Accurate prediction of disease risk based on genetic factors is an important goal in human genetics research and precision medicine. Advanced prediction models will lead to more effective disease prevention and treatment strategies. Despite the identification of thousands of disease-associated genetic variants through genome-wide association studies (GWAS) in the past decade, accuracy of genetic risk prediction remains moderate for most diseases, which is largely due to the challenges in both identifying all the functionally relevant variants and accurately estimating their effect sizes. In this work, we introduce PleioPred, a principled framework that leverages pleiotropy and functional annotations in genetic risk prediction for complex diseases. PleioPred uses GWAS summary statistics as its input, and jointly models multiple genetically correlated diseases and a variety of external information including linkage disequilibrium and diverse functional annotations to increase the accuracy of risk prediction. Through comprehensive simulations and real data analyses on Crohn’s disease, celiac disease and type-II diabetes, we demonstrate that our approach can substantially increase the accuracy of polygenic risk prediction and risk population stratification, i.e. PleioPred can significantly better separate type-II diabetes patients with early and late onset ages, illustrating its potential clinical application. Furthermore, we show that the increment in prediction accuracy is significantly correlated with the genetic correlation between the predicted and jointly modeled diseases. Genetic risk prediction plays a significant role in precision medicine. Accurate prediction models could have great impact on disease prevention and treatment strategies. However, prediction accuracies for most complex diseases remain moderate mainly due to the challenges in identifying and quantifying the effects of genetic variants from millions of markers, limited access to individual-level genotype data, and lack of efficient computational methods. Up to now, most methods have been focused on predicting disease risk using data from a single trait. With the discovery of genetic correlations among many complex diseases, incorporating data of genetically correlated diseases could have the potential to increase prediction accuracy. Current statistical methods are not able to fully exploit the richness of these kinds of data to take into account the shared genetic architecture. To make use of commonly available GWAS summary statistics, we propose a novel method to address these challenges by jointly modeling genetically correlated diseases and integrating genomic functional annotations. We demonstrate the substantial improvement in accuracy in both extensive simulation studies and real data analysis of Crohn’s disease, celiac disease and type-II diabetes. Furthermore, we show that the increment in prediction accuracy is significantly correlated with the genetic correlation between the predicted and jointly modeled diseases. Achieving accurate disease risk prediction using genetic information is a major goal in human genetics research and precision medicine. Accurate prediction models will have great impacts on disease prevention and treatment strategies. Varioushttps://github.com/yiminghu/PleioPred), a principled framework that integrates GWAS summary statistics of genetically correlated diseases with various types of annotation data and reference genotype panels to improve risk prediction accuracy. Incorporating data from related traits and functional annotations increases the effective sample size and statistical power to detect functionally relevant variants, especially when diseases share similar genetic architecture. We compare PleioPred with state-of-the-art single-trait PRS-based approaches and demonstrate its consistent improvement in risk prediction performance using real data of multiple complex diseases.Integrating external information, e.g. pleiotropy , 3, LD , and funWe first apply PleioPred to Crohn’s disease (CD), celiac disease (CEL) and type-II diabetes (T2D) by jointly modeling them with known correlated diseases (i.e. CD with Ulcerative Colitis (UC); CEL with UC; T2D with coronary artery disease (CAD)) and show a statistically significant improvement in prediction performance in independent validation cohort over single-trait models. By comparing two-trait prediction model with and without functional annotations in both simulation and real data analysis, we demonstrate that functional annotation may further improve the performance of joint modeling. Furthermore, we show that PRS calculated from PleioPred can effectively partition T2D patients by their age of onset, indicating the potential clinical usage of our approach, 17. Thr1 and N2 denote the sample sizes for the two diseases and M is the number of markers. We assume a linear model with genotype matrices, effect sizes (β and γ) and random errors (ε and δ) mutually independent as followsWe propose a Bayesian framework to incorporate functional annotations and pleiotropy. We assume throughout the report that the phenotypes of two diseases  instead , 19. Herρe measures the covariance within the overlapping individuals between two studies. Denote the LD matrix and marginal effect size estimator from GWAS as: Ns is the number of overlapping samples between the two studies. When Ns is relatively small, we can discard terms with We also assume that the effect sizes of different SNPs are independent. As for random errors, we assume thatu et al. , we can i and ρg: = cor, represents the genetic correlation between two diseases. This is equivalent to a multivariate random effects model with various variance components. Suppose that the whole genome is partitioned into K functional regions A1, …, AK. We assume that the effect size of a SNP depends on the functional regions it falls in and the effect sizes are additive in the overlapping regions. To be specific, we haveτjc denotes the variance of the effect size of SNPs on disease j falling in Ac alone. In the random effects model, the variance of effect size can be interpreted as heritability and thus for convenience, we will use heritability of SNP i instead of the variance of effect size in the rest of the manuscript.We first consider an infinitesimal model to account for a polygenic genetic architecture. We assume that the effect sizes follow a multivariate normal distribution:Methods. When all the parameters are specified, we can estimate the expectation of the effect sizes given the marginal effect size estimators of two diseases. The PRSs are defined asDetails on parameter estimation are described in ρg as a tuning parameter and the posterior expectation of the effect sizes can be calculated in closed form , joint normal and point mass  and joint point mass  [That is, the effect sizes of SNP disease) . AlthougFor both infinitesimal and non-infinitesimal models, we used a total of 61 different annotation categories, including functional genome predicted by GenoCanyon scores , GenoSkyWe compare the prediction performance of eight methods, corresponding to infinitesimal and non-infinitesimal versions of single-trait and two-trait approaches with and without functional annotations. As shown in , 13, LDpAnnoPred-inf/AnnoPred: single-trait prediction model with 61 functional annotationsLDpred-inf/LDpred: single-trait prediction model without functional annotations, corresponding to a special case of AnnoPred when assuming only one annotation covering the whole genomePleioPred-anno-inf/PleioPred-anno: two-trait prediction model with 61 functional annotationsPleioPred-inf/PleioPred: two-trait prediction model without functional annotations, corresponding to a special case of PleioPred-anno when assuming only one annotation covering the whole genomeAll of these methods studied require a pre-specified tuning parameter except for PleioPred and PleioPred-anno. To select a suitable tuning parameter, we divided the independent testing dataset  into two equal parts , and selected the tuning parameters by optimizing prediction accuracy on dataset A. We then evaluated prediction accuracy using the remaining half of testing data, i.e. dataset B. Finally, we repeated the analysis one more time by choosing the tuning parameter on dataset B while evaluating the prediction accuracy on dataset A. Results from these two separate analyses were averaged to quantify model performance. Ideally, the parameter should be tuned in an independent cohort and then evaluated in another independent cohort. However, it is very challenging to find two independent cohorts without any overlapping samples with the training GWAS and we therefore chose a cross-validation scheme. In real data analysis, tuning the parameter within the same cohort may lead to a little bit over-optimistic results due to possible shared confounders. However, the proposed non-infinitesimal models address this issue via a hierarchical Bayesian approach to avoid tuning parameter and thus result in more robust and generalizable estimation. Besides the methods discussed above, we have also compared the performance of proposed joint models with a recently developed multi-trait analysis tool (MTAG ). FollowA1 and A2. Denote the heritability of each trait as m1 and m2 (both 300). Causal variants were generated as follows: one third of causal variants were selected from A1, one third from A2 and the rest from (A1⋃A2)C, of which p of the causal variants was shared by both diseases (0.2 and 0.8). Effect sizes of causal variants were sampled from We first performed simulations to demonstrate PleioPred’s ability to improve risk prediction accuracy. We simulated traits from GERA (dbGaP access number phs000674.v1.p1) genotype data, which contains 61,172 individuals genotyped for 670,176 SNPs. More specifically, we randomly selected ~28,000 individuals as training set to calculate the summary statistics for disease 1 and another ~28,000 for disease 2. The remaining ~5000 individuals were used for testing. Throughout the simulation we used genotype data of chromosome 1  to generate phenotypes. We first generated two annotations and each annotation was simulated by randomly selecting 10% of the genome, denoted as Correlations between simulated and predicted traits of disease 1 were calculated from 50 replicates under different simulation settings. PleioPred-anno showed the best prediction performance in all settings . The percase = 6,333 and Ncontrol = 15,056, with samples from the Wellcome Trust Case Control Consortium (WTCCC) removed from the meta-analysis), a CEL GWAS with 4,533 cases and 10,750 controls [case = 6,687 and Ncontrol = 19,718). For the validation data, we merged the CD cases from WTCCC  and CEL cases from the National Institute of Diabetes and Digestive and Kidney Diseases study  with healthy controls from