs were eliminated if their call rates were lower than 0.99 in any of the three samples or if their genotype distribution in the two control datasets was significantly different from the one expected under Hardy-Weinberg proportions . In the absence of heterogeneity, the observed p-values are uniformly distributed, and the quantity −2*log follows a 2-df chi-squared r. Similarly to the Genomic Control lambda r is the ratio of the median of −2*log over the expected median of a 2df chi-squared distribution.Homogeneity between the two sets of controls (58BC and UKBS) was first tested for each MAF category using a 1 degree of freedom (d.f.) Mantel-extension test of the difference in MAF between subjects from the 58BC and UKBS collections, stratified by the 12 broad regions of the United Kingdom. Homogeneity of the two control datasets was assessed by the Genomic Control lambda http://genepath.med.harvard.edu/~reich/EIGENSTRAT.htm), was performed on the three pruned MAF sets and the correlation between the top principal components (PC) obtained in these different analyses were computed.In a next step, the SNPs in each MAF category  were first pruned on Linkage Disequilibrium (Plink options: “indep-pairwise 50 5 0.2”). Principal component analysis of the genotype data using SmartPCA from the Eigensoft package http://www.genetics.ucla.edu/software/admixture) was used to impute the region of the UKBS controls, assuming the region of origin of the 58BC controls was known. This supervised analysis was carried out for each MAF category with the same pruned MAF sets as for the PCA.To determine how much of the regional geographic information can be inferred from the genetic data, the Admixture software GC were computed from the observed chi-squared distributions or after transforming the p values obtained from EMMAX into a chi-square with one degree of freedom.The impact of rare variant stratification on the results of case-control association studies was evaluated in an extreme scenario of stratification where cases and controls were sampled from regions R11 and R12 in different proportions. Among the 146 individuals from region R11, 59 (40.4%) were assigned cases and the remaining individuals were assigned controls and among the 273 individuals from region R12, 150 (54.9%) were assigned cases and the remaining individuals were assigned controls. First a Cochran-Mantel-Haenszel (CMH) test accounting for the 2 different regions  was performed in each MAF category. Since this test adjusts exactly on the confounding factor introduced in the analysis, we used it as reference to assess the performances of the other tests. Second, the association test statistics in each MAF category were calculated either ignoring the stratification or after adjusting on the PCs derived from the PCA described above, using eigenstrat from the Eigensoft package Finally, a more realistic scenario where the type 2 diabetes cases were compared to all the controls was also investigated with the same methods except for the CMH test that was stratified on the12 regions instead of 2.Figure S1Map of UK with the 12 regions of origin, as defined by the WTCC1 study (reprinted from ref. 12 with permission from the authors).(TIF)Click here for additional data file.Figure S2Distribution of the number of rare and low frequency variants carried by each individual in the combined WTCCC control datasets.(TIFF)Click here for additional data file.Figure S3Distribution of the number of rare variant per individual in the 12 UK region.(TIF)Click here for additional data file.Figure S4Boxplots of the PC values per region for the first 3 PCs computed on the different pruned MAF sets.(TIF)Click here for additional data file.Figure S5Percentage of variance explained by the different principal components from the principal component analysis performed on the different sets of markers.(TIF)Click here for additional data file.Figure S6Pie charts showing the average posterior probabilities of UKBS controls from each of the 12 regions to belong to any of the 12 regions. A. when Admixture is run on the set of common variants, B. when Admixture is run on the set of low frequency variants and C. when Admixture is run on the set of rare variants.(PDF)Click here for additional data file.Figure S7true (in black) or another region Pother (in grey).Posterior probabilities for the UKBS individuals to belong to their true region of origin P These posterior probabilities were computed with Admixture true within each region.