Puccinia polysora Underw, is a destructive disease that can severely reduce grain yield in maize (Zea mays L.). Owing to P. polysora being multi-racial, it is very important to explore more resistance genes and develop more efficient selection approaches in maize breeding programs. Here, four Doubled Haploid (DH) populations with 384 accessions originated from selected parents and their 903 testcross hybrids were used to perform genome-wide association (GWAS). Three GWAS processes included the additive model in the DH panel, additive and dominant models in the hybrid panel. As a result, five loci were detected on chromosomes 1, 7, 8, 8, and 10, with P-values ranging from 4.83×10-7 to 2.46×10-41. In all association analyses, a highly significant locus on chromosome 10 was detected, which was tight chained with the known SCR resistance gene RPPC and RPPK. Genomic prediction (GP), has been proven to be effective in plant breeding. In our study, several models were performed to explore predictive ability in hybrid populations for SCR resistance, including extended GBLUP with different genetic matrices, maker based prediction models, and mixed models with QTL as fixed factors. For GBLUP models, the prediction accuracies ranged from 0.56-0.60. Compared with traditional prediction only with additive effect, prediction ability was significantly improved by adding additive-by-additive effect . For maker based models, the accuracy of BayesA and BayesB was 0.65, 8% higher than other models . Finally, by adding QTL into the mixed linear prediction model, the accuracy can be further improved to 0.67, especially for the G_A model, the prediction performance can be increased by 11.67%. The prediction accuracy of the BayesB model can be further improved significantly by adding QTL information . This study will provide important valuable information for understanding the genetic architecture and the application of GP for SCR in maize breeding.Southern corn rust (SCR), caused by  SCR wason areas  and obseon areas . The invon areas . The widon areas . With clon areas .The breeding of SCR resistant varieties is very important for disease management, which poses challenges for breeders. In China, several main cultivated corn varieties, such as Zhengdan958, Xundan20 and Xianyu335, have been identified to be susceptible to SCR . Indeed,P. polysora have been identified, including EA.1, EA.2, EA.3, and PP.3-PP.9 , which is based on genetic linkage disequilibrium (LD) in a panel including a large number of genotypes representing broadly natural variations, has been used as an alternative approach for exploring the molecular basis and identifying SNPs of complex quantitative traits . In maizGenomic prediction (GP), also known as genomic selection (GS), is a technology to predict the performance of plants without phenotyping, and has been proven to be effective in plant breeding . Gowda eIn this study, four DH populations with 384 accessions and their testcross hybrids with 903 accessions were used to perform GWAS and GP analyses for SCR resistance. The objectives of the current study were to (1) detect the significantly associated SNPs, and major QTL conferring SCR resistance; (2) predict SCR resistance trait with different GBLUP models; (3) test the predictive power of different marker-based models for resistance trait; and (4) estimate the GP accuracies using models with QTL information.22.1A total of 384 DH lines belonging to four DH populations were developed from four elite inbred lines Table 1 To test the SCR infection levels of the accessions, we planted the DH lines and hybrids in Huang-Huai-Hai summer corn planting region in China for phenotypic identification. This region is the main area where SCR occurs in China due to high temperature and rainy summer. The DHs were planted in Jinan (N37°42’ E117°27’) in 2021, Xinxiang (N35°9’ E113°47’) in 2018 and 2021; the hybrids were planted in Jinan in 2021, Jining (N35°6’ E116°31’) in 2020 and 2021, Xinxiang in 2020. We used the augmented experimental design, setting every 20 accessions as a block. Each block consisted of 19 rows and standard accessions were planted in random order. For the DHs, the standard accession was a susceptible inbred line C116A. For the hybrids, the standard accession was a susceptible commercial hybrids ZhengDan958. In the field, each accession was planted in a one-row plot for DHs and a two-row plot for hybrids at a spacing with 0.6 x 0.25 m spacing .2.2SCRRS for each accession was visually collected from the leaf area covered by lesions at 4 weeks after flowering .2.3The raw phenotypic data were analyzed using the linear mixed model with an R add-on package “lme4” . Best