Gossypium hirsutum L.). This research aims to reveal the genetic effects of six branch traits, including bottom fruit branch node number (BFBNN), bottom fruit branch length (BFBL), middle fruit branch node number (MFBNN), middle fruit branch length (MFBL), upper fruit branch node number (UFBNN), and upper fruit branch length (UFBL). Association mapping was conducted for these traits of 39 lines and their 178 F1 hybrids in three environments. There were 20 highly significant Quantitative Trait SSRs (QTSs) detected by mixed linear model approach analyzing a full genetic model with genetic effects of additive, dominance, epistasis and their environment interaction. The phenotypic variation explained by genetic effects ranged from 32.64 ~ 91.61%, suggesting these branch traits largely influenced by genetic factors.Genetic architecture of branch traits has large influences on the morphological structure, photosynthetic capacity, planting density, and yield of Upland cotton ( Gossypium hirsutum is one of the commercially grown species of cotton. In the past decades, thousands of analyses have been carried out to find what factors are important in cotton growth. Previous studies have revealed that branch traits were related to plant density, canopy structure, and photosynthetic capacity, thus influencing fiber quality and yield [nd yield ,2. Assocnd yield . Since aThe first research that utilized association mapping on plant genetics is in 2001 . Several1 hybrids in three environments. Different with previous studies on branch traits, the branches of cotton plant divided into three parts: upper, middle and bottom. This may help to find whether the branch traits of different parts have different genetic characteristics. PCR-based molecular markers SSRs (simple sequence repeats) from the cotton markers database (CMD) were extracted. Software QTXNetwork (http://ibi.zju.edu.cn/software/QTXNetwork/) was used in this study, which is based on mixed linear model approach [In this study, the association mapping was carried out for 872 SSR markers of 39 lines and their 179 Fapproach . And the. A randomized complete block design with three replications was employed in the field trials. Each block was settled with two rows, and each row was kept in a 5.00 m long and 0.70 m wide plot. The distance between plants was 0.25 m wide  in Anyang; the distance between plants was 0.10 m wide  in Alar. Six fruit branch architecture traits were analyzed from random selected 10 plants for each material in each replication, these traits are bottom fruit branch node number (BFBNN), bottom fruit branch length (BFBL), middle fruit branch node number (MFBNN), middle branch length (MFBL), upper fruit branch node number (UFBNN), and upper fruit branch length (UFBL).A tested mapping population is representative for part of Upland cotton cultivars in China’s cotton-growing regions. These cultivars or lines  were pro and theiet al. [http://www.cottonmarker.org/cgi-bin/panel.cgi). This database contains all publicly available cotton SSR markers, which provides a more efficient utilization of molecular marker resources and will help accelerate basic and applied research in molecular breeding and genetic mapping in Gossypium spp. Polymorphic information is acquired from a standard screening panel including Upland cotton cultivars and other tetraploid species. A total of 5,052 SSR primer pairs were examined to screen for polymorphisms among thirty-nine inbred lines parents. These SSR primer pairs included CGR, GH, HAU, NAU, BNL, DPL, C and MGHES primer series. Marker nomenclature consisted of a letter indicating the origin of the marker, followed by the primer number. SSR analysis was conducted following the procedure described by Yao et al. [QQ genotype); if parent 3, 4 had stripe, coded “1” for the genotypes of SSR of parent 3, 4 (or genotype qq), F1 from parent 1 and parent 2 is coded to “0”, F1 from parent 3 and parent 4 is coded to “1”, (or genotype Qq). For a couple of primer, only a stripe is coded for the same stripe to conducted association analysis. A total of 351 couple primers (872 difference stripes) showed polymorphic among the 39 Upland cotton varieties (or lines) in current study.The leaves of cotton were collected in the pots in March 2012. Two cotyledons were taken from two plants of each variety (or line). DNA samples were extracted from 39 parents as described by Paterson et al. . The dowo et al. . For a dk-th individual in the h-th environment (yhk) can be expressed by the following mixed linear model,μ is the population mean; eh is the fixed effect of the h-th environment; ai is the additive effect of the i-th locus with coefficient QQ, coded no stripe parent; −1 for qq stripe coded having stripe parent); di is the dominance effect of the i-th locus with coefficient Qq, 0 for QQ and qq, coded having stripe hybrid F1); aaij, adij, daij and ddij are the digenic epistasis effects between the i-th locus and j-th locus with coefficients QQ × QQ and qq × qq, −1 for QQ × qq and qq × QQ), QQ × Qq, −1 for qq × Qq), Qq × QQ, −1 for Qq × qq) and Qq × Qq), respectively; aeih is the additive × environment interaction effect of the i-th locus in the h-th environment with coefficient deih is the dominance × environment interaction effect of the i-th locus in the h-th environment with coefficient aaeijh, adeijh, daeijh and ddeijh are the digenic epistasis × environment interaction effects between the i-th locus and j-th locus in the h-th environment with coefficient εhk is the residual effect of the k-th line or hybrid in the h-th environment.The full genetic model for the phenotypic value of the http://ibi.zju.edu.cn/software/QTXNetwork/). The genotypic data  algorithm with 20,000 Gibbs sample iterations [The SSR-trait association analyses were performed based on the above mixed linear model, and genetic effects were estimated by newly developed software QTXNetwork based on GPU parallel computation  were detected for six branch traits in cotton. The number of QTSs for each trait were 2 ~ 6, including DPL0061-2 for BFBL and MFBL, HAU2273-1 for MFBNN, BFBNN and BFBL. For the six fruit branch traits, estimated heritability for genetic effects was listed in Cotton has a within-canopy structure, and the fruit branches of plants can be divided into three parts: bottom, middle, and upper. The within-canopy structure of cotton is adjusted and affected by genetic basis and environment, and different part has different genetic inheritance rules. A total of 20 significant QTSs   . CGR6795PEW-value lower than 1×10−5  suggested that heterozygote Qq of these two QTSs could have heterosis of MFBL in F1 hybrids.Six QTSs were significantly associated with MFBL . Among tTopping is a vital step in cotton cultivating because there is apical dominance, which causes imbalance growth. From Tables EW-value < 10−8)  . CGR5876e1 and e2. No epistasis effects were detected in these two traits. Increasing UFBL of F1 hybrid could be selected by large positive environment-specific dominance of HAU1434-1 in e1 or BNL4023-1 for different environments. Selecting genotypes QQ of CGR6848-1 or qq of HAU1081-3 could increase UFBL.A total of four QTSs were detected for UFBL , and all1 hybrids.Besides the genetic effects of each QTS, the maximum positive and minimum negative genotypic effects of the superior lines and superior hybrids were also predicted in three environments . For allQQ, qq), and heterozygote (Qq) also were predicted for four traits in three environments. For MFBNN, MFBL and BFBL, the predicted genotypic effects were positive for major-allele homozygote QQ, but negative for minor-allele homozygote qq. It indicated that the natural selection tends to increase the middle branch node number and length, and also bottom branch length. This tower-like pattern is an ideal plant type for manipulating the plant density, enhancing the total light energy efficiency of a population, and increasing the yield [QQ of BFBNN, BFBL, MFBNN and UFBL in e3 are significantly larger than them in e1 and e2. It may suggest that these traits would change in different environments and the environment in Alar is inclined to improve these traits. In Anyang, the high-yield variety is more tower-like. However, under the high-density condition in Alar, the middle and bottom fruit branch length need to be shorter and node number need to be less, and the upper fruit branch length needs to be longer and node number to be more. Thus, only by selecting different genotypes can breeders get high yield in different environments.In the meantime, the genotypic effects of homozygotes  breeding in different environments could obtain further improvements.S1 Data(GEN)Click here for additional data file.S2 Data(PHE)Click here for additional data file.S1 Table(DOCX)Click here for additional data file.S2 Table(DOC)Click here for additional data file.