(TIFF)Click here for additional data file.Figure S8Manhattan plots showing the association between T2D and the rare variants, detected without correction (“raw”), with the CMH test (“cmh”), after correction with the first 10PCs of the common (“PCA common”) and of the rare (“PCA Rare”) MAF sets, and after correction with Emmax on the common (“Emmax Common”) and the rare (“Emmax rare”) MAF sets.(TIFF)Click here for additional data file.Table S1Case and control repartition by region.(DOCX)Click here for additional data file.Table S2Description of the “others” SNPs according to the number of minor allele copies in the different samples.(DOCX)Click here for additional data file.Table S3 of homogeneity tests performed to compare allele counts in the two subgroups of controls. Genomic Control lambda values (λGC) are provided for the different MAF categories.(DOCX)Click here for additional data file.Table S4−4) between the 12 UK regions in the different MAF categories.Number and proportion of variants that differ the most Click here for additional data file.Table S5Repartition of the SNPs seen in only one region in each dataset, UKBS and 58BC. SNPs unique to each of the 12 regions are compared for their regional distribution in the two datasets and those found in the same region in the two datasets are highlighted.(DOCX)Click here for additional data file.Table S6P-values of the ANOVA comparing the values of the different PCs over the 12 region.(DOCX)Click here for additional data file.Table S72 values) between the first two PCs (PC1.x and PC2.x) obtained on the four disjoint subset x (x = 1 to 4) of 11,848 common variants.Correlation Click here for additional data file.Table S8GC obtained for the different tests of association performed on the type 2 diabetes dataset with the different sets of variants.Genomic control coefficient lambda λ(DOCX)Click here for additional data file.


SLC2A9 and the neighboring WDR1 on chromosome 4p16.1 gave suggestive evidence of gene-environment interaction with environmental tobacco smoke (ETS) among 259 Asian trios when the models included a term for GxE interaction. Multiple SNPs in these two genes were associated with increased risk of nonsyndromic CP if the mother was exposed to ETS during the peri-conceptual period (3 months prior to conception through the first trimester). When maternal ETS was considered, fifteen of 135 SNPs mapping to SLC2A9 and 9 of 59 SNPs in WDR1 gave P values approaching genome-wide significance (10−6<P<10−4) in a test for GxETS interaction. SNPs rs3733585 and rs12508991 in SLC2A9 yielded P = 2.26×10−7 in a test for GxETS interaction. SNPs rs6820756 and rs7699512 in WDR1 also yielded P = 1.79×10−7 and P = 1.98×10−7 in a 1 df test for GxE interaction. Although further replication studies are critical to confirming these findings, these results illustrate how genetic associations for nonsyndromic CP can be missed if potential GxE interaction is not taken into account, and this study suggest SLC2A9 and WDR1 should be considered as candidate genes for CP.Nonsyndromic cleft palate (CP) is one of the most common human birth defects and both genetic and environmental risk factors contribute to its etiology. We conducted a genome-wide association study (GWAS) using 550 CP case-parent trios ascertained in an international consortium. Stratified analysis among trios with different ancestries was performed to test for GxE interactions with common maternal exposures using conditional logistic regression models. While no single nucleotide polymorphism (SNP) achieved genome-wide significance when considered alone, markers in  Nonsyndromic cleft palate (CP) is a common birth defects and has a complex and heterogeneous etiology, involving both genetic and environmental risk factors FOXE1, ALX3, MKX, PDGFC, and SUMO1Genetic risk factors play an important role in the etiology of CP. A recent twin study in Denmark showed heritability of CP is as high as 90%, and the proband-wise concordance rate for CP among monozygotic twins was much higher compared to dizygotic twins: 33% vs. 7% MLLT3, SMC2, TBK1, ZNF236, and BAALC) showed statistically significant interaction with common maternal exposures, although no single SNP achieved genome-wide significance when such GxE interaction was ignored A few studies of CP have investigated potential GxE interaction for candidate genes and maternal exposure to cigarette smoking In this study, we performed stratified analysis of the CP case-parent trios from the International Cleft Consortium Research protocols were reviewed and approved by institutional review boards (IRB) at each institution, including IRBs