liijy is the mean phenotypic value of the ith DH or hybrid in the jth environment;where, μ is the overall mean of the trait; ig is the random effect of the ith accession; jl is the random effect of the jth environment; ig×jl is the random interaction effect between the ith accession and the jth environment; and ϵ is the random error.Heritability was calculated using variance components estimated from the above model. The following equation was used to estimate heritability on an individual plot basis,gV is the genotypic variance component, eV is the error variance, and l is the number of environments.Where 2.4http://www.cog-genomics.org/plink2/). The genotypes of hybrids were obtained with the cleaned SNPs  of DHs and testers using TASSEL V5.2 software (2) between two loci using plink software. Only SNPs with a MAF > 0.05 and less than 0.1 missing data were used to estimate LD. Principal component analysis (PCA) was used to assess the level of genetic structure using TASSEL software.Young leaves of all the DHs and the tester lines were sampled for DNA extraction using the CTAB method . Then, gsoftware . Pairwis2.5−6), where 34,037 is the total number of SNP markers  were considered to mark the same genomic region  method, as proposed by Liu et al.  was appl markers . Markersc region . The cor2.6The Genomic prediction was performed for the hybrid panel with three conditions, including 1) extended GBLUP models, 2) maker based prediction methods, and 3) prediction models with QTL calculated by GWAS as fixed effects.aG), dominant (dG) and epistatic relationship matrices. aG and dG matrices were calculated using the “sommer” package in R (“#”) of the following form: (i) additive-by-additive interactions (a#GaG); (ii) dominance-by-dominance interactions (d#GdG); and (iii) additive-by-dominance interactions (a#GdG), respectively : nμ+dudG+ϵy=1Model(G_D): nμ+auaG+dudG+ϵy=1Model(G_A_D): nμ+auaG+aauaaG+ϵy=1Model(G_A_AA): nμ+auaG+aduadG+ϵy=1Model(G_A_AD): nμ+auaG+dduddG+ϵy=1Model(G_A_DD): nμ+auaG+dudG+aauaaG+aduadG+dduddG+ϵy=1Model(G_A_D_E): y is the vector of phenotypic data; n1 is the n-dimensional vector of ones; μ is the overall mean; a, ud, uaa, uad, uddu are the vectors of random effects for additive, dominant, additive-by-additive, additive-by-dominance and dominance-by-dominance effects assumed to obey the normal distributions N having mean zero and variance where To further improve the prediction ability, we added QTL into the mixed linear model as fixed factors. Two representative models were selected, namely G_A and BayesB. We added additive localization maker and dominant localization maker obtained by GWAS into the model separately or together, including G_A_qa (G_A with additive GWAS SNPs), G_A_qd (G_A with dominant GWAS SNPs), G_A_qad (G_A with additive and dominant GWAS SNPs), BayesB_qa (BayesB with additive GWAS SNPs), BayesB_qd (BayesB with dominant GWAS SNPs), BayesB_qad (BayesB with additive and dominant GWAS SNPs). When the prediction was performed with additive QTL, homozygous genotypes with recessive allele combinations were coded as 0, homozygous genotypes with dominant allele combinations were coded as 2, and heterozygous genotypes were coded as 1. When the prediction was performed with dominant QTL, both types of homozygous genotypes were coded as 0 and heterozygous genotypes were coded as 1. The models can be described as,QTLaβaX+auaG+ϵy=Model(G_A_qa): QTLdβdX+auaG+ϵy=Model(G_A_qd): QTLadβadX+auaG+ϵy=Model(G_A_qad): QTLaβaX+Zaα+ϵy=Model(BayesB_qa): QTLdβdX+Zdα+ϵy=Model(BayesB_qd): QTLadβadX+Zadα+ϵy=Model(BayesB_qad): y is the vector of phenotypes; QTLa, XQTLd, XQTLadX are incidence matrices of additive localization makers, dominant localization makers and both, respectively; a, βdβand adβ are vectors of fixed effects for QTLa, XQTLdX and QTLadX, respectively; aG is the genomic relationship matrix corresponding to additive genotypic values; Z is a genotypic matrix for all markers; α is a vector of random regression coefficients of all the marker effects; and ϵ is a vector of residuals.where In this study, we used a five-fold cross validation approach to assess the ability of the tested GP models. Prediction accuracy was quantified using two methods, 1) the Pearson correlation between the input trait values and the genomic estimated breeding values (GEBVs) predicted from a given GS model evaluated in the test set, 2) the number of top 20% accessions intersections selected by GEBVs and true values derived by the total number of accessions in the test set. The process was repeated 100 times to eliminate the prediction error.2.7P < 0.05 was considered to be statistically significant.Data analysis was carried out with R