P ≤ 1.0 × 10−6). mLOY genome-wide association study signals exhibit polygenic architecture and demonstrate strong heritability enrichment in regions surrounding genes specifically expressed in multipotent progenitor (MPP) cells and HSCs (P ≤ 3.5 × 10−6). ChIP-seq data demonstrate that binding sites of FLI1, a fate-determining factor promoting HSC differentiation into platelets rather than red blood cells (RBCs), show a strong heritability enrichment (P = 1.5 × 10−6). Consistent with these findings, platelet and RBC counts are positively and negatively associated with mLOY, respectively. Collectively, our observations improve our understanding of the mechanisms underlying mLOY.Mosaic loss of chromosome Y (mLOY) is frequently observed in the leukocytes of ageing men. However, the genetic architecture and biological mechanisms underlying mLOY are not fully understood. In a cohort of 95,380 Japanese men, we identify 50 independent genetic markers in 46 loci associated with mLOY at a genome-wide significant level, 35 of which are unreported. Lead markers overlap enhancer marks in hematopoietic stem cells  is associated with age and smoking but also genetic factors play a role. Here, Terao et al. perform GWAS for mLOY in 95,380 Japanese men and identify 46 loci that overlap with hematopoietic stem cell enhancers and transcription factor binding sites critical for hematopoiesis. Age4 and smoking5 are well established risk factors for mLOY, however, the broader mechanisms that influence mLOY, including the stage(s) of hematopoietic differentiation during which mLOY arises, are not fully known. Genetic analysis can provide biological insight into the basis of this phenomenon. The same array-based assays can provide information about single-nucleotide polymorphism (SNP) genotype and, from intensity data of genome-wide probes, allow inference of mosaic events7. This has allowed previous studies to identify some genetic determinants underlying mLOY. Zhou et al. reported that mLOY is associated with a variant in the TCL1A gene locus8. Wright et al. identified a total of 19 loci associated with mLOY9, including TCL1A and other genes involved in cell cycle regulation and DNA damage response. Previous studies examined European populations, so genetic studies from an East Asian population would expand our knowledge of the genetic architecture underlying mLOY, in turn allowing us to make deeper biological inferences about mLOY based on expanded genetic findings.Mosaic loss of chromosome Y (mLOY)10. Previous studies reported that mLOY is associated with shorter life span and increased risk for cancer onset12. Other studies suggested that mLOY is associated with onset of acute myeloid leukemia (AML) or other hematological disorders14. However, Zhou et al. did not find significant differences in overall survival or cancer-specific survival in data from 5340 cancer cases8. No studies have analyzed the clinical significance of mLOY in Asian populations. Although the clinical significance of mLOY is not well established, clarifying the mechanisms of chromosome loss may provide a deeper understanding of clonal expansion during hematopoiesis, cellular ageing, and cancer development. Furthermore, there is a possibility that mLOY has a distinct clinical impact in Asian populations.The clinical significance of mLOY is still unclear15. We examine the genetic architecture of mLOY, performing the genome-wide association study (GWAS) of this condition in an East Asian population. To infer biological mechanisms driving mLOY, we conduct downstream analyses using our GWAS results, making inferences based on overlap of associated variants and polygenic mLOY heritibility with functional elements to pinpoint the cell types and gene pathways involved in mLOY. Furthermore, we conduct association studies between mLOY and survival data of the participants to evaluate the clinical significance of mLOY in an Asian population.Here, we use genotype array data from 95,380 Japanese males enrolled in the Biobank Japan Project (BBJ) to study mLOYThe data were generated in three separate batches due to advances in genotyping platforms during data collection. Detailed description of the samples is shown in Supplementary Table 9 to estimate mLOY in our data. We obtained logarithm of R ratio (LRR) probe intensity data across more than 1100 variants (depending on batch) in chromosome Y for each male subject. We used mean LRR (mLRR-Y) as a proxy for mean Y chromosome dosage in circulating blood cells of subjects . Hereafter, we use the term ‘mLOY GWAS’ to denote GWAS on mLRR-Y, as in Wright et al.9.We applied a method similar to that used in Wright et al.P < 1.0 × 10−100, Wald test in linear regression analysis, Fig. P = 7.5 × 10−10, Wald test in linear regression analysis). These associations are in agreement with previous studies5.We observed a strong association between age at DNA collection and mLOY (1 year increase in age associated with 2.2% standard deviation (SD) decrease in mLRR-Y signal, 17  and a reference panel of whole-genome sequenced individuals, including 2504 individuals from the 1000 Genomes project phase 3 and 1,037 Japanese18, with the use of ldsc software. This regression analysis suggested that mLOY is a highly polygenic trait and that departure of mean chi-squared statistics could be largely explained by polygenic effects . When considering only the 31 novel loci, this trend remained consistent; twenty-five variants were polymorphic and had MAF >0.5% in the UK population, and 23 out of the 25 variants had the same effect direction in the two studies , indicating strong genetic overlap in association with mLOY between the two populations.To further assess similarities and differences in the genetic architecture of mLOY across populations, we examined associations of the 46 loci with mLOY in 205 thousand male participants in the full UK Biobank release (Supplementary Table 20. We found a strong overlap between the variants and enhancer marks present in hematopoietic stem cells (HSCs)  showed overlap with enhancer marks in HSCs  Fig. . This fi23 using ldsc (see the Methods section). Superenhancer, H3K27ac, and transcription start site (TSS) were the top three categories with positive and significant heritability enrichment  using ATAC-seq data of hematopoietic progenitor cells and lineages at different differentiation stages26. Genes expressed in MPP and HSC, evidenced by open-chromatin state assessed by ATAC-seq, showed the strongest and the 2nd strongest heritability enrichment with mLOY, respectively  and common myeloid progenitor (CMP), as well as HSC27. Thus, we hypothesized that overlap of genetic associations with TF-binding sites in various hematopoietic cells may provide information about lineage- or context-specific influence on mLOY. We used available chromatin immunoprecipitation sequencing (ChIP-seq) data to help identify TFs involved in mLOY. We obtained a total of 37 ChIP-seq data sets derived from CD34-positive cells or HSCs . Binding sites of three transcription factors, namely, FLI1, GATA2, and RUNX1, showed significant overlap with regions positively enriched in mLOY heritability . Heritability enrichment in FLI1-binding sites was not seen in the 11 other cell types for which FLI1 ChIP-seq data were available, supporting the biological specificity of this result; heritability of mLOY is enriched in binding sites of FLI1 in CD34-positive cells  play a critical role in hematopoietic cell differentiation and function31 to develop into megakaryocytes and thus produce platelets rather than erythrocytes33. Therefore, we analyzed the association between mLOY and hematologic traits (including platelet count and red blood cell (RBC) count) using data from 57,987 subjects from whom complete blood counts (CBC) were available at the time of DNA collection. mLOY was positively associated with platelet count  associated with 0.03 SD decrease in mLRR-Y signal, P = 7.6 × 10−14, Wald test in linear regression analysis) and WBC count . PASCAL takes not only GWAS significant loci but whole-genome signals into consideration. We found that gene scores calculated based on the GWAS signal of mLOY showed the strongest and most significant enrichment in cell cycle pathways and a mitotic pathway  . There was no association between mLOY and overall survival  were more likely to have experienced an adverse outcome , Fig. Genome instability, including chromosome rearrangements and loss, is a central event in development of some cancers, so genetic determinants that increase susceptibility to mLOY may influence cancer risk. We therefore analyzed whether the associations between mLRR-Y and mortality were mediated by malignances. We found a significant association between mLOY and death due to lung cancer (9), we used the mean of LRR as a proxy of chromosome Y copy number. Using the mean, rather than the median, of LRR allows that some strongly deviated markers could unduly influence estimation of chromosome Y dosage. However, we found that the median and mean are strongly correlated (Spearman’s rho: 0.993) and lead to quite similar genetic association results . Since recent studies have revealed that mosaic events frequently occur systemicallyOur study also analyzed association between mLOY and survival at an unprecedented scale. While we could replicate a trend of poor outcome in subjects with a high burden of mLOY, the clinical significance of mLOY was not very apparent in our study. Since this is a large study to analyze effects of mLOY on clinical outcomes in an Asian population, it is possible that the clinical significance of mLOY is not the same across all populations. However, it is also possible that mLOY is associated with onset of specific types of cancer and/or context-dependent survival, such as poor outcome in specific diseases, which could not be fully captured by our population cohort.39, suggesting the strong overlap of susceptibility loci for mLOY between the two populations. Considering common genetic background of mLOY, susceptibility loci which are found significant only in one population suggest that the causal variants in these loci are polymorphic only in that population. In addition, taking advantage of genetic overlap seemed to help us to pinpoint shared causal variants of susceptibility loci.While different LD structure between Japanese and UK population made it difficult to quantify genetic similarities of mLOY between the two populations, we showed that significant variants found in the BBJ very often shared direction of effect on mLOY in the UKB. We tried to replicate 156 significant variants found in UKB, as a result, 92 out of the 100 variants which were polymorphic and passed QC showed shared direction in effectFurther in-depth analysis including trans-ethnic meta-analysis could reveal additional genetic components and context-specific clinical significance of mLOY. Because we showed mLOY shares genetic architecture across populations, trans-ethnic meta-analysis would be attractive to increase the number of associated loci and to obtain further biological insights from finer resolution functional inference. The association between mLOY and clinical outcomes should be replicated to resolve the clinical impacts of mLOY and develop management protocols for elderly populations. Disease-specific associations of mLOY should be analyzed in disease-specific data sets rather than population cohorts.40. In this study, we used genotype data from three different sets using four different arrays, namely, (1) HumanOmniExpressExome v1.0, (2) HumanOmniExpressExome v1.2, and (3) a combination of Illumina HumanOmniExpress v1.0 and Human Exome v1.0 or v1.1 BeadChips. A breakdown of the subjects and arrays is given in Supplementary Table We used 183,899 subjects in the BBJ project for selection of samples to analyze for this study. Written informed consent was obtained from all the participants. The study was approved by the ethical committees in the Institute of