the Resource for Genetic Epidemiology Research on Aging Cohort . For T2D, we trained the model on summary data from the Diabetes Genetics Replication and Meta-analysis study  [case = 22,233 and Ncontrol = 64,762)[case = 662 and Ncontrol = 517) [To further illustrate the improvement in risk prediction accuracy, we first applied PleioPred to Crohn’s disease (CD), celiac disease (CEL) and type-II diabetes (T2D). We jointly modeled CD with ulcerative colitis (UC), CEL with UC, and T2D with coronary artery disease (CAD). We trained PleioPred using publicly accessible GWAS summary statistics and evaluated risk prediction performance using individual-level genotype and phenotype data from cohorts independent from the training GWAS samples. The training summary statistics for the two autoimmune disease include the training summary statistics are from the International Inflammatory Bowel Disease Genetics Consortium   and the = 64,762). Samplesl = 517)  were useWe evaluated the effectiveness of the per-SNP heritability estimated from functional annotations of the two autoimmune diseases  with well-powered testing cohorts . Interestingly, not only the per-SNP heritability of the testing diseases (CD and CEL) but those of related diseases (UC) could effectively identify SNPs with large effect sizes  and consCorrelations between the calculated PRS and disease status (COR) for different approaches and area under the ROC curve (AUC) are summarized in Since COR only measures the global discriminating power of prediction method, it might not be the best evaluation metric for risk prediction approaches, with which it is of more use to stratify the population into clinically meaningful groups, 17, 29.In the non-infinitesimal two-trait model, the major contribution to improved performance came from pleiotropy. That is, the variants that are causal in both diseases would be prioritized and those are not causal or have smaller effect sizes in both diseases would be given lower effect size estimation. Therefore, incorporating a genetically correlated disease is equivalent to integrating a functional annotation and its effectiveness and power depend on the genetic correlation between two diseases. When the two diseases are very similar and share a large amount of causal and non-causal variants, adding less effective annotations may dilute the signals and lead to lower prediction accuracy. This aligns with our results in Tables Our work demonstrates that pleiotropy and functional annotations can effectively improve the performance of genetic risk prediction. PleioPred jointly analyzes genetically correlated diseases and diverse types of annotation data with GWAS summary statistics to upweight causal SNPs shared between diseases and with a higher likelihood of functionality, which lead to consistently better prediction accuracy for multiple complex diseases. Besides prediction accuracy, PleioPred can better stratify population into different risk groups and has greater potential in clinical usage. Our method is not without limitation. First, despite consistent improvement compared with existing PRS-based methods, AUCs for most diseases remain moderate. In order to effectively stratify risk groups for clinical usage, our model remains to be further calibrated using large cohorts with measured environmental and clinical risk factors . Second,1 and N2 denote the sample sizes for the two diseases and M is the number of markers. We further assume a linear model with genotype matrices, effect sizes (β and γ) and random errors (ε and δ) mutually independent.Assume the phenotypes of two diseases ρe measures the covariance within the overlapping individuals between two studies. Denote the LD matrix and marginal effect size estimator from GWAS as: Ns is the number of overlapping samples between the two studies. When Ns is relatively small, we can discard terms with ρe and obtain the exact number of overlapping samples. 2) The off-diagonal term ρe is still at the magnitude of ρe can be estimated via LDSC if NS is known. However, including the covariance matrix of Assume that the effect sizes of different SNPs are independent. As for random errors, we assume thatation in , we can  samples . 4) In pi and ρg: = cor, representing the genetic correlation between two diseases. Suppose that the whole genome is partitioned into K functional regions A1,…, AK. Specific annotations used in PleioPred were described previously , which ij where Cj is a constant calculated from the following equationSpecifically for each disease, we use We do not directly use he model . Such pehe model . Therefohe model , we use b (e.g. an LD block) and the corresponding genotype matrices are Xb and Zb and sample correlation matrices is b for the two diseases, which are usually close to zero since the region b is relatively small and can be safely rounded to zero in calculation. We choose the size of b using the standard described in [In the GWAS setting, ribed in .ρe as a tuning parameter and the posterior expectation of the effect sizes can be calculated as:Finally, we treat In practice, 13, we i to two diseases follow a mixed distribution with normal , joint normal and point mass  and joint point mass . Although we do not have closed form solution for the posterior expectation of the effect sizes, we can use Gibbs sampler to sample from the posterior distribution of the effect sizes to estimate the posterior expectation. The joint posterior distribution of βi and γi given βi−, γi− and That is, the effect sizes of SNP d11 represents the number of SNPs that are causal in both diseases, d10 and d01 represent the number of SNPs that are causal in only one disease and d00 denotes the number of non-causal SNPs from previous sampling step. To ensure convergence, we shrink the posterior probability of being causal if the estimation of heritability at current step of either disease is larger than the heritability estimated from the GWAS summary statistics. That is, j in the ith iteration. And simulations showed the algorithm yields fast convergence and high accuracy in estimation . And we recommend using at least one thousand unrelated individuals with the same ancestry for which summary statistics datasets are obtained from following the same guideline of .The study was approved by YALE UNIVERSITY HUMAN INVESTIGATION COMMITTEE with approval number 100 FR1 and 100 FR27.https://github.com/yiminghu/PleioPredPleioPred software: https://github.com/yiminghu/AnnoPredAnnoPred software: http://genocanyon.med.yale.edu/GenoCanyon: http://genocanyon.med.yale.edu/GenoSkylineGenoSkyline: Supplemental data include two figures and six tables and detailed description of GWAS summary statistics and validation cohorts.S1 FigGenetic correlations were estimated using LDSC and sign(TIFF)Click here for additional data file.S2 FigGenetic correlations were estimated using LDSC. (AAM: a(TIFF)Click here for additional data file.S1 TableFor two-trait prediction models, we jointly modeled CD with UC, CEL with UC, and T2D with CAD.(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 TableData were generated from real genotype data of chromosome 1 with 29,596 individuals for both traits. We random selected 300 out of 41,334 SNPs as causal variants with 1/3 shared between two traits. We simulated in total 6 scenarios corresponding to different heritability of two traits. In each setting we use the maximum of mean squared error (MAX_MSE) of effect sizes of 41,334 SNPs to evaluate the estimation accuracy.(XLSX)Click here for additional data file.S6 TableData were generated from real genotype data of chromosome 1 with 29,596 individuals for both traits. We random selected 300 out of 41,334 SNPs as causal variants with 1/3 shared causal variants. N_s: the number of overlapping individuals between diseases; rho_e: the covariance between random errors of two traits on the same individuals (see (XLSX)Click here for additional data file.S7 Table(XLSX)Click here for additional data file.S1 Text(DOCX)Click here for additional data file.


Dicentrarchus labrax) is one of the most important species for European aquaculture. Viral nervous necrosis (VNN), commonly caused by the redspotted grouper nervous necrosis virus (RGNNV), can result in high levels of morbidity and mortality, mainly during the larval and juvenile stages of cultured sea bass. In the absence of efficient therapeutic treatments, selective breeding for host resistance offers a promising strategy to control this disease. Our study aimed at investigating genetic resistance to VNN and genomic-based approaches to improve disease resistance by selective breeding. A population of 1538 sea bass juveniles from a factorial cross between 48 sires and 17 dams was challenged with RGNNV with mortalities and survivors being recorded and sampled for genotyping by the RAD sequencing approach.European sea bass (P < 1e06). Weighted genomic best linear unbiased predictor provided additional support for the QTL on chromosome 3 and suggested that it explained 4% of the additive genetic variation. Genomic prediction approaches were tested to investigate the potential of using genome-wide SNP data to estimate breeding values for resistance to VNN and showed that genomic prediction resulted in a 13% increase in successful classification of resistant and susceptible animals compared to pedigree-based methods, with Bayes A and Bayes B giving the highest predictive ability.We used genome-wide genotype data from 9195 single nucleotide polymorphisms (SNPs) for downstream analysis. Estimates of heritability of survival on the underlying scale for the pedigree and genomic relationship matrices were 0.27  and 0.43 (0.29–0.57), respectively. Classical genome-wide association analysis detected genome-wide significant quantitative trait loci (QTL) for resistance to VNN on chromosomes (unassigned scaffolds in the case of ‘chromosome’ 25) 3, 20 and 25  contains supplementary material, which is available to authorized users. Dicentrarchus labrax) is a popular and valuable species for Mediterranean aquaculture, with a production volume of more than 150,000 tons [European sea bass  sequencing is a reduced representation high-throughput sequencing technique for the concurrent detection and genotyping of single nucleotide polymorphisms (SNPs) in multiplexed samples, each containing a unique nucleotide barcode . RAD seqThe aim of this study was to investigate genetic resistance to VNN in sea bass juveniles, using a RAD sequencing approach to generate genome-wide SNP data from 1538 individual disease-challenged fish. Heritability estimates were obtained using both pedigree and genomic relationship matrices for survival status  on the underlying liability scale. GWA approaches were used to test associations of both individual SNPs and genomic regions with resistance to VNN. Finally, genomic prediction of breeding values