This analysis (a) works for random sample data, pedigree data, or a mix of both; (b) is highly efficient in both run time and memory requirement; (c) accommodates both univariate and multivariate traits; (d) works for autosomal and x-linked loci; (e) correctly deals with missing data in traits, covariates, and genotypes; (f) allows for covariate adjustment and constraints among parameters; (g) uses either theoretical or single nucleotide polymorphism (SNP)–based empirical kinship matrix for additive polygenic effects; (h) allows extra variance components such as dominant polygenic effects and household effects; (i) detects and reports outlier individuals and pedigrees; and (j) allows for robust estimation via the t-distribution. This paper assesses these capabilities on the genetics analysis workshop 19 (GAW19) sequencing data. We analyzed simulated and real phenotypes for both family and random sample data sets. For instance, when jointly testing the 8 longitudinally measured systolic blood pressure and diastolic blood pressure traits, it takes Mendel 78 min on a standard laptop computer to read, quality check, and analyze a data set with 849 individuals and 8.3 million SNPs. Genome-wide expression QTL analysis of 20,643 expression traits on 641 individuals with 8.3 million SNPs takes 30 h using 20 parallel runs on a cluster. Mendel is freely available at  In this paper, we demonstrate the capabilities of Mendel on the Genetic Analysis Workshop 19 (GAW19) sequencing data.The classical variance component model has been a powerful tool for mapping quantitative trait loci (QTLs) in pedigrees. Polygenic effects are effectively modeled by introducing an additive genetic variance component operating on the kinship coefficient matrix. With unknown or dubious pedigree structure, global kinship coefficients can be accurately estimated from dense markers using either the genetic relationship matrix (GRM) or the method of moments. In GWAS (genome-wide association studies), the 2 alleles of a SNP (single nucleotide polymorphism) shift trait means and can be tested as a fixed effect. However, fitting a variance component model is computationally challenging, especially when it has to be done for a large number of markers. In the newly released version of the Mendel software , Option T-variate trait Y ∈ ℝn × T over a pedigree of vec(Y) into a vector v and the corresponding covariances into a matrix Σ and represents the loglikelihood of a pedigree asΣ = 2Σa ⊗ Φ + Σd ⊗ Δ7 + Σh ⊗ H + Σe ⊗ I. Here Φ is the global kinship matrix capturing additive polygenic effects, and Δ7 is a condensed identity coefficient matrix capturing dominance genetic effects. For Φ, Mendel can use (a) the theoretical kinship matrix from provided pedigree structures; (b) SNP-based estimates for the kinship of pairs of people within each pedigree; or (c) SNP-based estimates for the entire global kinship matrix ignoring pedigree information. To estimate kinship coefficients from dense SNP data, Mendel employs either the GRM or the method of moments [H has entries hij = 1 if individuals i and j are in the same household and 0 otherwise. Individual environmental contributions and trait measurement errors are incorporated via the identity matrix I. QTL fixed effects are captured through the mean component υ = Aβ for some predictor matrix A and vector of regression coefficients β. To test a SNP against a T-variate trait, A is augmented with T extra columns holding the allele counts at the SNP, and the corresponding regression coefficients are jointly tested for association [p values (top 10 by default) are further tested by the more accurate, but slower, likelihood ratio method, thus achieving a good compromise between speed and power for large-scale QTL analysis. We refer readers to our companion manuscript [QTL association mapping typically invokes the multivariate normal distribution to model the observed entclass1pt{minima moments , 4. The ociation . For lonMAP4 gene on chromosome 3 is evaluated from the 200 simulation replicates of the trivariate traits systolic blood pressure (SBP) and diastolic blood pressure (DBP). Type I errors are evaluated from the univariate Q1 trait, which does not involve a major gene. Our analysis includes covariates sex, age, BPmed, smoke, and their pairwise interactions, and uses the theoretical kinship matrix as the additive polygenic variance component. We constrain the covariate effects to be equal across 3 time points. Table The power to detect the 6 functional variants in the i, DBPi, i = 1, 2, 3, 4). Our model includes covariates sex, age, BPmed, smoke, and their pairwise interactions, and we constrain the covariate effects to be equal across 4 time points. The log-likelihoods of the null model (no SNPs included) using the theoretical kinship, GRM within pedigrees, or GRM across all individuals are −11675.95, −11696.90, and −11698.71, respectively, indicating that the provided pedigree information captures additive genetic effects adequately. The results summarized below use the theoretical kinship matrix.Our analyses are based on the genotype calls for 959 individuals (464 directly sequenced and the rest imputed) provided in the chrNN-geno.csv.gz files. SBPs and DBPs measured at 4 time points are available for 1389 members from 20 extended families. The largest family contains 107 individuals; the smallest, 27. Genotypes at 8,348,674 SNPs were available on 959 of the individuals. We analyzed all SNPs and pedigrees together for the 8-variate trait  of 0.05 is 4.19 × 10−8 or 7.38 on the log10 scale.To read in all the data and run standard quality control (QC) procedures took just under 5 min. QC excluded 10,603 SNPs and 110 individuals based on genotyping success rates below 98 %. The remaining 8,338,071 SNPs and 849 individuals were analyzed. The subsequent ped-GWAS analysis ran in 73 min for all results reported in Fig. p <10−22, indicating possible genotyping error. The remaining 2 significant SNPs occur at 118,783,424 and 118,767,564 base pairs, respectively, on chromosome 11. Both show a minor allele frequency (MAF) of 0.02778 in 413 founders. Because the MAFs in all 849 individuals are higher than 0.03, they were not removed in the filtering stage.Table Genome-wide measures of 20,634 gene expression levels in peripheral blood mononuclear cells from the first study examination are provided for 643 individuals in the family data. The formidable task of exhaustive expression quantitative trait locus (eQTL) analysis  can be easily managed using Mendel. We submitted 20 parallel jobs to a cluster and finished the complete analysis in approximately 30 h.− 13.In all eQTL runs, SNPs and individuals with genotyping success rate equal to or less than 0.98 are excluded from analysis. Rare variants with MAF entclass1pt{minimaA second data set consists of exome sequence calls, blood pressure phenotypes at a single time point, and simulated phenotypes on a large set of unrelated individuals. Like the family data set, these individuals are Mexican Americans; however, they were independently ascertained and do not overlap with the family data set.The data set provides 200 simulation replicates of the trait SBPs and DBP. However, GAW19 organizers did not distribute the exact simulation details, except to state that “The set of causal variants is somewhat different since this is exome data rather than the full sequence data that was provided last time, and so not all of the GAW18 variants, regulatory ones in particular, are present in the new data set.” This precludes a precise size and power study.For ease of comparison, we tested 5 of the 6 variants displayed in Table p values were calculated for 52,314 SNPs. Accordingly, the genome-wide significance threshold is 9.56 × 10−7 or 6.02 on the log10 scale.The phenotypes SBP and DBP measured at the first examination are available for 1943 unrelated American Mexicans. We analyzed all SNPs and bivariate traits . To read in all the data and run standard QC procedures took 1 min and 16 s. QC excluded 10,191 SNPs and 93 individuals based on genotyping success rates below 98 %. The remaining 1,701,575 SNPs and 1850 individuals were analyzed. GRM calculated from whole genome SNPs was used to adjust for polygenic effects. The subsequent ped-GWAS analysis ran in 37 min and 5 s and included all of the results plotted in Fig. Estimated environmental effects and their interactions and variance components under the null model (no SNPs included) are listed in Table http://www.genetics.ucla.edu/software. Pedigree GWAS (Option 29) in Mendel proves to be an extremely efficient and versatile implementation for large-scale QTL analysis. Most competing programs ignore multivariate traits and outliers altogether. See Zhou et al [All analyses in this article use Mendel v14.3, which is freely available at ou et al  for a siou et al  and GEMMou et al  programs


The large biological distance between genetic risk loci and their mechanistic consequences in the tissue of interest limits the ability to establish functionality of susceptibility variants for genetically complex traits. Such a biological gap may be reduced through the systematic study of molecular mediators of genomic action, such as epigenetic modification. Here, we report the identification of robust genetic estimators of whole-blood CpG methylation, which can serve as intermediate molecular traits amenable to association testing with other genetically complex traits. We describe the relationship between these estimators and gene expression, demonstrate their genome-wide applicability to association testing even in the absence of individual genotypic data, and show that these estimators powerfully identify methylation-related genomic loci associated with polygenic traits and common diseases, such as schizophrenia. The use of genetic estimators for blood DNA methylation, which are made publically available, can serve as a valuable tool for the identification of epigenetic underpinnings of complex traits. This promise is being increasingly fulfilled. For example, cancer research has benefited dramatically from the discoveries related to the human genome2, mainly because the genomic mechanisms leading to the development of many cancers are amenable to direct observation. However, the situation is slightly different in disorders for which the underlying molecular events are not easily accessible, as is the case for mental disorders3. Advances in the development of high-throughput genotyping and analytical software, and the launch of large collaborative efforts have led to the identification of numerous well-validated genetic risk factors for such common disorders. However, the functional relevance of most discovered loci and the molecular mechanisms behind the reported genetic association signals remain elusive4.Improving understanding, diagnosis, and therapy of human disease has been one of the central promises of the human genome project4. For example, in such common neuropsychiatric disorders as schizophrenia, genetic susceptibility variants are significantly enriched in promoter and enhancer regions and point to a functional link between disease-associated noncoding single-nucleotide polymorphisms (SNPs) and transcriptional regulation in the brain5. The integration of transcriptomics data in the study of the genetic factors of complex