at The Johns Hopkins School of Public Health, University of Iowa, University of Pittsburgh, Utah State University, and all foreign collaborators. The review process for the consortium was approved by Johns Hopkins’ IRB. Written informed consent was obtained from parents. Case-parent trios were drawn from an international consortium which conducted a GWAS using a case-parent trio design to search for genes controlling risk of nonsyndomic, isolated oral clefts −5) from Hardy Weinberg equilibrium (HWE) among parents within recruitment site or across European and Asian populations separately. This QC process flagged 14.6% of all SNPs (mostly for low MAF), leaving ∼498 K SNPs available for analysis.The Center for Inherited Disease Research (CIDR) genotyped DNA samples using Illumina’s 610 Quad platform and 99.1% passed CIDR quality control (QC) Maternal exposure information, including cigarette smoking, ETS, multivitamin supplementation, and alcohol consumption was collected through direct interview of mothers. Only Asian sites collected complete information on ETS. Environmental exposures were defined as being exposed from three months prior to pregnancy through the first trimester. The question measuring ETS status during certain periods asked “did someone smoke in your home, workplace or any other place near you?”. Maternal exposures were assessed as simple yes/no responses. See Table II in Beaty et al. (2011) for details of the exposure rates for all CP trios. The proportion of infants exposed to maternal cigarette smoking and alcohol consumption was very low among Asian mothers (around 4%), so only maternal ETS and multivitamin supplementation could be analyzed in this group. The proportion of exposure to ETS and multivitamin supplementation among Asians were 40.3% and 20.2%, respectively.2 for all SNPs using the Haploview program, and was used to identify linkage disequilibrium (LD) blocks MAFs were computed using parents only. Pairwise linkage disequilibrium (LD) was measured as ri)] = βG(Gi)+ βGxE(GixEi), where G = 0, 1, or 2 stands for the number of risk alleles in the case:“pseudo-control” set (representing a 1∶3 matching), andwhere E = 0 or 1 reflects unexposed or exposed mothers, respectively. A 2 degree of freedom (df) likelihood ratio test (LRT) for joint effects of G and GxE interaction was first performed, followed by a 1 df LRT for GxE interaction alone. The 2 df test examines the inherited effect of the SNP after taking into account effects of GxE interaction, while the 1 df test focuses exclusively on GxE interaction. We used RR(CP|G no E) = exp(βG) to represent the estimated RRs of being a case with one copy of the risk allele in the absence of maternal environment exposures, while RR(CP|G and E) = exp(βG+βGxE) reflects the RR of being a case carrying one copy of the risk allele in the presence of maternal exposure.All autosomal markers were examined using the conditional logistic regression model assuming an additive model of inheritance. The log-odds of being the observed case in the i-th trio is modeled as: logit[P.A conventional search for marginal gene (G) effects in the total sample of 550 CP trios, as well as in the stratified analysis of trios of Asian and European ancestry, showed no markers achieved significance at a genome-wide level (df ), as well as the combined effects of gene (G) and gene-environment (GxE) interaction (LRT with 2 df). This screening process yielded no significant signals among European trios  among 259 Asian trios clustered on chromosome 4p16, especially in the 1 df test for GxETS interaction. 10(P) from the 1 df LRT for GxETS interaction was plotted , where conditional logistic regression models were used to estimate effects of GxE interaction alone (LRT with 1 10(P) for the conventional family-based test of SNP effects ignoring exposure . In the top half of 10(P) are shown for each autosomal SNP from both the 2 df test of G and GxE interaction together (red dots) and the 1 df test for GxE interaction alone (blue dots). Dashed lines connect P-values from the marginal test ignoring exposures (below the mid-line) to those models considering GxE interaction (above the mid-line). As seen in P values approaching genome-wide significance level in tests for GxETS interaction, including 15 SNPs in SLC2A9 and 9 in WDR1 on chr. 4p16.1 .Although none of 135 SNPs mapping to  df test . SNPs rsSLC2A9 along with P values from the LRT for both the 2 df and 1 df test. Here, the apparent “risk allele” became the target allele  compared to a similar heterozygous child of unexposed