Medical Science, the University of Tokyo and RIKEN Center for Integrative Medical Science. Most of the subjects had already been genotyped using genome-wide genotyping arraysUsing log-R ratio (LRR) generated by Illumina GenomeStudio software, mean LRR in Y chromosome (mLRR-Y) was calculated and used as a proxy of mLOY as follows. We extracted only male subjects and reclustered the subjects based on their probe signal intensities in variants on chromosome Y. This step was performed separately for each type of array. We did not use intensity data of Human Exome BeadChip to avoid batch effects within the same subjects. We obtained LRR for all variants on chromosome Y excluding the pseudoautosomal regions, and subjects and variants with missing rate higher than 5% (restricted to the Y chromosome) were excluded from mLRR-Y calculation. As a result, 1268, 1305, and 1162 variants remained for calculation of mLRR-Y in the three batches described above, respectively. We set LRR in variants with missing genotypes as missing. We then standardized LRR in each variant, and calculated mean of LRR in each subject across variants on chromosome Y. The mLRR-Y was standardized per batch and used as a signal reflecting mLOY in the subjects. We took this approach to avoid strong influence of limited number of variants with extreme values of LRR. To confirm that our data did not suffer from noise due to variants with extreme LRR, we also took median of LRR signals in each individuals among the variants and conducted GWAS with the use of median LRR instead of mLRR-Y.r2 of 0.5) and conducted principal component (PC) analysis to project subjects in PC1 and PC2 space, included in the reference panel mentioned below (939 samples) or showing a missing rate higher than 2% (0 sample at this stage). Finally, we obtained data of 95,380 males whose probe intensity data in the Y chromosome was available for subsequent analyses. SNPs with missing rates more than 1%, Hardy–Weinberg equilibrium P-values <1.0 × 10−6 or heterozygote calls <5 in each of the three arrays were excluded.We excluded subjects found to be genetically identical to other subjects (321 samples), showing discrepancy between reported sex and inferred sex based on genotypes of variants on X chromosome (1245 samples), found to be outliers from the EAS (Japanese and Chinese) cluster (121 samples) in the analysis where we merged GWAS data with 1000 Genomes Project genotype data, pruned variants by excluding variants in moderate LD with other variants (with cutoff level of 41 and whole-genome sequence data (x30) of 1037 Japanese subjects16  >0.3 (to ensure imputation accuracy) and minor allele frequency >0.005 for association with mLOY. We applied the Bayesian mixed-model using bolt-lmm44 (URL). Age, arrays, smoking, and disease status  were included as covariates  by restricted maximum likelihood estimation (REML) to compute variance of genetic components.9. We conducted conditional analyses to confirm that two loci were independently associated with mLOY when the boundary of the two regions were <1 Mbp apart. If significant associations were observed in conditional analyses and adjacent loci were apart by >200 kbp but <1 Mbp, we regarded the two loci as different.Two associated loci on the same chromosome were regarded as different if a genome-wide significant marker at one locus was at least 1 Mbp apart from those in the other locus. This definition was also applied to regard significant loci in the BBJ as the same as or different from those described by Wright et al.P < 5.0 × 10−8) to the conditional analyses to define significant associations.We applied conditional analyses to identify independent signals in a single locus or adjacent loci. We incorporated dosages of a variant whose effect we would like to condition on as a covariate in linear mixed model. We applied the same threshold 1 of genotyping arraysr2 = 0.80), for this locus. A significant level of associations was set based on Bonferroni’s correction.We analyzed overlap between lead variants in significant loci associated with mLOY and enhancer marks in cells by Haploreg (URL) to infer cell types important for mLOY. Briefly, enrichment of lead SNPs for mLOY in enhancer histone marks in cell types was evaluated by comparing estimated overlap based on pruned variants in the 1000 Genomes Project with minor allele frequencies >0.05 in any population. The enrichment significance was computed by binomial test. Since Haploreg requires rs id of SNPs which is not available for Chr2:136879065, we used rs6751768, which is in strong LD with Chr2:136879065 (35 (URL) which takes LD structure of nearby genes into consideration. To avoid overestimation of GWAS significant variants, we calculated gene score for pathway analysis by PASCAL by using the sum of statistics of variants in single genes rather than the maximum of the statistics. Bonferroni’s correction accounting for all of the pathways  was used to set a threshold of statistically significant enrichment (P < 0.05/1077).We conducted pathway analysis with the use of the PASCAL software18. We regarded intercept in LD score regression <1.05 or ldsc ratio (an index estimating confounding bias of GWAS statistics) <0.3 as no confounding bias18.To evaluate the polygenic effect on mLOY and assess confounding bias leading to inflation of median chi-square statistics, we used LD score regression analysis with the use of ldsc software23 by ldsc. Briefly, the full baseline model contains coding, intronic, UTR, promoter, enhancer regions, histone marks, open-chromatin regions, and their extended regions, none of which are specific to any cell types23. Although ldsc uses chi-square statistics which are calculated from different distribution from that of bolt-lmm44, we confirmed similar results of ldsc between bolt-lmm chi-square statistics and normal linear regression chi-square statistics (with the same covariates as bolt-lmm). Thus we showed results of analyses with the use of chi-square statistics in bolt-lmm. We also applied to the analyses another full baseline model of ldsc recently reported including information of LD-related annotations, synonymous, and nonsynonymous annotations, ancient sequence age, and conserved function across species24.We evaluated enrichment of heritability of histone marks in cell groups or detailed cell types in each cell group by conditioning on the full baseline model described in Finucane et al.45 of mLOY and quantitative trait or malignancy susceptibility . We used GWAS of malignancy whose summary statistics are available in the BBJ36 . While samples were overlapped between traits, a genetic correlation estimated by ldsc is shown not to be affected by sample overlap since sample overlap does not change LD score45.We also used ldsc software to assess genetic correlation46 .We conducted Mendelian randomization analysis to assess causal relationship between mLOY and AST which showed a significant genetic correlation with mLOY  version 2.1 with default settings (q < 0.01). Through this analysis, we obtained a total of 2856 ChIP seq data. LD scores of transcription factor binding were constructed by extending 500 bp from the peaks in ChIP seq. We conducted partitioning heritability of GWAS data of mLOY by ChIP seq using ldsc. We first extracted 37 ChIP seq data, in which HSC was analyzed for transcription factor binding based on the results of enrichment analysis of significant variants in cell-specific enhancer marks and of cell-type or group analyses of partitioning heritability. We partitioned heritability of mLOY with the use of the LD scores of transcription factor bindings and the full baseline model by Finucane et al.23. In addition, we also analyzed the data with the use of the latest full baseline model described above.We used the ChIP-seq data in the previous report+ cells, we used LDSC-SEG48, a method recently developed to estimate heritability enrichment of gene expression (or open chromatin) in various tissues and cell types by taking advantage of tissue- and cell-specific eQTL data, which are available in the widest range of tissues and cell types. We used data from Corces et al.26 who generated ATAC-seq data of hematopoietic cell lineages, including CD34+ hematopoietic stem progenitor cells. We computed Japanese LD scores of cell-specific gene expression based on the ATAC-seq data by referring to European annotations for the analyses (we obtained very similar results regardless of the origin of LD scores). In this analysis, we used the full baseline model by Finucane et al.23 as baseline of LD scores. In addition, we also analyzed the data with the use of the latest full baseline model described above.To evaluate the important cell types among the CD3437. If a death was reported, a detailed search was conducted to identify causes of death coded by ICD10 by accessing the national vital registration system at the Japanese Ministry of Health, Labor, and Welfare. Further details are written elsewhere37. We extracted cancers with >1000 deaths overall, and analyzed lung, colon, esophagus, gastric, pancreas, hematologic and prostate/testis cancer as specific malignancies. To analyze associations between mLOY and malignancy mortality, we excluded subjects having had malignancy at registry, without information of follow-up period or with follow-up <1 year to exclude potential undiagnosed cancers and other fatal diseases. As a result, 54,887 subjects with follow-up period of mean 8.0 years and standard deviation of 2.4 years remained for the analyses. During the follow-up periods, 12,410 deaths were observed. We used the survival package of R statistical software. We set subjects who did not die during follow-up as controls and evaluated associations between mLOY and mortality of overall or specific diseases. In addition to the use of mLRR-Y signals as a quantitative trait, we used subjects with the lowest 3, 5, 10, and 20% of mLRR-Y signals as categorical variables and compared with subjects whose mLRR-Y signals not reaching the lowest 20%. The 20% cutoff was determined by the latest UKBB mLOY study which reports 20% of male subjects in the UKBB were positive for mLOY39. We used Cox proportional hazards regression for survival analysis to estimate associations between mLOY and the cause of death adjusting for age at DNA collection, data batches, disease status, and smoking.The living status  of a total of 141,612 BBJ subjects with one of 32 diseases was prospectively followed for more than 10 years after DNA collectionWe analyzed a total of 57,987 subjects for associations between mLOY and CBC data for inference of biological insights. We z-transformed CBC data to assess associations. Age, smoking, disease status, and data set were used as covariates in the association study. To test the hypothesis that subjects carrying high mLOY signals were strongly associated with CBC data, we took subjects carrying top 1, 3, 5, and 10% of mLOY signal . We divided all subjects in this study into two groups (binary traits), with or without top 1, 3, 5, and 10% of mLOY signals and associated the binary traits with the CBC data mentioned above together with covariates of age, smoking, disease status, data set with the use of logistic regression analysis.http://www.1000genomes.org/; for GWAS catalog, see https://www.ebi.ac.uk/gwas/; for LDSC and SEG-LDSC, see https://github.com/bulik/ldsc/; for PASCAL, see https://www2.unil.ch/cbg/index.php?title=Pascal; for Minimac, see https://genome.sph.umich.edu/wiki/Minimac; for Haploreg, see https://pubs.broadinstitute.org/mammals/haploreg/haploreg.php; for JENGER, see http://jenger.riken.jp/en/; for R, see https://www.r-project.org/; for Plink1.9, see https://www.cog-genomics.org/plink2; for bolt-lmm, see https://data.broadinstitute.org/alkesgroup/BOLT-LMM/; for LCR, see ftp://ftp.1000genomes.ebi.ac.uk/vol1/ftp/release/20130502/supporting/low_complexity_regions/hs37d5-LCRs.20140224.bed.gz.For 1000 Genomes Project, see Further information on research design is available in the Supplementary InformationReporting SummaryPeer Review File