traits has significantly improved our understanding of their genetic basis6. Thus, methods that reduce the gap between genetic susceptibility and its functional consequences are expected to increase our understanding of the genetic underpinnings of genetically complex traits.One of the main reasons for the limited ability to establish functionality of susceptibility variants is the large biological distance between a genetic polymorphism and its related mechanistic consequences in the tissue of interest. Such biological gap may be reduced by the study of molecular mediators of genomic action, such as gene expression. These methods capitalize on the joint additive effects of cis-markers on a given expression trait to estimate gene expression from individual genotypes. At the population level, the derived genetic estimates represent an intermediate molecular trait, amenable to association testing with the phenotype under study. This approach can be viewed as genetic correlation testing for which a significant association is interpreted as existence of shared co-localizing genetic factors between the complex phenotype and the investigated expression trait.Genetic estimators for gene expression have been recently proposed in this context10. High-throughput methylomic profiling studies have highlighted the strong local genetic regulation of DNA methylation15, with possibly multiple co-localized markers contributing independently to variation in DNA methylation at individual CpG sites16.Here we report the generation of robust genetic estimators of epigenetic regulation as an attempt to provide insights into the molecular basis of polygenic traits by minimizing the biological gap between genetic variation and its functional impact. We focused on DNA methylation  sites), the most extensively studied epigenetic modification to date, which directly regulates important molecular processes such as gene expression, imprinting, and chromosomal inactivationWe generated genetic estimators of DNA methylation (DNAm), that allow testing for localized shared genetic contributions between DNAm variation and complex traits. We demonstrate their applicability even to studies providing summary SNP statistics only, and show exemplarily that such estimators result in the identification of epigenetic underpinnings of a common neuropsychiatric disease.17, and from elderly adults .Whole-blood methylomic profiles and genotypic data were obtained from healthy young adults recruited in the course of two separate studies conducted in Basel, previously describedN = 533 participants  and the independent Basel Cognitive dataset (BASEL2) included a total of N = 319 participants . The study protocols were approved by the ethics committee of the cantons of Basel-Stadt and Basel-Landschaft. All participants gave written informed consent after complete description of the study protocols. Subjects were free of any neurological or psychiatric condition and did not take medication at the time of the experiment.The Basel Imaging dataset (BASEL1) included 18. The entire study protocol was approved by the local ethics committees at the University of Bonn, Bonn, Germany; the University of Hamburg, Hamburg, Germany; the University of Duesseldorf, Duesseldorf, Germany; the University of Heidelberg/Mannheim, Mannheim, Germany; the University of Leipzig, Leipzig, Germany; and the Technical University of Munich, Munich, Germany. Before participation written informed consents were collected from all subjects. Participants were followed-up in 1.5-year intervals and received cognitive testing at each follow-up19. Out of the ACD cohort a subsample comprising 302 subjects  with available whole-blood methylomic data and genotypic data was used in this study. After methylomic and genotypic samples quality control, a total of N = 288 subjects  were included in analysis. Subjects were free of any neurological or psychiatric condition.The ongoing German Study on Ageing, Cognition, and Dementia (ACD) started in 2003 and consists of 3327 non-demented elderly subjects over 75 years of age who were randomly selected from the general-practice registry in six German cities 17. Briefly, methylomic profiling was performed using the Illumina HumanMethylation450 array. Samples of non-European ancestry were identified using Hapmap references population genotypes and excluded from analysis . The β-values were calculated from SWAN normalized intensities20. Subsequently, β-values were M-transformed and adjusted for processing plate effect (z-transformation), age, sex, and the main sources of technical variations inferred from principal components analysis17. The β-values with detection p-value > 0.05 were considered as missing. Individual CpG sites were excluded based on the following criteria: non-CpG context, non-autosomal probes, probes with a SNP mapping to the target CpG site or with three or more SNPs within the 50-mer probe > 0.01) (based on RnBeads package annotation), multi-mapping or polymorphic CpGs (MAF > 0.01 in European population) reported in refs.22, and probes with missing rate ≥5% in final samples. Prior to analysis, missing values were imputed using the R package impute (https://bioconductor.org/packages/release/bioc/html/impute.html) with k = 10.A detailed description of methylomic profiling protocols can be found in Milnik et al.p > 0.05 (none detected). An additional subject processed on a single plate was further excluded from analysis. This yielded a total N = 297 samples for analysis. Methylation values were pre-processed using the wateRmelon package23. First, CpG sites with beadcount <3 in 5% of samples and/or sites with detection p > 0.05 in 1% of study samples were excluded. The β-values were next normalized using the dasen algorithm, logit transformed, adjusted for technical covariates (plate and Sentrix ID) using ComBat24, and finally adjusted for age, sex, and the six first principal component analysis axes.The Illumina HumanMethylation450 array was used to quantify DNA methylation in bisulfite converted genomic DNA from whole-blood samples. Each sample consisted of one technical probe. Subjects were excluded based on the following criteria: (1) inconsistency between reported and methylome estimated gender (two subjects excluded); (2) exceeding more than four s.d. from the mean on one of the two first principal components (one subject excluded); (3) inconsistency between actual genotypes and those inferred from methylomic data (none excluded); and (4) subjects with more than 1% of sites with detection 25. In each testing dataset, we compared EstiMeth model performance before and after further linear regression adjustment of DNAm for the estimated cell type proportions.Cell type proportion estimates  were obtained for each sample using the EpiDISH-CIBERSORT approach26 . In the BASEL1 dataset, approximately 5 million imputed SNPs with MAF > 0.05, Hardy–Weinberg equilibrium (HWE) p-value > 0.0001, and imputation score R2 > 0.8 were retained for training genetic models of DNAm estimation. To allow complete evaluation of the trained models, all selected markers were considered in the BASEL2 dataset.DNA was isolated from saliva sample and genotyped using the Affymetrix Genome-Wide Human SNP array 6.0 following the manufacturer’s protocol. Genotype imputation was performed independently for each BASEL1 and BASEL2 dataset, on the University of Michigan Imputation Serverp-value > 10−6, a MAF > 0.01, and a call rate > 95% were included. This led to a SNP reduction from 932,703 to 606,260 before the imputation. Genotype imputation was performed on the University of Michigan Imputation Server26.DNA was isolated from whole-blood samples and genotyped using the Illumina Infinium OmniExpressExome-8v1.3 Kit following the manufacturer’s protocol. Illumina’s GenomeStudio software was used to export the genotyping raw data into plink format. Variant and sample quality control was performed before imputation. Samples were excluded if their ancestry was non-European, if samples were related, if they had an outlying heterozygosity rate, or if they had a sample call rate < 98%. SNPs with a HWE R2 < 0.5. Models with less than 50% SNP coverage were discarded from analysis (n = 1061), yielding a total of 85,170 models evaluated.For evaluation of EstiMeth models, SNPs were filtered out based on the following criteria: (1) inconsistency of allele pairs between EstiMeth models and imputed genotypes, (2) MAF < 0.01, and (3) genotype imputation cis-SNPs within ±1 Mbp, were considered for analysis. At each of these individual CpG sites, an elastic net27 genetic additive model was fitted between all encompassing imputed cis-SNPs, and adjusted DNA methylation signal.A total of 395,014 CpGs, measured in both BASEL1 and BASEL2 datasets and encompassed by more than one 28 with α elastic net constraint fixed to 0.5. Default standardization of genotypes (mean centering and unit variance) was applied within the training procedure which resulted in slight improvement of model performance .Genotypes were coded as: 0: homozygous for the major allele, 1: heterozygous, and 2: homozygous for the minor allele. Models were implemented using the glmnet R packager2 between the model estimate—linear combination between elastic net inferred β-coefficients and observed genotypes—and the actual adjusted DNAm signal; for the training dataset, r2 refers to cross-validation performance.Model performance was assessed using Pearson’s squared correlation r2 in training dataset = 0.94%; minimum r2 in testing dataset = 1.37%).We derived a set of robust genotype-based estimators for DNAm—i.e. EstiMeth models—as follows: (1) all models exhibiting a significant association between the elastic net-derived cross-validation estimator and the actual values in the BASEL1 training dataset  < 0.05 across all non-null models); (2) among those, all models exhibiting a significant association between the elastic net-derived estimator and the actual values in the BASEL2 testing dataset (FDR < 0.05); (3) all models resulting in a positive correlation between actual and genotype-based estimated value in the testing dataset. This yielded a total of 86,710 models likely reflecting a robust genetically driven DNAm signal at the corresponding CpG (minimum observed 29 for estimating genetic correlation between EstiMeth model and a trait based on genome-wide association study (GWAS) summary statistics solely. Specifically, consider a given EstiMeth model comprising weights W at p SNPs. Let Tg denote the t-value between the EstiMeth linear combination and the trait. Let ∑p be the observed covariance matrix of the p SNPs, and Z the vector of standardized coefficients obtained from testing each SNP for association with the trait ).We relied on the approach recently proposed by Barbeira et al.29, Tg is equivalent to Zg:k;As described by Barbeira et al.k;p has to be estimated from a reference population, which leads to the approximation:In the absence of genotypes, the This approximation has two potential caveats.29, removal of the R2 ratio can lead to remarkable underestimation of Tg for SNPs with large effect sizes. This deviation was notably observed when comparing EstiMeth and MetaMeth approaches on DNAm signal, which implicate large effect sizes. Considering the actual sample’s covariance matrix, the exact statistic derived