software (Version 3.6.2). Microsoft Excel for Mac (Version 16.50) was used for collation of phenotypic data. Tukey’s test and Students’ t-test were performed to assess the significance of differences between values, and 33.1P<0.05), with the mean SCRRS was 6.02. In the hybrid panel, the scores ranged from 3.65 to 6.08, with a mean of 4.97. The most resistant subgroup was POP2/C229, with the mean SCRRS was 5.39. In particular, the DHs and hybrids were planted at different locations, so we didn’t make a comparison between the two panels. The broad-sense heritability (2H) analysis revealed that the 2H in the DH panel and the hybrid panel were 0.64 and 0.54, respectively, suggesting that the phenotypic variation in the two panels was genetically controlled.We evaluated the SCRRS in 384 DH lines and 903 hybrids under three and four environments, respectively. The results indicated that there were abundant phenotypic variations within each panel , 34,037 SNP markers for 384 DH genotypes were available for further analysis. The 903 hybrid genotypes were imputed by their parents. The molecular diversities among the DH lines and hybrids were examined by applying principal coordinate analysis  ranging from 6.30 to 40.61. These SNPs were distributed on chromosomes 1, 8 and 10, with the candidate regions Chr1: 181,330,348-188,255,567, Chr8: 13,140,413-18,429,572, Chr10: 2,656,837-4,990,741, respectively (P) were ranged 7.17-37.12, the effects were -0.16, 0.14 and -0.5  plot implied that the population structure and family relatedness were well controlled in the three GWAS jobs . Interestingly, G_A is better than other models for top selection, which is different from previous reports  were selected to test the effect of adding QTL as fixation factors (4SCR is a major disease widely existing in maize, which can cause large yield loss and occur in a wider geographical range . TherefoUnlike the natural line based GWAS analysis, we used the population derived from four bi-parent DH and their testcross hybrid populations. In previous studies, the background of the GWAS homozygous population formed by multiple artificial populations is more controllable, which has been confirmed in the NAM population . This meRp genes mainly functioned in SCR resistance in previous studies, there was evidence that quantitative genes also contributed to SCR resistance (RppC (RppQ (RppD (RppS/RppK (RppM (It was found that although dominant sistance . Five sisistance Table 3.ce (RppC  and othepC (RppQ , RppD (ZpQ (RppD , RppS/RpppS/RppK , RppM (WpK (RppM . The staIn recent years, GP is a commonly used method to reduce costs and workload in plant and animal breeding programs, especially when combined with DH technology, breeding efficiency can be further improved . HoweverSince the heredity of plant resistance seems to be controlled by dominant genes, GP models based on the genetic relationship matrix may have limited predictive power. We tried maker based GP models and found that most of them had comparable predictive power to G_A, including RRBLUP, BRR, BL and BayesC Figure 6Based on the results of GWAS and GP, we further added candidate loci resulting from association analysis into the prediction model as fixed factors Figure 75P-values ranging from 4.83×10-7 to 2.46×10-41. On the other hand, to improve the selection efficiency of resistant materials in breeding, several GP methods were performed to explore predictive ability for SCRRS in hybrids, including extended GBLUP with different genetic matrices, maker based prediction models, and mixed models with QTL as fixed factors. We found that adding additive-by-additive effect to GBLUP model, selecting BayesA or BayesB model, adding QTL into the mixed linear prediction model will improve the prediction performance. The results will provide important valuable information for understanding the genetic architecture and the application of GP for SCR in maize breeding.SCR occurs widely in maize and brings great loss to yield. Here, we developed the DH panel with 384 lines and the hybrid panel with 903 testcross hybrids. SCRRS of accessions were collected with multi-year and multi-location field testing. Using GWAS analytical pipeline, five QTL loci were detected on chromosomes 1, 7, 8, 8, and 10, with The original contributions presented in the study are included in the article/JL and DC: investigation, data processing, and writing. SG, CC, YuwW, YZ, XQ, ZL, and DW: investigation, data collection and editing. WL and YuaW: managing the project, review and editing. CL and SC: managing the project, editing the manuscript, and funding acquisition. All authors contributed to the article and approved the submitted version.