The initial preference task (IPT) is an implicit measure that has featured prominently in the literature and enjoys high popularity because it offers to provide an unobtrusive and objective assessment of self-esteem that is easy to administer. However, its use for self-esteem assessment may be limited because of weak associations with direct personality measures. Moreover, moderator effects of sample- and study-related variables need investigation to determine the value of IPT-based assessments of self-esteem.N = 17,777) originating from 60 studies. Summary effect estimates and subgroup analyses for potential effect moderators  were calculated by means of meta-analytic random- and mixed-effects models. Moreover, we accounted for potential influences of publication year, publication status (published vs. not), and participant sex in a weighted stepwise hierarchical multiple meta-regression. We tested for dissemination bias through six methods.Conventional and grey-literature database searches, as well as screening of reference lists of obtained articles, yielded a total of 105 independent healthy adult samples (r = .102), indicating conceptual independence of these two constructs. Effects were stronger when the B-algorithm was used for calculation of IPT-scores and the IPT was administered only once, whilst all other moderators did not show significant influences. Regression analyses revealed a somewhat stronger  effect for men. Moreover, there was no evidence for dissemination bias or a decline effect, although effects from published studies were numerically somewhat stronger than unpublished effects.There was no noteworthy correlation between IPT-based implicit and explicit self-esteem (We show that there is no noteworthy association between IPT-based implicit and explicit self-esteem, which is broadly consistent with dual-process models of implicit and explicit evaluations on the one hand, but also casts doubt on the suitability of the IPT for the assessment of implicit self-esteem on the other hand. Personality psychology has been striving in the past to develop measures that are unobtrusive , easy to administer, and yet provide valid assessments of traits. Such ideas can be traced back to at least the 1960s . On theOn the other hand, in dual-process models implicit and explicit self-esteem are viewed as expressions of different largely independent cognitive processes e.g., ,10). Whi. Whi10])These different models lead to different expectations for explicit and implicit self-esteem associations. Whilst in common-core models a substantial association between these two constructs is expected, dual-process models suggest only weak correlations.An approach that has gained particular popularity for the assessment of implicit self-esteem is the initial preference task (IPT), as popularized by the procedure of Kitayama and Karasawa , perhapsIPT-based assessments of implicit self-esteem continue to enjoy considerable popularity in the literature. However, despite this, several conceptual questions about the IPT remain unanswered, particularly in terms of its usefulness for the assessment of self-esteem. In the extant literature, IPT scores are frequently treated as an indicator for the “self-evaluative climate” , whilst explicit self-esteem scores are considered to be an indicator for the “self-evaluative weather” .k = 19) showed that correlations between IPT-based scores and explicit self-esteem were small  or the decline effect .Potentially includable studies were initially coded independently by two researchers respectively  or twice by the same researcher [JP]. Correlation coefficients, sample sizes, sample percentage of men, mean participant ages, and publication years were recorded, and primary studies were coded into categories according to IPT exposure (single vs. double administration of the IPT), administration order of measures , publicZs and were subsequently backtransformed for ease of interpretation, following standard practice for r-based meta-analyses. Initially, we used random-effects estimators for the calculations of (subgroup) summary effect sizes. We consciously decided against using fixed-effect models because of the expected functional non-equivalence of studies .Prior to all analyses, correlation coefficients were transformed to Fisher s; e.g., , pp. 83–s; e.g., . FinallyIt should be acknowledged that many of the identified studies did not focus on the assessment of the relationship between the IPT and explicit self-esteem as their primary goal, which makes the occurrence of “traditional” publication bias less likely . However, summary effect-inflating mechanisms of selective reporting  are well-documented ,33 and wWe used seven methods to detect different forms of dissemination biases. For all these calculations, data were restricted to published results only . First, we visually inspected funnel plot asymmetry . Second,p-curve and p-uniform) that are based on the observed distributions of published significant p-values . Because only published and nominally significant values are considered, this makes effect estimates arguably insensitive to non-retrievable unpublished (and therefore likely non-significant) results and makes it possible to assess more insidious forms of dissemination bias such as p-hacking .Finally, we used two recently developed detection methods for dissemination bias . In the presence of a non-zero effect, p-value distributions should be significantly right-skewed, which can be assessed by either binomial tests  or continuous tests. The evidential value of a study set can be assessed by evaluating whether the observed p-value distribution is flatter than the theoretical p-value distribution at 33% power. Finally, effect sizes can be estimated by minimizing a loss function, thus yielding a curve (with a certain effect size associated to it), that most closely resembles the observed p-curve . This ip-uniform method [p-hacking by comparing the distribution of conditional p-values  with a uniform distribution. The population effect is estimated by obtaining the summary effect size that fits closest to a conditional p-value distribution. In a similar manner, confidence intervals for the summary effect are calculated. Moreover, a significance test of the population effect can be obtained by comparing the observed p-value distribution with a uniform distribution.A similar idea has led to the development of the m method , which ap-curve and p-uniform have been developed in the context of fixed-effect models and have been shown to systematically overestimate summary effects in presence of moderate to large between-study heterogeneity [p-values that are associated with effect sizes showing differing signs. Therefore, prior to data analyses, we decided to use only p-values associated with positive effect sizes , to provide an upper threshold of the population effect. All analyses were performed in SPSS, the open Source Software R [p-curve (www.p-curve.com [p-uniform web application (available from https://rvanaert.shinyapps.io/p-uniform/). We provide the code for all our calculations in the Online Supplement , and thpplement , exceptiurve.com ).N = 17,777; 35.4% men) were included in the meta-analysis. Mean ages of participants ranged from 18.4 to 37.7 years (weighted mean age = 25.1), and participants were from 14 different countries . The IPT was administered in pen-and-paper format (k = 42) or on a computer . In all, 62 samples used the B-, 26 the I-, 3 the R-, 3 the Z-, and 2 the S-algorithm to calculate IPT scores . For the assessment of explicit self-esteem, all studies used self-report questionnaires, with the Rosenberg Self-Esteem Scale (k = 90) being the most frequently reported measure. Characteristics and correlation coefficients of all included samples are detailed in the Online Supplement  between implicit and explicit self-esteem, indicating that the IPT shares about 1% of variance with explicit measures  = 1.04, p = .309; see I2 values  were small to medium-sized , thus iQ(1) = 3.40, p = .065; see uppermost two blocks of Q(1) = 2.426, p = .119), or rating type  = 2.88, p = .090). Interestingly, IPT scores obtained by using the B-algorithm correlated significantly stronger with explicit self-esteem than IPT scores obtained with any other algorithm  = 10.94, p < .001). Still, I2 values remained non-trivial , thus indicating some extent of true between-study heterogeneity. Moreover, double administration of the IPT yielded weaker associations with explicit measures than single administration  = 6.66, p = .010).Further subgroup analyses revealed no influence of administration order . However, because variance explanation of the models in all three steps of the regression analyses remained below the triviality threshold, our analysis indicates a lack of substantial influence of any of these three included predictors . A similar stability of the overall evidence was observed when categorizing in regard to publication status .Sensitivity analyses did not show noteworthy effects of single studies on summary effect size estimates  and last name IPT scores . However, these summary effects were based on a comparatively small number of samples (k = 18).Finally, we investigated correlations between first and last name IPT scores with explicit measures separately in a subset of our data, yielding trivial effects for first (p = .608), Sterne and Egger’s regression approach (p = .873), or the trim-and-fill method . Ioannidis and Trikalinos test of excess significance [p = .429), although more significant studies were observed than expected .Visual inspection of the funnel plot did not suggest evidence for publication bias in the present meta-analysis . Similarificance  did not p-curve analysis revealed no evidence for p-hacking, but showed that the available data provide evidential value . However, the included significant positive studies on average were underpowered  was somewhat stronger than the conventional meta-analytic estimate, as based on all studies. Evidently, this is due to the omission of significant negative effects within the p-curve on the one hand, and the assumption of a fixed-effect model on the other hand.Results from our p-uniform calculations, similar results were obtained. There was no evidence for p-hacking (p = .610), and the summary effect estimate was r = .154 (95% CI: .085 to .200). Again, the stronger summary effect, as compared with the conventionally calculated summary effect-size estimate, can be attributed to the necessary omission of all negative effect sizes that were nominally significant and the adoption of fixed-effect estimators.For the p-curve and p-uniform illustrate that these methods may be useful for the detection of several forms of dissemination bias, but might be less suitable and informative in the context of meta-analyses investigating small summary effects . However, it should be noted that both methods performed comparatively well when comparing their effect estimates with conventional meta-analytic estimates, when only effect sizes with positive signs were included in the random-effects (r = .140) and fixed-effect calculations (r = .138).The results from r = .102). This finding is consistent with an earlier meta-analytic estimate , but co = .115; . AssociaThese findings can be interpreted in two ways. On the one hand, the lack of a noticeable association between implicit and explicit self-esteem could indicate that both constructs, conceptually or practically, are unrelated. This may mean that implicit and explicit self-esteem are orthogonal dimensions that represent different constructs, a notion that already has received some support in the literature  and is On the other hand, our findings may indicate that the IPT is an unsuitable measure for the assessment of implicit self-esteem which appears to be supported by evidence from recent studies . This cIt has