from Eq. Tg 7. We found empirically λs = 0.1 to achieve conservative results, at the cost of decreased power. Unless otherwise specified, all reported results were obtained using λs = 0.1Secondly, the divergence between the reference population and actual covariance structures can lead to biased estimates. Using Eq. ∑pref were inferred from the publicly available 1000G reference genotypes (http://ftp.1000genomes.ebi.ac.uk/vol1/ftp/release/20130502/) considering N = 503 samples from European populations. SNPs with allele pair mismatching alleles observed in the BASEL1 dataset were discarded, yielding a total of 5,059,361 markers referred as 1000G SNP panel (99% of markers from BASEL1 dataset). Elastic net models were re-trained on the BASEL1 sample using the 1000G SNP panel. Models not reaching the minimum r2 initially observed in the training and BASEL2 testing datasets were excluded from MetaMeth benchmarking analyses . Overall, we observed comparable performance of the EstiMeth models implemented on the BASEL1 and 1000G SNP panels .The SNPs covariance matrices n = 2,228,898 markers). Models reaching the minimum r2 initially observed in the training and BASEL2 testing datasets were retained, yielding n = 82,885 models, showing performance comparable to the EstiMeth models implemented on the BASEL1 dataset .To ensure sufficient coverage of EstiMeth models for the MetaMeth scan of GWAS summary statistics imputed from HapMap reference panel, we additionally provide EstiMeth models inferred from a restricted SNP panel. Elastic net models were re-trained on the BASEL1 sample using the SNPs overlapping between 1000G, HapMap SNPs, and BASEL1 imputed SNPs  while further adjusting expression values for increasing number of principal components;31 this procedure was repeated until no increase in the number of identified eQTLs was observed anymore, leading to 23 components retained for final adjustment of expression values. Only genes annotated to RefSeq identifiers were considered for analysis. The annotation was based on the manufacturer’s information (GPL17586-45144) curated using the UCSC database version Oct 2015. This yielded a total of 21,186 autosomal genes entering subsequent analyses.Blood samples were collected using PAXgene Blood RNA Tubes . Expression profiles were obtained for  2.0 see , providiN = 397,731 sites out of 397,947 CpGs from BASEL1 sample). Statistical association testing was performed using Pearson’s correlation test. Genome-wide significant associations were identified using Benjamini–Hochberg FDR correction. Expression signals were optimally processed for preserving genetic effects (see paragraph Data processing). In order to check whether this procedure possibly biased the over-representation of EstiMeth genetically driven CpGs among identified associations, the genome-wide CpG-gene association scan was re-conducted on expression data adjusted for main confounders only . This analysis led to the identification of 11,760 significant associations (FDR < 0.05), implicating 8530 CpGs, among which 74% involved EstiMeth CpGs, convergent with results obtained from the primary analysis.The relationship between DNAm and expression traits was examined considering for each gene all CpGs located within ±1 Mbp from gene boundaries . DNAm-expression associations were also examined under adjustment for EstiMeth models: DNAm was adjusted for EstiMeth estimated values using linear regression, and next tested for association with gene expression.32 were downloaded from https://www.med.unc.edu/pgc/files/resultfiles/scz2.snp.results.txt.gz. GWAS summary statistics for inflammatory bowel disease (IBD) obtained from meta-analysis across 34,652 European samples33 were downloaded from https://www.ibdgenetics.org/downloads.html, file: EUR.IBD.gwas_info03_filtered.assoc); summary statistics for rheumatoid arthritis (RA) obtained from meta-analysis across 58,284 European samples34 were downloaded from http://plaza.umin.ac.jp/~yokada/datasource/software.htm (file: RA_GWASmeta_European_v2.gz); summary statistics for Alzheimer’s disease (AD) obtained from meta-analysis across 54,162 European samples35 were downloaded from http://web.pasteur-lille.fr/en/recherche/u744/igap/igap_download.php (file: IGAP_stage1.txt); summary statistics for Height obtained from meta-analysis across 253,288 European samples36 were downloaded from http://portals.broadinstitute.org/collaboration/giant/index.php/GIANT_consortium_data_files#GWAS_Anthropometric_2014_Height. MetaMeth scans for SCZ, AD, IBD, and RA were conducted considering EstiMeth models implemented on the BASEL1 SNP panel  and corresponding SNP covariance structure inferred from BASEL1 dataset. MetaMeth analysis of height GWAS summary statistics was conducted considering EstiMeth models implemented on the HapMap SNP panel  and covariance structure inferred from BASEL1 dataset. SNPs with allelic mismatch between GWAS report and EstiMeth models were discarded. For each analysis, models reaching a SNPs coverage greater or equal to 80%  were retained . For each analysis, multiple testing adjustment was performed using Bonferroni method for the number of tests conducted.GWAS summary statistics of Psychiatric Genomics Consortium (PGC) schizophrenia (SCZ) analysis https://redgar598.shinyapps.io/BECon/ 37. Briefly, these metrics report, for each CpG, the coefficient of variation (CV) of β-values in whole blood, and correlation coefficients between blood and each of three brain tissues , derived from 63 paired methylomic samples (16 unique subjects). As reported in the original publication37, a CpG was considered as potentially informative between blood and brain tissues if it met the following criteria: (1) sufficient inter-individual variability in whole-blood DNAm characterized by a CV > 0.1; (2) concordance between whole blood and at least one brain tissue, characterized by absolute Spearman's correlation value >0.36 for BA7, >0.4 for BA10, and >0.33 for BA20 . Significance of enrichment of informative CpGs across EstiMeth CpGs was assessed using 10,000 permutations, each of which consisted of counting the number of informative CpGs within a randomly sampled n-set of CpGs .We downloaded summary statistics of concordance of CpG signals between blood and brain from , who underwent both whole-blood methylomic profiling and genome-wide SNP assessment. Prior to analysis, the DNAm signal was adjusted for technical and biological confounders , and genotypes were imputed using the Michigan imputation server26 .Our reference dataset comprised cis-SNPs  and adjusted DNAm signal at each individual CpG site . From 395,014 CpG sites investigated, a total of 236,923 non-null models  could be fitted, with cross-validation r2 accounting on average for 6.9% of variance of the DNAm signal.In the reference sample, a elastic net model was trained between common cis-markers that are likely to impact on DNAm at a given CpG site16. We compared the fraction of variance of DNAm explained by the elastic net models  with the fraction of variance explained by the single best methylation quantitative trait loci (mQTL) identified at each CpG site. We observed substantial gain in average r2 retrieved by the multiple regression elastic net over single-marker univariate testing  was close to the maximum variance in DNAm that can theoretically be explained by common SNPs. In addition, per-CpG cross-validation r2 showed high correlation with reported SNP-based (r = 0.53) and total heritability (r = 0.62) estimates across all modeled CpGs. Among CpGs for which no elastic net model could be fitted , lower SNP-based heritability was observed, with an average of 4%.Unlike univariate testing, the elastic net approach allows for simultaneous modeling of the joint effects of multiple N = 319 healthy young adults . The correlation of model performance between training and testing samples across all modeled CpGs was high (r = 0.96)  was very close to the corresponding performance of the training sample (r2: 6.9%). These findings demonstrate high stability and generalization capability of the implemented genetic models. A set of 86,710 genetic models for DNAm estimation was identified as highly robust, showing significant (FDR < 0.05) and consistent correlation with DNAm across the two independent BASEL1 and BASEL2 datasets  . We observed high correlation (r = 0.83) of EstiMeth model performance between the BASEL1 training and the ACD BONN dataset. In the ACD BONN dataset, the models accounted on average for 13.9% (mean testing r2) of DNAm . This result further supports the robustness of the derived models in whole blood.The EstiMeth models were additionally tested in an independent dataset comprising whole-blood methylomic profiles from r2 that was very close to the original distribution . This resulted in an overall average distribution of r > 0.99) before and after adjustment for estimated cell type proportions  .Each EstiMeth model corresponds to a CpG that is likely to be under strong genetic control. Given the role of DNAm in the regulation of gene expressionN = 397,731 sites). We identified 26,925 significant associations (FDR < 0.05), involving 6160 genes and 17,867 CpGs. Among these CpGs, we observed significant over-representation of EstiMeth CpGs .First, we performed genome-wide association testing between DNAm and expression levels of genes located within ±1 Mbp of any CpG site  CpGs are more likely to correlate with expression of co-localizing genes. This observation might also reflect the existence of shared genetic contributions between EstiMeth CpGs and the expression of their co-localizing genes.We also observed that EstiMeth CpGs, which were associated significantly with gene expression, were over-represented in shores . Given that gene expression was measured in the BASEL1 dataset, all EstiMeth models were re-implemented using the independent BASEL2 dataset as reference to prevent overfitting . Subsequently, a total of 2 million EstiMeth gene pairs were tested for association. We observed substantial deviation of genetic association signals from the null uniform distribution   Fig. . This suProvided availability of individual genotypic data in a given study sample, EstiMeth values can be readily obtained as the linear combination between the weights provided herein (derived from the BASEL1 dataset) and the observed SNPs Fig. .29. Based on this body of work, we extended the EstiMeth models to a ‘MetaMeth’ approach that allows genetic correlation testing from GWAS summary statistics  EstiMeth SNPs’ weights, (2) the standardized GWAS summary statistics , and (3) the covariance structure of the SNPs included in the EstiMeth model   Fig. . The impds) Fig. . This laZ-statistic should be close to the T-value obtained by testing directly association between height and the corresponding EstiMeth estimated DNAm values. Using the SNP covariance structure from the BASEL2 dataset, i.e., the actual population structure, the correlation between genetic correlation statistics was close to 1  and MetaMeth  genetic correlation approaches by considering height as the complex trait under study. Under quasi-interchangeability of the two approaches, the MetaMeth o 1 Fig. . We nexto 1 Fig. , supportp-value obtained per run yielded a 5% quantile equal to 7.4e−07 . This indicates that under realistic settings the proposed