With the development and application of super rice breeding, elite rice hybrids with super high-yielding potential have been widely developed in last decades in China. Xieyou9308 is one of the most famous super hybrid rice varieties. To uncover the genetic mechanism of Xieyou9308’s high yield potential, a recombinant inbred line (RIL) population derived from cross of XieqingzaoB and Zhonghui9308 was re-sequenced and investigated on the grain yield (GYD) and its three component traits, number of panicles per plant (NP), number of filled grains per panicle (NFGP), and grain weight (GW). Unconditional and conditional genome-wide association analysis, based on a linear mixed model with epistasis and gene-environment interaction effects, were conducted, using ~0.7 million identified SNPs. There were six, four, seven, and seven QTSs identified for GYD, NP, NFGP, and GW, respectively, with accumulated explanatory heritability varying from 43.06% to 48.36%; additive by environment interactions were detected for GYD, some minor epistases were detected for NP and NFGP. Further, conditional genetic mapping analysis for GYD given its three components revealed several novel QTSs associated with yield than that were suppressed in our unconditional mapping analysis. Xieyou9308 is one of the most famous super hybrid rice varieties with a grain yield as high as 12.23 t/ha1. However, the genetic basis underlying this high yield potential remains largely unclear. In order to fuel the further successes of super rice breeding programs, continued efforts to dissect the genetic basis of economically-important traits will be necessary.Rice is a fundamentally important staple crop, and improving rice yields has remained a major goal in world agriculture. Super hybrid rice shows great advantages in grain yield and biomass in comparison with conventional rice varieties. Since its inception in China in 1996, super rice breeding program has achieved tremendous increases in rice yields4. However, owing to the insufficient density of polymorphism markers, the QTLs reported in these studies could typically only be localized to very large chromosomal regions, where still may harbor considerable amounts of genetic variants5. This restricts the consequent application of these QTLs in marker assisted breeding to some extent.Economically, the most important agronomic trait for rice is grain yield (GYD). GYD exhibits complex genetics, as it is known to be an integrated quantitative trait that is influenced variously by yield component traits and by the environment. Several QTL linkage mapping studies with Xieyou9308 have used conventional molecular markers to explore the causal loci that are responsible for the phenotypic variation of economically-important traits12. Huang et al.9 re-sequenced 517 rice landraces and used GWAS methods to analyze putative causal relationships between 14 agronomic traits and ~3.6 million SNPs, from which they identified three loci associated with tiller number, two loci associated with spikelet number, two loci associated with grain width, and five loci associated with grain length. A subsequent study from Huang et al.12 reported 32 new loci associated with 11 agronomic traits based on a natural population of 950 worldwide rice varieties. Another GWAS based on 413 diverse accessions of O. sativa from 82 countries identified 234 loci associated with 34 agronomic traits using 44,100 identified SNP variants11.Partly impelled by advances in sequencing technologies and the resulting improvements in genotyping, genome-wide association study (GWAS) strategy has become one of the primary approaches used to identify causal genes underlying phenotypic variation. GWAS is particularly attractive because it offers hope for rapidly narrowing the region where a causal gene might lie. Although pioneered by human geneticists, GWAS is also being appealingly applied to plants including rice13 to study developmental quantitative genetics; it was later extended for the analysis of the genetic contributions of component traits to an integrated trait at the molecular level15.These studies confirm that GWAS is a powerful approach that can be used in rice to identify genetic variants associated with complex traits with high resolution. However, most of these studies were focused on detecting genetic variant exhibiting additive genetic effects without consideration of gene-environmental and gene-gene interactions which were thought to be very important for complex traits. In addition, the cryptic population structure in the rice natural population (collected landraces) which would increase the false positive associations also haunted the researchers. Moreover, although increasing numbers of association studies have attempted to map the casual genes for yield traits of rice, most of these studies dissected traits separately, without considering genetic correlations between traits. As yield traits are known to be interrelated, exploring genetic correlations among these traits should provide additional insights into the genetic basis of grain yield. Conditional genetic analysis is a methodology first introduced by ZhuIn this study, the derived recombinant inbred line (RIL) population of Xieyou9308, which should theoretically have no deleterious issues relating to population structure, were re-sequenced and used for both genome-wide association mapping and for conditional association mapping for GYD and its three constitutive traits. The analysis was based on a saturated mixed linear model that included both epistasis and gene-environmental interactions. Further, a conditional methodology was adopted to identify additional candidate regions that likely contribute to grain yield. Our results provided some information that should be of use in efforts seeking genetic improvement of yield potential in rice.As shown in Table In total, there were 24 SNPs detected significantly  with accumulated explanatory heritabilities varying from 43.06% to 48.36%. There was an additive by environment interaction detected in grain yield (GYD), and some epistatic effects were detected for NP and NFGP (Table h2 = 10.91%), and additive by environment interaction which showed opposite genetic effects in the two different locations. For NP, the total heritability (43.35%) mainly consisted of additive heritability (41.03%) from 4 QTSs whose individual heritability was quite large, especially for rs28989077 (h2 = 18.54%). The remaining heritability was from one pair of additive by additive epistasis effects (rs20829501/rs9429313). All the main additive effects were negative; only one epistasis was positive, and its genetic effect size was relatively small as compared with the main additive effects  in these detected SNP loci would increase the number of filled grains. Additionally, there was a pair of positive epistasis interactions (rs645267/rs23681930) detected; and their individual main additive exhibited opposing genetic effects (rs645267 was negative while rs23681930 was positive). For GW, 7 SNPs, all with only additive effects, were found; in aggregate, these QTSs accounted for 48.36% of phenotypic variation. Of particular note, the SNP located on chromosome 3 (rs18572583) contributed 15.19% of the phenotypic variation and should thus be considered to be a very important candidate locus for subsequent breeding efforts.All significant QTSs with additive effects for yield conditioned on each of its components are presented in Table Comparing the results of the unconditional and conditional association mapping for GYD Table , three phttp://rice.plantbiology.msu.edu/index.shtml), of the 39 significantly QTSs detected for yield traits from the unconditional and conditional mapping, 18 QTSs were located within known annotated genes  that is known to play a critical role in communication between the plant cell wall and the cytoplasm18 and has been shown via functional studies in Arabidopsis to be involved in various functions such as cell expansion20. The QTS rs28989077 associated with NP is located in the LOC_Os03g50780 gene, which encodes a protein containing a PHD finger domain. PHD finger domains are thought to play an important role in the regulation of chromatin or transcription22. SNP rs20829501 is another NP-associated QTS in the LOC_Os07g34770 gene. A previous study23 reported that the function of LOC_Os07g34770 may relate to rice seed dormancy, but evidence for its possible association with NP is, to our knowledge, new in the literature. In addition, the rest of the detected QTSs that are not located in known genes but they are near some sensible genes. For instance, rs41315645, found in our study to be related to filled-grain numbers, is located ~12 kb downstream of the LOC_Os01g71310 gene, which exhibits the same gene function as the known cloned gene Gn1a . Gn1a encodes a cytokinin oxidase/dehydrogenase that degrades bioactive cytokinins; and reduced expression of Gn1a can lead to the accumulation of cytokinins and thus increase the number of grains24.According to the latest version of rice genome annotation  population that is generated from random mating of recombinant inbred (RI) strains would be ideal, since it contains more heterozygous loci as well as more kinds of combination of genes in different positions on genome which are basic requirements for analyzing dominance, dominance-related epistasis effects.In the last decade, genome-wide association method have been a primary tool for dissecting complex traits, especially for human diseases. Such methods have also become appealing and affordable in plant research programs owing to dramatically-reduced costs for genomic technology services. Even though genome-wide association studies (GWASs) have led to some promising scientific discoveries, they have encountered the ‘missing heritability’ problem. This refers to the situation where identified genetic variants (mainly SNPs) only explain a small proportion of the expected heritability estimated from classical pedigree analyses. It has been suggested that the failure to evaluate genetic interactions  is a reasonable explanation for this phenomenonYD Table , which mYD Table . There w29. Here, we adopted this methodology to analyze the genetic interrelationships between rice yield and its three components, and further detected some additional QTSs for final yield by conditioning on its component traits. Grain yield in rice can be viewed as the integration of some quantitative component traits, which, as proposed by Piepho30, can be represented by observed primary characters like number of panicles (NP), number of filled grains (NFGP) and grain weight (GW). This integrated character also complicates the causal gene mapping for final grain yield, especially because of the negative correlations between the components. Thus, it has been thought more effective to dissect its component traits individually, as these probably have simpler genetic control and can exclude the influence of the other components. In this study, we first performed genome-wide association mapping for all four traits separately. There were a total of 24 significant unconditional