Saccharomyces cerevisiae. The genetic variation of 971 published isolates and their growth ratios under 35 medium conditions were analyzed by genome-wide association analysis, and the precise p-value threshold for each phenotype was calculated. Risk markers for the above 35 phenotypes were obtained. By estimating the genotype of F1 hybrids according to that of the parents, the PRS of 613 F1 hybrids was predicted. There was a significant linear correlation between the maximum growth rate at 40 °C and PRS in F1 hybrids and their parents , which indicates that PRS can be used to estimate the production performance of individuals and their hybrids. Our method can provide a reference for strain selection and F1 prediction in cross-breeding yeasts, reduce workload, and improve work efficiency.The cultivation of hybrids with favorable complex traits is one of the important goals for animal, plant, and microbial breeding practices. A method that can closely predict the production performance of hybrids is of great significance for research and practice. In our study, polygenic risk scores (PRSs) were introduced to estimate the production performance of  Saccharomyces cerevisiae) strains with preferred characteristics from multiple parental strains by sexual hybridization. Cross-breeding of industrial strains, such as baker’s [Cross-breeding is one of the effective ways to obtain new yeast strains with superior traits. The production of excellent hybrids through cross-breeding has led to a continuous and substantial increase in global agricultural productivity ,2,3. It  baker’s , sake [6 baker’s , has bee baker’s . TherefoMany complex diseases in human beings are caused by both genetic and environmental factors. Moreover, most of them are affected by multiple genes , so theoHowever, PRS is only used to identify the individuals with clinically significant increased risks, primarily for the early warning of important human traits for adjunctive treatment . In the The goal of this study is to identify risk markers related to the production performance of yeasts, increase the variance explained by phenotypic diversity, and achieve the accurate prediction of phenotypes in F1 hybrids. In this paper, it is proposed to introduce PRS into breeding research and to screen out high-potential parents based on the parent’s trait performance. In order to predict the phenotype of the next generation of hybrids, we estimate the offspring genotype according to parental genotype and then estimate its PRS.S. cerevisiae genomes and the growth ratio of their F1 hybrids without any genetic marker through spore-to-spore mating. The method consisted of three main steps. First, to identify risk markers associated with the growth ratio, we downloaded the published GWAS summary results regarding the association between 83,794 variant markers and growth ratios under 35 medium conditions. We screened out the risk markers by calculating the precise p-value. Then, by estimating the genotypes of F1 hybrids according to the parental genotypes, we calculated their PRS. Finally, the potential of F1 was judged according to the value of PRS. We developed a method for predicting the growth ratio of hybrid F1 and validated it with 52 wild-type homozygous S. cerevisiae isolates to obtain phenotype association loci. The isolates included in this project were carefully selected from providers and references including 23 kinds of ecological and 312 different geographical origins from around the world [http://1002genomes.u-strasbg.fr/files/ accessed at 19 December 2017and 30 March 2017 respectively.To calculate the PRS of one individual, we needed to obtain the risk loci associated with each trait. We used a dataset of 1011 he world . EcologyS. cerevisiae isolates was a gift from Prof. Fengyan Bai, Institute of Microbiology, Chinese Academy of Sciences. Their work provided the detailed information about the SNPs of these isolates [S. cerevisiae that has been documented to date [S. cerevisiae S288c was used as the reference genome (version R64-1-1) and was downloaded from the National Center for Biotechnology Information (NCBI). The phenotypic data  were measured for 613 F1 hybrids and their parents without any genetic marker by spore-to-spore mating between pairs of the 52 wild S. cerevisiae strains gifted from Liang S [The testing dataset with variant calls of 266 isolates . They we to date . The gen Liang S .GEMMA 0.98.3 with a linear mixed model and p-values from the Wald test to account for the 35 phenotypes. Then, we computed the variance explained by our significantly associated markers [PRSice-2 [p-value thresholds according to the results of GWAS and provide the best-fit PRS and p-value significance threshold. Then, we used it to calculate the PRS of each isolate and obtained the precise p-value threshold (PT) in order to explain a higher variance. Markers with a p-value below PT were screened to form a dataset with risk loci associated with the phenotype by in-house Python scripts.Since the phenotypic data we obtained were already normalized, and the genomic variants had also been filtered, we could perform the genome-wide association analysis (GWAS) directly. We subjected 971 isolates with MAF > 5% to the performed genome-wide association analysis by  markers  by an in markers . The metPRSice-2  was usedPRSs were generated by multiplying the genotype dosage of each risk loci by its respective weight and then summing across all variants in the score using in-house Python scripts.For homozygous SNP, there is ideally only one allele that is passed down to the next generation. However, for heterozygous loci, we cannot accurately determine which allele is passed on to the offspring. Assuming that To measure the degree of heterosis, F1 was divided into groups according to the above three parameters, and the PRS difference between groups