MetaMeth yields conservative association statistics.In a second stage, we estimated the Type I error rate of the MetaMeth approach. We performed a genome-wide MetaMeth scan on 1000 phenotypes generated from a normal distribution. The distribution of the minimum r2 = 7.3% yielding an association detectable at 50% power under Bonferroni adjustment for multiple testing). Over all CpGs, the MetaMeth achieved lower average power (44.8%) as compared to the EstiMeth method .We first applied MetaMeth on summary statistics obtained from the recently published schizophrenia PGC large-scale mega-analysis of GWAS resultsp-value < 5.78e−07). For the majority of these hits , the corresponding EstiMeth model included at least one marker exhibiting a GWAS association p-value that would have reached a genome-wide GWAS Bonferroni adjustment significance threshold (p < 5e−08) . Significant associations (Bonferroni adjusted p < 0.05 for the number of CpGs investigated within a given MetaMeth scan) were identified in each GWAS investigated  (Supplementary Tables p < 5e−08) was located within ±1 Mbp of the CpG site  and/or Height (n = 46) with an important fraction located on chromosome 6 (66%) within or nearby the extended MHC locus , 10 (BA10) and 20 (BA20) samples across N = 16 subjects37. We observed significant enrichment of CpGs previously reported as concordant between whole-blood and brain tissues37 among EstiMeth CpGs  . This suggests that a significant subset of the identified genetically driven CpGs show consistent DNAm pattern between blood and brain tissue.Recently, subsets of CpGs showing co-varying patterns between blood and brain tissue DNAmWe generated genetic estimators of epigenetic regulation—EstiMeth—that leverage genetic contributions to DNAm in whole blood to identify epigenetic underpinnings of complex traits. EstiMeth models together with MetaMeth and 1000G reference structure programs are made publicly available. By capitalizing on multiple co-localized genomic loci likely to impact on the DNAm signal, we identified a set of genetic estimators accounting on average for a modest, yet highly consistent fraction of variance in DNAm across independent samples.12. Here, integration of both methylomic profiles and gene expression data revealed that EstiMeth models accounted for a substantial fraction of the shared phenotypic variance between both molecular traits. This suggests that, in line with a recent report42, local genetic variations represent an essential factor underlying the observable inter-individual relationship between gene expression and DNAm at adjacent CpG sites. Importantly, the identified associations do not always imply direct causality between genetically driven DNAm and gene expression, as the EstiMeth models possibly include SNPs exerting independent effects on each trait12.Inter-individual variation in DNAm correlates with variation in expression levels of co-localizing genes possibly through shared genetic factors29. This approach, applied to recent large-scale GWAS results for schizophrenia32, resulted in the identification of 469 significant associations. This suggests the existence of shared genetic contributions between whole-blood DNAm and schizophrenia risk which is consistent with recent reports44. Of note, it cannot be excluded that the identified associations can also be partly driven by genetic loci exerting independent effects on each trait. A majority of the identified associations implicated genome-wide significant GWAS hits, whilst encompassing slightly less than half of the 105 genomic regions associated with schizophrenia32. In analogy to the findings obtained in the schizophrenia GWAS, the MetaMeth approach revealed significant associations with AD, RA, IBD, and Height, with the majority of the detected signals pointing to genome-wide significant GWAS markers. Importantly, each association suggests shared genetic contributions between a given trait and whole-blood DNAm variation at a specific CpG site. These results altogether highlight the potential of MetaMeth to decipher, from large-scale GWAS results, trait-associated loci that are putatively mediating their effect through methylation at given CpG sites, and to prioritize specific genomic loci for downstream functional validation.We also combined the genetic estimators for DNAm with recently proposed methods that allow applicability of these estimators to SNP summary statistics solely 37. Thus, the provided genetic estimators might also serve as a valuable tool for the study of co-variation patterns between peripheral and brain tissue DNAm, whenever intra-individual multi-tissue samples are not available.Given the tissue-specific nature of DNAm, no direct and mechanistic link can be inferred between the identified MetaMeth association signals for schizophrenia and DNAm patterns observed in brain tissue. In line with previous results, we nevertheless observed that CpGs showing concordant DNAm patterns across whole-blood and brain tissue were enriched among genetically driven EstiMeth CpGsOn the side of limitations, it should be stressed that the EstiMeth models were inferred and tested on moderately sized whole-blood samples. For about one-third of the investigated CpGs, characterized though by lower average SNP-based heritability, no elastic net model could be fitted from our training sample. Thus, additional local genetic contributions to DNAm might be detected with increasing sample sizes.The fraction of variance explained by the EstiMeth models refers to DNAm signal after adjustment for main confounders. As for any omics dataset, such confounders are usually unknown and estimated empirically in a study-specific manner. This might ultimately impact on the fraction of variance in DNAm that can be retrieved by the derived genetic estimators. For instance, in our study, we observed that these estimators showed, on average, higher performance on a testing sample as compared to the training sample. Thus, although high stability was globally observed between performance of the models across the investigated samples, inference on multiple independent datasets, and multiple tissues, is warranted to fully appreciate their generalizability.7. In addition, the derived genetic estimators were built on cis neighboring SNPs only. Although we globally observed high consistency of the inferred models’ performance with published SNP-based heritability estimates, the performance was on average lower than the reported common SNP heritability. This gap might be explained by additional trans genetic components likely to contribute to inter-individual variability in DNAm44. Improved accuracy might thus be achieved by extending the modeling to trans genetic components, as was recently shown for gene expression45.We also note that we generated a genetic estimator of DNAm at each single CpG site. Although this provides a straightforward way of annotating the models, it also results in certain redundancy of the estimators for highly correlated CpG sites. This in turn leads to a number of inferred estimators, which, unlike genetic estimators for gene expression, allow only for a moderate reduction of multiple testing burden in GWAS49, we cannot totally rule out a possible contribution of this mark to the detected signals reported herein.We would also like to stress that the 450k array used in this study captures both methylation (5mC) and hydroxymethylation (5hmC). Even though the 5hmC mark remains strongly underrepresented in whole-blood tissueConcerning the MetaMeth extension, we could derive empirical settings that showed appropriate control of Type I error in the investigated sample, yet at the cost of decreased average power of detecting genuine associations. Robustness of the derived statistic is also tightly linked to the genetic discrepancy between the reference and study population, which might not be easily evaluated in practice. This calls for assessment of the stability of the approach on larger independent samples from varying populations.In conclusion, we provide genetic estimators for DNAm in whole blood that can effectively complement genetic estimators for gene expression to gain insight into the molecular underpinnings of complex traits.Supplementary InformationSupplementary Table 2Supplementary Table 3Supplementary Table 4Supplementary Table 5Supplementary Table 6Supplementary Table 7


Parental education is the strongest measured predictor of offspring education, and thus many scholars see the parent–child correlation in educational attainment as an important measure of social mobility. But if social changes or policy interventions are going to have dynastic effects, we need to know what accounts for this intergenerational association, that is, whether it is primarily environmental or genetic in origin. Thus, to understand whether the estimated social influence of parental education on offspring education is biased owing to genetic inheritance (or moderated by it), we exploit the findings from a recent large genome-wide association study of educational attainment to construct a genetic score designed to predict educational attainment. Using data from two independent samples, we find that our genetic score significantly predicts years of schooling in both between-family and within-family analyses. We report three findings that should be of interest to scholars in the stratification and education fields. First, raw parent–child correlations in education may reflect one-sixth genetic transmission and five-sixths social inheritance. Second, conditional on a child’s genetic score, a parental genetic score has no statistically significant relationship to the child’s educational attainment. Third, the effects of offspring genotype do not seem to be moderated by measured sociodemographic variables at the parental level (but parent–child genetic interaction effects are significant). These results are consistent with the existence of two separate systems of ascription: genetic inheritance (a random lottery within families) and social inheritance (across-family ascription). We caution, however, that at the presently attainable levels of explanatory power, these results are preliminary and may change when better-powered genetic risk scores are developed. If researchers studying educational attainment merely want to describe the extent to which children resemble parents on this dimension of stratification, they need not concern themselves with the mechanisms by which such an intergenerational correlation is obtained. However, if scholars seek to explain how this social fact comes into being and, furthermore, wish to know whether policies that affect the distribution of education in one generation will have distributional consequences in the next generation, then whether the observed parent–child correlation in education reflects social inheritance or genetic inheritance should be of utmost importance. If family resemblance in educational attainment is socially oriented, then changes in the distribution of education in one generation will have important implications for the distribution of education in the next . Howeveoverall correlation between siblings, for instance, that measures the relative openness or closure of a stratification system , some sociologists have persuasively argued that we should abandon raw or adjusted