mothers (solid circles). For the two most significant SNPs (rs3733585 and rs12508991) being a heterozygous child of an exposed mother was associated with a 2.58-fold increase in risk , but not among children of unexposed mothers . The 1 df LRT for GxETS interaction in this conditional logistic regression model approached genome-wide significance (P = 2.26×10−7).Regression coefficients from the conditional logistic regression model provide an estimate of exposure specific RRs under this additive model. When both G and GxE terms were included in the conditional logistic regression model, RRs were also calculated for both exposed and unexposed heterozygous carriers of the apparent risk allele. WDR1 on chr. 4p16.1 is located next to SLC2A9 and encompasses 59 SNPs. Like SLC2A9, none of these SNPs achieved genome-wide significance levels alone, however, a block of 9 SNPs (spanning 213 kb) showed suggestive GxETS interaction in the 1 df test for GxE interaction . eraction . SNPs rsExamining the imputed genotypes generated by the GENEVA Coordinating Center GE>2.5).Similar analysis for potential GxE interaction with maternal multivitamin supplementation in these same Asian CP trios showed no significant GxE interaction. Because the exposure rate for maternal multivitamin supplementation was lower in this sample of Asian CP trios (∼20%), however, this sample had less statistical power to detect GxE interaction unless the causal allele were highly polymorphic (MAF>0.15) and the true interaction effects were at least as large as those seen in test of GxETS interaction (RRSLC2A9 and WDR1) showed P-values approaching genome-wide significance when GxETS interaction was incorporated into the analysis of Asian trios. Our results suggested SLC2A9 and/or WDR1 located at position 9 Mb on chromosome 4p16.1 may influence risk of nonsyndromic CP through interaction with maternal exposure to ETS, though independent replication studies are still needed to confirm these findings. Our study did not yield any compelling evidence of GxE interactions approaching genome-wide significance among trios of European ancestry.While the initial GWAS of 550 CP case-parent trios stratified by European and Asian ancestry did not yield any markers achieving genome-wide significance (i.e. when GxE interaction was ignored), multiple markers in two adjacent genes on chr. 4p16.1  is downstream from SLC2A9 and it is highly conserved in eukaryotes and promotes cofilin-mediated actin filament disassembly WDR1 has an important role in unidirectional cell migration by promoting cofilin activity. Protein aggregates of actin and cofilin in the brains of twins with dystonia and CL/P were described by Gearing, et al. (2010) WDR1 and nonsyndromic oral clefts, they suggest a possible biological mechanism involving disruption of cell migration during development of the palate. The SLC2A9 gene  is located on chromosome 4p16.1, and encodes a member of the SLC2A facilitative glucose transporter gene family, which is critical for maintaining glucose homeostasis. Multiple association studies across several populations showed consistent findings that this gene is associated with uric acid concentration and risk of gout SLC2A9 may reflect its close physical proximity to WDR1. We also performed the GxETS analysis using imputed genotype data in this chromosomal region among Asian trios, and the imputed genotypes yielded greater significance  in the region  should be considered as candidate genes for nonsyndromic CP.The SLC2A9 and WDR1. Exposure rate of ETS among Asian mothers in this sample was as high as 40%, reflecting the high prevalence of smoking among Asian males (about 60%) We acknowledge the suggestive GxETS interactions on chr. 4p16.1 region seen in the present study require further confirmation in independent samples. However, adequate sample size will be a challenge. Our results argue maternal ETS appears to increase risk of nonsyndromic CP in Asian cases carrying certain genotypes in File S1Supporting information. Figure S1.1: Manhattan plot with P values from likelihood ratio tests with 1 degree of freedom testing for GxSmoking interaction among 272 European CP trios. Figure S1.2 Manhattan plot with P values from likelihood ratio tests with 1 degree of freedom testing for GxAlcohol consumption interaction among 272 European CP trios. Figure S1.3 Manhattan plot with P values from likelihood ratio tests with 1 degree of freedom testing for GxMultivitamin supplementation consumption interaction among 272 European CP trios. Figure S2: Q-Q plot with P values from likelihood ratio tests with 1 degree of freedom testing for GxETS interaction among 259 Asian CP trios . The gray shaded region indicates 95% confidence band for order statistics. The numbers on the top axis indicate the respective locations for (ordered) expected –log10 p-values.  