QTSs detected and the two or three highly significant QTSs for each trait were found to be located within or near annotated genes, most of which are predicted to have functions conceivably associated with target traits  and corresponding gene functional analysis in Arabidopsis, which revealed its regulation role for plant cell growth16. Additionally, the conditional mapping analysis indicated that rs26302731 is supposed to be independent of the panicle number trait. The QTS rs8203251 is another reliable candidate locus, although it was not located in an annotated gene. It is quite special; it is the only QTS found to be independent of all three components and to exhibit a very high heritability (h2 = 10.91%). The nearest gene to it was LOC_Os04g14620 (715 bp away) that encodes a retrotransposon protein belonging to the Ty3-gypsy subclass. Retrotransposons seemed ubiquitous in our results, as they were associated with all four yield traits  and conceivable gene functions as described in candidate gene analysis section. The QTS rs41315645 is highly correlated with filled-grain number (h2 = 8.16%) and near a gene (~12 kb away and there is no SNP in this gene) that exhibits the same function as the cloned gene Gn1a which has been demonstrated to have a function in influencing grain number24; it should thus be considered a quite reliable candidate for grain number in this population. Novel loci from the conditional mapping also have high potential to be reliable candidates for grain yield along with the analysis of corresponding gene function. For instance, rs3063720 is located in the OsWAK gene; studies in Arabidopsis have shown that this gene functions in cell expansion during plant development20 and thus it is a high potential candidate for breeding.As for practical breeding, we detected some high potential candidates for these yield traits. For grain yield, rs26302731 appears to be a reliable candidate locus due to its high heritability (13 lines was developed from the super hybrid Xieyou9308 via the single seed descent (SSD) method, with XieqingzaoB (XQZB)  as the maintainer line and Zhonghui9308 (ZH9308)  as the restorer line. The inbred lines were planted in Lingshui, Hainan province and in Hangzhou, Zhejiang province in 2009, respectively. Four rice yield traits, including grain yield per plant (GYD), panicle number per plant (NP), number of filled-grains per panicle (NFGP), and the weight of 1000 grains (GW) were measured. Based on the mixed linear model approach implemented in the software of QGAStation31, the total genotypic values were predicted for the calculation of genetic correlation between traits. Calculations of the summary statistics of the phenotypic data, as well as analysis of the data distributions and correlation coefficients were performed using the R (v3.2.2) statistical software32.A recombinant inbred line (RIL) mapping population consisting of 138 F33. SNPs were identified between the individuals and the reference genome by using SAMtools software34, with settings as follows: base quality ≥30, mapping quality ≥20, and the maximum sequence depth ≤1000. Finally, a total of 701,867 SNPs were identified for the 138 RILs and used in the subsequent association studies. The filtration of SNPs and LD pattern analysis have been demonstrated in our another study35 based on this RIL population. It has shown that the LD decay rate was estimated approximately 1,000 kb on whole genome-wide. It is noteworthy that associations in this population would not be affected by population structure issues, as these progenies are from the same ancestry (the cross of XQZB and ZH9308), and the relatedness among these lines is distributed evenly .DNA re-sequencing was conducted at the Beijing Genome Institute (BGI) for the 138 inbred lines with 2X coverage and the parent lines with 10X coverage. The latest version of the Nipponbare sequence was used as the reference genome. Subsequently, sequence alignment was performed between the re-sequencing data and the reference genome using BWA softwarea) and additive by additive epistasis (aa) as fixed effects, the environment (e) which is mostly uncontrollable as random effects, and thus their interactions  also as random effects. The genetic model for the phenotypic value of the k-th genotype in the h-th environment (yhk) can be expressed by the following mixed linear model,μ is the population mean; ai is the additive effect of the i-th gene (QTS) with coefficient xik, fixed effect; aaij is the additive by additive epistasis effect of the i-th QTS and the j-th QTS with coefficient xik · xjk, fixed effect; eh is the main effect of the h-th environment, random effect; aehi is the additive by environment interaction effect of the i-th QTS and the h-th environment with coefficient uhik(=xhik), random effect; aaehij is the interaction effect of the aaij and the h-th environment with coefficient uhijk(=xhik · xhjk)), random effect; and εhk is the random residual effect of the k-th line in the h-th environment.In this study, we adopted a saturated genetic model with additive  potentially associated with the trait were kept for each chromosome according to their testing accuracy from high to low. Finally, based on the screened SNP subsets, association mappings were conducted for each trait using the mixed linear approach implemented in QTXNetwork37 software. In this procedure, first significant testing for each individual SNP and for all possible SNP pairs were performed using F-test which is permutation-based to control the experiment-wise type I error rate at 0.05, and then stepwise model selection was conducted to pick out the relatively high explanatory significant candidates for the final full model (1). Finally, all the parameters and corresponding standard errors of model (1) were estimated via Markov chain Monte Carlo (MCMC) with 20,000 Gibbs sampler iterations. Based on the estimated genetic component effects , the heritability of each QTS in each genetic component was calculated and the summation of all detected QTSs for the trait is regarded as the total heritability.Based on the above mixed linear model, both unconditional and conditional genetic mapping were performed for grain yield and its three components. For conditional association mapping, the conditional phenotypic values of grain yield given its components (T1|T2) were first produced by software of QGAStation 2.0


Expression quantitative trait (eQTL) studies are a powerful tool for identifying genetic variants that affect levels of messenger RNA. Since gene expression is controlled by a complex network of gene-regulating factors, one way to identify these factors is to search for interaction effects between genetic variants and mRNA levels of transcription factors (TFs) and their respective target genes. However, identification of interaction effects in gene expression data pose a variety of methodological challenges, and it has become clear that such analyses should be conducted and interpreted with caution. Investigating the validity and interpretability of several interaction tests when screening for eQTL SNPs whose effect on the target gene expression is modified by the expression level of a transcription factor, we characterized two important methodological issues. First, we stress the scale-dependency of interaction effects and highlight that commonly applied transformation of gene expression data can induce or remove interactions, making interpretation of results more challenging. We then demonstrate that, in the setting of moderate to strong interaction effects on the order of what may be reasonably expected for eQTL studies, standard interaction screening can be biased due to heteroscedasticity induced by true interactions. Using simulation and real data analysis, we outline a set of reasonable minimum conditions and sample size requirements for reliable detection of variant-by-environment and variant-by-TF interactions using the heteroscedasticity consistent covariance-based approach. Gene-gene and gene-environment interaction effects on common human traits and diseases have been difficult to identify . Part ofIn this study we analyzed blood gene expression and genotype data from 121 subjects in the ECLIPSE Study , 8 to teUsing simulation we investigate these issues by quantifying the performance of five analytical strategies to detect interaction: standard linear regression, two heteroscedasticity-consistent covariance estimates, dichotomizing the predictors, and a saturated model. More specifically, we assessed the robustness of these approaches when heteroscedasticity has been induced through interaction effects while varying sample size, minor allele frequency and the magnitude of the main and interaction effects simulated. We identify minimal conditions necessary for valid tests of interaction in eQTL studies. Finally, for illustration purposes, we also present the results from the TF by SNP interaction screening in ECLIPSE. This real data analysis confirms the findings of our simulations, highlighting that standard approaches might have severely inflated type I error rate. Moreover, we observed that the list of significant associations changed dramatically across approaches, especially when comparing analyses of transformed versus untransformed gene expression data, stressing that the two sets of analyses capture different patterns in the data.step 3 in rkt) in particular, as the latter approach is commonly applied in eQTL studies. Applying rkt on expression data can have several advantages. First, if the data show deviation from normality , rkt can increase the statistical power to detect the linear marginal effect of a predictor. In brief, non-linear transformation can achieve a normal and homoscedastic distribution of points around the regression line, potentially allowing for a larger amount of the outcome variance to be captured, thus increasing power [rkt can also decrease power in certain scenarios [rkt is that it addresses outlying values while preserving sample size. Expression data often has noise-induced outliers  because of experimental artifacts or stochastic properties of the biological system, which can lead to an increased rate of type I and type II errors [Gene expression data are heavily pre-processed . We assung power , 21. Howcenarios . Indeed,cenarios , 24. AnoI errors . The nairkt might have a stronger impact on Type I and Type II error rates when testing for interaction [rkt can dramatically impact the interpretation of interaction effects. In particular, while differences in significance before and after transformations are expected to be relatively minimal when interaction effects are small , this is not necessarily the case when the variance explained by predictors is large. Consider for example the generative model defined in Y depends on a SNP G, an exposure E interacting with G (mRNA levels of a transcription factor in our case), and the residual ε follows a skewed-normal distribution with mean 0 and variance 1 . Note that for simplicity, we assume the covariate Z has no effect (γz = 0) on Y. In the absence of interaction effect (γGE = 0), if E and G explain a relatively large amount of the variance of Y  can induce a statistical interaction between G and E. For illustration, we plotted in G and E, but the rank-normal transformed data does not. Note that we considered a non-normal residual as it can be an argument for applying a rank-based inverse normal transformation, but similar issues might arise when the residuals are normally distributed. Figs B-C inHowever, in contrast to screening for marginal effects, eraction , 26. MorE, unknown, and drawing ε, the residual from a normal distribution with variance scaled so that the variance of Y is one for all scenarios simulated. For simplicity we also assumed that E and Z follow normal distributions with mean 0 and variance 1. We tested for interaction between G and the non-interacting factor Z in a series of replicates simulated in the presence or absence of main effects for G, E and Z, as defined in The second major challenge we found is that while weak interaction effects between two risk factors are unlikely to have a noticeable impact on the conditional distribution of the outcome, this is not the case for moderate to strong interactions. For an interacting SNP, this will be expressed through heterogeneity of variance of the outcome residual by genotypic class, a property that has been proposed as a target for interaction screening  , 18, 19.