mobility rates  as measures of openness and meritocracy. Rather, stem cf.  but rathstem cf. . In thisstem cf. .1With these concerns in mind, ascertaining the proportion of a quantitative trait—such as IQ, education, or income—that is due to genetic variation has long been of interest to a wide range of social and behavioral scientists, despite the controversy surrounding such estimates  and not her genetic bequest. Such a possibility is raised by the robust literature showing that prenatal environment matters dearly to children’s development and ultimate socioeconomic success  contributions to offspring educational attainment remain unmeasured; genotype—a measured variable—is not included. As such, we cannot directly assess each component  along with parental (or other) characteristics to see how intergenerational genetic and environmental correlations may mediate each other. Furthermore, in both twin and adoptee study designs, 2Moderation of genotype by environment has long been an interest of social scientists. By way of example, The article proceeds as follows: Availing ourselves of two data sets with molecular genetic markers as well as educational information for parents and offspring , we first estimate overall latent heritability of education using an approach that relies on unrelated individuals (genomic-relatedness-matrix restricted maximum likelihood estimation [GREML]). We then utilize results from independent genome-wide studies of education to calculate a genomic risk score (GRS) for those two samples. Finally, we ascertain whether the inclusion of this genomic risk score substantially alters parameter estimates for parental education variables on offspring education and whether this genomic risk score moderates the effect of other, sociodemographic variables. In the following, we detail this novel approach to interrogating genetic mediation and moderation in models of educational inheritance.The recent collection of genetic markers from respondents of large and representative samples of adults has opened up an opportunity for researchers to directly confront and measure one of the two main “lurking” variables that threaten to bias traditional models of socioeconomic attainment . Many novel approaches are possible as a result of the direct measurement of individual genetic variation. In the present study, we deploy two.First, rather than fixing the values of genetic relatedness  in the twin based models, genome-wide similarity among biological siblings has provided comparable estimates of heritability without the strong assumptions that accompany the twin model . More imThe most important shortcoming of GREML estimates is that they still focus on a latent quantity (heritability) that cannot be used to directly test whether genotype mediates or moderates observed phenotypic relationships across generations. To do that, we need a measured—rather than latent—indicator of genotype. One method would be to test each measured allele separately, but this approach is seriously hobbled by the combination of weak effects of individual alleles on something as complex, distal, and polygenic as educational attainment. Instead, the solution at present is to collapse all the information from thousands or millions of markers into a single scalar that can then be easily deployed. This scale is known as a GRS and requires extremely large sample sizes that vastly exceed those available to any single social scientific study.p < 5 × 10−8) and replicated in the independent samples, these explained a trivial amount of the total variance in years of schooling or college attendance. Relaxing the significance threshold for SNPs included in the genetic risk score for educational attainment continually increases the predictive power. When all SNPs are taken into account, this single scalar can explain between 2 and 3 percent of the variance in years of schooling. This suggests that to the extent that it is associated with genotype, educational attainment—as we might expect—is driven by many small effects across the entire genome. This finding has further been replicated in new samples with stricter controls and the deployment of sibling fixed effects models  should significantly lower the coefficient on parental education. This is a direct test of the genetic transmission hypothesis that improves on adoption and kinship studies, which may confound prenatal effects with genetic ones, as well as studies that control for IQ, which itself is affected by social environment .Two and a half percent is a relatively small contribution to our understanding of educational outcomes, especially when compared to the published meta-analyses that find that genetic factors account for up to 40 percent of the variation . There aWe also investigate whether the effects of offspring genotype interact with the socioeconomic conditions of the parental household—specifically with maternal education. That said, an ideal test would be examine if the underlying genotype interacts with exogenous environmental shocks, such as school or tax policy interventions . We knowThe data for the present study come from the second- and third-generation respondents of the Framingham Heart Study (FHS) as well as from the Health and Retirement Study (HRS).We describe the specifics of the genotyping for each data set in SD = 17.10 years). The third-generation respondents of the FHS who are included in our sample  are just under a decade younger at 39.49 years of age on average, with concomitant lower variability as well (SD = 7.67 years). Meanwhile, the HRS sample is much older, by design, with a mean age of 68.17 years and a standard deviation of 10.5 years by virtue of its cohort design (we randomly select a wave for each respondent). While the age distribution does vary considerably, the sex ratio is almost the same, ranging from 50 to 58 percent female across the samples. Finally, the mean education levels also vary between the different studies for a variety of reasons, including attrition, region, age, and cohort effects. The FHS displays the highest mean education levels for both the respondents and their parents. This may be due to the fact that Massachusetts is a state with high average educational levels as compared to the nation writ large. For example, the mean rate of college graduation was highest in Massachusetts of all the states in the United States at 38.2 percent in 2009; meanwhile, the nation as a whole had a mean bachelor degree attainment rate of 27.9 percent  with the inclusion of maternal education as a measure , we do not find that the parameter estimate for maternal education drops substantially—only 3.33%. If the proper scaling factor is 5 , maternal genotype matters.For now, we turn to the question of whether maternal genotype rather than offspring genotype is the key omitted variable. To test this possibility, we add parental genotype to the model to see if it has a direct effect on offspring educational attainment alone as well as net of parental education and offspring genotype and/or whether it explains part of the effect of parental education. In model 4 of the FHS data in R2 = 0.026). Despite a slightly larger effect for genotype and a slightly smaller effect for maternal education, when we compare across models in the HRS, the story is much the same as it was for the FHS sample. Namely, comparing models 2 and 3, we see that the coefficient for genotype drops by about a third in magnitude when maternal education is held constant—a slightly smaller drop than seen for the FHS data. Likewise, when we compare the coefficients for maternal education in model 1 to those with GRS controlled for in model 3, we find that it has dropped by 3.8 percent. Here, if we scale up to 20 percent heritability  and 50 percent relatedness, this would mean 14.4 percent of the intergenerational association between one parent and her offspring in educational attainment can be accounted for by genetic factors.When we perform a similar exercise with data from the HRS, we find that a corroborating story emerges. In this data set, we do not have the genotypes of the parents, so we can only answer the question of whether offspring genotype biases or is biased by observed maternal education. The story that emerges is much the same. Both maternal education (model 1) and respondent genotype (model 2) predict offspring education when run separately. In model 1, each additional year of maternal schooling results in three-tenths of an additional year of school for the offspring. Likewise, in model 2, we see that a 1 standard deviation change in genetic score of the offspring is associated with 0.41 additional years of schooling. The score is more predictive for the HRS than for the FHS sample .Finally, it could be the case that alleles are nonrandomly distributed across social groups, making the genetic effect spurious. For example, imagine group A has higher education on average than group B for historical, cultural, or economic reasons. Meanwhile, group A also scores higher on the polygenic risk score for education for random reasons of genetic drift. It could appear that the polygenic risk score causes educational attainment when it is really just acting as a proxy for socially observable differences. To address this concern, we run sibling fixed effects models. By comparing full siblings from the same family, concerns about genetic–environmental confounding are obviated because the differences in polygenic risk score between siblings stem wholly from random processes in reproduction. We do not have sibling data in the HRS, so we confine this analysis to the FHS sample. In A different story emerges when we look at the effect of the coefficient itself. Here we find that the point estimate from the within-family regression is larger than in the between-family regressions. Within families, we see that for each additional standard deviation in GRS relative to one’s sibling, the educationally more endowed sibling completes 0.32 more years of schooling. But comparing unrelated individuals across families, the difference in schooling is only 0.27 years. In other words, it may be the case that any reinforcing effect on social stratification that the between-family distribution of genetic ability has on the reproduction of educational attainment across generations due to genetic assortative mating is compensated for by the greater effect of genetic endowment on schooling within families  cf. . How canFinally, as a robustness check, in 5 does—contrary to ilibrium .) LastlyWith these rationales in mind, we are the first researchers to deploy a polygenic risk score to model the transmission of educational attainment from parents to children. This approach avoids the confounding of genetic effects with prenatal environmental effects from which adoption studies suffer. Also, this approach complements twin models, which suffer from limits with respect to external validity and may confound exogenous pre- or postnatal environmental factors that covary with genetic relatedness. Finally, deploying explicitly measured genotype in models allows us to do a formal mediation analysis that is not possible in the variance portioning exercises inherent to the twin or adoption studies. By comparing across models of intergenerational educational inheritance with and without genotype