was compared. MPH (mid-parent heterosis) > 0 was considered to show heterosis, BPH (best-parent heterosis) > 0 was considered to show significant heterosis, and DEP (depression) > 0 was considered to show decline. The formula is as follows:The normality was verified by Kolmogorov–Smirnov test. We performed linear fitting on the PRS and phenotype data of 52 candidate parents and 613 F1 hybrids and output at a 95% confidence interval. All tests were two tailed with an alpha threshold of 0.05. Statistical analyses were conducted in R v3.6.0.https://github.com/DYqwert/pyprs/ accessed on 1 July 2022.The scripts for calculating PRS for parents, gametes, and any F1 hybrids were deposited in GitHub at p < 5 × 10−8 as the high-confidence significant threshold, we found 12 SNPs associated with YPD40 (R2 = 0.33) (2 = 63.97%)  A,B. When 63.97%) C,D. Acco2 = 0.2582, p-value = 1.203 × 10−4), indicating that there was a good linear correlation between PRS and phenotype , and there was also a significant difference between the PRS of the strains that showed depression and the other strains . However, there was no significant difference in PRS between the strain with best-parent heterosis and the other strains   C. Our reAchieving trait prediction of F1 hybrids is of great significance for cross-breeding, whether in terms of industrial applications, experimental costs, or genetic research. Our method enables the efficient prediction of traits in the progeny of hybrids, and we confirmed the correlations with the experimental results. This method can accurately predict the phenotype of hybrid generation with only the parental phenotype and genome and without hybridization experiments being conducted. Moreover, this method is not only applicable to the production traits mentioned in this paper, but also to other important complex traits . It is hPRSs are similar to narrow heritability in that they represent the aggregate and additive effects of segregating loci with small effect to some degree ,28. ConsS. cerevisiae [For homozygous SNP, ideally only one allele is inherited by the next generation. However, for heterozygous loci, we cannot accurately determine which allele is passed on to the offspring. Our method may underestimate or overestimate the effect of homozygous loci. Simply put, under the assumption that there are only two alleles, the offspring can only have three genotypes. Considering the amount of calculation, we only need to estimate the minimum and maximum PRS of different F1 genotypes, and the obtained interval can be used as a breeding reference. Theoretically, the variance of PRS mainly comes from the genotype difference produced by uncertain gametes, so, with the increase of uncertain genotypes, the variance of the estimated PRS will increase. In addition, our method cannot yet predict the heterosis of hybrids. However, our results show that PRS may be used to judge whether heterosis exists, although it cannot be used to judge the degree of heterosis. Heterosis is an important reason for cross-breeding research, so the prediction of F1 heterosis is also crucial. However, the complementation of the allelic variation and the variation in gene content and gene expression patterns are likely to be an important contributor to heterosis . There irevisiae . Althougrevisiae , it is dThe prediction of complex traits in hybrids is of great significance for production cost, experimental cost, and genetic research relating to breeding. This method can effectively predict the phenotypes of F1 hybrids, and we confirmed the correlation with experimental results, which may be helpful for the cross-breeding of fungi.


In complex diseases, the phenotypic variability can be explained by genetic variation (G), environmental stimuli (E), and interaction of genetic and environmental factors (G-by-E effects), among which the contribution G-by-E remains largely unknown. In this study, we focus on ten major neuropsychiatric disorders using data for 138,383 United States families with 404,475 unique individuals. We show that, while gene-environment interactions account for only a small portion of the total phenotypic variance for a subset of disorders , they explain a rather large portion of the phenotypic variation of the remaining disorders: over 20% for migraine and close to or over 30% for anxiety/phobic disorder, attention-deficit/hyperactivity disorder, recurrent headaches, sleep disorders, and post-traumatic stress disorder. In this study, we have incorporated—in the same analysis—clinical data, family pedigrees, the spatial distribution of individuals, their socioeconomic and demographic confounders, and a collection of environmental measurements.  •G-by-E interactions contribute to the etiology of neuropsychiatric disorders•Environmental quality is associated with the risk of neuropsychiatric disorders•Geographic locations explain a part of variability of neuropsychiatric disorders•Identifying specific G-by-E interactions might be the future of personalized medicine Zhang et al. show that gene-environment interactions account for a significant portion of the phenotypic variance of common neuropsychiatric disorders: over 20% for ADHD, migraine, and anxiety/phobic disorder and close to 30% for recurrent headaches, sleep disorders, and post-traumatic stress disorder. G × E (“the G-by-E effect”). However, measuring such interactions in real-world data has proved rather difficult.(1)The data would need to contain the complete germline genomic sequence for a large number of individuals. While such human datasets are available today, our ideal data would link all study individuals into a unified genetic pedigree, which would allow for the inference of genetic models associated with the vertical trait transmission.