been argued that one explanation for small correlations between IPT-based implicit self-esteem and explicit self-esteem measures may be due to the low reliabilities of the IPT, which invariably must limit the observable strength of the correlation coefficient. Other causes, such as unique method variance or differences in conceptual approaches between explicit and implicit measures have also been cited as potential causes for such small correlations ,51.B-algorithm than for any other algorithm used. Because the B-algorithm does not control for individual response tendencies that are controlled for in other algorithms , this mIn a different vein, stronger correlations of single than double administrations of the IPT with explicit measures may be due to the already mentioned low retest reliability of the IPT on the one hand (which makes it more difficult to detect true effects), but also to responders increasingly recognizing the intended purpose of the IPT, on the other hand. This finding is consistent with those of a previous study . The forAnother meaningful factor may be that indirect measures such as the IPT may tap into states rather than traits . This mPreviously reported differences of administration order , indicatInterestingly, effect sizes were somewhat  stronger for ratings of letter attractiveness than for letter liking. This finding is consistent with the idea that liking and attractiveness evaluations may reflect different domains of implicit self-esteem .p-hacking.As expected, the regression coefficients indicated decreasing strengths of correlations over time  althougAlthough the above discussed causes are likely candidates to account for the small-to-trivial correlation between the IPT and explicit self-esteem scores, the implications for the use of the IPT (at least as a measure for implicit self-esteem) are somewhat disheartening. The suboptimal IPT stabilities and its conceptual ambiguity limit the evidential value that can be derived from IPT-based assessments.B-algorithms did not allow for meaningful comparisons of the B-algorithm with other calculation methods. Still, the present investigation suggests that the B-algorithm yields scores that might be more meaningfully associated with explicit self-esteem than scores from other popularized algorithms.Of course, a more detailed assessment of differences between the use of specific algorithms for implicit self-esteem score calculations would have been desirable. However, the comparatively low application numbers of non-k = 5) which may impair comparability between the observed effects. However, there was no significant difference between subgroup summary effects (p > .05).Some of the available studies used a compound measure of birthday number liking and the IPT as an indirect measure , althoup-curve- and p-uniform-based effect estimates. Both methods have been shown to overestimate effect sizes in presence of moderate between-study heterogeneity [p-values that are associated with hypothesis non-conforming effect directions  cannot be included in p-curve or p-uniform effect estimations, thus necessarily causing effect inflation of summary effects.Another point that needs to be noted is that the observed between-study heterogeneity limits the validity of ogeneity , which mIt would have been desirable to compare the results of our meta-analysis with the results of the samples that had been included in Krizan and Suls’ study . HoweverBased on the present findings, the validity of implicit self-esteem as measured by the IPT appears to be unclear. This may be partly due to the fact that many of the recommendations pertaining to the administration of the IPT e.g., ,12,14) h,14 h12,1In all, we show that there is no noteworthy association between IPT-based implicit and explicit self-esteem. These findings broadly support dual-process models of implicit and explicit evaluations but may also be due to suboptimal psychometric properties of the IPT on the one hand, and lacking validity of the IPT on the other hand. So far, the latent construct as measured by the IPT remains unclear. Further examination of IPT-based correlates with behavioral data may shed light on the meaning and nature of IPT scores.S1 Text(DOC)Click here for additional data file.S2 Text(DOCX)Click here for additional data file.S1 Table(DOCX)Click here for additional data file.S2 Table(DOC)Click here for additional data file.


DNA mutations that confer late‐life effects on female reproductive performance. This should lead to increased levels of mitochondrial genetic variation on reproduction at later‐life stages. We tested this hypothesis using thirteen strains of Drosophila melanogaster that each possessed a different mitochondrial haplotype in an otherwise standard nuclear genetic background. We measured fecundity and egg‐to‐adult viability of females over five different age classes ranging from early to late life and quantified the survival of females throughout this time period. We found no significant variation across mitochondrial haplotypes for the reproductive traits, and no mitochondrial effect on the slope of decline in these traits with increasing age. However, we observed that flies that died earlier in the experiment experienced steeper declines in the reproductive traits prior to death, and we also identified maternal and grandparental age effects on the measured traits. These results suggest the mitochondrial variation does not make a key contribution to shaping the reproductive performance of females.While numerous studies have demonstrated that mitochondrial genetic variation can shape organismal phenotype, the level of contribution the mitochondrial genotype makes to life‐history phenotype across the life course remains unknown. Furthermore, a clear technical bias has emerged in studies of mitochondrial effects on reproduction, with many studies conducted on males, but few on females. Here, we apply a classic prediction of the evolutionary theory of aging to the mitochondrial genome, predicting the declining force of natural selection with age will have facilitated the accumulation of mt To create the strains, mitochondrial haplotypes from each of these regions were placed alongside an isogenic nuclear background  by Clancy , we are unable to determine whether any detected mitochondrial genetic variation is sensitive to epistatic interactions with nuclear genetic variation. Our current study will therefore provide an important proof‐of‐principle of the applicability of the classic evolutionary theory of aging to the mitochondrial genome and serve as an important foundation for follow‐up studies that assess age‐related mitochondrial genetic effects across a broader array of nuclear genetic backgrounds.We note that this experimental design is highly controlled to allow us to home in on phenotypic effects that map unambiguously to the mitochondrial genome. One limitation of this design, however, is that by constraining our inferences to the one isogenic nuclear background  on a potato‐dextrose agar medium and were maintained under a constant 25°C and 12‐hr light‐dark cycle. To control for parental age effects, the grandparents of the focal flies were 2 or 3 days old and the parents 1 or 2 days old at the time of reproduction. Because grandparental and parental ages were not evenly distributed across classes, we combined these into a composite categorical variable with three levels for statistical analyses .w1118 isogenic strain for 24 hr, and then each female was moved to a separate “laying vial” for 20 hr. These laying vials each contained a plastic spoon filled with 1 ml of medium, stained black  to increase visibility of white eggs. Following this 20‐hr period, each focal female was then transferred to a “holding” vial containing a small amount of fresh medium and subsequently transferred to a fresh holding vial every 48 hr until the next measurement period.Virgin focal female flies were collected within 6 hr of their eclosion into adulthood and maintained in individual vials. On day 2 of their adult lives, these females were provided with ad libitum access to yeast. On day 3, each focal female was exposed to 2–4‐day‐old “tester” males of the D. melanogaster  associated with a given set of eggs, dead adults were included in the count as long as no part of them remained within the pupal case. While we treat egg‐to‐adult viability of the maternal clutch as a trait corresponding to a reproducing female's performance, the likelihood of each egg to progress through the larval and pupal stages and successfully eclose is a product of both maternal effects and direct effects on the individual developing zygote. As maternal effects have been found to have a strong influence on egg‐to‐adult viability in Drosophila propagation (14–28 days). Given that mortality rate increases exponentially at around day 35 of adult life in these strains  an additional four times for each focal female, with each assay interspersed by approximately 8 days. We therefore assessed each focal female's clutch viability and fecundity at an adult age of 4, 12, 20, 28, and 35 days. We tested an average of 60 female flies per mitochondrial strain, divided among three experimental blocks, for a total of 850 focal flies at the start of the experiment. Each experimental block was separated in time by either one or two generations of 3.1lme4 package , and performed the same model reduction process, although without the observation‐level random effect. The final reduced model of the transformed data contained the same terms and was qualitatively similar to the final binomial model  was included as the response variable instead of as a fixed covariate. As before, we used log‐likelihood ratio tests and maximum likelihood estimation to evaluate the significance of effects included in the final model, and we retained several nonsignificant random effects  to accurately reflect the hierarchical structure of the data set.We then performed a similar process of model reduction to test for relationships between fecundity, mitochondrial haplotype, and female age using a generalized linear mixed model with a Poisson distribution in coxme package . We divided the data into five subsets based on focal female age, each isolating measurements from a particular age group . We then fitted each to a simplified binomial model that tested for effects of fecundity and parental/grand‐parental ages (as fixed effects) and mitochondrial haplotype, duplicate, block, and observation number (as random effects) on clutch viability. We repeated these models with fecundity instead of clutch viability, using simplified Poisson models of the same form (except removing number of eggs from the fixed effects). We then estimated the proportion of variance explained by mitochondrial haplotype at each of the five ages using formulae and R code described in Nakagawa and Schielzeth  and John4Drosophila. Our final model indicated that clutch viability decreased with age  was provided to females. Females in the Camus and Dowling  study weRegardless, the patterns of sexual antagonism across haplotypes revealed in Camus and Dowling  and the Drosophila model system.In sum, our results suggest that mutation accumulation in the mitochondrial genome is not a key driver of reproductive trait senescence in females. Indeed, we did not uncover mitochondrial genetic variation affecting any of the traits measured in this study, a finding that reinforces the emerging evidence that functional effects of mitochondrial genetic variation are often male‐biased .The dataset used in this study is available through Figshare (R.K. assembled and analyzed the data, wrote the initial manuscript draft, and contributed to revisions. J.P. and M.F.C. contributed to initial project design, collected the data, and performed preliminary analyses. D.D. contributed to project design, supervised data collection, and contributed to data analysis and manuscript revisions. Click here for additional data file.