controlled for, we are able to come to some tentative conclusions. First, when we include offspring genotype to control for spurious effects of parental education due to parent–offspring similarity in genetic educational endowment, we find in two different data sets that the coefficient for maternal education (our focus) or paternal education  is indeed slightly attenuated. The amount of attenuation is trivial, and a Hausman test reveals it not to be significantly different from zero. However, if we accept the point estimates as accurate and make a few other assumptions  endowment , genetic stratification is not an accurate description of the interplay between genes and social status. ndowment . If thisr = 0.22 among FHS parents and 0.22 among HRS spouses), the within-family differences in genetic stock that generate observed social mobility  partially counteract any between-family effects of the distribution of genetic stock, educational attainment, and assortative mating at the parental level. While assortative mating means that there is indeed greater variance between families on genotype than within families (the sibling r in FHS is 0.59), the actual strength of the effect (which is greater within families) may be due to the fact that small differences in endowment between siblings generate a very elastic social response of differentiation within the household. That is, siblings may engage in niche formation that accentuates the differences in genotype, or it may be the case that parents differentially invest and create larger differences as the endowments of their various offspring are revealed to them through interaction over the course of childhood. In other words, the randomness of recombination and segregation of alleles during sexual reproduction along with the within-family accentuation of endowment effects serve to help counteract any cross-familial social sorting by genotype to help “reset” the genetic playing field for the next generation.However, in our analysis, we find that despite a moderate degree of assortative mating on educational genotype  does not appear to hold true. An important caveat to all this analysis is that heritability—that is, genetic effects—is, of course, highly contingent on social structure, whether measured latently through kin correlations or directly by a GRS. Indeed, heritability is not a fixed parameter across time and place but is always a “local perturbation analysis” estimate, as cogently argued by Lastly, parental genotype has no net effect on offspring educational attainment once genetic transmission  and parental years of schooling are controlled for. That is, parents’ genes are not leading to social advantages above and beyond their own schooling. The counterfactual of genetically advantaged parents having Appendix A and B


Understanding human mating patterns, which can affect population genetic structure, is important for correctly modeling populations and performing genetic association studies. Prior studies of assortative mating in humans focused on trait similarity among spouses and relatives via phenotypic correlations. Limited research has quantified the genetic consequences of assortative mating. The degree to which the non-random mating influences genetic architecture remains unclear. Here, we studied genetic variants associated with human height to assess the degree of height-related assortative mating in European-American and African-American populations. We compared the inbreeding coefficient estimated using known height associated variants with that calculated from frequency matched sets of random variants. We observed significantly higher inbreeding coefficients for the height associated variants than from frequency matched random variants (P < 0.05), demonstrating height-related assortative mating in both populations. Physical location, race, religion, ancestry, socioeconomic status (SES) and physical characteristics all influence mate choice9. Assortative mating, a phenomenon in which people choose mates with similar phenotypes to theirs in terms of physical traits and/or socio-cultural factors, is the most common deviation from random mating in Western societies11. Assortative mating studies have examined a wide array of factors for diverse purposes11. In general, age, education, race, religion and ethnic background show the strongest degree of assortative mating19. In addition to underlying biological traits, patterns of mate selection is often affected by the distribution of wealth and socioeconomic status, and taken together can impact on genetic structures of traits in a population if they are associated with genetic variation21.Human mate choice is relevant to a wide range of scientific disciplines, including biology, sociology, population genetics, evolutionary biology, and psychology22. A key outcome of assortative mating is that it increases homozygosity of variants associated with traits that affect mate choice and causes an increase in genetic variance in a population and the corresponding trait variance, but does not change the allele frequencies unless the genetic variants are under differential selection5. When a trait forms a basis on which to select mates, it will inflate the estimated heritability for this trait based on parent-offspring studies24. If parental traits are correlated, then the offspring will have a higher probability of having the same alleles that affect the trait compared to their genomic backgrounds. In contrast, when estimating the heritability from twin studies, it is assumed that monozygotic (MZ) twins are genetically identical and share 100% of their genetic patterns, and dizygotic (DZ) twins share half of their genomes. Therefore, assortative mating does not affect trait correlation between MZ twins because MZ twins are genetically identical, but increases the correlation between DZ twins. As a result, assortative mating reduces the difference between MZ and DZ correlations, and which may lead to an underestimated heritability, if mating patterns are ignored26.From the population genetics perspective, assortative mating can affect heritability estimates, create correlations among traits that were initially unrelated and affect trait variance within and between families16. Without accounting for assortative mating in genetic association studies, spurious associations may be observed for loci involved in the assortative mating process, and thus lead to an inflated false positive rate28. Another important aspect of assortative mating is that it increases the correlations between relatives for traits involved in mate choice, thereby increasing between-family variance11. Without properly modeling assortative mating, parameter estimates in association studies could be biased. Lastly, variants involved in assortative mating may be incorrectly eliminated from analyses because they violate Hardy-Weinberg equilibrium.Assortative mating can create correlations between previously uncorrelated traits when these traits are involved in the mating selection preference10. And because height has been associated with a range of health problems, such as cancers29, heart disease30, stroke31 and Alzheimer’s disease32, understanding how mate choice affects genotypes associating loci may help us to interpret results for these other traits as well. The estimated heritability of height is approximately 0.80 based on full-sib pair analysis33, but may be overestimated due to shared common environmental factors. Large GWAS studies identified common variants that together explain 50% to 60% of the heritability of adult height36. Genome wide association studies have identified about 700 variants associated with human height in individuals of European-ancestry37. These variants cumulatively explain approximately one fifth of the phenotypic variation in height and provide the most complete description of the genetic bases of a polygenic effect in humans. Although numerous height loci have been identified by GWA studies in Europeans, fewer have been reported in African-American populations, possibly because of smaller sample sizes and small estimated effect sizes of individual variants39. There is some debate whether spouse similarity for height can be explained by ancestry assortative mating40. Sebro et al.3 noted ancestry assortative mating in European Americans reflects a North-South European cline, which correlates with height. A recent study by the same group indicated that the height-related assortative mating is smaller than that for assortative mating by ancestry41. Thus, it is unclear whether assortative mating for height can be separated from the assortative mating for ancestry. Since assortative mating for height will only affect loci that contribute to height variation (and those in linkage disequilibrium with them), the genotype distributions of the identified height associated variants can be used to evaluate the evidence of assortative mating. In this study, we sought to quantify the genetic bases of height-related assortative mating by estimating the inbreeding coefficients of the height associated variants as compared to expectations for non-height associated loci. Simply, we tested the hypothesis that height associated variants have larger inbreeding coefficients than those for other loci in the genome. Results consistent with this hypothesis can provide complementary evidence that these variants are in fact height associated as it has previously been shown that deviations from Hardy Weinberg Equilibrium can provide independent evidence for association45.Among the traits that affect mate choice, e.g., education, SES, skin color, height is one that has been shown to be highly heritable, has a polygenic architecture, and is well studied genetically46. We first calculated the height correlations between spouses. Table The Cleveland Family Study (CFS) is an epidemiologic longitudinal study of participants who reside in Cleveland, Ohio. CFS recruited 645 European-Americans from 139 families and 652 African-Americans from 147 families34. These 697 independent variants are located in 432 loci, and their corresponding genes are enriched in biological pathways for human skeletal growth. Among the 697 height-associated SNPs, 196 and 270 SNPs were directly genotyped in ARIC and CFS cohorts, respectively. An additional 315 and 325 SNPs could be replaced by proxy SNPs based on LD (r2 > 0.9) derived using the 1000 G reference panel, which provides 511 and 595 height-associated SNPs for the two European-American cohorts, respectively   3) (See P < 5 × 10−5) identified from the GWAS of the Women’s Health Initiative (WHI)39 for the height-related assortative mating analysis. The number of SNPs genotyped in African-American cohorts range from 158 to 168 . We calculated the correlation between effect size and inbreeding coefficient using the 521 genome wide significant SNPs and their corresponding inbreeding coefficients. We did not observe a significant correlation . Our result indicates that inbreeding coefficient is independent of the effect size of height associated variants, and the estimated average inbreeding coefficient is likely underestimated when only top of height associated markers are used for analysis.We observed negative average inbreeding coefficients for randomly selected SNPs in most of our studied cohorts