δ) by genotypic class, resulting in inflation of the type I error rate of the interaction tests between G and Z. This is in agreement with previous work, also showing type I error inflation when misspecifying the main genetic effect [G and Z) can also worsen the type I error inflation  can induce spurious interaction effects with other non-interacting factors. Note that heteroscedasticity generated by interaction would only be a limited concern for the test of the marginal genetic effect. Indeed G being involved in an interaction means it is related to the outcome tested, and while power and effect estimation might be impacted, a marginal effect association signal with G would likely represent a true signal.c effect –30. Varistep 1 and 2 in Z, and using a saturated model that includes non-linear main effects of the predictors. For the latter approach we simply included in the model a main effect for Z2 and for each genotypic class (G = 1 and G = 2).We then extended our simulations to assess the validity of five approaches in the presence of a strong interaction between the SNP tested and an unmeasured factor. As before, we assumed that the gene expression data have been corrected for technical artifacts but not rank transformed , and assuming alternatively presence or absence of a main effect for Z. The magnitude of the G × E interaction effects and the main effects of the predictors  were generated at random for each replicate. As shown in the QQplots from Fig D-K inλ close to 1 and only minor or no inflation of low p-values when using a sample size of 1000 or greater and common SNPs (CAF ≥ 0.3).We compared the robustness of the five approaches across a series of one million simulated replicates for the null model of no interaction between analyses , 4, 6), a priori list of TFs and significant SNP-gene pairs from the ECLIPSE cis eQTL analysis. We followed the pre-processing procedure of cis-effect on the expression of that gene assuming an additive genetic effect and using a score test as implemented in the GGTools software [q-value for association less than or equal to 0.01. From these results we selected the most significant SNP for each Affymetrix probe set, resulting in a total of 2,982 cis-eQTL SNPs associated with 3,334 target probe sets. As observed in other studies, the variance of the residualized expression phenotypes explained by cis-eQTL SNPs can be much larger than those observed for quantitative phenotype in human GWAS [Fig A inr2 obtained from marginal genetic model for the 3,334 pairs. The average equals 0.45 with a maximum r2 of 0.87. In comparison, under a null model with the same total number of tests and using the same p-value threshold, we would expect to observe a distribution of effects to have a mean r2 of 0.14 and a maximum of approximately 0.25.To illustrate these effects in real data, we conducted a two-step screening approach to identify interaction effects between cis-eQTL SNPs and candidate TFs in a genome-wide expression dataset from 121 subjects in the ECLIPSE Study . Interacsoftware , and to man GWAS . Fig A icis-eQTL SNPs selected at step one were tested for interaction with the expression level of candidate TFs obtained from the publication by Vazquerizas et al [target probe set was nominally significant (p<0.05). Also, to avoid confounding by a cis-effect of a SNP on two genes in close physical proximity, all TFs within 10Mb of a candidate cis-eQTL SNP were not tested for interaction with that SNP and its target gene. Among 1494 TFs, 1292 TFs represented by 2,896 probesets were available for analysis in the ECLIPSE study. As shown in Fig A intarget gene explained by candidate TFs was high, with an average r2 of 0.35. Overall, there were 745,943 trios  to be screened for interaction effects. For each of these trios we performed the standard linear regression on non-rank transformed data (std) and inverse-normal rank-transformed data (rkt), and we considered for both approaches the HC3 correction of the effect estimate variance to account for heteroscedasticity .In step two, all as et al . To reduFig L inp-values, as measured by the genomic control . There were 151, 244, 4, and 75 significant interactions after correction for multiple comparisons , for std, h3, rkt and rkt.h3, respectively. While a few interactions were significant or near significant across all tests, most showed strong heterogeneity. p-value and rank. Unsurprisingly, all SNPs from target gene. For example, rs8109474 explained 63% of the variance of target probe set 218824_at (PNMAL1). The significance of the interaction was also strongly correlated with the strengths of the marginal association between the candidate TF and the target probe set. As shown in λGC value for the std interaction test increases to almost 2 when focusing on the candidate TFs showing the strongest association with the target gene. While some of the observed λGC inflation might due to a true enrichment for interaction effects, a substantial part of the association is likely due to statistical artifacts. Conversely, the rkt test, which corrects for the effect of outliers and potentially reduces inflation caused by interaction between SNPs and unmeasured factors (Table A inλGC = 1.17). In addition, rkt appears to be stable when focusing on TFs with increasing association with the target. Assuming strongly associated TFs are more likely to have biological interaction with cis-eQTL SNPs, this flat curve raises the potential concern that, in agreement with our simulations, interaction effects on the original scale might be removed by the rkt transformation.step 3 in Genomic data, and gene-expression data in particular, offer new opportunities to identify gene-gene and gene-environment interactions. In this study we attempted to screen for SNP by TF interaction on gene-expression using data from the ECLIPSE study, and we describe two methodological issues related to the detection and interpretation of statistical genomic interactions. First, interaction effects are scale-dependent and commonly applied pre-processing steps that perform non-linear transformation of expression data can induce or remove statistical interaction, making interpretation of results more challenging. Second, the effect sizes observed in eQTL data are substantially larger than those observed for genetic association with complex human traits and diseases. Assuming interaction effect sizes are similarly large, our simulations show that their presence can induce substantial heteroscedasticity, which itself can impact the robustness of interaction test screening. While heteroscedasticity and scale-dependent effects have been discussed in a broader context, recent screening for interaction effects in gene expression data have not specifically addressed these issues , 4, 6. Wrkt . We also observed in simulated data that heteroscedasticity induced by true interaction effects is partly reduced after applying ror rate , 26. Morray data . For thecis-cis interaction effects should be interpreted with caution, as an observed statistical interaction may reflect a haplotype effect. While our analysis focused on SNP-by-TF interactions, SNP-SNP interactions would likely face the issues discussed in our study, as the increased type I error rate we observed was driven by the hidden interaction between the SNP tested and an unmeasured quantitative trait, independently of the other tested interacting factor (another SNP in a SNP-SNP interaction screening).Our simulations also demonstrate that an interaction between two factors can induce spurious statistical interaction effects between those factors and other non-interacting factors, leading to the paradoxical situation where the interaction effect screening can be invalid under the scenario of strong interaction. Exploring alternative solutions, we found that interaction effect screening can likely be performed safely among common SNPs  in large sample sizes  using the HC3 correction, while for smaller sample size (N ≥ 1000), there will remain uncertainty on the validity of association signal. This result is complementary to previous publications highlighting other challenges in genomic interaction screening. In particular, there has been controversy regarding the validity of previously reported , 42. TheWe acknowledge that the proposed strategy does not necessarily represent the optimal solution. To fully address scaling and robustness issues, future work might explore alternatives to the HC3 correction that better model the data  and also assess the impact of common pre-processing practices such as log transformation of raw expression values, quantile normalization , adjustmY as a function of a SNP G, an exposure E and a covariate Z using the following generative model:γ0, γG, γE, γZ and γGE are the intercept and the effects of G, E, Z and the interaction effect between G and E, respectively; and ε is the residual. We set the minor allele frequency of G at 0.1, and generated E using a normal distribution with mean 0 and variance 1. We considered two scenarios. In the first one, G and E have only main effects, each explaining 40% of the outcome variance, but they do not interact (γGE = 0). In the second scenario, only E has a main effect (γE ≠ 0) and (γG = 0), while G has no main effect but influences Y through its interaction with E. The residual ε is generated following a right-skewed normal distribution and is scaled so that the variance of Y equals 1. For each scenario we plotted Y and rkt(Y) as a function of E, where rkt is a rank-based inverse normal transformation function. The rkt transformation was performed using the R function rntransform from the GenABEL R package. We then estimated the effect of E on both Y and rkt(Y) by genotypic class using standard