for resistance to VNN was tested using several approaches to evaluate the potential of genomic selection for genetic improvement of resistance to VNN in seabass.The population of fish for the VNN disease challenge was obtained by artificial fertilization of 18 dams and 49 sires from the Ferme Marine de Douhet breeding nucleus . Five factorial mating blocks, each comprising 9 to 10 sires and 3 to 5 dams, were created in February 2014. The fertilized eggs of each dam were transferred to individual incubators. Following egg hatching, equal numbers of larvae from each incubator were transferred in a single tank and reared in common environmental conditions.5 50% tissue culture infective dose (TCID50) per ml of the W80 betanodavirus strain, which was produced and titered in striped snakehead cells (SSN-1), as previously described [The fish (at a size of ~ 10 g) were challenged at the Unité de Pathologies Virales des Poissons—ANSES facility . Autopsies and extensive bacteriological and virological analyses were carried out on receipt of fish to confirm their health status. After 4 weeks of acclimatization, 1990 individuals distributed in three tanks were immersed for 2 to 3 h in static seawater, containing 1 × 10escribed . Strain escribed . A negatDNA was extracted from fin samples of the challenged fish using the REALPure genomic DNA extraction kit (Durviz S.L.) and treated with RNase. Each sample was quantified by spectrophotometry (Nanodrop), quality-assessed by agarose gel electrophoresis, and finally diluted to a concentration of 20 ng/µL in 5 mmol/L Tris, pH 8.5 using a Qubit Fluorometer (Invitrogen).SbfI (that recognises the CCTGCA|GG motif) −  using 6 U Sbf I per µg genomic DNA in 1 × Reaction Buffer 4 (NEB) at a final concentration of 1 µg DNA per 50 µL reaction volume. Reactions  were then heat-inactivated at 65 °C for 20 min. Individual specific P1 adapters, each with a unique 5–7 bp barcode, were ligated to the Sbf I-digested DNA at 20 °C for 60 min by adding 1.8/0.6 µL of 100 nmol/L P1 adapter, 0.45/0.15 µL of 100 mmol/L rATP (Promega), 0.75/0.25 µL 10 × reaction buffer 2 (NEB), 0.36/0.12 µL T4 ligase  and reaction volumes for each parental/offspring sample were completed to 45/15 µL with nuclease-free water. Following heat inactivation at 65 °C for 20 min, ligation reactions were slowly cooled down to room temperature (over 1 h), then combined in appropriate multiplex pools. Shearing (Covaris S2 sonication) and initial size selection (300 to 600 bp) by agarose gel separation was followed by gel purification, end repair, dA overhang addition, P2  paired-end adapter ligation, library amplification, as in the original RAD protocol [The protocol for RAD library preparation followed the methodology originally described in Baird et al. . Brieflyprotocol , 34. A vprotocol . FollowiGCA_000689215.1 using the Bowtie2 program [P < 1e–06; parental samples) were discarded.Sequence reads of low quality, with a missing restriction site, or with ambiguous barcodes and PCR duplicates were discarded. The remaining reads were aligned to the European sea bass reference genome  assembly program . Aligned program . The lik program  implemenParentage assignment was performed with the R/hsphase program  using alI the identity matrix.Variance components were estimated using the R/BGLR software . The procument}G  for certThe parameters of this model were estimated by Monte Carlo Markov chain (MCMC) Gibbs sampling . Convergence of the resulting posterior distributions was assessed both visually (inspecting the resulting MCMC plots) and analytically using the R/coda v0.19-1 software . Heritabd models , 46.To test the association of individual SNPs with resistance to VNN, a ‘classical’ genome-wide association study (CGWAS) was performed using the R/gaston software . The mixInitialize Calculate Estimate GEBV using GBLUP;Estimate the SNP effects from GEBV based on the equation Calculate the weight for matrix Normalize the weights of SNPs such that the total genetic variance remains constant;Loop to step (d) (three iterations).In addition to the CGWAS approach, weighted genomic best linear unbiased predictor (WGBLUP) was performed  to estim follows :InitialiThe percentage of additive genetic variance explained by each genomic region was estimated by non-overlapping windows of 0.5 Mb as follows:This analysis was performed using the THRGIBBS1F90 program from the BLUPF90 software suite , 52 to eTo assess the potential of genomic selection for improved resistance to VNN in sea bass breeding programs, the accuracy of GEBV was assessed and compared to EBV obtained with pedigree-based approaches. Missing genotypes for the SNPs that passed QC filters were imputed using FImpute . Severalsoftware .Six-fold cross-validation was performed in order to test prediction accuracy of correctly classifying animals in the validation set as resistant or susceptible. The dataset was randomly split into sequential training  and validation sets (n = 218). The number of survivors and mortalities in each validation set was proportional to the overall survival of the challenged population. In the validation sets, the phenotypes of the animals were masked, and their (genomic) estimated breeding values—(G)EBV—were estimated based on the prediction model derived from the training set. This cross-validation procedure was repeated five times. Receiver operator characteristic (ROC) curves were used to assess the efficacy of classifying the animals as survivors or mortalities, using either the pedigree- or the genomic-based models. The area under the curve (AUC) metric , 56 was The challenge study was conducted for 7 weeks, with mortalities recorded daily. Characteristic clinical signs of VNN were observed in each disease-challenged tank. In this experiment, the total percentage of mortality reached 48% (ranging from 40 to 56% depending on the tank), with four successive peaks of mortality ;  and 2.83 million (s.d. = 1.38 million) sequence reads passed the QC filters for the parental and offspring samples, respectively. The mean number of putative RAD loci identified was 45,631 (s.d. = 7099) and 43,538 (s.d. = 4543) for parents and offspring, with mean coverages of 68× (s.d. = 32) and 26× (s.d. = 12), respectively. The RAD loci were distributed relatively evenly across the sea bass genome assembly  comprised 140 full-sib families (48 sires and 17 dams), with 1 to 32 animals per family and a mean size of 9 (s.d. = 8). The contribution of individual dams to the population ranged from 1 to 267 animals, with a mean of 77 (s.d. = 68), while the contribution of sires ranged from 1 to 66, with a mean of 27 (s.d. = 18). Further testing of parentage assignment results using FImpute identified four animals as potentially mis-assigned. These individuals were discarded, which left 1293 animals originating from 48 sires and 17 dams in the final dataset used for the subsequent genetic analyses. The overall survival of these individuals in the VNN challenge was 42%  using the pedigree relationship matrix and at 0.43  using the genomic relationship matrix.P < 1e–05; R2: 0.03–0.05; Fig. In the CGWAS, SNPs that exceeded the genome-wide significance level were located on chromosomes 3, 20 and 25  Table , Fig. 4.prior genomic resources [European sea bass is a farmed species of paramount importance for Mediterranean aquaculture. Breeding for improved genetic resistance to VNN offers a promising avenue for reducing economic losses due to this disease and for improving animal welfare. A small number of family-based selective breeding programs exist for sea bass, with growth and disease resistance as the major target traits. Applying genomic information to selective breeding schemes facilitates direct selection for favorable alleles at major QTL (marker-assisted selection) and/or incorporation of genome-wide markers into the prediction of breeding values (genomic selection). Genomic prediction methods have been repeatedly shown to increase selection accuracy compared to pedigree-based approaches in aquaculture , 30, 57,esources . RAD seqesources .Our study is the first application of high throughput sequencing to study genetic resistance of sea bass to VNN. The estimated heritability of resistance was moderate to high (ranging from 0.27 to 0.43). The heritability estimate obtained by using the pedigree relationship matrix (0.27) was in accordance with a recently estimated heritability (0.26) for resistance to VNN in several sea bass populations, also using pedigree . These sThe CGWAS identified genome-wide significant QTL in several genomic regions . The single SNP CGWAS approach may lack statistical power to detect QTL when compared to methods in which all SNPs are used simultaneously, because of a false assumption of independence between SNPs . WGBLUP The genomic region that explained the highest percentage of additive genetic variance in the WGBLUP (~ 4%) was located on chromosome 3 and was also detected in the CGWAS. However, this may be an overestimation of the explained additive variance because threshold models often lead to overestimates of genetic variance . In spitThe results from the genomic prediction approach used in the current study were encouraging for practical implementation of genomic selection for genetic resistance in sea bass. For traits like disease resistance, which cannot be measured directly on selection candidates, genomic selection benefits from the use of within-family genetic variation, compared to pedigree-based BLUP, which uses between-family genetic variation only . ImproveWe applied RAD sequencing to study the genetic basis of resistance to VNN in a large sample of juvenile sea bass derived from a commercial breeding program. RAD-derived SNPs allowed us to perform pedigree assignment in this batch-spawning species, estimate genetic parameters, perform GWAS, and test genomic selection. Genome-wide significant QTL were identified with minor to moderate effects on host resistance, on chromosomes 3, 20 and on an unassigned genome scaffolds. Genomic prediction using the RAD genotype data was effective, demonstrating significant improvement in prediction accuracy, and facilitating classification of surviving and mortality fish with a success rate of 70% using the cross-validation approach. This highlights the utility of genotyping-by-sequencing for genomic prediction of disease resistance in aquaculture species, and demonstrates that genomic selection can be an effective method for improving resistance to one of the most problematic infectious diseases in sea bass aquaculture.Additional file 1: Table S1. VNN challenged sea bass. Phenotypic information of VNN challenged sea bass and pedigree structure.Additional file 2: Table S2. Identified SNPs. Sequence information of identified SNPs.Additional file 3: Table S3. SNP location. Location of SNPs on the sea bass reference genome v1_0.