Table , althoug48. The North-South European admixture can be clearly observed   analysisved Fig. . We thenved Fig.  and calc−3 and 4.2 × 10−3 for ARIC European and CFS European, respectively. For the five African-American cohorts, the estimated inbreeding coefficients range from 8.62 × 10−3 to 2.477 × 10−2. The estimated inbreeding coefficients using all height-associated loci are approximately equivalent to the average of inbreeding coefficient for the single locus analysis, as expected. We observed that the inbreeding coefficients estimated using height associated variants fall in the right tails of the inbreeding coefficient distributions calculated using randomly sampled allele frequency matched SNPs  for all the cohorts, and they are all statistically significant  and PC-loading products (P = 6.33 × 10−56 for PC1 and P = 5.06 × 10−41 for PC2) (Table We further assessed assortative mating for height by regressing pairwise linkage disequilibrium (LD) score on the products of the first two PC loadings and the product of effect sizes of height associated variants in the ARIC European cohort, a method demonstrated to be robust with respect to population structure51, with estimates of correlation between spouse-pairs ranging from 0.24 to 0.4. We observed that the estimated inbreeding coefficients for height associated variants were consistently larger than that for frequency matched random markers using either single or multiple locus analyses in both European Americans and African Americans. Since assortative mating can be affected by socio-demographic factors, Laurent et al.4 suggested to use the genome wide distribution as a control. We estimated the inbreeding coefficients across the genome in the studied cohorts  score on the products of the first two PC loadings and the product of effect sizes of height associated variants in the ARIC European cohort. We observed significant association between LD and height effect size after adjusting for the PC loadings of the first two PCs , and this may result in negative average inbreeding coefficient estimates. (2) In F1 populations, the homozygote frequency will decrease by an amount of the variance of frequency among subpopulations . In admixed populations, there can be many subjects whose parents are from different ancestries, even if defined as European. For example, the ARIC cohort probably has numerous samples where one parent was from Northern Europe and the other from Southern Europe , further providing evidence of height-based assortative mating in the ARIC European cohort (Tables 54) that may contribute to its variation33, it is possible that some of our randomly selected SNPs are actually associated with height. If this is the case, then our resampling analyses are conservative in testing for assortative mating. Nonetheless, we found evidence for height related assortative mating in all studied cohorts. It should be noted that our method cannot differentiate active assortative mating from passive assortative mating, i.e., that related to social or geographical homogamy.To further investigate the negative inbreeding coefficients, we analyzed the ~2,500 and ~5,000 most significant height associated SNPs from the GIANT height genome wide association study. The estimated inbreeding coefficients became more positive on average with an increasing number of height-associated SNPs. Increasing the number of marginally significant height SNPs in the estimates of inbreeding coefficients increased the difference with respect to the random SNPs . The genotype data from the Candidate Gene Association Resource (CARe) consortium were downloaded from the dbGaP.61. Four examinations over 16 years included measurements of sleep apnea, anthropometry, and other related phenotypes, as detailed previously61. The CFS (dbGaP phs000284.v1.p1) includes 645 European Americans in 139 families who were genotyped on the OmniChip 2.5 M array. The ARIC data were downloaded from dbGaP database (dbGaP phs000090.v1.p1). The ARIC study, sponsored by the National Heart, Lung and Blood Institute (NHLBI), is a prospective epidemiologic study designed to investigate the etiology and natural history of atherosclerosis, the etiology of clinical atherosclerotic diseases, and variation in cardiovascular risk factors, medical care and disease by race, gender, location, and date. It includes 9,707 independent subjects genotyped by Affymetrix 6.0 array.The European cohorts included Cleveland Family Study (CFS) and Atherosclerosis Risk in Communities (ARIC). The CFS is a family-based longitudinal study starting in 1990 comprised of index cases with laboratory diagnosed sleep apnea, their family members, and neighborhood control families62. CARe has assembled samples from 9 community-based cohorts representing four ethnic groups: European-American, African-American, Hispanic, or Chinese-American, as described in detail62. The African-American samples for our assortative mating analysis were obtained from five CARe cohorts: Atherosclerosis Risk in Communities (ARIC: dbGaP phs000280.v1.p1), Coronary Artery Risk Development in Young Adults (CARDIA: dbGaP phs000285.v2.p2), Cleveland Family Study (CFS: dbGaP phs000284.v1.p1), Jackson Heart Study (JHS: dbGaP phs000286.v1.p1), Multi-Ethnic Study of Atherosclerosis (MESA: dbGaP phs000283.v1.p1), a detailed description of each cohort can be found in63. Genotyping for those cohorts was performed with Affymetrix 6.0 array.The African-American samples are from the Candidate Gene Association Resource (CARe) consortium39 in both European-American and African-American populations to determine the degree of height-based assortative mating. The remaining SNPs were considered for use in a comparison group. For the set of non-height associated loci, we excluded SNPs in each individual dataset that had either a call rate (CR) < 0.95, a minor allele frequency (MAF) < 0.01 or 58. Individuals with a missing genotype rate > 0.1 were also removed. After QCs, ~600,000 markers remained in European-American cohorts for analysis. For the five African-American cohorts, ~800,000 markers passed QCs. Since our analysis assumed all markers are independent, we pruned SNPs using PLINK58 (r2 < 0.1). After pruning, the number of SNPs in analysis were between 68,453 and 65,069 for ARIC and CFS European-American cohorts, and between 119,725 and 189,966 SNPs for African-American cohorts, respectively. The minor allele frequency distributions for height associated variants and all variants across the genome are shown in Supplementary Figs All data quality controls (QCs) were performed for each cohort separately, and only autosomal loci were used. We selected the height associated variants from the most recent GWAS64 and excluded one individual of each pair with an estimated kinship coefficient >0.025. The final sample sizes were presented in Table 65 that requires allele frequency distributions in ancestral populations, which were not available for our European American cohorts. Since the estimated kinship coefficients from GCTA and REAP are highly correlated and we only estimated kinship coefficients, it should have little effect for the inbreeding coefficient estimates. Therefore, the difference in method should not affect our conclusions.To ensure the estimated inbreeding coefficients were not confounded by the related family members, we selected unrelated founders for the family-based cohorts (CFS and JHS). To avoid cryptic relatedness, we estimated the pairwise kinship coefficient among individuals using genome wide SNPs in each cohort by software GCTA5. In either case, the genotype frequencies can be written as:5. Both inbreeding and assortative mating will increase homozygote and decrease heterozygote frequencies. An inbreeding coefficient ranges between Assume that a marker with two alleles A and a, and the corresponding three genotypes are aa, Aa, or AA, with allele frequency 66 which maximizing the following log likelihood (logl):Assuming Note that the allele frequency is unaffected by inbreeding and assortative mating. Thus, we can maximize the inbreeding coefficient using an estimated allele frequency To test whether assortative mating exists in each cohort, we calculated the inbreeding coefficients when estimated using resampled frequency matched variants across the genome after excluding the height associated loci. Since these resampled SNPs are less likely to be height associated, the distribution of estimated inbreeding coefficient from resampling should reflect the distribution without assortative mating on this trait. We further performed a two sample T-test as well as a Kolmogorov–Smirnov test (KS-test) to compare the height-associated SNPs with the randomly selected frequency matched SNPs.We extended the maximum likelihood method to estimate the inbreeding coefficient at a set of height-associated loci. Consider a set of When a set of SNPs contributes to trait variation involved in assortative mating, the estimated inbreeding coefficient equation  will be The authors wish to acknowledge the support of the National Heart, Lung, and Blood Institute and the contributions of the research institutions, study investigators, field staff and study participants in creating this resource for biomedical research. The following nine parent studies have contributed parent study data, ancillary study data, and DNA samples through the Broad Institute (N01-HC-65226) to create this genotype/phenotype data base for wide dissemination to the biomedical research community:Jackson Heart Study (JHS): Jackson State University (N01-HC-95170), University of Mississippi (N01-HC-95171), Tougaloo College (N01-HC-95172); Multi-Ethnic Study of Atherosclerosis (MESA): University of Washington (N01-HC-95159), Regents of the University of California (N01-HC-95160), Columbia University (N01-HC-95161), Johns Hopkins University (N01-HC-95162), University of Minnesota (N01-HC-95163), Northwestern University (N01-HC-95164), Wake Forest University (N01-HC-95165), University of Vermont (N01-HC-95166), New England Medical Center (N01-HC-95167), Johns Hopkins University (N01-HC-95168),Harbor-UCLA Research and Education Institute (N01-HC-95169).The Atherosclerosis Risk in Communities Study is carried out as a collaborative study supported by the National Heart, Lung, and Blood Institute contracts N01-HC-55015, N01-HC-55016, N01-HC-55018, N01-HC-55019, N01-HC-55020, N01-HC-55021 and N01-HC-55022, and grants R01HL087641, R01HL59367, R37HL051021, R01HL086694 and U10HL054512; National Human Genome Research Institute contract U01HG004402; and National Institutes of Health contract HHSN268200625226C. Infrastructure was partly supported by Grant Number UL1RR025005, a component of the National Institutes of Health and NIH Roadmap for Medical Research; Cleveland Family Study (CFS): Case Western Reserve University (RO1 HL46380-01-16); Coronary Artery Risk in Young Adults (CARDIA): University of Alabama at Birmingham (N01-HC-48047), University of Minnesota (N01-HC-48048), Northwestern University (N01-HC-48049), Kaiser Foundation Research Institute (N01-HC-48050), University of Alabama at Birmingham (N01-HC-95095), Tufts-New England Medical Center (N01-HC-45204), Wake Forest University (N01-HC-45205), Harbor-UCLA Research and Education Institute (N01-HC-05187), University of California, Irvine ; Supplementary Figures