Supplemental Digital Content is available in the text. The genetic basis of left ventricular (LV) image-derived phenotypes, which play a vital role in the diagnosis, management, and risk stratification of cardiovascular diseases, is unclear at present.The LV parameters were measured from the cardiovascular magnetic resonance studies of the UK Biobank. Genotyping was done using Affymetrix arrays, augmented by imputation. We performed genome-wide association studies of 6 LV traits—LV end-diastolic volume, LV end-systolic volume, LV stroke volume, LV ejection fraction, LV mass, and LV mass to end-diastolic volume ratio. The replication analysis was performed in the MESA study (Multi-Ethnic Study of Atherosclerosis). We identified the candidate genes at genome-wide significant loci based on the evidence from extensive bioinformatic analyses. Polygenic risk scores were constructed from the summary statistics of LV genome-wide association studies to predict the heart failure events.P<1×10−8. Three loci were replicated at Bonferroni significance and 7 loci at nominal significance (P<0.05 with concordant direction of effect) in the MESA study (n=4383). Follow-up bioinformatic analyses identified 28 candidate genes that were enriched in the cardiac developmental pathways and regulation of the LV contractile mechanism. Eight genes  supported by at least 2 independent lines of in silico evidence were implicated in the cardiac morphogenesis and heart failure development. The polygenic risk scores of LV phenotypes were predictive of heart failure in a holdout UK Biobank sample of 3106 cases and 224 134 controls .The study comprised 16 923 European UK Biobank participants  without prevalent myocardial infarction or heart failure. We discovered 14 genome-wide significant loci  at a stringent We report 14 genetic loci and indicate several candidate genes that not only enhance our understanding of the genetic architecture of prognostically important LV phenotypes but also shed light on potential novel therapeutic targets for LV remodeling. Prognostically important left ventricular imaging phenotypes are highly heritable (~22% to 39%).A total of 14 genetic susceptibility loci (8 of which are unique) enriched in the cardiac developmental pathways and regulation of contractile mechanism are discovered in the largest genome-wide association study of cardiovascular magnetic resonance-derived left ventricular phenotypes.The polygenic risk scores of left ventricular phenotypes are predictive of heart failure events independently of clinical risk factors.The findings from this study not only enhance our understanding of the genetic basis of prognostically important left ventricular phenotypes in the general population but also underscore the intricate genetic relationship between these endophenotypes and the pathogenesis of the heart failure syndrome.The prioritized genes in the genome-wide significant loci should be followed up in the functional studies to aid the development of potential novel therapies for heart failure.The polygenic risk scores of left ventricular phenotypes may have a role in personalized risk stratification pending further validation of clinical robustness in future studies.1 Globally, both incidence and prevalence of heart failure are increasing due to improved survival from other contributory cardiovascular diseases in an aging population. The diagnosis and treatment of heart failure is in part based on left ventricular (LV) functional and structural parameters derived from cardiac imaging. Although the impact of modifiable risk factors on LV structure and function is well established, our current understanding of the genetic component of these imaging phenotypes is limited.Heart failure is a clinically heterogeneous condition associated with a substantial mortality, morbidity, and economic burden to the society.3 were hampered by the lack of a standardized measurement protocol in the phenotyping process and reliance on 2-dimensional echocardiography (ECHO) with inherent dependency on geometric assumptions and adequate acoustic window. These shortcomings can be overcome by using the individual-level data from a single large study such as the UK Biobank, which also provides accurate and reproducible imaging phenotypes from cardiovascular magnetic resonance (CMR) imaging, considered to be a reference standard for the assessment of cardiac morphology.4Previous large-scale genetic association studies of LV imaging phenotypes6 In addition, LV mass to end-diastolic volume ratio (LVMVR) represents geometric remodeling of the left ventricle, and an elevated LVMVR reflects concentric remodeling or hypertrophy associated with adverse outcomes.7 Systematic genome-wide scanning for loci associated with the LV image-derived measurements is a vital first step, which will advance our understanding of their genetic basis in a general population and may inform novel diagnostic and targeted therapeutic opportunities. In this study, we conducted genome-wide association studies (GWASs) to identify the genetic loci for 6 clinically relevant CMR-derived LV imaging phenotypes.Although multiple indices of LV structure and function can be measured from CMR images, 5 parameters, LV mass (LVM), LV end-diastolic volume (LVEDV), LV end-systolic volume (LVESV), LV stroke volume (LVSV), and LV ejection fraction (LVEF), are frequently used in clinical practice and carry prognostic information.http://www.ukbiobank.ac.uk/register-apply/).The data including GWAS summary statistics, analytic methods, and study materials will be returned to the UK Biobank. The UK Biobank will make these data available to all bona fide researchers for all types of health-related research that is in the public interest, without preferential or exclusive access for any person. Please see the UK Biobank’s website for the detailed access procedure .Genotypes directly called by 2 closely related, purpose-built arrays known as UK Biobank Axiom Array (825 927 markers) and UK BiLEVE Axiom Array (807 411 markers) were imputed to ~92 million variants using 2 reference panels . Since our primary aim was to investigate the genetic basis of LV image-derived phenotypes, we excluded individuals with prevalent myocardial infarction, heart failure, or LVEF <50% to minimize the confounding influence of these preexisting conditions. Additional sample quality control measures were outlined in Methods in the online-only Data Supplement .The detailed CMR protocol and analysis methods have been described previously,Methods in the online-only Data Supplement . We estimated the heritability explained by the genotyped variants (hg2 SNP [single nucleotide polymorphism]) and bivariate genetic correlation (rg) using a variance component method implemented in BOLT-REML software.10 We next performed the discovery GWAS of each LV trait using a linear mixed-model method by BOLT-LMM software,11 under an additive genetic model with ~7 million imputed genetic variants with minor allele frequency ≥5% and imputation quality score >0.3. Both heritability analysis and GWAS models were adjusted for age, sex, height, weight, systolic blood pressure corrected for antihypertensive medication use (by adding 15 mm Hg), phenotype-derivation method , array type (UK Biobank versus UK BiLEVE array), and imaging center . The untransformed LV phenotypes that showed evidence of positive skewness normalized well after rank-based inverse normal transformation . We used these rank-based inverse normal transformed phenotypes in all primary analysis models for heritability, genotypic correlation, and GWAS. In addition to consideration for the multiple testing of genotypes involved in a single GWAS, we had to consider multiple hypothesis testing with our 6 distinct, albeit correlated, LV traits. The effective number of phenotype-association tests estimated by the Galwey method was 3.3. However, we set a more stringent threshold for genome-wide significance at P<5×10−8/5=1×10−8 given the absence of a large replication cohort of comparable size. Genome-wide significant loci were defined by the most significant variant (known as the sentinel or lead variant) and their proxies (correlated variants) in linkage disequilibrium (LD) r2>0.1 in a 1 Mb region.The detailed analysis strategy is outlined in Methods in the online-only Data Supplement, Conditional Analysis and Percentage Variance).We also performed conditional analysis to determine the presence of secondary independent signals within the GWAS loci and nested linear regression analyses to calculate the percentage variance explained by the lead variants . We also repeated the association analyses with untransformed LV traits while controlling for the same covariates as the primary analysis to obtain more comprehensible effect sizes (β), which are in the same unit of measurements as the LV traits . Since the ratio of LV mass to LVEDV0.67 (concentricity0.67) was previously shown to be more correlated with both LV wall thickness and systolic blood pressure than the standard definition of concentricity (LVMVR),12 we repeated the association analysis with this phenotype. Furthermore, potential mediating effects of systolic blood pressure and sex were explored by incorporating the lead variant and covariate interaction terms in the primary models, using the mixed-model method implemented in the MMAP software (https://mmap.github.io/). Bonferroni correction was applied on the interaction P values to adjust for the number of variants tested.As a sensitivity analysis, we adjusted the primary analysis models with additional cardiovascular risk factors, namely diastolic blood pressure corrected for antihypertensive medication use (by adding 10 mm Hg), body mass index as a measure of obesity (replacing weight in the primary model to avoid collinearity), smoking status, regular alcohol use, dyslipidemia, and diabetes mellitus , a total of 4383 individuals from the MESA study  were included in the look-up analysis. Further details on the design and analysis of MESA cohort are available in Methods in the online-only Data Supplement.We performed the association analyses for all our sentinel variants in both European and non-European ancestries of the MESA study (Multi-Ethnic Study of Atherosclerosis).P<5×10−8) reported in published literature on closely related phenotypes  and performed a lookup of these variants in our GWAS results. We cross-referenced our sentinel variants and their close proxies (LD r2≥0.8) with Phenoscanner database v2 (http://www.phenoscanner.medschl.cam.ac.uk/) and presented the variants that showed strong associations with other traits at P<5×10−8.14 We also interrogated the GeneAtlas database (http://geneatlas.roslin.ed.ac.uk/) to assess the associations of our variants with other traits in the UK Biobank.15We searched PubMed to collate all genome-wide significant variants .We employed an integrative bioinformatics approach to compile the functional information at both variant and gene levels. Significant genomic loci were annotated using multiple lines of evidence including the presence of coding variant, gene expression data, chromatin interaction analyses, knockout models, and literature review (16 to construct the polygenic risk score (PRS) of each LV trait based on the effect sizes derived from the LV GWASs and predicted the risk of heart failure event in the remainder of the UK Biobank cohort. LDPred considers the tuning parameter known as the fraction of causal variant (ρ). To choose the best unbiased ρ, we first split the UK Biobank dataset into the training  and test  sets. The final PRS constructed from the best-fit ρ value was used to predict heart failure in the holdout