indicates the expected value, on the –log10 scale, for the minimum  p-value). Figure S3.1 LD plots for SLC2A9 among 259 Asian CP trios. Black squares represent r2 = 1; gray squares represent 0<r2<1; white squares represent r2 = 0. Figure S3.2 LD plots for WDR1 among 259 Asian CP trios. Black squares represent r2 = 1; gray squares represent 0<r2<1; white squares represent r2 = 0. Figure S4: P values from likelihood ratio test with 1 degree of freedom testing for GxETS interaction after including the imputed SNPs among Asian CP trios. Circles represent imputed genotypes using 1000 Genomes as a reference population and squares represent observed SNPs. Table S1.(DOCX)Click here for additional data file.


Distributed robustness is thought to influence the buffering of random phenotypic variation through the scale-free topology of gene regulatory, metabolic, and protein-protein interaction networks. If this hypothesis is true, then the phenotypic response to the perturbation of particular nodes in such a network should be proportional to the number of links those nodes make with neighboring nodes. This suggests a probability distribution approximating an inverse power-law of random phenotypic variation. Zero phenotypic variation, however, is impossible, because random molecular and cellular processes are essential to normal development. Consequently, a more realistic distribution should have a y-intercept close to zero in the lower tail, a mode greater than zero, and a long (fat) upper tail. The double Pareto-lognormal (DPLN) distribution is an ideal candidate distribution. It consists of a mixture of a lognormal body and upper and lower power-law tails.Saccharomyces cerevisiae to seven different probability distributions: DPLN, right Pareto-lognormal (RPLN), left Pareto-lognormal (LPLN), normal, lognormal, exponential, and Pareto. The best model was judged by the Akaike Information Criterion (AIC).If our assumptions are true, the DPLN distribution should provide a better fit to random phenotypic variation in a large series of single-gene knockout lines than other skewed or symmetrical distributions. We fit a large published data set of single-gene knockout lines in S. cerevisiae fits a double Pareto-lognormal (DPLN) distribution better than any of the alternative distributions, including the right Pareto-lognormal and lognormal distributions.Phenotypic variation among gene knockouts in A DPLN distribution is consistent with the hypothesis that developmental stability is mediated, in part, by distributed robustness, the resilience of gene regulatory, metabolic, and protein-protein interaction networks. Alternatively, multiplicative cell growth, and the mixing of lognormal distributions having different variances, may generate a DPLN distribution. Developmental homeostasis and robustness are related concepts having very different histories. Developmental homeostasis, the older of the two concepts, has two independent aspects: canalization and developmental stability Hsp90Developmental stability is thought to be mediated by heterozygosity Distributed robustness involves the complexity of gene regulatory, metabolic, and protein-protein interaction networks. If a link in a network is broken, it may (in many cases) be bypassed with little impact on fitness P(k)≈k−γ, where P(k) is the probability that a node (or vertex) has k links (or edges) and γ is a coefficient that reflects the declining frequency as k increases. Inverse power-law distributions are monotonically decreasing and they have long (fat) tails. Other proposed distributions, such as truncated power-law and stretched exponential distributions, also suggest scale-free behavior, but only over a part of the network If distributed robustness is the main contributor to developmental stability, then the topology of interactions among genes, proteins, and metabolites should be critically important but see . The degR to perturbation of a particular node (or link) in a gene regulatory, metabolic, or protein-protein interaction network is proportional to the node's connectedness, k. This is true for protein-protein interactions involving single-copy genes and synthetic lethal interactions involving all genes R to a random perturbation will then be given by P(R)≈R−γ. In addition, assume that random