linear regression.We generated an outcome γGE, the interaction effect between G and E, so that the variance of the outcome explained by the interaction τG×E varies from 0 to 30%, where τG×E = var(γGEGE) / var(Y). Note that τG×E is similar to the standard definition of variance explained by interaction effects as all predictors are standardized, however this would not be the case for unstandardized predictors [G, E, or Z explain the same amount of variance as the interaction effect. We draw ε, the residual of Y, from a normal distribution with mean 0 and variance scaled so that the unconditional variance of Y equals 1. From this model we generated a series of 10,000 independent replicates of 400 individuals and we conducted a test of G and Z from the model:To explore the impact of true interaction effects, we then generated a series of data using edictors . For simγG = γE = γZ = 0), including a main effect of G (γG ≠ 0), a main effect of E (γE ≠ 0), or a main effect of G (γZ ≠ 0). We first evaluated the relationship between τG×E and δ the residual variance of the outcome from ε from δ (see Supplementary Note). We then derive for each simulated scenario the type I error rate α of βGZ, the interaction tests between G and Z, at a p-value threshold of 0.05, defined as Ns the number of simulations equals 10,000 and pGZ is the p-value of the interaction effect.We generated multiple series of data from this model in the absence of main effects  are modelled using additional terms. Various saturated models can be built. In these analyses we defined a model that includes a main effect of Z2 and encodes the main effect of the genotype using two dummy variables corresponding to G = 1 and G = 2. We tested Z and G, using its ordinal coding:The last correction entails using a saturated model where the main effects of the interacting factors  are randomly sampled from a uniform distribution . Unless otherwise specified, continuous variables  were drawn randomly from a normal distribution or right-skewed normal distribution, both with mean 0 and variance 1. The residual ε was further scaled so that the variance of Y explained by the simulated predictors in E, Z and ε) we also performed simulations while using a normal distribution only for all replicates. We also compared scenarios where the either the true interacting exposure E or the tested interacting exposure Z have a main effect against scenarios where they have no main effect. Finally, we varied the sample size from 100 to 5,000 and the frequency of the coded allele for G from 0.05 to 0.5. Overall, our simulations covered 96 scenarios.We generated a series of 1 million replicates using the model from step1 in step2 in in process). ECLIPSE expression data has been previously submitted to GEO as part of another project (229 samples) with GSE76705. Note that the ECLIPSE dbGaP submission  will also contain links to the GEO expression data.Study participants included 121 COPD cases genotyped as part of the ECLIPSE study  using thS1 File(PDF)Click here for additional data file.


The resurrection approach is a powerful tool for estimating phenotypic evolution in response to global change. Ancestral generations, revived from dormant propagules, are grown side by side with descendent generations in the same environment. Phenotypic differences between the generations can be attributed to genetic change over time. Project Baseline was established to capitalize on this potential in flowering plants. Project participants collected, froze, and stored seed from 10 or more natural populations of 61 North American plant species. These will be made available in the future for resurrection experiments. One problem with this approach can arise if nonrandom mortality during storage biases the estimate of ancestral mean phenotype, which in turn would bias the estimate of evolutionary change. This bias—known as the “invisible fraction” problem—can arise if seed traits that affect survival during storage and revival are genetically correlated to postemergence traits of interest. The bias is trivial if seed survival is high. Here, I show that with low seed survival, bias can be either trivial or catastrophic. Serious bias arises when (i) most seeds deaths are selective with regard to the seed traits, and (ii) the genetic correlations between the seed and postemergence traits are strong. An invisible fraction bias can be diagnosed in seed collections that are family structured. A correlation between the family mean survival rate and the family mean of a focal postemergence trait indicates that seed mortality was not random with respect to genes affecting the focal trait, biasing the sample mean. Fortunately, family structure was incorporated into the sampling scheme for the Project Baseline collection, which will allow bias detection. New and developing statistical procedures that can incorporate genealogical information into the analysis of resurrection experiments may enable bias correction. Richard Lenski and associates have applied it in their ongoing evolution experiment with Daphnia galeata hatched from resting eggs retrieved from sediments in Lake Constance, Hairston et al.  cannot be ignored. Here, the process generating missingness changes in intensity and/or direction with the process under study Figure c. With r2z that is expressed in mature plants. A very large, random sample of seeds was collected from a natural population, dried, frozen, and then revived at a later date. These are grown side by side with a descendent generation. All descendent seeds germinate, but fraction q of the ancestors fails to revive. Back at the time of collection (time 0), the potential mean value for focal trait z within the ancestral sample was z¯0, which is the proper baseline for testing evolutionary change in z. However, z is expressed at time t, after revival and emergence, when only 1‐q of the ancestral sample remains. Finally, assume that failure depends on seed trait y. To simplify calculations, assume z and y are normally distributed with zero mean and unit variance.To illustrate the potential invisible fraction bias, suppose the following. We are interested in some focal trait z¯t, differ from z¯0? Drawing on basic quantitative genetic theory /(1–q), where p(y*) is the probability of drawing an individual measuring below y* from a normal distribution.Equation z¯t can deviate dramatically from z¯0 when mortality is high and the genetic covariance is strong. Under a “worst‐case scenario” , the baseline to measure evolutionary change is off by 2 SDs. However, the bias is very weak (~0.01 SD) when mortality is only 5% and the genetic correlation is 0.25. At moderate mortality rates and genetic correlations, truncation selection can still distort the baseline by 0.1 to 0.4 SDs  generates low bias, even under strong genetic correlations.where To repeat, if seed germination failure is very low, bias will be trivial. But the bias under high failure rates can be either trivial or catastrophic, depending on how strongly mortality genetically correlates with the focal trait. One cannot determine the strength of this correlation from an unstructured sample of propagules. However, if genealogical relationships within the ancestral sample are known, the potential postemergence phenotype of a failed propagule can be inferred from phenotypes of its surviving relatives . Also consider vector w, which is the survivorship status of all individuals at the time that z is expressed . Their joint probability density is Recently, Steinsland et al.  offered d contains parameters for the differences across generations, m the parameters for the survival process, and a the breeding values for z. Thus, the combined model includes a conditional model for the data, p, generated from the animal model of quantitative genetics . This model structure implies that the association between the trait of interest and the failure to revive is induced by additive genetic effects  occurs during the early nesting stage, even before the spots are fully formed.where the vector This sort of analysis can be applied to a resurrection experiment if the relatedness among the stored propagules is known. This condition is met in the Project Baseline collection because the stored seeds are packaged by maternal sibships . Germination failure during the refresher generation can be recorded, and information on all subsequently expressed traits for the failed seeds entered as missing values in the data set. An SPM model may then be used to estimate the level of divergence between ancestor and descendant samples (and their hybrids) due to additive genetic variance, which quantifies the evolutionary response to selection exerted by global change.4A crucial assumption in resurrection experiments is that the resurrected individuals are a random sample of genotypes from the ancestral generation (Bennington & McGraw, SD, even when seed mortality is high. A genetic correlation between storage survival and the trait mean signals that the invisible fraction of the sample cannot be ignored when estimating the ancestral phenotypic mean.The calculations presented above indicate that under a worst‐case scenario, the estimated phenotypic mean for a late‐life trait can be highly biased by a strong genetic correlation to seed storage tolerance. However, when seed mortality is related to additional, uncorrelated factors, and/or when the genetic correlation to storage tolerance is weak, the bias is weak. Under some reasonable assumptions, estimates of the baseline mean will be off by less than 0.1 Methods to identify and potentially correct an invisible fraction bias depend upon genealogical information. Resurrection experiments have addressed evolutionary change in a variety of ecologically important traits (see Franks et al., Daphnia (Hairston et al., It is also parsimonious to conclude adaptation when focal traits simply have no functional relationship to processes that would influence propagule survival and emergence. Resistance to cyanobacteria toxins in Pleiotropic effects of loci expressed during both early and late stages are one source of an invisible fraction problem, but studies on germination rates in crop cultivars suggest a second path—genetically mediated maternal effects. Crop varieties with larger seeds commonly have higher germination rates, especially under stressful conditions such as high temperature or saline soils (Krishnasamy & Seshu,Fruiting phenology in plants presents another example of a genetically mediated maternal effect that could produce an invisible fraction problem. If seeds are collected too early in the season, those from late‐fruiting plants will not have accumulated their full complement of cryoprotectants Walters, . When stca. year 2065, future investigators will be able to use family structure to estimate the range of potential bias.Although low germination does not lead inevitably to a strong bias, high germination precludes it. Some studies using the resurrection approach have reported similar germination rates in the ancestral and descendant generations (Franks et al.,  Click here for additional data file.