GxG) and gene-by-environment (GxE) interaction. In the past decades, an explosion of high throughput technologies enables omics studies at multiple levels . The analyses of large omics data, especially two-loci interaction analysis, are very time intensive. Integrating the diverse omics data and environmental effects in the analyses also remain challenges. We proposed mixed linear model approaches using GPU (Graphic Processing Unit) computation to simultaneously dissect various genetic effects. Analyses can be performed for estimating genetic main effects, GxG epistasis effects, and GxE environment interaction effects on large-scale omics data for complex traits, and for estimating heritability of specific genetic effects. Both mouse data analyses and Monte Carlo simulations demonstrated that genetic effects and environment interaction effects could be unbiasedly estimated with high statistical power by using the proposed approaches.Precise prediction for genetic architecture of complex traits is impeded by the limited understanding on genetic effects of complex traits, especially on gene-by-gene ( GxG) and gene-by-environment (GxE) interactions, such as chicken comb typeGxG and GxE interactions.Both natural and experimental populations harbor an array of phenotypic variations because of the complicate genetic architecture underlying quantitative traits. It is well documented that the genetic basis responsible for phenotypic variability consists of individual causal genes and interacting networks, with their specific effects in multiple environmental conditions. Gene-by-gene . At each level it is possible to construct interaction networks associated with complex traits (including diseases)5678GxE interactions1819202223GxG and GxE interactions by experimental data involving multiple environments (or treatments). However, with the recent development of high-throughput genotyping technologies, genetic association analyses have become common tools for uncovering causal genetic variants and networks at the whole-genome level27282930GxG and GxE at transcript levels are ignored. Despite intensive efforts to explain genetic variation of quantitative traits, which have identified a great number of genetic variants and transcripts for various complex traits, we still fall short of understanding the mechanism of the genetic architecture of complex traits.Linkage analyses and association analyses are two genetic mapping approaches used to assess the relation between the genotypic and phenotypic variations on a population scale. Taking advantage of conventional molecular markers, efficient statistical methods of QTL (Quantitative Trait Locus) mapping have become pervasive13141516GxE interaction  estimating gene effects of individual and epistasis loci detected in previous process by method of Monte Carlo Markov Chain via Gibbs Sampling24In this study, mixed linear model approaches are proposed to identify genetic effects of individual loci, epistasis effects of pair-wise loci , as welleraction , which in = 528 mice). Differences in the phenotypes are evident in the parental strains. For example, the maternal strain C57BL/6J exhibits lower anxiety- and fewer stress-related effects than the paternal strain DBA/2J, which exhibits greater fear-related responsesWe applied our proposed statistical methods for mapping QTLs, QTSs, and QTTs to searching for the genetic mechanism of anxiety in 71 BXD recombinant inbred (RI) strains of mice  and Q2 (within 169.1 Mb ~ 169.8 Mb) were on chromosome 1, and Q3 (within 44.6 Mb ~ 53.9 Mb) was on chromosome 11. These three loci were confirmed by QTS association analysis with precision location . Two extra QTS sites were also discovered on chromosome 11 (Q4 at 35.3 Mb and Q5 at 36.5 Mb). The QTS mapping matched well with exact position of identified SNP and higher power than QTL mapping. For the three loci detected by QTL and QTS mapping, only one was confirmed by QTT mapping (Q2 at 169.1 Mb), but another one was revealed nearby (Q6 at 155.5 Mb). It is apparent that QTT mapping can only discover transcript loci at the time when they are expressed.As shown in QQ1 was identified with similar predicted effects by both QTL mapping (D1Mit291 × rs3659789) and QTS mapping (D1Mit291     × rs3717220). Compared with the QTL mapping, QTS mapping appeared to have higher statistical significance. Because no transcription QQ1 was detected on chromosome 1, there might have been no significant association of transcript epistasis QQ1 at the time when the tissue used for mRNA extraction was collected. There was another transcript epistasis QQ2 (ILM100060136 × ILM1740047) that was detectable only by QTT mapping.As shown in Q1, Q2, Q3, Q4, and Q5) were assumed to control the simulated trait. Four of the five QTSs were involved in the three pairs of two-way interactions, denoted QQ1 for Q1 × Q3, QQ2 for Q1 × Q4, and QQ3 for Q3 × Q4. The whole-genotype individuals were investigated in three environments. The individual SNPs and interactions were set to account for as much as 20% in total heritability (SE) were also calculated for inferring un-biasedness of estimation of genetic effects.A simulation study with 200 replications was conducted. The BXD mouse genetic map was used to generate three simulated populations for mapping QTLs, QTSs, and QTTs. Initially, we generated a simulated population for QTS mapping with 200 RIL genotypes consisting of 2,320 SNPs covering 2,037.6 cM. Five QTSs  were supposed to control the phenotype variation. Meanwhile, three pairs of two-loci combinations  between the four transcript loci were assumed to be associated with the simulated trait. The 200-genotype individuals were tested in three environments. The total heritability was equal to 20%. Detailed information is listed in SE) were also calculated as for QTLs/QTSs mapping.A second simulation population was generated for mapping QTLs, including 506 microsatellite markers drawn from the entire 2,320 markers within each observation sample. Other parameters had the same settings as described above. A third simulation population was created for mapping QTTs, including 200 genotypes, with each composed of 2,320 transcript loci, using the same map as the mouse genetic map. Four transcript loci  than QTL linkage analysis (95%). Furthermore, the positions and genetic effects could be estimated more precisely by QTS association analysis. For a locus with a relatively large effect, both methods could yield an unbiased estimate. However, there were obvious differences between the two approaches for estimating genetic effects and positions of loci with relatively small heritability. For locus Q5, the smaller standard error (SE) of the estimated position indicated that QTS association analysis could define a more precise position than QTL linkage analysis. Because of the precise identification of position, the estimated effects of the locus may be closer to the parameters by the QTS association method. The estimated additive and additive-by-environment interaction effects of locus Q5 were also relatively accurate by QTS mapping. Likewise, the more precise estimation and smaller SE of the general additive effect of individual locus Q4 revealed that QTS mapping (SE = 0.56) could obtain more accurate estimates than QTL mapping (SE = 1.13).The Monte Carlo simulation demonstrated that mixed linear model approaches could robustly estimate positions and effects for QTLs, QTSs, and QTTs. The simulation results of mapping QTLs and QTSs are listed in GxE interaction effects. Individual transcript loci could be detected with statistical power higher than 83.0%, and the power for detecting epistasis was 100% in all cases. The estimates of genetic effects and environment interaction effects were close to the parameter setting with very small SEs for individual transcript loci as well as two-transcript loci interactions. Because QTT association analysis could identify the transcript loci efficiently, we could obtain unbiased estimates of QTT main effects and QTT by environment interaction effects.Detailed simulation results for mapping QTTs are listed in We used three GPU servers to test the performance. The first one consisted of 2 NVIDIA GTX480 cards running on an Intel® core™ i7 × 980 with 3.33 GHz (Gigahertz) CPU using 12 GB (Gigabyte) DDR3 host memory. The second one consisted of 4 NVIDIA GTX680 cards running on an Intel® core™ E5645 with 2.40 GHz CPU using 48GB DDR3 host memory. The third one consisted of 4 NVIDIA Tesla K20c cards running on an Intel® core™ E5645 with 2.40 GHz CPU using 48GB DDR3 host memory. We compared the running time of three implementation versions, and measured the time of the whole procedure including the input, one-dimension search, two-dimension search, effect estimation, and the output as the comparing time. We implemented multi-GPU computing in two-dimension search. First we divided the whole SNP pairs into parts according to the number of GPUs and assigned each part to one GPU. Each GPU finished its tasks in loops. The speed-up results of GPU implements over single-thread CPU implementation are summarized in QQ, Qq, and qq), supposing the existence of linkage between the flanking markers and the unobserved loci. However, in artificially generated lines such as recombinant inbreeding lines (RILs) or doubled haploid lines (DHLs) derived from two parental lines, the abundant recombination may eliminate linkage over generations. Besides, it may be difficult to infer the probability of three genotypes in mapping QTLs for populations derived from multiple parental lines. The QTS association analyses rely on the retention of adjacent DNA variants over many generations. As a result, it is appropriate to detect loci for natural populations and complicated experimental designs by QTS association analyses.Traditionally, linkage analyses can detect the causal individual QTLs and epistasis. Linkage mapping has discovered many QTLs affecting various quantitative traits. Because of the recent development of high-throughput genotyping technologies and identification of highly dense SNPsQ2 and Q5 in Q5 in SEs of estimated position than the QTL linkage analyses. In addition, when analyzing the data of the mouse on chromosome 11, the QTS association mapping detected two significant SNPs in the region of the QTL mapped by the linkage study. It is revealed that QTS association analysis has advantages over linkage analysis for efficiency and accuracy in mapping loci.For advanced populations, such as recombinant inbred lines (RILs) and near-isogenic lines (NILs), the linkage between the flanking markers and unobserved markers is reduced, as a few generations increase the recombination frequencyDiscovered loci such as QTSs can subsequently be used to predict phenotypic values and QTS effects in an independent population, and it typically provides some improvement in classifying phenotypic values over random decision-making. In public health, it is useful to determine whether individuals are in an at-risk group. Owing to the accuracy of locus position and effect estimation, and the ease of discovery of loci with low heritability, the effective and efficient QTS association can improve the genetic predictor.On the other hand, transcript association can detect causal transcript loci efficiently. In contrast to QTS association analysis and QTL linkage analysis, the genotypic variants of QTT association are continuous gene expression data. The high statistical power and unbiased estimation indicates that QTT association is also a useful approach to map individual transcripts and pair-wise interaction, which are significantly associated with the quantitative traits. In addition, the approach could also be extended to mapping quantitative trait protein (QTP) and quantitative trait metabolite (QTM)For mapping quantitative trait SNP (QTS) or quantitative trait transcript/protein/metabolite (QTT/QTP/QTM), mixed linear model approaches can be used to detect loci significantly associated with phenotypic variation51525354k-th subject in the h-th environment can be expressed by the following mixed linear model:h-th environment; i-th locus effect with coefficient QQ, -1 for qq, and 0 for Qq in QTS mapping, and using expression values in QTT/P/M mapping); i × locus j with coefficients QQ × QQ and qq × qq, -1 for QQ × qq and qq × QQ in QTS mapping, and using expression values i-th locus in the h-th environment with coefficient i × locus j in the h-th environment with coefficient k-th individual in the h-th environment.Mixed-model approach for QTL mapping24n × 1 column vector of phenotypic values and n is the number of sample observations; v-th random vector v-th random vector n × 1 column vector of residual effects.The mixed linear model can be presented in matrix notation:i-th individual locus, we used the following mixed linear modelF-test step by step based on the Henderson method IIIF-valueIndividual locus detection. To test significance of the Epistasis loci detection. In order to search all possible epistasis interacting loci when s individual locus has been selected by the first step, we conduct an exhausted two dimension (2D) genome scan by the following statistical model.where the parameters have the same definitions as in Equation F-test is performed to test all possible pairs. The pairs of loci with maximum F-value larger than the predefined threshold value  method57P-value for controlling the experiment-wise type I error. Stepwise selection was performed on all the significant peaks selected from the F-statistic profile, which meets the significance level  were exploited. The framework is shown as In two-dimension search, one pair of loci was tested by one GPU thread. Because of the high throughput technology, the pair number can be very huge. We implemented the interaction scan on multi-GPU platforms. We have drawn How to cite this article: Zhang, F.-T. et al. Mixed Linear Model Approaches of Association Mapping for Complex Traits Based on Omics Variants. Sci. Rep. 5, 10298; doi: 10.1038/srep10298 (2015).