developmental variation is a normal (and necessary) component of development, such that zero variation is impossible for continuous traits Assuming that distributed robustness contributes to developmental stability and robustness, what should the distribution of random phenotypic variation  look like? Perturbing a highly connected node  has a greater phenotypic effect than perturbing a node with only a few links kk. The power-law then is the probability density function associated with the cumulative distribution function given by Pareto's law. Both have fat upper tails. Gene expression data sets in yeast, mouse, and human cells follow a Pareto-like probability distribution The Pareto distribution is the name given to a cumulative distribution function that has a power-law tail. In the context of networks, the value of the Pareto cumulative distribution function is the number of nodes having degree greater than a priori reason to expect a fat lower tail. The left Pareto-lognormal (LPLN) distribution, on the other hand, lacks a fat upper tail (it has a fat lower tail) Alternative distributions include the right and left Pareto-lognormal distributions, as well as the normal, lognormal, Pareto, and exponential distributions. The right-handed Pareto-lognormal (RPLN) distribution resembles the DPLN, but has a fat upper tail and a lognormal lower tail Saccharomyces cerevisiae (Baker's yeast) is an ideal species in which to examine the predictions of network topology and developmental instability. Its genome has been sequenced and the degree distributions of its metabolic, protein-protein interaction, and gene regulatory networks roughly approximate the predicted inverse power-law distribution S. cerevisiae fits a double Pareto-lognormal distribution better than several other skewed and symmetrical distributions.Working with 4,718 strains of haploid single-gene knockouts ν) and variance (τ2), and power-law scaling exponents for the right (α) and left tails (β). The probability density function, dPlN , isg(y) is a normal-Laplace distributionR(z) is the Mill's ratio, φ is the probability density function for the standard normal distribution N. . See .S. cerevisiae single-gene knockouts to DPLN, right Pareto lognormal (RPLN), left Pareto lognormal (LPLN), normal, lognormal, Pareto, and exponential distributions. For the normal, lognormal, Pareto, and exponential distributions, we used maximum likelihood estimators of the parameters . For the DPLN, RPLN, and LPLN distributions, we used two independent algorithms, the Downhill Simplex Method in Multidimensions  AIC is a measure of the relative goodness of fit of a statistical model. The models are ranked by their AIC values, where AIC = −2 ln(L)+2d. ln(L) is the value of the log likelihood function for a particular model, while d is the number of parameters in a model. A corrected version for finite sample sizes is n = the sample size. The smaller the AIC value for a distribution, the more likely it is that the distribution fits the data the best. Because AIC values are relative, the AIC differences (Δi) are calculated: AIC) is the smallest AIC value among all of the models. AIC is estimated for each of i models. Akaike weights (iw) reflect the normalized likelihood of the models given the data We used the Akaike Information Criterion  look close by eye.The phenotypic potential of ibutions  and 2. Tibutions . The relThere are two major differences between the DPLN and the RPLN, LPLN, and lognormal distributions . The DPLThe robustness of living organisms is thought to arise from redundancy and distributed robustness Networks consist of nodes and links P(k) of nodes follows a power law, P(k)≈k−γ, distribution. Most nodes have few links, but a few hubs may have hundreds or thousands of links. The hubs connect the less connected nodes to the system. These systems are typically scale-free A highly connected node is a hub. In many biological networks, or parts of these networks, the connectivity Drosophila and CaenorhabditisOther degree distributions have also been fitted to biological networks, including truncated power-law, exponential, and stretched exponential distributions Saccharomyces cerevisiae, the balanced distribution of nodes and hubs buffers phenotypic variation In yeast, S. cerevisiae genetic networks exist in multiple copies, which would blunt the effect of a mutation in just one copy. Consequently, capacitors of phenotypic variation are more likely to be single-copy hubs. But even these single-copy hubs are likely to be idiosyncratic capacitors. Based upon