N=108 976), we carried out a genome-wide association study (GWAS) of responses to the question, ‘Over the last two weeks, how often have you felt tired or had little energy?’ Univariate GCTA-GREML found that the proportion of variance explained by all common single-nucleotide polymorphisms for this tiredness question was 8.4% (s.e.=0.6%). GWAS identified one genome-wide significant hit . Linkage disequilibrium score regression and polygenic profile score analyses were used to test for shared genetic aetiology between tiredness and up to 29 physical and mental health traits from GWAS consortia. Significant genetic correlations were identified between tiredness and body mass index (BMI), C-reactive protein, high-density lipoprotein (HDL) cholesterol, forced expiratory volume, grip strength, HbA1c, longevity, obesity, self-rated health, smoking status, triglycerides, type 2 diabetes, waist–hip ratio, attention deficit hyperactivity disorder, bipolar disorder, major depressive disorder, neuroticism, schizophrenia and verbal-numerical reasoning (absolute rg effect sizes between 0.02 and 0.78). Significant associations were identified between tiredness phenotypic scores and polygenic profile scores for BMI, HDL cholesterol, low-density lipoprotein cholesterol, coronary artery disease, C-reactive protein, HbA1c, height, obesity, smoking status, triglycerides, type 2 diabetes, waist–hip ratio, childhood cognitive ability, neuroticism, bipolar disorder, major depressive disorder and schizophrenia . These results suggest that tiredness is a partly heritable, heterogeneous and complex phenomenon that is phenotypically and genetically associated with affective, cognitive, personality and physiological processes.Self-reported tiredness and low energy, often called fatigue, are associated with poorer physical and mental health. Twin studies have indicated that this has a heritability between 6 and 50%. In the UK Biobank sample ( The first and last authors of the present study grew up in South Lanarkshire in Scotland, where fatigue was often self-reported in terms of feeling ‘wabbit’. The Scots word wabbit encompasses both peripheral fatigue, the muscle weakness after a long walk, and central fatigue, the reduced ability to initiate and/or sustain mental and physical activity, such as we might experience while having flu. Throughout the paper, we refer mainly to the single English words ‘fatigue’ and/or ‘tiredness’ as the construct captured by the question, but the Scottish vernacular word is a good reminder of the subjective ‘feel’ of fatigue.1 These findings are similar to a London-based survey of general practice patients in England, aged 18–45 years, with 15 283 respondents, where 36.7% reported substantial fatigue, 18.3% substantial fatigue of >6 months duration and 1% fulfilled the diagnostic criteria for CFS.2 Two other large surveys of US workers and community-dwelling adults aged 51 years and over report fatigue rates of 37.9%  and 31.2%  respectively.4 In an early review of fatigue epidemiology, Lewis and Wessely5 argue that fatigue ‘is best viewed on a continuum’, and the continuous distribution of fatigue in the general population is supported by the Pawlikowska et al.2 study. Fatigue is also a common presentation in primary care. In a survey of 1428 consultations to 89 general practitioners in Ireland, fatigue prevalence was 25% and the main reason for attendance in 6.5%.6Fatigue is a common complaint. In a Dutch adult, general population survey with 9375 respondents, 4.9% reported short-term fatigue (<6 months duration), 30.5% chronic fatigue (>6 months duration) and 1% fulfilled diagnostic criteria for chronic fatigue syndrome (CFS).1 and poorer self-rated health status.7 There are less clear associations between age and fatigue, with some studies reporting a small but significant positive correlation between age and fatigue,2 whereas others report no association6 or a negative association.7 There is a clearer link with the Fried phenotype of frailty in older adults,8 which has significant associations with mortality. The frailty phenotype comprises weakness (as measured by grip strength), weight loss, reduced mobility, reduced walking speed and fatigue.9Demographically, higher levels of self-reported fatigue are associated with female sex, lower socioeconomic status10 and fatigue has strong cross-sectional associations with type 2 diabetes11 and increased body mass index (BMI).12 Fatigue is consistently associated with poorer physical and mental health status. It is one of the most common symptom complaints of cancer patients. For those undergoing treatment, prevalence estimates vary between 25 and 99%, and 25 and 30% of survivors report long-term fatigue.13 Fatigue is also a significant symptom of, to name just a few conditions, primary biliary cirrhosis,14 multiple sclerosis,15 rheumatoid arthritis,16 primary Sjogren’s syndrome17 and Parkinson’s disease.18 It is associated with chronic disease in general, and there is a linear relationship between number of chronic diseases and self-reported fatigue.19 Fatigue is also associated with depression,20 with self-reported psychological distress,21 and with the personality trait of neuroticism.23Fatigue is associated with a number of lifestyle-related factors and conditions. Smoking is a risk factor for fatigue24 and administration of interferon-alpha produces depression and/or fatigue in the majority of patients receiving it as a treatment.25 Hypothalamic-pituitary-adrenal axis dysregulation in the form of hypocortisolaemia, blunted diurnal variation and blunted stress reactivity have been found in the cross-sectional studies of CFS patients . Other popular candidate aetio-pathological mechanisms for fatigue include serotonin pathways, circadian dysregulation, autonomic dysfunction,17 5HT neurotransmitter dysregulation, alterations in ATP metabolism and vagal afferent activation.24 Some authors have suggested that, rather than being located with one biological system, fatigue represents a systemic dysregulation of the interaction between these systems.27Research into the biological mechanisms of fatigue has focussed on a few key areas. Fatigue is associated with the cytokine-mediated inflammatory response, particularly interleukin-1beta and interleukin-6. These latter have been shown, for instance, to be elevated in cancer patients,28 More integrative models are predicated on the notion of allostatic load, the psychophysiological work done to adjust to stress and its impact upon the body’s self-regulatory systems. As such, these models complement biological accounts of fatigue and provide potential pathways for integrating psychosocial and biological findings.29 Multifactorial accounts and models of fatigue exist in multiple sclerosis,30 primary biliary cirrhosis,14 obesity,31 diabetes,32 frailty33 and cancer.13 These multifactorial models postulate that fatigue is likely to be the product of physiological factors , psychosocial factors , lifestyle and behavioural factors , illness consequences  and the interaction of these contributors.At the other end of the biopsychosocial spectrum, psychosocial models of fatigue focus on the role that the individual’s response to their symptom may serve in perpetuating it. For instance, in a cross-sectional study of 149 patients with multiple sclerosis, illness-related cognitions and behaviours were associated with a higher level of fatigue independent of neurological impairment.et al.34 suggest that findings are inconclusive, and are hampered by phenotypic heterogeneity, lack of power and poor study design. For example, the candidate gene studies included in the Landmark-Høyvik paper had sample sizes between 2 and 248 individuals, and the results have not been replicated. Twin studies have shown the heritability of fatigue to be between 6 and 50% with a higher concordance in monozygotic twins than dizygotic twins.36 One of these studies36 did not show any sex-specific patterns of genetic influences in a Swedish sample, whereas the other one35 showed differences in the amount of variance explained by the genetic effect for males and females. Around half the variance in males was explained by the genetic effects compared to only a fifth of the variance in females. In a study of fatigue, insomnia and depression in 3758 twins (893 monozygotic pairs and 884 dizygotic pairs), the best model was a common pathway model, suggesting that the high association between the symptoms (correlations of 0.35–0.44) was mediated by an underlying common factor whose variation was 49% genetic and 51% unique environmental.37 This study showed that unique specific variance in fatigue was 38% genetic and 62% unique environmental, which supports a previous study, suggesting that fatigue is largely attributable to additive genetic factors.38 Genome-wide association studies (GWAS) have shown an association between single-nucleotide polymorphisms (SNPs) in genes associated with impaired cognitive abilities 40 and the circadian clock 40 and CFS, but this was in a sample of just 42 cases of CFS and 38 controls, lacking statistical power to detect genome-wide findings.Research into the genetics and epigenetics of fatigue has tended to focus on genes associated with the biological mechanisms described above, and done so usually within fatiguing illnesses such as those listed above. Candidate gene studies have suggested several genes to be involved in CFS, particularly genes involved in the immune system and Hypothalamic-pituitary-adrenal axis. Reviewing this literature, Landmark-Høyvik et al.:41 ‘fatigue can be conceptualised as a final common end point for psychological and biological processes. Fatigue is therefore both heterogeneous (occurring across different conditions) and multifactorial’. Given that, it could be argued that it is futile to search for a shared genetic contribution to tiredness, as it may not exist. However, in line with other fatigue research programmes42 and the research cited above, we judge that the best way to approach this complexity is to conduct large, well-designed studies focussing on specific areas of the biopsychosocial spectrum, and that to date no large study has done this at the genetic level.To sum up in the words of Landmark-Høyvik per se, not accounted for the factors in questions 2–4 below?Is there a direct genetic contribution to self-reported tiredness Is tiredness genetically linked to proneness to health-related traits?Is tiredness genetically linked to a systemic proneness to poor health?Is there a genetic relationship between the personality trait of neuroticism and tiredness?Tiredness can be the result of external factors—such as poor sleep—or inherent factors—such as personality traits or poor health. It is therefore important that we clarify the scope of the present study in terms of what questions we can ask, and how definitively we can answer them. By averaging tiredness across a large sample and performing a GWAS, the present study will primarily pick upon the genetic links between tiredness and inherent factors. These are likely to be various, so we will seek to bring some clarity to what we consider to be the likely genetic heterogeneity of tiredness by posing the following questions:With regard to questions 2 and 3, it is important to remember that a positive answer may constitute more than the obvious conclusion that the presence of an illness phenotype is inevitably accompanied by tiredness. Our analyses of UK Biobank data capture genetic predisposition to illness rather than its actual presence; we will address this in our polygenic prediction sensitivity analysis.The aim of the present study, then, is to understand further the genetic contribution to self-reported tiredness and/or low energy. We conducted a genome-wide association analysis, in the UK Biobank sample, of a response to a single item question: ‘Over the past two weeks, how often have you felt tired or had little energy?’ On the basis of the foregoing literature overview, we also investigated pleiotropy with physical- and mental health-related traits, and we specifically investigated pleiotropy with factors associated with allostatic load as a first step towards answering question three above. The current study design, using >100 000 UK Biobank participants, directly addresses the main limitation from the previous studies by substantially increasing the sample size. In addition, we complement this with SNP-based heritability estimates of tiredness, sex- and age-stratified analysis, and an examination of the genetic overlap of tiredness with many health-related traits.http://www.ukbiobank.ac.uk).43 A total of 502 655 community-dwelling individuals aged between 37 and 73 years were recruited in the United Kingdom between 2006 and 2010. Baseline assessment included cognitive testing, personality self-report, and physical and mental health measures. For the present study, genome-wide genotyping data were available for 112 151 participants  after quality control (see below). They were aged from 40 to 73 years . UK Biobank received ethical approval from the Research Ethics Committee (REC reference for UK Biobank is 11/NW/0382). This study has been completed under UK Biobank application 10279. UK Biobank is a large resource for identifying determinants of human diseases in middle-aged and older individuals .An imputed data set was made available as part of the UK Biobank interim data release. The 1000 Genomes phase 3 and UK10K haplotype reference panels were merged and the genotype data imputed to this merged reference panel. Further details can be found at the following URL: Published summary results from international GWAS consortia were gathered to derive genetic correlations using the linkage disequilibrium (LD) score regression method and perform polygenic profile score analysis between the UK Biobank tiredness variable and the genetic predisposition to multiple health-related traits. Details of the health-related variables, the consortia’s websites, key references for each consortium and number of subjects included in each consortium’s GWAS are given in Spearman’s rank correlation coefficients were calculated between responses to the tiredness question, grip strength, forced expiratory volume in 1 s, height, BMI, self-rated health, verbal-numerical reasoning and neuroticism, all of which were measured phenotypes in UK Biobank. Details on measurements of these phenotypes can be found in the https://mathgen.stats.ox.ac.uk/genetics_software/snptest/snptest.html#introduction. An additive model was specified using the ‘frequentist 1’ option. Genotype uncertainty was accounted for by analysing genotype dosages.A total of 111 749 individuals answered the tiredness question and had genotypic information. After visual inspection of the distribution of the UK Biobank tiredness variable no exclusions were made. Prior to analysis, tiredness was adjusted for age, sex, assessment centre, genotyping batch and array, and 10 principal components for population stratification. Genotype–phenotype association analyses were conducted using SNPTEST v2.5.1 ref.  and can 48 grip strength, forced expiratory volume in 1 s, neuroticism,49 verbal-numerical reasoning.50 We specifically examined whether any variants associated with tiredness were also associated with grip strength, self-rated health and neuroticism because we judged these to provide some coverage of physical and mental resilience in UK Biobank.Genetic association analyses were also performed on the following UK Biobank phenotypes to perform further analyses: self-rated health,51 This analysis included only unrelated individuals, using a relatedness cutoff of 0.025 in the generation of the genetic relationship matrix.To estimate the proportion of variance explained by all common SNPs in tiredness, univariate GCTA-GREML analysis was performed.52 using the summary GWAS statistics for tiredness. SNPs were assigned to 18 062 genes using the National Center for Biotechnology Information build 37.3. The gene boundary was defined as the start and stop site of each gene. To account for LD between the SNPs used, the European panel of the 1000 Genomes data  was used. A Bonferroni correction was used to control for 18 062 tests .Gene-based associations were derived using MAGMA,et al.;53 more details on this method can be found in the The summary statistics from the GWAS on tiredness was partitioned into functional categories using the same data processing pipeline as Finucane 55 Bivariate LD score regression was performed between tiredness and 29 health-related traits. Polygenic profile score analysis was performed on 26 of the 29 health-related traits, as this method requires independent samples to provide the summary GWAS information from which the polygenic profile score is computed.Genetic associations between tiredness and health-related variables from GWAS consortia were computed using two methods, LD score regression and polygenic profile score analysis. Each provides a different metric to infer the existence of loci contributing to pairs of traits. LD score regression was used to derive genetic correlations between two traits; this tests the degree to which the polygenic architecture of one trait overlaps with that of other traits. Polygenic profile score analysis was used to test the extent to which individual differences in the tiredness phenotype in UK Biobank could be predicted by polygenic profile scores predictive of the health-related traits from other GWAS consortia. Both of these methods are dependent each on trait being polygenic in nature, that is, where a large number of variants of small effect contribute towards phenotypic variation.Bivariate LD score regression56 This technique examines the correlational structure of the SNPs found across the genome. In the present study, LD score regression was used to derive genetic correlations between tiredness and health-related traits using the GWAS results of 25 large GWAS consortia and four UK Biobank phenotypes. The data processing pipeline devised by Bulik-Sullivan et al.55 was followed. To ensure that the genetic correlation for the Alzheimer’s disease phenotype was not driven by a single locus or biased the fit of the regression model, a 500-kb region centred on the APOE locus was removed and this phenotype was re-run. This additional model is referred to in the tables and figures as ‘Alzheimer’s disease (500 kb)’.This was used to quantify the extent of genetic overlap between tiredness in UK Biobank and 29 health-related traits.Polygenic profile scores46 Polygenic profile scores were created for 25 health-related traits in all genotyped participants using PRSice.57 Prior to creating the scores, SNPs with a minor allele frequency <0.01 were removed and clumping was used to obtain SNPs in linkage equilibrium with an r2<0.25 within a 200 bp window. Five polygenic profile scores were created for each trait including SNPs according to their significance of association with the relevant trait at P-value thresholds of P<0.01, P<0.05, P<0.1, P<0.5, and all SNPs.The UK Biobank genotyping data were recoded from numeric  allele coding to standard ACGT coding using a bespoke programme developed by one of the present authors (DCML).58 Sensitivity analyses were performed to test whether the results were confounded by individual’s neuroticism levels, their self-rated health scores or a diagnosis of major depressive disorder. This was done by adjusting the models for the neuroticism and self-rated health scores. Individuals with a probable diagnosis of major depressive disorder were excluded from the sensitivity analysis, based on the diagnostic method formulated by Smith et al.59 Further details can be found in the Regression models were used to examine the association between the polygenic profile scores and tiredness in UK Biobank, adjusting for age at measurement, sex, genotyping batch and array, assessment centre, and the first 10 principal components for population stratification. All associations were corrected for multiple testing using the false discovery rate (FDR) method.52Gene-based associations for tiredness were compared with gene-based results for other UK Biobank health-related traits that, in the present report’s results, showed a statistically significant genetic correlation with tiredness, using previously described methods.On the basis of the age and sex distribution for tiredness , furtherThe code used to run the analysis is available from the authors upon request.A total of 108 976 individuals from UK Biobank with genotypic data answered the question ‘Over the past two weeks, how often have you felt tired or had little energy?’, referred to hereinafter as ‘tiredness’. There were 51 416 individuals who answered ‘not at all’, 44 208 individuals responded ‘several days’, 6404 individuals answered ‘more than half the days’ and 6948 individuals responded ‘nearly every day’. Correlations indicated that individuals who reported feeling more tired tended to have lower grip strength, lower lung function, poorer self-rated health, lower scores for verbal-numerical reasoning and shorter stature . CorrelaP=1.36 × 10−11) on chromosome 1  and 6.86 × 10−8  for each peak, respectively. The peak on chromosome 1 contains three genes . The peak on chromosome 17 contains one gene (PAFAH1B1). The