test dataset using a logistic regression model controlled for age, sex, body mass index, systolic and diastolic blood pressure adjusted for antihypertensive medication use, smoking status, regular alcohol use, dyslipidemia, diabetes mellitus, and 15 genetic principal components. We also explored the prospective association between LV-PRS quintiles and incident heart failure in the test dataset using multivariate Cox proportional hazards models adjusted for the same covariates as the logistic regression models. Further information on PRS is available in Methods in the online-only Data Supplement (Polygenic Risk Prediction of Heart Failure Events).We used the LDPred toolTable I in the online-only Data Supplement. The mean±SD age of the cohort 62.5±7.5 years, and 45.8% were men. The primary analysis comprised a total of 16 923 European individuals with a maximum sample size of LVEDV (n=16 920), LVESV (n=16 920), LVSV (n=16 917), LVEF (n=16 923), LVM (n=16 920), and LVMVR (n=16 884). Approximately 25% of the CMR studies were manually analyzed, and the remainder were segmented by a deep learning algorithm. The reproducibility of both manual and automatic measurements was very high (intraclass correlation coefficient ranged from 0.88 to 0.98).The overall study design is illustrated in Figure 2g SNP) estimates were observed for the structural traits such as LVEDV and LVESV (both at 39%), followed by LVM at 34% and LVMVR at 33%, while the functional traits such as LVSV and LVEF had lower heritability . The genotypic correlations between LV traits ranged from very high (rg=0.92 between LVEDV and LVSV) to very low . We assigned a single sentinel variant with the lowest GWAS P value for each locus and plotted the LocusZoom plots for all sentinel variants . Variants at several loci were associated with more than 1 LV trait. The TTN locus was associated with 4 LV traits , and the BAG3 and MTSS1 loci were shared across more than 1 trait , which were not shared with other LV traits. No significant locus was found for LVSV. In total, 8 unique loci were identified. There was no evidence of secondary independent variants achieving the prespecified criteria at any loci in conditional analyses (Table II in the online-only Data Supplement). The percentages of trait variance explained by the sentinel variants were small as expected given the limited number of significant loci for each trait .We discovered a total of 14 genomic loci defined by a 1 Mb region—3 loci each for LVEDV, LVESV, and LVMVR; 4 loci for LVEF; and 1 locus for LVM—at a stringent SH2B3 locus for LVEDV, where the GWAS P value of sentinel variant (rs7310615) became significantly attenuated . The β estimates and the P values of our primary results and the analyses with untransformed LV phenotypes were highly correlated (ρ=0.98–1.0 for β and ρ=0.94–0.99 for P) with no significant attenuation of GWAS P values (−log10 P primary/−log10 P secondary<1.5) (Table IV in the online-only Data Supplement). The absolute effect sizes in the models with untransformed phenotypes ranged between 1 to 2 mL for LVEDV and LVESV and ~0.5% for LVEF per allele (Table P<1×10−8) in the sensitivity analyses with concentricity0.67 index. There was no significant interaction between systolic blood pressure and the lead variants (Table V in the online-only Data Supplement). In contrast, male sex significantly mediated the effects of lead variants in the TTN locus in the direction of larger LVEDV  and LVESV  and higher LVM  (Table VI in the online-only Data Supplement).The secondary analysis models, additionally adjusted for other cardiovascular risk factors, produced results generally congruous with the primary analyses, except for the iant rs730615 becaP<0.0036 [0.05/14]) and 7 loci at nominal significance (P<0.05 with concordant direction of effect) in at least 1 of the MESA ethnic subcohorts (Summary Characteristics in Table VII in the online-only Data Supplement). The rs200712209 variant associated with LVESV and rs34866937 variant associated with LVEF—both in MTSS1 locus—were replicated in the European subset of MESA study after Bonferroni correction. Three other variants tagging TTN, BAG3, and ZNF592 loci were nominally associated with LVESV, LVEF, and LVMVR traits in the MESA European cohort (Table VIII in the online-only Data Supplement).Out of 14 locus-trait associations discovered in the UK Biobank, we validated 3 loci at Bonferroni significance  for the corresponding CMR traits in our GWAS (Table IX in the online-only Data Supplement). The rs10774625 variant reported by Wild et al2 for ECHO-derived LV end-diastolic diameter was in high LD (r2=0.95) with the sentinel variant at SH2B3 in our LVEDV GWAS. Previously unvalidated rs34866937 variant at the MTSS1 locus, reported by Kanai et al for ECHO-derived LV end-systolic diameter and ECHO-derived LVEF in a Japanese population, was genome-wide significant for CMR-derived LVESV and LVEF in our European GWAS.3 For ECG-LV hypertrophy traits, 13 previously reported variants were nominally associated with our CMR-derived LVM (Table X in the online-only Data Supplement).For ECHO traits, 2 previously reported variants in the 14 The variants in the SH2B3 locus for LVEDV was associated with multiple risk factors that could mediate the cardiac remodeling process such as blood pressure/hypertension, cholesterol/low-density lipoprotein level, diabetes mellitus, and smoking status. The variants in the CLCNKA and BAG3 loci for LVEF and LVESV were associated with dilated cardiomyopathy (DCM) (Table XI in the online-only Data Supplement). We also interrogated the Gene Atlas PheWAS database, which reported the association results of hundreds of traits in the UK Biobank with our sentinel variants. The sentinel variant in the SH2B3 locus (rs7310615) was again found to be highly associated with the presence of hypertension (P=5.9×10−46) and ischemic heart disease (P=4.8×10−14) in the UK Biobank (Table XII in the online-only Data Supplement).We also explored the association between our sentinel variants and their proxies with other traits from published GWASs using Phenoscanner.Figure VIII in the online-only Data Supplement). Out of 18 exonic variants, 12 were nonsynonymous and were located in the BAG3, ALPK3, TTN, SH2B3, NMB, and WDR73 genes. The missense variant, rs2234962, in the BAG3 gene for LVESV and LVEF was predicted to be damaging by at least 2 prediction tools.At variant-level annotation, we identified a total of 238 candidate variants for all LV traits .18 Of these variants, 2 (rs2175567 and rs17598603) were intronic for the NMB gene, and the other (rs7237) was located in the 3’ UTR region of the WDR73 gene. The expression quantitative trait locus analysis in the GTEx (Genotype-Tissue Expression) dataset revealed that rs35006907, a close proxy of the sentinel variants in the MTSS1 locus for LVESV and LVEF, was associated at false discovery rate <0.05 with the MTSS1 gene expression in left ventricle and left atrial appendage tissues.19 Additionally, rs2070458, a proxy variant in the DERL3 locus for LVMVR, was associated with the MMP11 gene expression in LV tissue (Table XIII in the online-only Data Supplement).Among 220 noncoding variants, 52 were located in promotor histone marks, 148 in enhancer histone marks, and 82 in DNase I sites, and 13 altered the binding sites of regulatory proteins. We also found 6 noncoding variants that were highly conserved in vertebrates according to site-specific phylogenetic analysis (SiPhy) software.Table XIV in the online-only Data Supplement). A summary of all variant-level annotations is presented in Table XV in the online-only Data Supplement. The gene prioritization, gene-set enrichment, and pathway analyses for the LV traits did not yield any significant results. However, in the tissue-specific enrichment analysis using the data from the Roadmap Epigenomics project, there was a significant enrichment of our genome-wide significant LV variants within the regions of DNase I hotspots in fetal heart tissue .We explored the long-range interaction influence of the sentinel variants and their proxies in the long-range chromatin interaction (Hi-C) data of aorta, left ventricle, and right ventricle, and found 11 potential target genes (2≥0.8), 6 were prioritized by expression quantitative trait locus data in cardiovascular tissues, 11 were prioritized based on long-range chromatin interactional analyses, and 6 were prioritized by availability of knockout models (Table XVI in the online-only Data Supplement). A summary of prioritized genes for all LV traits is depicted in Figure Table XVII in the online-only Data Supplement).20At gene-level annotation, we identified a total of 28 candidate genes at 8 unique loci: 5 genes were prioritized by presence of nonsynonymous variant .We explored the predictive ability of PRSs derived from the genetic variants associated with LV traits to predict heart failure events in an independent test sample of the UK Biobank cohort . All LV-PRSs (except LVM-PRS) were significantly associated with heart failure. The PRS quintiles of LVEDV and LVESV were associated with higher odds of heart failure (odds ratio [OR] 1.25–1.41 for the top 20% versus bottom 20% group), while the opposite pattern was observed for LVEF- and LVMVR-PRSs across all levels of adjustments for potential confounders including age, sex, body size, and cardiovascular risk factors  were shared between more than 1 LV traits, resulting in the discovery of 8 unique loci, of which 6 were novel for LV imaging traits. The follow-up analysis of our sentinel variants in an independent multiethnic cohort (MESA) showed strong support for 2 loci (MTSS1 and BAG3) at the level of Bonferroni significance, while 3 other loci  achieved nominal support. Our enrichment analyses revealed that the regulatory variants associated with the LV loci are highly enriched in the fetal heart tissue, and the candidate genes for these loci are involved in the cardiac developmental pathways and regulation of the LV contractile mechanism.This is the largest individual-level GWAS to date investigating the genetic architecture of prognostically important LV phenotypes derived from CMR. The key strength of this study is the combination of a standardized, highly precise, and reproducible phenotyping process with a high-quality dense genotype dataset in a cohort of ~17 000 individuals free from myocardial infarction and heart failure. This strategy yielded a total of 14 locus-trait associations. Three loci  in a large population of unrelated white individuals. A significant proportion of LV phenotypic variability was explained by the genotype (ranging from 22% to 39%), and the structural traits such as LVEDV or LVM had a noticeably higher heritability than more functional traits such as LVEF. The relatively lower heritability estimates in these functional traits could be due to the inflated interpersonal variations secondary to differences in the loading conditions and chronotropic and inotropic states.23 The heritability estimates of CMR-derived LV traits were overall higher than previously reported values in other complex cardiovascular traits such as resting heart rate (h2g=21%),24 and comparable ECHO traits .3 However, the heritability of the ECHO trait was calculated using the summary-level data with LD score regression approach, which tends to produce lower estimates than the variance component method  as in our study. The pattern and magnitude of genotypic correlations between LV traits mostly mirrored the corresponding phenotypic correlations except for the relationship between LVSV and LVEF, where the genotypic correlation was absent despite a moderate phenotypic