evolutionary simulations of gene-regulatory networks, Siegal et al. t−1 actively participates in the production of cytoplasm at time tOur results, the close fit to the DPLN, are consistent with the hypothesis that network topology, and hence distributed robustness, plays a role in developmental stability. Nevertheless, it is unlikely to play the only role. Levy and Siegal Lu and King In addition to these alternative explanations for the DPLN, we have not accounted for the better fit to the DPLN over the RPLN. The lower tail of the distribution of phenotypic potential appears to fit a power-law distribution, but with a positive slope. Allometric relations, such as the scaling of metabolic rate with mass, are the best-known scaling relationships having a positive slope Other researchers have examined the statistical distribution of developmental errors, but have done so with radially or bilaterally symmetrical traits in natural populations of multicellular organisms. Van Dongen and Møller How does the DPLN alter our understanding of networks and organismal evolution? All yeast single-gene knockouts (or loss-of-function mutations) are heritable, by definition, but not all of the phenotypic variation generated by such knockouts is heritable. Most knockouts barely increase phenotypic variation beyond the cloud of random, non-heritable, developmental noise. This is the variation generating the lower tail of the DPLN. The knockouts in the upper tail of the distribution, however, represent heritable variation in developmental noise. Such heritable variation should be accessible to natural selection, which could then fine-tune developmental noise to maximize fitness. Consequently, by understanding the complex relationships between gene regulatory, metabolic, and protein-protein interaction networks and phenotypic variation, we may eventually begin to understand why organisms are not less variable (or more variable) than they already are.The close fit of phenotypic variation in single-gene knockouts of yeast to the DPLN distribution suggests that disruption of most nodes has a minor, but significant, impact on phenotypic variation. This impact is greater than one would expect from the RPLN, LPLN, and lognormal distributions. Consequently, the DPLN distribution suggests that more random phenotypic variation is potentially heritable than one would expect under, say, a lognormal distribution, or less random phenotypic variation is heritable than one would expect under a normal distribution.Arabidopsis thaliana, Drosophila melanogaster, and multicellular colonies of S. cerevisiae. The gene deletion and RNAi lines exist, and the methods of estimating random phenotypic variation in plants The generality of our results will have to await further research on random phenotypic variation of gene deletion and RNAi lines of multicellular organisms, such as S. cerevisiae. Yeast are unicellular eukaryotes, but colonies on agar plates behave somewhat like multicellular organisms. Palkova and colleagues CCR4 gene increases phenotypic variation among cells and also increases the irregularity of entire colonies An obvious extension of our study to multicellular organisms should begin with α and β approach infinity? And what will the distribution of phenotypic variation look like in a population of yeast in which each clone is a product of sexual reproduction? Will it approach the lognormal distribution? Or will it fit the normal distribution, as Van Dongen and Moller In conclusion, we have demonstrated that the DPLN fits the distribution of random phenotypic variation of yeast single-gene knockouts better than several competing distributions. This result is consistent with the hypothesis that distributed robustness operating in a noisy developmental system buffers phenotypic variation, at least in part. It is also consistent with the hypothesis that the DPLN arises from multiplicative cell (or cytoplasmic) growth and the mixing of lognormal distributions having different variances. Moreover, these hypotheses, one a biological hypothesis and the other a statistical hypothesis, are not mutually exclusive. Further research will be necessary to distinguish between them. Finally, it will be important to refine the behavior of the DPLN for future models of phenotypic variation. For example, how will the DPLN change if the nodes experience only minor perturbation? Will it approach a lognormal distribution instead, as Appendix S1Errata in the original article on the double Pareto-lognormal distribution by Reed.(DOCX)Click here for additional data file.