CRY/TYW3 locus has previously been associated with circulating resistin levels, a hormone associated with insulin resistance, inflammation, and risk of type 2 diabetes and cardiovascular disease.60SLC44A5 encodes a solute carrier protein and is important for metabolism of lipids and lipoproteins, and has been associated with birth weight in cattle.61PAFAH1B1 encodes a subunit of an enzyme that has important roles in brain development and spermatogenesis. Mutations in this gene cause the neurological disorder lissencephaly.62There was one genome-wide significant SNP  of the phenotypic variation of tiredness as measured in UK Biobank.DRD2, PRRC2C, C3orf84, ANO10 and ASXL3, that attained genome-wide significance for tiredness  were significant across phenotypes. Grip strength showed less overlap, with only C3orf84 being nominally associated with grip strength. Of the five genes examined here, C3orf84 was associated with each of these four phenotypes. Whereas the genetic correlations between these traits (see below) are likely to encompass multiple genic and non-genic regions, as well as unique points of overlap between pairs of phenotypes, the variants found in the C3orf84 represent a point of the genome where the genetic architecture of these four traits converges.In addition, each of these genes was also nominally significant in a GWAS of neuroticism, with P=0.0004). By clustering the histone marks into tissue-specific categories, we found significant enrichment for variants found in the central nervous system (P=0.0002).From the full baseline model using 52 annotations, only evolutionarily conserved regions were found to be enriched for tiredness . This ans system . This carg=0.20), C-reactive protein (rg=0.17=0.02), HbA1c (rg=0.25), obesity (rg=0.21), smoking status (rg=0.20), triglycerides (rg=0.13), type 2 diabetes (rg=0.18), waist–hip ratio (rg=0.28), attention deficit hyperactivity disorder (rg=0.27), bipolar disorder (rg=0.14), major depressive disorder (rg=0.59), neuroticism (rg=0.62) and schizophrenia (rg=0.25). Negative significant (FDR corrected) genetic correlations were found between high-density lipoprotein (HDL) cholesterol (rg=−0.11), forced expiratory volume in 1 s (rg=−0.12), grip strength (rg=−0.16), longevity (rg=−0.39), self-rated health (rg=−0.78) and verbal-numerical reasoning (rg=−0.14). These genetic correlations suggest that there are common genetic associations between tiredness and multiple physical- and mental health-related traits. LD score regression was used to test whether genetic variants associated with health-related traits also contribute towards tiredness in UK Biobank. β’s between 0.008 and 0.026) in UK Biobank: BMI, low-density lipoprotein (LDL) cholesterol, coronary artery disease, C-reactive protein, HbA1c, obesity, smoking status, triglycerides, type 2 diabetes and waist–hip ratio. Higher polygenic profile scores for HDL cholesterol and height predicted lower tiredness .The full results including all five thresholds can be found in β’s between 0.008 and 0.028). Polygenic profile scores for childhood cognitive ability showed a negative association with tiredness (β=−0.011).Of the mental health traits, higher polygenic profile scores for bipolar disorder, neuroticism, major depressive disorder and schizophrenia were associated with increased tiredness , C-reactive protein, HbA1c, triglycerides, waist–hip ratio, childhood cognitive ability and schizophrenia remained significant (after FDR correction), indicating that these associations are not wholly confounded by scores for neuroticism. Similar analyses controlling for self-rated health indicated that the following associations with tiredness are not wholly confounded by self-rated health: bipolar disorder, neuroticism, major depressive disorder and schizophrenia. N=7364) from all individuals with sufficient information about their mental health to make a probable depression diagnosis , the associations between tiredness and eight polygenic profile scores remained significant (after FDR correction), compared to nine in the full model, the association between type 2 diabetes and tiredness became non-significant after excluding individuals with probable diagnosis of major depressive disorder (N=725), the association between tiredness and the polygenic risk score for diabetes remained significant, indicating that this association is independent of self-reported morbidity for that disorder.When excluding individuals with a probable diagnosis of major depressive disorder  showed that polygenic profile scores for the following traits contributed independently to the association with tiredness: BMI, HDL cholesterol, triglycerides, waist–hip ratio, childhood cognitive ability, major depressive disorder, neuroticism and schizophrenia. The scores together accounted for 0.25% of the variance in tiredness .N=57 165) in females and 8.2%  in males. h2=19.8%, s.e.=6%, N=10 798) and males aged 60–70 years . Genome-wide association analysis indicated no significant sex differences between males and females, but did show some significant age differences in males =0.04–0.26, P=0.0074) and females , as the confidence intervals were overlapping. Also, no significant differences in the genetic correlations were found between waist–hip ratio and tiredness for males  and females , with overlapping confidence intervals.GCTA-GREML analysis was used to test for possible differences in the heritability estimates for tiredness in different age/sex groups. The proportion of variance in tiredness explained by all common genetic variants using GCTA-GREML was 9.4%  have previously been associated with insulin resistance, inflammation, risk of type 2 diabetes, metabolism of lipids and lipoproteins, and cardiovascular disease.16 These genes are consistent with the identification of regions associated with both tiredness and metabolic irregularities, and perhaps more broadly with ‘metabolic syndrome’ and ‘allostatic load’. PAFAH1B, within a suggestive peak on chromosome 17 has important roles in brain development.17 This is consistent with the identification of regions associated with both tiredness and cognitive traits, and the finding of significant enrichment for variants found in the central nervous system.In answer to our first research question—is there a direct genetic contribution to self-reported tiredness 53 suggesting that these are important loci where common additive SNPs cluster to produce phenotypic variation in many traits, as explored in more detail in the paper by Hill et al.67 The range of factors—affective, cognitive, behavioural and physical—that are genetically associated with tiredness is in itself remarkable, and confirms the observation of Landmark-Høyvik et al.,34 quoted in the introduction, that the related construct of fatigue is aetiologically heterogeneous and multifactorial. No overlap has been found with genes  identified in previous GWAS of fatigue;40 however, the sample size of these studies was too small to have enough power to detect statistically significant differences. The present study did not show significant associations for candidate genes previously identified.34Evolutionarily conserved regions were found to be enriched for association with tiredness, consistent with findings for other quantitative traits including disease status,38 This study estimated the SNP-based heritability of self-reported tiredness at 8.4%, and also examined age- and sex-specific heritability. No differences were found between males and females, but the results suggested a higher heritability in males aged between 40 and 50 years, compared to males between 60 and 70 years. Previous twin studies have shown inconsistent results regarding the sex-specific heritability. One study reported a higher heritability for prolonged fatigue (fatigue for more than one month) in males,36 whereas another reported a higher heritability for ‘interfering’ fatigue (fatigue for >5 days) in females.35 One study reported no sex differences in the heritability of chronic fatigue.36 In summary, the answer to our first question is that, whereas tiredness is, as expected, largely causally heterogeneous, there may be a small but significant, direct genetic contribution to tiredness proneness.The results of the present study add to the body of evidence that tiredness has a genetic underpinning.et al,34 quoted in the introduction, that the related construct of fatigue is aetiologically heterogeneous and multifactorial. This may seem a relatively trivial finding whether we assume that it simply reflects the sum of genetic factors that are primarily associated with other more specific phenotypes, which cause tiredness in one way or another. However, it is important to recall that the biobank data capture illness propensity rather than actual morbidity. In our sensitivity analysis, we controlled for the presence of type 2 diabetes and found that the genetic link between type 2 diabetes and tiredness remained significant. This would indicate that, for this health marker at least, tiredness and illness proneness are genetically related irrespective of the presence of morbidity. Similarly, the genetic association between tiredness and longevity would argue for a non-trivial link between self-reported tiredness and a more general tendency to poor health.In answer to question two—is tiredness genetically linked to proneness to health-related traits?