Manihot esculenta Crantz) is a clonally propagated staple food crop that feeds hundreds of millions. We quantified the amount and nature of nonadditive genetic variation for three key traits in a breeding population of cassava from sub-Saharan Africa using additive and nonadditive genome-wide marker-based relationship matrices. We then assessed the accuracy of genomic prediction for total (additive plus nonadditive) genetic value. We confirmed previous findings based on diallel crosses that nonadditive genetic variation is significant for key cassava traits. Specifically, we found that dominance is particularly important for root yield and epistasis contributes strongly to variation in cassava mosaic disease (CMD) resistance. Further, we showed that total genetic value predicted observed phenotypes more accurately than additive only models for root yield but not for dry matter content, which is mostly additive or for CMD resistance, which has high narrow-sense heritability. We address the implication of these results for cassava breeding and put our work in the context of previous results in cassava, and other plant and animal species.In clonally propagated crops, nonadditive genetic effects can be effectively exploited by the identification of superior genetic individuals as varieties. Cassava ( Efforts to improve cassava genetically with cutting edge methodologies including transgenic and genomic selection (GS) approaches are underway thanks to new genomic resources (http://www.nextgencassava.org). Vegetatively propagated crop  breeding can exploit nonadditive genetic effects by identifying superior clones as varieties  are strong, particularly for root yield traits . Breeding gains have indeed been slow in cassava  genomic selection breeding program. Further, we assess the accuracy of predicting total genetic value using the additive and nonadditive models. We discuss the origin of nonadditive genetic variance in cassava, its potential effect on cassava breeding, and its role in genomic selection strategies for cassava improvement in the future.http://www.nextgencassava.org). The IITA’s Genetic Gain (GG) collection contains 694 historically important clones, most of which are advanced breeding lines although some are classified as superior landraces. These lines have been selected and maintained clonally since 1970  in Nigeria for a total of 24,373 observations. Each GG trial comprises a randomized, incomplete block design replicated one or two times per location and year. Since materials have been occasionally lost and new, selected materials are continuously added to the GG, the number of clones trialed in a given year changes gradually across years, generally increasing. The sample sizes, number of replicates, and number of clones from the GG in each of the trials (location-year combinations) are provided in Table S3. Further, information about the germplasm analyzed, including data regarding the genetic structure of the population, have been published previously  at some loci relative to others . ConsequTable S2). Clones were assigned to each location so as to equally represent each family in every environment.Cycle 1 progenies were evaluated in a single clonal evaluation trial during the 2013–2014 field season across three locations . For the C1 clonal trial, planting material was only available for one plot of five stands per clone, so each clone was only planted in one of the three locations . Most GG trials measured DM by the oven drying method although some trials used the specific gravity method. Dry matter content is expressed as a percentage of the fresh weight of roots. Fresh root weight (RTWT) is measured in kilograms per plot and is natural-log transformed to achieve normally distributed, homoscedastic residuals in all presented analyses. Trait distributions are presented in Figure S2.For both datasets, we analyzed three traits: MCMDS, DM, and RTWT. MCMDS was scored on a scale of 1 (no symptoms) to 5 (severe symptoms). We note that the distribution of MCMDS is skewed toward low disease severity (http://phytozome.jgi.doe.gov) and described by the International Cassava Genetic Map Consortium (2 > 20) were removed. If there were not at least two reads at a given locus for a given clone, the genotype was set to missing and imputed. SNP marker data were converted to the dosage format  and missing data were imputed with the glmnet algorithm in R (http://cran.r-project.org/web/packages/glmnet/index.html). Similar to the approach of q = 1 in glmnet), with the tuning parameter λ selected by fivefold cross-validation. We used 114,922 markers that passed these filters with a minor allele frequency >1% to construct GRMs as described below.We used genotyping-by-sequencing (GBS) to obtain genome-wide SNP marker data (nsortium . We remoG) using the formula of Z is a mean-centered matrix of dimension n individuals by m SNP markers. To obtain Z, we subtract 2(ip − 0.5) from the marker dosages, where the dosages are coded −1 for aa, 0 for Aa, +1 for AA, ip is the frequency of the second allele (A) at the ith locus, and iq = 1−ip. The a (or 0) allele refers to the reference genome allele. The G matrix was calculated using the A.mat function in the rrBLUP package , is H is a mean-centered dominance deviation matrix with the same dimensions as Z. To obtain H, we score heterozygotes as 1 and homozygotes as 0, and subtract the mean (2iqip) from the scores. We made a custom modification (available at ftp://ftp.cassavabase.org/manuscripts/) to the A.mat function to produce the D* matrix.We constructed a matrix to capture dominance relationships using the formulation originally proposed by D* dominance matrix was shown by D, defined as W is a marker matrix with markers coded 0 for aa, 2ip for Aa, and 4ip − 2 for AA and then centered on the mean, 2ip2. Although our focus in the present study is not on the prediction of breeding value, the matrix D has been shown by G. For this reason, we tested the D and D* matrices and provide comparison of their results. Except where explicitly comparing matrices, we use D to indicate the dominance matrix D* as in The A#A) and additive-by-dominance (A#D) relationships in this study.Finally, we constructed relationship matrices that capture epistasis by taking the Hadamard product  of matrices . For simTable S2).We used several approaches to estimate the relative importance of additive and nonadditive effects in the Genetic Gain and Cycle 1 datasets. In the first analysis, we analyzed the multi-year, multi-location GG data with a single-step mixed-effects model. Since the entire historical phenotype dataset is large  and was relatively unbalanced in sample size across years and locations, we only analyzed data from trials with >400 individuals. This filter resulted in a dataset of 7745 observations from three locations  and 8 yr . All 694 genotyped GG clones were represented in this dataset , I is the identity matrix and The models we fit were similar to those described in G is the additive genetic relationship matrix and D equal to the dominance relationship matrix and E took the form either of the A#A matrix (additive-by-additive) or the A#D matrix (additive-by-dominance) and the epistatic variance ε is the residual variance, assumed to be random and distributed X, loc.yearZ, repZ, addZ, domZ, and epiZ are incidence matrices relating observations to the levels of each factor. We list the different models fit in The genetic variance component terms included regress package in R (regress function finds restricted maximum likelihood (REML) solutions to mixed models using the Newton–Raphson algorithm.The formulation described above was used to fit the subset of the GG historical data described above in a single model. For the C1 progenies only a single season was available and therefore we fit all data together in a single model. Since the C1 trials were conducted across three locations but with no replications we fit the same model for C1 as GG excluding the replication term. The models described above were fit using the age in R . The regk – 2*ln(likelihood), where k = number of parameters estimated]. In addition, we calculated the Bayesian Information Criterion . We also examined the log-likelihood of each model and the proportion of variance explained by genetic factors (H2). The precision of variance component estimates and the dependency among estimates was examined using the asymptotic variance–covariance matrix of estimated parameters, provided by regress (V). We report standard errors for each variance component, defined as the square root of the diagonal of V. We also converted V into a correlation matrix [F, as in F is defined as −1/2VL−1/2L and L is a diagonal matrix containing one over the square root of the diagonal of V. We use F to assess the dependency of variance components estimates, especially for comparing results among traits and datasets.For each trait, in both the C1 and GG we identified a “best fit” model among the models listed in N = 47, unique location-year combinations) separately. This provided us with 47 estimates of additive, dominance, and epistatic variance. We examine the distribution of variance components estimates. As in the multi-environment models, within-trial models were fit with regress in R.We used only a subset of the GG trials to estimate variance components in the single-step multi-environment model described above. In addition, we were able to analyze the entire historical GG data by testing each trial . We used each fold in turn for validation by removing its phenotypes from the training population and then predicting them. We calculated accuracy as the Pearson correlation between the genomic prediction and the BLUP . Genomic predictions were made using the EMMREML R package  and the Cycle 1 (C1). For each trait, in each dataset, we first identified the best fitting model of the five tested  on the bTable S4, and Table S5). Based on the guidelines of The AIC-selected best model for MCMDS included additive-by-dominance epistasis (A×D) in both GG and C1. For RTWT, the model with additive-by-additive epistasis (A×A) fit best in the GG but a simpler dominance only (Dom) model was selected in the C1 dataset. Finally, for DM the additive only (Add) model was best in the GG but additive plus dominance (A+D) was selected in the C1 dataset. The BIC criterion places a steeper penalty on increasing the number of parameters. Nevertheless, BIC selected the same model as AIC in all cases except for RTWT in the GG dataset, where the additive plus dominance model was preferred (H2), the H2 was higher in C1 compared to GG. This can be seen most easily in H2) is partitioned among variance components in the C1 and GG . We also noted that the additive only model had the highest H2 for all traits in the GG dataset, but C1 models with nonadditive components always had at least slightly higher H2.We noted that for every trait, when comparing the model achieving the highest broad-sense heritability . In contrast, nonadditive components accounted for the majority of genetic variance for RTWT, with H2 between 0.21 and 0.33. Dominance was significant in all models tested for RTWT in both datasets and epistasis was significant in the GG dataset. MCMDS had the highest H2 compared to the other traits (0.66–0.89) and was similar to RTWT in that dominance and/or epistasis