correlation (rp=0.39 vs rg=−0.01). The finding may suggest dissimilar genetic architecture between these 2 functional traits, which should be validated in an independent cohort. Most genomic loci observed in our study were specific for the LV traits except for the SH2B3 locus (associated with LVEDV), which appeared to be highly pleiotropic and associated with multiple cardiovascular risk factors. This finding may explain the substantial weakening of the sentinel variant’s association P value in our secondary analysis additionally adjusted for a wider range of cardiovascular risk factors.Although the LV image-derived phenotypes were known to be heritable, their reported heritability varied widely, ranging from 15% to 84% for LVM, which may reflect the methods used including monozygotic and dizygotic twins, siblings, nuclear, and complex families.TTN (titin) gene emerged as a strong candidate causal gene for 4 LV traits . The pivotal function of TTN in the maintenance of sarcomere assembly, stretch sensing and signaling, passive stiffness adjustment, and active force generation corresponds well with our finding of TTN being an important gene for both structural and functional LV imaging traits.25 Several titin-truncating variants have been found in 10% to 20% of DCM cases and may have a role in the pathogenesis of DCM in these individuals.26 These titin-truncating variants have been reported to occur at much lower frequencies in the general population ,27 and were found to be associated with larger LV volumes.28 In our study including variants with minor allele frequency ≥5%, we found several missense variants (but no protein truncation variants) in the TTN locus (Table XIII in the online-only Data Supplement), which were all predicted to be benign by the pathogenicity prediction tools.Among several candidate genes, we highlighted the functional roles of a few potential causal genes based on the bioinformatic analyses and literature review. The BAG3 (BCL2 associated athanogene 3) gene appears to be a likely candidate gene that is involved in modulation of the 2 volumetric traits (LVEDV and LVESV) and the derived LV functional index (LVEF). BAG3 encodes an antiapoptotic protein expressed in the heart and skeletal muscle and serves as a cochaperone of the heat shock protein family.29 It is essential for the homeostasis of filamin and influences myocyte contraction through interaction with the b1-adrenegic receptor and the L-type calcium channel.31 Mutations in BAG3 gene have been implicated in DCM pathogenesis with the myocardial tissues displaying evidence of myofibril disarray and relocation of BAG3 protein in the sarcomeric Z-disc.32 In our cohort of individuals with preserved LVEF, free from known heart failure or DCM, we found a missense mutation  in the BAG3 gene, which was reported to be damaging by 2 in silico prediction tools. The same missense variant has been indicated as the sentinel variant in a DCM GWAS,33 underlining the shared genetic basis of LV volumetric phenotypes and DCM. Our long-range chromatin interaction (Hi-C) analysis flagged another potential candidate gene at the BAG locus called GRK5 (G protein-coupled receptor kinase 5). GRK5 regulates cardiac development through the mammalian target of rapamycin (mTOR) pathway in zebrafish.35 Its expression level in the myocardium is elevated in heart failure, and a nonsynonymous polymorphism of GRK5 appears to be protective of heart failure through inhibition of β-adrenergic receptor signaling.37 In addition, GRK5 is a known drug target for β-blockers and antihypertensive agents (Table XIV in the online-only Data Supplement). At the CLCNKA locus for LVEF, we indicate HSPB7 (heat shock protein family B member 7) as a likely candidate given its recognized role in cardiogenesis by modulating actin filament assembly and known association with heart failure development.40 Decreased cardiomyocyte proliferation and abnormal sarcomere morphology were observed in HSPB7 knockout mice.The MTSS1 locus for CMR-derived LVESV and LVEF has previously been reported for comparable ECHO-derived LV traits.3 The sentinel variant at the MTSS1 locus is in the intergenic region. However, its close proxy  is located in the DNase I hypersensitive site in the cardiac tissue and is associated with expression of the MTSS1 (metastasis suppressor protein 1) gene in LV and left atrial appendage tissues. This gene is involved in cytoskeletal signaling pathway and encodes a scaffold protein that regulates actin dynamics.42The ALPK3  gene in the ZNF592 locus is expressed in the developing heart and involves in cardiomyocyte differentiation.43 The ALPK3 knockout mouse model exhibited evidence of cardiac-specific phenotypic changes such as LV dilatation and hypertrophy. Another potential candidate gene at the same locus is NMB (neuromedin B), which is associated with regulation of eating behavior and obesity.44 This gene has previously been highlighted as a candidate gene in a GWAS investigating the ECG indices of LV hypertrophy,45 in which the sentinel variant was moderately correlated (LD r2=0.39) with our LVMVR sentinel variant. Last, the proxy variant (rs2070458) of the DERL3 locus for LVMVR was in cis-expression quantitative trait locus (cis-eQTL) with the MMP11  gene expression in the left ventricle. MMP11 belongs to the family of proteolytic enzymes that regulate extracellular matrix and play a role in the development of myocardial fibrosis and ventricular remodeling.47The GWAS of remodeling phenotype, LVMVR, produced 3 genetic loci that were not shared with other LV traits. The TTN, BAG3, and MTSS1) that were shared across multiple structural and functional LV traits encode essential proteins involved in the construction and maintenance of sarcomeric infrastructure. In contrast, the variation of LVMVR, the LV remodeling trait, was determined by the genetic loci containing candidate genes implicated in cardiomyocyte differentiation and extracellular matrix homeostasis.Altogether, several key candidate genes in our GWAS loci  phenotype in the heart failure cases in our cohort. Interestingly, and contrary to the epidemiological evidence of association between LVM and incident heart failure,50 the LVM-PRS was not predictive of heart failure in our study. Although LVM appeared to be highly heritable in our genome-wide heritability analysis (h2g SNP=34%), only a single locus was discovered at P<1×10−8 (percentage variance explained=0.1%). Thus, the limited statistical power may have curtailed the predictive ability of LVM-PRS.Despite a limited number of loci found in this study, the PRSs constructed from LVEDV, LVESV, LVEF, and LVMVR were predictive of heart failure events in the remainder of the UK Biobank cohort. This finding reinforces the fundamental role of the LV imaging endo-phenotypes in the pathogenesis of heart failure. The directionality of association between PRSs and heart failure events was generally concordant with prior expectations  except for the PRS derived from LVMVR, where higher scores were correlated with lower odds of heart failure. LVMVR is a geometric phenotype where higher values are indicative of concentric remodeling or concentric hypertrophy of the left ventricle. Despite the conventional wisdom of higher LVMVR being associated with an increased risk of adverse cardiovascular outcomes, a prospective longitudinal study in the general population did not find a positive correlation between LVMVR and heart failure events.We acknowledge some limitations in our study. Despite being the largest GWAS of CMR image-derived LV phenotypes, the relatively small discovery sample size translated to the discovery of a few loci explaining <0.5% of trait variance per trait. Additionally, the current sample size restricted our analysis to common variants with minor allele frequency ≥5%. However, the expected expansion of the CMR sample size to 100 000 in the UK Biobank, together with the highly optimized automatic image segmentation pipeline, will lead to future studies with statistical power to detect more genetic loci at a lower minor allele frequency threshold. Furthermore, the upcoming exome sequencing data from the UK Biobank may allow us to investigate the role of rarer, protein truncating, variants in a general population. Of note, 3 out of 8 unique loci discovered in the UK Biobank were not replicated in MESA. Therefore, the evidence for these susceptibility loci should be considered preliminary. Second, although we have performed a limited look-up of our loci in MESA for additional support, our findings should be formally validated in a larger cohort.In summary, the findings from this study not only enhance our understanding of the genetic basis of prognostically important LV phenotypes in the general population but also underscore the intricate genetic relationship between these endophenotypes and the pathogenesis of heart failure syndrome, which may lead to potential novel therapeutic targets and personalized risk stratification strategy in the future.This research has been conducted using the UK Biobank Resource under Application 2964. The authors wish to thank all UK Biobank participants and staff.Dr Aung is supported by a Wellcome Trust Research Training Fellowship (203553/Z/16/Z). Drs Petersen, Neubauer, and Piechnik acknowledge the British Heart Foundation for funding the manual analysis to create a cardiovascular magnetic resonance imaging reference standard for the UK Biobank imaging resource in 5000 CMR scans (PG/14/89/31194). This work was part of the portfolio of translational research of the National Institute for Health Research Biomedical Research Centre at Barts and The London School of Medicine and Dentistry; Drs Cabrera, Barnes, Warren, Munroe, and Petersen acknowledge support from this center. Dr Petersen also acknowledges support from the “SmartHeart” Engineering and Physical Sciences Research Council program grant (EP/P001009/1). Drs Piechnik and Neubauer are supported by the Oxford National Institute for Health Research Biomedical Research Centre and the Oxford British Heart Foundation Centre of Research Excellence. This project was enabled through access to the Medical Research Council eMedLab Medical Bioinformatics infrastructure, supported by the Medical Research Council (grant No. MR/L016311/1). Dr Fung is supported by The Medical College of Saint Bartholomew’s Hospital Trust, an independent registered charity that promotes and advances medical and dental education and research at Barts and The London School of Medicine and Dentistry. The UK Biobank was established by the Wellcome Trust medical charity, the Medical Research Council, the Department of Health, the Scottish Government, and the Northwest Regional Development Agency. It has also received funding from the Welsh Assembly Government and the British Heart Foundation. MESA and the MESA SHARe project are conducted and supported by the National Heart, Lung, and Blood Institute in collaboration with MESA investigators. Support for MESA is provided by contracts HHSN268201500003I, N01-HC-95159, N01-HC-95160, N01-HC-95161, N01-HC-95162, N01-HC-95163, N01-HC-95164, N01-HC-95165, N01-HC-95166, N01-HC-95167, N01-HC-95168, N01-HC-95169, UL1-TR-000040, UL1-TR-001079, UL1-TR-001420, UL1-TR-001881, and DK063491. Funding for SHARe genotyping was provided by National Heart, Lung, and Blood Institute contract N02-HL-64278. Genotyping was performed at Affymetrix  and the Broad Institute of Harvard and the Massachusetts Institute of Technology  using the Affymetrix Genome-Wide Human SNP Array 6.0.Dr Petersen provides consultancy to Circle Cardiovascular Imaging Inc, Calgary, Canada. The other authors report no conflicts.