—we can answer in the affirmative. The range of factors—affective, cognitive, behavioural and physical—that are genetically associated with tiredness is in itself remarkable, and confirms the observation of Landmark-Høyvik 68 including cholesterol, triglycerides, HbA1c, waist–hip ratio, BMI, obesity and type 2 diabetes. Several of these factors are biomarkers of allostatic load.62 The concept of allostatic load has been used in the context of both physical and mental ill health, including the symptom of fatigue. Conceptually, allostatic load represents the cumulative, physiological ‘wear and tear’ of a prolonged response to a stressor. Allostatic load has been shown to be a reliably-measurable multi-variate construct,70 with first-order factors comprising cardiovascular, immune, metabolic, anthropometric and neuroendocrine markers.29 It is hypothesised that, in response to threats to homeostasis, the body’s self-regulatory mechanisms, such as the sympathetic–adrenal medullary axis and the hypothalamic pituitary adrenal axis, have the potential to ‘overcompensate and eventually collapse upon themselves’,29 with consequences for morbidity and mortality.This takes us into the territory of question three—is tiredness genetically linked to a systemic proneness to poor health? To begin to answer this, we examined the genetic associations between tiredness and putative markers of allostatic load. Tiredness showed significant shared heritability with a range of factors associated with the metabolic syndromeIn our current analysis, we included metabolic , anthropometric  and cardiovascular/respiratory  markers of allostatic load. The results showed significant shared genetic aetiology, as measured by both LD score regression and polygenic profile score analysis, between tiredness and most of the metabolic and anthropometric markers, though not the cardiovascular/respiratory markers. This raises the possibility that the genetic overlap between tiredness and these physiological factors may be due to a biological propensity to an over-compensatory physiological stress response. This suggestion will require further investigation, because a more parsimonious explanation of these links would be that there is a genetic link between tiredness and multiple, separate genetic determinants of poor physical health. However, the substantial genetic correlations between these traits, and between these traits and tiredness provide some evidence that the allostatic load concept does have coherence at the genetic level.et al.,49 also using this UK Biobank sample, supports that the physiological and affective dimensions of poor health overlap in neuroticism. That paper showed that polygenic profile scores for several physical and mental health traits—BMI, coronary artery disease, smoking status, bipolar disorder, borderline personality, major depressive disorder, negative affect and schizophrenia—significantly predicted neuroticism. In the present study, when tiredness polygenic profile score analyses were adjusted for neuroticism, the associations between tiredness and mental health disorders (bar schizophrenia) were largely attenuated, whereas most of the metabolic and anthropometric associations remained significant. This suggests that it is the propensity to neuroticism, rather than the specific propensity to these disorders, that accounts or mediates the tiredness associated with mood disorders. Watson and Pennebaker,71 discussing competing models of how negative affectivity is related to self-reported physical and emotional well-being, found that it is associated as much with the former as with the latter, and that negative affectivity might better be conceptualised as a general tendency to experience both somatic and emotional distress. This concept of a general tendency to what they termed somatopsychic distress could explain the pleiotropy observed in the present study between neuroticism and tiredness.Fourth, to answer the question on the genetic associations between tiredness and the personality trait of neuroticism, which is the tendency to experience negative affective states, these were indeed strongly correlated, both phenotypically and genetically. This may represent a separate route to fatigue, a predominately affective one, and/or it may overlap with the physiological factors described above. A recent paper by Gale et al.,49 investigating shared genetic aetiology between neuroticism and physical and mental health, where there were more and stronger genetic associations between neuroticism and mental health than between neuroticism and physical health. If we take self-rated health to be a marker, to some extent, of actual physical health , then this would suggest that when physical health is adjusted for, polygenic profile scores for neuroticism and its associated negative affective states, continue to make a unique contribution to tiredness.That neuroticism may also be a distinct route to fatigue is supported by the fact that when the polygenic profile score analysis is adjusted for self-rated health, all associations between polygenic profile scores for physical health and tiredness are attenuated to the point of non-significance, whereas the relationship between tiredness, and polygenic profiles for neuroticism, major depressive disorder and bipolar disorder remain significant. This is consistent with the study of Gale et al.,49 the only significant result between neuroticism and physical disease state was a significant association with the polygenic risk score for coronary artery disease, which is suggestive of an overlap of affective and cardiovascular stress responses. This multifactorial understanding of fatigue would also allow us to incorporate childhood cognitive ability (reduced ability to problem solve), smoking status  and grip strength  into a more general model that is suggestive of shared genetic variance between stress proneness , the physiological response to stress (biomarkers), behavioural responses (smoking), self-reported tiredness, disease and mortality.72 However, as with our discussion of allostatic load, these links are suggestive not conclusive, and will require further empirical and theoretical investigation.These proposed affective and physiological routes to fatigue may not be mutually exclusive. The allostatic load model, and the multifactorial models of fatigue described in the introduction, postulate that individual differences in personality, cognition and behavioural responses to stress, and socio-cultural factors, affect the physiological stress response. An increased propensity to experience distress, as captured in the concept of neuroticism, would imply that there is increasing propensity to over-respond to stressors and thus to physiological dysregulation. In the study by Gale The large sample size of the present study is a strength of this study, providing powerful and robust tests of shared genetic aetiology between tiredness, and physical and mental health. A second strength is that all genetic samples were processed on the same platform at the same location. The use of summary data from many international GWAS consortia provided foundations for a comprehensive examination of shared genetic aetiology between tiredness and a wide range of health-related phenotypes.The study has some limitations. The amount of variance explained by the polygenic profile score analysis was small, which would be expected as not all SNPs are genotyped. The SNPs that were genotyped do not necessarily accurately tag the causal genetic variants. All analyses were restricted to individuals of white British ancestry, because the sample does not have enough power to generalise results for individuals with different backgrounds. Also, the sample consisted of middle- and older-aged adults, thus limiting its generalisability to the adult population as a whole. However, as mentioned in the introduction, there are no clear age-related differences in levels of self-reported fatigue. This could be taken as an indication that the phenomenon is fairly stable across the adult life course, at least at the level of phenotype. Whether the genetic determinants are different in younger adults is a topic for future research.73 observed, an objective measure of fatigue is ‘an unattainable holy grail’. Almost all the studies cited in the introduction have used subjective self-reports. The self-report measures used vary widely, with there being several validated fatigue measures, and many of the reported studies use either double- or single-item questionnaires and/or single item visual analogue scales. This in itself may account for some of the inconsistency in fatigue research, though the demographic studies cited at the beginning of this article, using a wide variety of measures from single questions7 to a well-validated fatigue questionnaire,2 produced similar findings. However, our findings of genetic associations of fatigue will need replication with better validated multi-item measures.A further limitation of the present study is the fact that tiredness was measured by self-report; that is, that we were looking for objective correlates of a subjective construct. However, as Wessely42 Like the psychosocial and biological fatigue research cited in our introduction, this work is predicated on the notion that, whereas fatigue shows up as a response to many physical and psychosocial stressors, its determinants may be shared across conditions. As such, we should distinguish between the effective cause of fatigue (the illness/stressors that set it going), and the material and formal causes .74 Whereas the effective causes might be various, the material and formal causes are likely to be more limited and shared across individuals and precipitating conditions. Even if this is not the case, we judge that the present study has gone some way to specifying the nature of the heterogeneity of tiredness at the genetic level, and that there are several non-trivial insights that will require further investigation, specifically: the links between tiredness and illness proneness as distinct from actual morbidity; the genetic coherence of the allostatic load concept and its contribution to tiredness; and the nature of the shared genetic and phenotypic links between tiredness and the personality trait of neuroticism. In terms of the genetic contributions to this complex phenomenon, the current study is probably best seen as the first attempt to use a large and relatively well-powered GWAS to identify these areas for future research.Perhaps a more serious concern is the one signalled in the introduction: that fatigue is too causally heterogeneous a trait to meaningfully study at the genetic level. To address this, it is worth situating this research in the context of other recent and ongoing fatigue research, such as the recently announced National Institute of Health Mechanisms of Fatigue programme. The latter, while acknowledging that fatigue ‘is a common co-morbid condition in a multitude of disease conditions’, is attempting to define whether ‘molecular, cellular or imaging signatures of fatigue can be defined’.Being genetically predisposed to a range of mental and physical health complaints also predisposes individuals to report that they are more tired or lacking in energy. This study confirms that self-reported tiredness is a partly heritable, heterogeneous and complex phenomenon that is phenotypically and genetically associated with affective, cognitive, personality, health and physiological processes. This study also served as a first step in testing some genetic hypotheses from the allostatic load model, finding suggestive links between tiredness and three genes on chromosome one associated with allostatic processes and considerable genetic overlap between tiredness and allostatic markers. We can foresee more tests of these links as more genome-wide genotyping data become available.