were always significant where included. While nonadditive genetics were the majority of H2 in GG, they were much less important in C1 for MCMDS.On the basis of genetic variance captured, DM had F) to ascertain the dependency of variance component estimation. The correlation between genetic variance components was always negative and was, in general, of greater magnitude in the GG compared to the C1 . Correlations between additive and dominance components were greatest in the A+D models (range −0.81 to −0.83 in the GG and −0.5 to −0.61 in the C1). Correlations between additive and dominance components dropped in models with epistasis . Correlations between additive and A×A epistatic variances (range −0.09 to −0.29) and A×D epistasis (range −0.07 to −0.22) were low. Correlations between dominance components and epistasis were higher, ranging from −0.28 to −0.64 with A×A epistasis and −0.36 to −0.69 with A×D epistasis.We examined the asymptotic correlation matrices of parameter estimates (D* (results described above) and D revealed very similar results. In almost every case, AIC and BIC selected the same best fit model for D and D*. The exception was RTWT in the C1 dataset where the A+D model was preferred over the dominance only model when using the D matrix instead of D* (Table S4 and Table S5). The AIC and BIC are on the whole slightly lower for the models using the D matrix, indicating a better fit to the data. As expected, the correlation between additive and dominance parameter estimates is of smaller magnitude for all analyses with D compared with D* . However, the correlation between additive and epistatic as well as between dominance and epistatic variances is always of greater magnitude with D. Finally and as expected, models using the D matrix generally explain the same amount of genetic variance as those with D* but partition a smaller portion to dominance . We noted that for RTWT in the C1 dataset, models with D actually achieve a slightly higher broad-sense heritability. Because of the similarity of results, we focused the remainder of our analyses and discussion on the results from the D* matrix, henceforth referred to only as D.Comparison of the two alternative dominance matrices etc.) across these trials are summarized in Table S12 and results for each individual trial-model combination are given in Table S13. Table S10) and found them to agree overall with the results of the one-step multi-environment models . By model, improvements in the correlation between total value and phenotype over the additive only model were 7, 7, and 8% for A+D, A×A, and A×D, respectively. The additive only model predictions were on average 12% less accurate in the C1 than in the GG. Total genetic value predictions were less accurate by 12% in the C1 relative to GG. The models we fit for genomic prediction involved the estimation by EMMREML of weights, used to create a single kernel that is the weighted average of multiple original kernels and corresponding to the partitioning of genetic variance among the kernels. The average total weight given to nonadditive components for both DM and MCMDS was 0.41 but was 0.92 for RTWT.We used cross-validation to assess the prediction accuracy for total genetic value from the five models  in both vs. DM, however, suggest that this weakness did not strongly affect our results. Further, we found that multi-component models incorporating nonadditive effects predict observed phenotypes more accurately than additive only models for root yield but not for DM content, which has primarily additive inheritance, or for CMD resistance, which has high narrow-sense heritability. We address the implication of these results for cassava breeding and put our work in the context of previous results in cassava, other plant, and animal species below.In clonally propagated crops, nonadditive genetic effects can be effectively exploited by the identification of superior genetic individuals as varieties. For this reason, we quantified the amount and nature of nonadditive genetic variation for key traits in a genomic selection breeding population of cassava from sub-Saharan Africa. We then assessed the accuracy of genomic prediction of additive compared to total (additive plus nonadditive) genetic value. Using several approaches and datasets based on genome-wide marker data, we confirmed previous findings in cassava based on diallel crosses nonadditive genetic variation is significant, especially for yield traits (Our results indicate strong nonadditive (mainly dominance) variance for root yields and mostly additive inheritance of root DM content. These findings confirm the conclusions of numerous diallelic studies conducted with both Latin American  of allele frequencies at some loci relative to others in populations undergoing bottlenecks (https://www.cog-genomics.org/plink2) and found the two generations to be similar.One of the more interesting aspects of our study relative to previous ones is the comparison between a parental generation (the Genetic Gain) and their offspring (Cycle 1), a collection of full- and half-sib families. From GG to C1, the tlenecks , inbreedtlenecks , or truntlenecks  should cProbably the strongest explanation for the difference in genetic variance components between GG and C1 is the family structure (135 full-sib families from 83 outbred parents). In a population of full-sibs three quarters of the dominance variance is expressed within families and all of it for half-sib populations . The suggestion is therefore that the quality and vigor of the seedling plant giving rise to the C1 clones may influence their performance in the 2013–2014 trial. We further caution that comparison of GG and C1 may be biased by the disproportionate amount of data from different locations and years available for the GG.D* matrix, which is correlated with the G matrix, or the D matrix, which is theoretically orthogonal to G. We suggest therefore that prediction models that do not explicitly incorporate nonadditive components may achieve gains in the short term that break down over the long term  values would provide a less biased, more accurate selection of parents for crossing.In our study, when additive and nonadditive kernels were used together, the variance explained by the additive component, particularly for RTWT, decreased. One interpretation of this result is that the additive component alone absorbs some nonadditive variance. Similar results have been obtained by other researchers, leading to similar conclusions (ong term . Our preh2 traits and without inbred cassava, using the kinds of models presented in this paper, good parents can be selected based on additive predictions and total genetic value can be predicted for the identification of potential commercial varieties, all based on the combination of marker and preliminary field trial data (e.g., Nonadditive variation is prevalent in cassava, especially for low-heritability traits. This has many important implications for cassava breeding. It explains, in part, why GGs have been slow (ta e.g., . Nonaddi


N=9942) is used to estimate a classical twin model, a genomic-relatedness-matrix restricted maximum likelihood (GREML) model on twins and estimates polygenic scores of age at first birth on childlessness. Results show that the variation in individual differences in childlessness is explained by genetic differences for 47% in the twin model and 59% for women and 56% for men using the GREML model. Using a polygenic score (PGS) of age at first birth (AFB), the odds of remaining childless are around 1.25 higher for individuals with 1 SD higher score on the AFB PGS, but only for women. We find that different sets of genes influence childlessness in men and in women. These findings provide insight into why people remain childless and give evidence of genetic sexual dimorphism.Previous research has found a genetic component of human reproduction and childlessness. Others have argued that the heritability of reproduction is counterintuitive due to a frequent misinterpretation that additive genetic variance in reproductive fitness should be close to zero. Yet it is plausible that different genetic loci operate in male and female fertility in the form of sexual dimorphism and that these genes are passed on to the next generation. This study examines the extent to which genetic factors influence childlessness and provides an empirical test of genetic sexual dimorphism. Data from the Swedish Twin Register ( Additive genetic variance in fitness implies natural selection in populations, with the underlying assumption that alleles leading to higher reproductive success are passed on with a higher frequency in future generations.2 The erroneous misinterpretation of Fisher’s Fundamental Theorem of Natural Selection that genetic variance in fitness should be close to zero has resulted in less attention to the study of genetics and reproduction.3 Fisher argued that reproductive fitness is moderately heritable in humans, with a growing number of twin and family studies showing reproduction to be 25–50% heritable.1 Previous research has found genetic influences on fecundity and reproductive desires4 with a recent GWAS isolating 12 genetic loci implicated in the timing and number of children.5Over the last decades, human reproductive research has increasingly focused on biodemographic and genetic factors.6 There are likewise sex differences in biological makeup, processes and diseases implicated in infertility and behavior. For women, ovulatory problems, tubal damage, endometriosis, cervix cancer and polycystic ovary syndrome are prominent causes of infertility, with sperm defects and testicular cancer being central factors for men.7 These diseases are partly heritable.9 There is also a behavioral component to sexual dimorphism, since genes are implicated in different ways in relation to educational level and certain personality traits, including sociability, impulsivity and emotionality.10 These traits, which potentially have different effects on male and female fertility13 have also been shown to have a heritable component in previous research.14 Isolating the extent of sexual dimorphism in childlessness fosters a better understanding of why genetic variation in this trait still exists.Reasons for genetic effects on childlessness could be gene–environment interaction, non-additive genetic effects, or new mutations that restore any genetic variance lost to selection. Another hypothesis is that sexual dimorphism or in other words differences in secondary sex characteristics, operates since genes contributing to male childlessness are inherited via the female lineage and those for female childlessness via the male lineage.15 Third, heritability , as well as sex differences, are estimated and contrasted using three different methods (see 5 to assess the influence of SNPs (single-nucleotide polymorphisms) on childlessness for men and women at the molecular genetic level. SNPs are variations in a single nucleotide that occur at a specific position in the genome, where each variation is present to some degree within a population.16 The twin method enables us to compare results found in other countries and time periods. DZ twins share between 35 and 65% of their segregating genes,17 which is assumed to be 50% in twin studies. The GREML method uses actual measured genetic similarity between twins, resulting in more precise estimates of heritability  were genotyped. Between 1998 and 2002 data was collected from twins born between 1911 and 1958. Between 2004 and 2008 a subset of SALT participants were genotyped for the TwinGene project.18 We restrict our analyses to TwinGene participants to ensure comparability of results between our different methodological techniques.This study uses data from the Swedish Twin Registry (STR) which is compiled from the national birth registry.19 and no men in our sample had a first child after the age of 50. The TwinGene sample contains 10 909 individuals. After age restrictions, 9942 individuals remained, with 4534 men and 5408 women coming from a total of 6330 different families, 3612 complete twin pairs and 2718 individuals for whom there is only one twin from the pair in the sample.We include women aged 45 and older and men 50 and older, since <0.05% of children are born to mothers older than 4518 If blood samples were available for both twins, genetic-based analyses were used to determine zygosity. This was not possible in two cases. In the TwinGene data, in some cases only one twin of a pair participated and was genotyped. Furthermore, in the case of presumed MZ pairs, also only one of each MZ pair was genotyped. In these two cases, zygosity was determined based on the responses to two questions. ‘During childhood, were you and your twin partner as alike as ‘two peas in a pod’ or not more alike than siblings in general?’ and, ‘How often did strangers have difficulty in distinguishing between you and your twin partner when you were children?’. If individuals responded ‘as alike as two peas in a pod’ and that strangers got confused ‘almost always or always’ or ‘often’, they were classified as MZ. This measure was tested by use of DNA markers and is accurate in 99% of the cases.20Monozygotic (MZ) and dizygotic (DZ) twin pairs were distinguished using two different methods.21 which is required for the GREML analysis. For quality control, SNPs with a minor allele frequency <1%, a higher missing rate than 0.03 and that failed the Hardy-Weinberg equilibrium for a threshold of 10−6 were removed. The first 20 principal components are included as covariates to adjust for population stratification.22The individuals were genotyped using the Illumina OmniExpress 700 K chip, imputed to the 1000 genome imputation panel. After imputation we selected SNPs from the HapMap3 panel since this SNP set was optimized to capture common genetic variation,Women are considered childless if they have no children who are living and no children who are dead (stillborn children are not counted as children who are dead). Men are considered childless if they have no children who are living. This results in a small discrepancy between the measurement of childlessness for men and women and for that reason we do robustness checks using only living children for men and women.To test heritability and sex differences of childlessness we used three methods: twin and GREML models and polygenic scores, illustrated in 23 This model assumes an underlying normal liability distribution that divides individuals into the two groups of childless versus not childless. Thresholds  for dividing these groups were estimated based on the proportion of childless individuals. The tetrachoric correlation of the liabilities in childlessness among MZ and DZ twin pairs was estimated using trait concordances.23 These correlations were then used to estimate the contribution of genetic and environmental factors in the same way covariances are used for continuous traits. In all twin models we control for birth year.To quantify the genetic contribution to childlessness (a binary trait), we estimated a liability threshold model.24 When MZ correlations are more than twice the DZ correlations, an ADE model is estimated, which tests for dominant genetic effects, since D correlates perfectly for MZ twins but only 0.25 for DZ twins. Since they are confounded, C and D cannot be estimated simultaneously in univariate models. The A, C and D parameters were estimated using a model-fitting approach in which A, C and D factors were dropped in a stepwise fashion from the full model (ACE model or ADE model) and sub models were compared to the full model by hierarchical chi-square tests. The difference in the goodness-of–fit (–2 log likelihood) between the sub- and full model is approximately chi-square distributed, with degrees of freedom equal to the difference in degrees of freedom. The model with the lowest Akaike’s information criterion (AIC=X2 –2df) reflects the optimal balance between goodness-of-fit and parsimony.To test for genetic and environmental influences of childlessness, ACE, ADE, AE and CE models were fitted, which estimate the effect of additive genetic factors (A), non-additive/dominance genetic factors (D), shared (common) environmental factors (C) and individual (unique) environmental factors (E). The latter also contains measurement error. As shown in 25 Qualitative sex difference refers to whether different genes influence childlessness for males and females, tested by fitting a model in which the genetic correlation between opposite sex twin pairs was freely estimated and a model in which the genetic correlation is set at 0 (indicating independent genetic effects by sex) and by comparing these models to one in which the genetic correlation was fixed at 0.5 (indicating no sex differences). A better fit of the model with the genetic correlation set to 0 thus indicates that different genes are implicated in male and female childlessness.To examine quantitative and qualitative differences in the genetic and environmental etiology between males and females, sex limitation models were applied.26Quantitative sex difference refers to different proportions of additive genetic (A), shared environmental (C) and individual specific environmental (E) influence. We first ran a heterogeneity model in which the A, C and E parameters can differ between males and females followed by a homogeneity model where parameters for A, C and E are fixed as the same for the sexes. Differences between the goodness-of-fit of models were tested as described previously. For all twin models we used the OpenMx package in R.27 As childlessness is a binary trait, the liability threshold model applies. The estimate of variance explained by SNPs on the observed scale is transformed to that on the underlying continuous scale.28 We controlled for the first 20 principal components as well as birth year.A second method used to estimate heritability is the genomic-relatedness-matrix restricted maximum likelihood (GREML) method on twins, which simultaneously considers the additive effect of all genotyped SNPs. The GREML method contains two steps. First, for each pair of individuals, the genetic similarity is estimated based on similarity in SNPs. Second, this genetic relatedness is used as the input as a random effect in a mixed linear model in which the genetic relatedness explains phenotypic similarity. This is done by a comparison of a matrix of pairwise genomic similarity to a matrix of pairwise phenotypic similarity.29 We estimated narrow sense heritability (h2), commonly estimated in twin or family studies, and heritability based on genotyped SNPs (h2snp). To estimate both h2 and h2snp, two covariance matrices were used: the identity-by-descent (IBD) and identity-by-state (IBS) matrices. The IBD matrix only includes individuals with relatedness above 0.05, for whom similarity of measured SNPs is an indicator of similarity over the whole genome. In the IBD matrix, genetic similarity for unrelated individuals (relatedness <0.05) is set to 0. The IBS matrix includes all individuals, but uses only information on unrelated individuals, because the information on related individuals is already captured by the IBD matrix. The IBS matrix thus captures only the genetic covariance for the SNPs in the genotyping array. We applied the joint model, which includes both the IBD and IBS matrices. The IBS matrix estimated h2snp and the IBD matrix estimates additional effects within families (h2–h2snp), which together provide an estimate for narrow sense heritability (h2).In this paper, we used a recently developed method that allows heritability to be estimated using both related and unrelated individuals.et al. for sex differences in schizophrenia.30 The GCTA software31 was used for the GREML analysis.To examine whether the same or different genetic variants are implicated in male and female childlessness, bivariate GREML analysis were conducted with male childlessness considered as the first trait and female childlessness as the second trait, also used by Lee 32 Different risk scores are created depending on P-value cutoffs, from using only genome wide significant SNPs  to including all genotyped SNPs . Polygenic scores are created with the PRSice tool in PLINK.33 An LD threshold of 0.1 and a distance threshold of 250 kb are used, indicating that if two SNPs are included in the PGS that have a correlation of 0.1 or greater, or a distance of 250 kb or smaller, one of the two SNPs is removed. The original sample of the GWAS from which we create the PGS included the STR sample. For that reason we used the GWAS results from the sample excluding STR and based our PGS on these results. We will run logistic regression models on childlessness with the standardized polygenic scores as independent variable controlling for year of birth and years of education. Only one individual from each twin pair is included in these analyses to meet the criteria of independent observations.The third method we used to assess the influence of genes on childlessness was creating the polygenic scores (PGS) for number of children ever born (NEB) and the age at which people have their first birth (AFB) and examine to what extend these PGS influence childlessness. The PGS is the sum of the risk alleles weighted by their effect size and is thus a summary measure of genetic variants that increase the risk for a trait.To assess sex differences in the effect of the polygenic risk score on childlessness fitted a logistic regression model including an interaction between the polygenic risk score and sex.34 Around 14.3% of the men in the sample were childless, which is lower than the overall rate in Sweden, which ranged between 17 and 20% in the period studied.34 The correlation among MZ twins was in all cases higher than the correlation in DZ twins  and when comparing model 1 and 3, dropping A resulted in a borderline significant reduction in model fit (P=0.072). The best fitting model for females is thus model 2—the AE model. The estimated heritability in this model was 0.48 (95% CI 0.33–0.62). For males, when contrasting model 5 with 6 and 9 with 10, we see that dropping C or D did not result in a significantly decreased model fit (P=1 and 0.461 respectively). Comparing model 5 and 7 shows that dropping A resulted in a significant drop in model fit (P=0.017), suggesting that the best fitting model for males is the AE (model 6). A heritability estimate of 0.46 (95% CI 0.30–0.61) indicates that almost half of the variance in childlessness is attributed to genetic factors. For both sexes, there was no significant effect of shared environment, with the individual environment estimated