Random-effects models are a popular tool for analysing total narrow-sense heritability for quantitative phenotypes, on the basis of large-scale SNP data. Recently, there have been disputes over the validity of conclusions that may be drawn from such analysis. We derive some of the fundamental statistical properties of heritability estimates arising from these models, showing that the bias will generally be small. We show that that the score function may be manipulated into a form that facilitates intelligible interpretations of the results. We go on to use this score function to explore the behavior of the model when certain key assumptions of the model are not satisfied — shared environment, measurement error, and genetic effects that are confined to a small subset of sites.The variance and bias depend crucially on the variance of certain functionals of the singular values of the genotype matrix. A useful baseline is the singular value distribution associated with genotypes that are completely independent — that is, with no linkage and no relatedness — for a given number of individuals and sites. We calculate the corresponding variance and bias for this setting. Genome-Wide Complex-Trait Analysis, known as GCTA, introduced by Jian Yang and collaborators in 2010 in , has ledIn this paper we seek to settle these basic questions.n respondents and p genetic markers, we go beyond order n, and show this intrinsic bias to be negligible in practice.For “Simple GREML”, defined below, with We present interpretable expansions for bias and standard error drawing on eigenvalue theory, depicting the contrasts between standard errors in the absence and in the presence of population stratification.For less simple settings, we consider known sources of bias including shared environment and measurment error, and characterize and bound bias arising fromobserved causal genetic variants at a subset of sites atypical with respect to their linkage statistics, andunobserved causal genetic variants.In a companion paper , we consThe data for GREML are assays of very large numbers of Single Nucleotide Polymorphisms (SNPs) in the genomes of individuals along with measurements of a putatively heritable trait. The model that GREML fits via the technique of Restricted Maximum Likelihood is defined in Section 2. For simplicity, we refer to it as “the GREML model”. It is an example of a “linear mixed model,” in which the contribution of SNPs to trait values are treated as random effects.  Alternative estimation methods for the model such as LD-score Regression and Haseman-Elston regression have also come into wide use, bringing up statistical issues paralleling those we examine here for GREML.Mixed models form a natural framework for the estimation of total heritability for traits whose variability is determined by a wide variety of sites, rather than by specific identifiable SNPs that each have strong influence. GREML found notable application in the GCTA work by Yang and Visscher and associates to identify “missing heritability” in height , 49 and The goal of these methods is to estimate total additive heritability, without the overfitting that arises in attempts to identify specific loci influencing a trait. As we have said, most examination of pitfalls – including two papers , 55 withet al. et al. [e [et al.  and 19]et al. ) is unnecessary as soon as we interpret the determinant as a product of squared singular values. Furthermore, in the case when a singular value is exactly zero, which occurs automatically when using de-meaned SNPs, the conditions for applying Sylvester’s Theorem are not satisfied.) Similarly, under the assumptions of the model, the iz are independent normal random variables, with variances θ−1 is positive.We observe here that  claim  for all i are unity.The Z sum to 0 induces one singular value of 0. It corresponds to the constant left singular vector with all entries equal to The normalization that makes each column of We use the symbol Cov to represent the empirical covariance of the elements of two n-dimensional vector arguments. Similarly, we use Var with a vector argument for the empirical variance of the elements. When the vector elements are themselves random variables the output of Cov and of Var are themselves univariate random variables.kτ(ψ) to be a rescaled version of the empirical k-th central moment of the elements of the vector iw(ψ); that is, for k ≥ 2We define We also defineNote that if we definekτ(ψ) is the central moment of these iw̃. Hence kτ(ψ) is well behaved at ψ = 0. It is bounded by the maximum of ψ > 0 also by ψ−k. We write kτ with no argument for kτ(ψ0). An important quantity in the scaling of errors in our estimates will beiw(ψ0) ∈ , we know ψ0 ∈  is a convex function of w̄ ≥ 1−ψ0 and τ1 ≤ 1. Formulas for τ1 and τ2 and τ3 under various assumptions about the singular values of the genotype matrix Z are derived in Section 5.Since + 2 (cf. ). For fiψ̂) in Theorem 3.1 proved in θ into the two-parameter log likelihood leads to a one-parameter “profile log likelihood”, namelyWe collect our main results about the asymptotic behavior of the MLE for heritability  satisfiesFurthermore, for ψ0 ∈ 53] centeThe question that needs to be asked is this: Given the simplifications that we know underlie the GREML model, should we expect approximately sensible inferences to follow from approximately well specified data? We consider three types of deviation from the model:Shared environment;Measurement error;A small number of causal loci that are responsible for the influence of genes on phenotype, while the large majority of SNPs have no influence.C clones produce C − 1 zero singular values and one singular value of size C.) The usual practice of working with the GREML model recognizes these problems: from the outset, population stratification has been addressed with principal component analyses and cryptic relatedness by removing samples with suspiciously high kinship . We then simulated genotypes for n =2,000 or 10,000 individuals by independently assigning a random number of minor alleles to each individual and site, according to the binomial distribution with the appropriate MAF. The genotypes corresponding to each site were then normalized to have mean 0 and variance 1. This was our genotype matrix Z.To illustrate this effect, we conducted simulations in the independent setting. We took k sites to be causal and independently simulated 1,000 datasets using Z, these causal SNPs and heritability either 0.25, 0.5 or .75. The heritability was then estimated for each dataset, according to the standard MLE procedure described in Section 3. We then repeated this procedure for 100 different random choices of the causal SNPs.We then selected a random subset of *ψ, the asymptotic heritability estimate for a given set of causal SNPs, we use a standard random-effect model. Specifically, if ijψ̂ is the estimated heritability for the j-th simulated dataset derived from the i-th set of causal SNPs, we assumeTo empirically estimate variance of ijε are i.i.d. Gaussian, each with an unknown variance parameter fit using lme4  byIn order to find expressions for the empirical moments across t = s2 stands for the eigenvalues corresponding to the singular values, and dG is the limiting empirical measure of the eigenvalues, concentrated on the interval  where μ conventionally placed at zero and rescaling by μ so that dG has unit mass on .Here iw is given by the value of ζM(ζ)/μ and the average of ζ2M′(ζ)/μ when we plug in ζ = −(1 − ψ)/ψ = −1/ϕ, making 1/(1−ζ) equal the heritability ψ. Averages of higher powers of iw are given by expressions in higher-order derivatives of M(ζ)/μ. Equation 2.1.1 of , we haveSpecifically, for small /(1 − ζ) = ψ, and −ζ = (1 − ψ)/ψ, evaluating ζM/μ we find that the mean over i of iw is given up to second order in μ byWhen 1M by ζ yieldsDifferentiating i of iw is given byIt follows that the scaled variance over We also haveHigher-order moments follow by successive differentiation./(1 − ζ). The variance is μ, and to second order in μ the third central moment is +μ2 and the fourth central moment 2μ2. Evaluating M(ζ)/μ at ζ = 0 shows that the mean of the reciprocal eigenvalues is 1/(1−μ), and successive differentiation reveals a variance of μ/(1− μ)3 and a third central moment of 2μ2/(1 − μ)5 for the reciprocal eigenvalues.Central moments of the eigenvalues themselves around their mean of unity can be found by collecting terms in powers of 1For the stratified setting, a great variety of scenarios come under consideration. Stratified populations are expected to have genotype matrices with some or many eigenvalues substantially larger than those in the independent setting, and large eigenvalues entail large numbers of small ones, since the mean is unity./β and β with weights β/(β +1) and 1/(β + 1). This two point-mass distribution, with its mean of unity, has variance (β −1)2/(β +1), close to β when β is large. Moments over i of iw come out to beAmong the simplest stylized models for eigenvalues arising in a stratified population, one posits eigenvalues concentrated at two reciprocal values 1β, the mean of iw is close to 1 and the variance of iw is close to 1/β. In contrast to the independent setting, where the variance of iw is roughly proportional to the eigenvalue variance, in this stylized model for the stratified setting, the variance of iw is roughly inversely proportional to the eigenvalue variance. Implications for bias and variance for GREML heritability estimates have been described in Section 3.2.For large In the simple setting when assumptions are satisfied, we have shown that threats to the accuracy of GREML heritability estimates arise not from bias but from potentially large standard errors. Our findings run counter to some recent criticisms of GREML.We have also evaluated the bias arising from fixed but unknown structured subsets for causal SNPs. This can be substantial in principle, but seems likely to be disabling in practice. We have argued that the structures that amplify bias are likely to be the exception rather than the rule. In a separate work  we also Standard errors for GREML estimates of heritabilities depend on the dispersion in the squared singular values of the genotype matrix. In this regard, an idealized baseline case, the independent setting, is something like a worst-case scenario. Here, drawing on eigenvalue theory, we have given explicit expansions for standard error, as well as bias, in terms of the ratio of respondents to SNPs. Implications of our formulas have been reviewed in Section 3.3. Departures from the independent setting which augment the dispersion of the squared singular values can improve the statistical properties of the estimates, but only up to a point and only at a cost in substantive interpretability. Linkage disequilibrium augments dispersion. Unexpunged population stratification augments dispersion. Their relative roles and their signatures are not yet clear. A priority for future research is analysis of empirical genotype matrices and their sets of singular values, the natural next step in elucidating the statistical properties of random effects models for genetic heritability.