slightly above 50%.To estimate heritability in the twin model, univariate ACE models were estimated separately by sex. For males, ADE models were also estimated, since for male MZ twins, the tetrachoric correlation is more than twice as large as for male DZ twins, which is an indicator of dominant genetic effects. Both goodness-of-fit and parameter estimates for each model are listed in rg) between men and women was different from the theoretical value of 0.5 or from 0. As we did not find any shared environmental factors, we did not test whether the shared environmental correlation was different from the theoretical value of 1 and thus focused on testing the sex limitations on our AE models. When the genetic correlation could be freely estimated in model 12, the estimate is 0.142. Model 13 in which the genetic correlation was set to 0.5 has a significantly lower model fit (P=0.023). Model 14 in which the genetic correlation was set to 0  has the best model fit, indicated by a value of –1.090 for the AIC. For this reason we adopt this model with the genetic correlation set to 0.To examine whether there were different genetic influences on childlessness for males and females we fitted sex limitation models. Goodness-of-fit statistics as well as parameter estimates are displayed in model 12 to 16 of To test for quantitative sex differences, we examined whether the values for additive genetic influences (A) and individual environmental influences (E) could be set as equal between the sexes. This would indicate that the influence of the additive genetic and individual environment is equally important for men and women. Model 15, the homogeneous model, had a lower AIC value than the heterogeneous model 14 of –3.939 and for that reason the values for A and E were set as equal between men and women.P-value=0.000), leaving the final best fitting model to be model 15. This was the model in which the genetic correlation between men and women was set to 0 without any effect of common environmental factors and equally high heritability estimates for men and women, with heritability estimated at 0.47 (95% CI 0.37–0.58) and individual environmental influences at 0.53 (95% CI 0.42–0.63)  see . This inIn the next step, we examined heritability in twins using the GREML method . The estTo further examine whether the same genes influence male and female childlessness, bivariate GREML models on childlessness were fitted to estimate the genetic correlation between childlessness by sex. The results are displayed in the bottom panel of P-value of 5 × 10−8) we find no significant effect on childlessness. For all other PGS’s we find a significant effect with odds ratios of around 1.25. This indicates that the odds of remaining childless are about 1.25 times as high for individuals with a 1 standard deviation higher score on the AFB genetic risk score. Individuals with a greater risk of having a higher age at first birth are thus more often childless.We then tested the effect of genes on childlessness by fitting logistic regression models on childlessness and testing the effect of the PGS of AFB and NEB. To test the sex differences in the effect of the polygenic risk score on childlessness, The measure of childlessness for men and women are not exactly the same. For women both living children as children who are dead are taken into account, while for men only children who are still living. Furthermore, only men over the age of 50 are included while women over the age of 45 are included. We fitted sex limitation models as well as the logistic regression models using the PGS on the measure on living children for men and women as well as on all men and women over 45 and over 50 to examine if this influences the results. Results are displayed in the The goal of this study was to examine sex differences in the genetic influence on childlessness. We provide clear evidence that there are different genetic influences on childlessness for men and women. Although the level of the heritability of childlessness is approximately equal for both sexes, the actual genes that have a role vary. We infer this by applying classical twin modeling, the GREML method and a molecular genetic PGS approach. Future research should investigate which pathways genetic factors influence male and female childlessness. The question remains as to whether they are mainly physiological, behavioral, or whether gene–environment interactions work differently for men and women. For example, since women have a shorter reproductive window, the postponement of childbearing may have a larger impact on genetic factors influencing female childlessness.We contrasted three different methods and compared their results in relation to male versus female childlessness. In the first classical twin method, we found that almost half of the variation (47%) in childlessness was due to genetic variation and that different genes influence male and female childlessness. We then applied the GREML method on twins. The main difference between the twin and GREML methods is that in the GREML method, genetic similarity between DZ twins is not assumed to be 50%, but measured on actual SNP similarity. Although the differences are not statistically significant, we find slightly higher heritability estimates of 59% with the GREML than the twin method, and also isolate that different genes influence male and female childlessness. Finally, using a PGS for AFB we found that genes previously found to be related to fertility timing are also related to childlessness for women, but not for men.13 and Denmark .35 One previous study on the STR found sex limitations in genetic influences on the total number of children,36 which is in line with our findings. We extend this study, however, by looking at the different reproductive trait of childlessness instead of number of children or the age at first birth, use a broader birth cohort of Swedish twins born between 1911 and 1958 (instead of 1915–1930 in Zietsch and colleagues36) and examine sex differences using three different methods.When comparing this study to previous twin studies on childlessness, we find comparable estimates of heritability in Finland (0.39 for women and 0.50 for men)5 In that study, out of the 12 independent loci isolated for human reproduction, two had a sex-specific effect. All signals found for AFB and two of the three signals for NEB had a consistent direction across the sexes. Using both LD score bivariate regression and GREML bivariate analyses that study found a high genetic correlation among men and women for both traits. It is notable, however, that for AFB, the LD score regression results suggested that there were in fact sex-specific variants for AFB  and that genetic risk scores for NEB only significantly predicted childlessness in women and not in men , where only some sex-specific genetic effects in fertility were reported .37 This makes it implausible that there are shared environmental family influences that make opposite sex siblings more dissimilar than same sex twin pairs. Furthermore, also our results from the PGS on unrelated individuals confirm our findings.We argue that different genes influence childlessness in males and females. A counterargument might be that differences in childlessness similarity in opposite sex twin pairs are not due to different genetic influences, but rather to different family socialization processes. However, we find no shared family influences in same sex twin pairs which is in line with previous research that does not find that family characteristics such as sociodemographic background, family religiosity or socialization influence male and female fertility differently.38 Previous research that examined this found no systematic differences between childlessness among twins and in the general population.39 It is thus very likely that the lower percentage in our male sample is not attributed to the difference between twins and the general population, but rather differences in the measurement or response rates related to male reproduction. Another concern in twin studies is whether DZ twins share their environment to the same extent as MZ twins, referred to as the equal environment assumption (EEA). For several outcomes, this assumption has been tested by comparing the influence of perceived and actual zygosity, which gained plausible support.40 Another study found that even though MZ twins share their environment to a higher extent than DZ twins, controlling for this rarely results in a significant reduction of the heritability estimate.41 Furthermore, previous research on unrelated individuals also found heritability of fertility traits.42 This indicates that estimates from the twin study might be an overestimate of the actual heritability, but that the overestimation is unlikely to be severe.A shortcoming of this study is that we were unable to distinguish between voluntary (childfree) and involuntary childlessness, which might result in heterogeneity within the group of childless individuals. Genetic factors could influence the desire or predisposition to have children, biological fecundity or other pathways leading to childlessness. However, for the sake of examining whether genetic factors can be passed on to the next generation by sex differences, these findings are relevant regardless of our lack of distinction between (in)voluntary childlessness. A more general concern often raised with regard to twin studies, is the question of whether the trait of interest is the same amongst twins compared to the overall population. In this sample we find that the proportion of women who remain childless is equal to the overall proportion of childless women in Sweden. For men, the percentage in our sample is lower than the national percentage.29 However, given that in contrast to Zaitlen et al29 we only include pairs of twins in our study, this issue should not impact our results. Second, dominant genetic effects might bias narrow sense heritability estimates upwards in the GRM models.29 Our twin models report no evidence for dominant genetic effects for childlessness—which is in line with the findings from recent reproductive1 and molecular genetics research.5 Third—and as discussed previously—shared environmental influences amongst siblings might influence fertility and correlate with genetic relatedness, inflating heritability estimates. Zaitlen et al29 find no evidence for a bias due to shared environmental influences when introducing this approach to the literature for several traits including number of children—in line with findings from twin studies.41 Given the similarity of our findings from both the twin and GREML modeling approach, we are confident that our results are robust, also since twin models account for shared environmental influences and dominant genetic effects on childlessness.Finally, there are three concerns for potential inflation of heritability estimates in the GREML models we apply. First, ascertainment bias from the overrepresentation of cases in case–control studies cannot be corrected for if extended genealogical data is used.35 but uniquely identified genetic sexual dimorphism, which may be one of the explanations for previous findings on the moderate heritability of fertility.This study has confirmed findings from previous research in showing a genetic influence on childlessness,