(2)For each study participant, the data would contain complete phenotypic profiles across all human traits. This is very challenging, as myriads of phenotypic characteristics, which change throughout individuals’ lives, would have to be recorded. Currently—at best—human observational data contains snapshots of medical histories and collections of biometric, metabolic, and clinical measurements for each individual, for a limited window of their ontogenetic timeline, usually capturing a few years (or less) of each timeline.(3)For each individual, the data would document a complete record of exterior environmental events and interventions, including exposures to changes in climate, tidal waves of uncountable bacterial, viral, fungal, and protozoic encounters, billions of environmental molecular species entering the individual’s body over time, and exposure to electromagnetic fields and the bombardment of elementary particles, as well as the individual’s diet, exercise routines, and social support structure. These factors are typically the worst-documented part of human life, because the set of relevant stimuli is astronomically vast and must be recorded continuously from conception to death.The study of phenotypic trait heritability is one of the most important topics in biology. Heritability is the proportion of the overall trait variance that can be explained by genetic variation under an explicitly defined genetic penetrance model. In practice, heritability has been used to indicate the strength of a trait’s response to artificial selection in domesticated organisms. As expected, this is not very productive when attempting to artificially select for traits with low heritability. Since the earliest days in the field, geneticists have imagined the possibility of the existence of complex interactions between genetic variation and environmental stimuli, often denoted as genotype × environment × phenotype × time data matrix, it would be used to fit a battery of increasingly complex mathematical models encapsulating the probability of observing a specific phenotype, given genetic and environmental inputs. The models that we are comparing represent alternative theories of how genetics, environments, and their interactions contribute to disease onset. The degree of each model’s fit to the data for a disease then explicitly quantifies the corresponding theory’s value with respect to the disease.Were we able to generate a gigantic Generating such a gargantuan dataset for a practical-size cohort of at least a few thousand individuals is prohibitively expensive at this time . Because these imaginary, ideal datasets are not available—and unlikely to be generated in the near future—the real-life heritability human disease estimates rely on (1) access to simplified-structure, cheaper datasets and (2) mathematical models with strong, simplifying assumptions permitting inference from incomplete data. There are three major groups of mathematical approaches—twin, pedigree, and genetic association studies—which constitute the modern toolbox for dissecting disease etiology.This type of data includes limited phenotypic descriptors (disease or no disease) and data regarding genetic relatedness between twins , with 100% and 50% genetic similarity of MZ and DZ twins, respectively. With the strong assumption that the environment is identical for both individuals in each twin pair, we can then use a simple model to attribute disease status in concordance to the twins’ genetic similarity.11These limited phenotypic data include disease or no-disease statuses for each family member. Genetic data are reduced to a pedigree structure, in which siblings share half of the genetic variants with each parent and with each other. No explicit environmental data are provided. Model assumptions can include the same environment for all individuals described in the dataset (earlier models), or distinct shared environments for siblings, spouses, families, and individuals (in the more recent and sophisticated models).In this case, the genetic data include individual-level genotypes for a large number of participants, possibly with knowledge of family structure for a subset of individuals. Phenotypic data involves disease status. Typically there are no environmental data available, and individual-specific environments are implicitly assumed to be identical for all participants.One should expect that each simplifying assumption in a mathematical heritability model results in biased parameter estimates. In twin analyses, all concordant disease states between twins are explained genetically. Therefore, we would expect that heritability estimates from twin data would be the highest. On the one hand, association studies focus on the explanatory power of common genetic variation—therefore, by design, heritabilities estimated with association data are smaller than estimates that would be obtained from total genetic variation . On the other hand, association analysis typically ignores environmental data, which means that heritability estimates should be inflated with respect to hypothetical association studies with explicit environmental data included. Family pedigree analyses incorporate both limited genetic and limited environmental data and thus promise better-balanced heritability estimates. Keeping the strengths and weaknesses of the currently available tools in mind, we expect that richer data and more complex models are needed in order to dissect the influence of environment and genetics on human traits.To represent genetics we will use family trees, as in the pedigree studies mentioned above. We will implicitly represent environmental influences in random effects, associated by the predetermined environmental relationship . More interestingly, we will construct models that consider gene-environment interactions and compare them with their counterparts in the absence of the mixed-effect regression’s interaction term . On the e2), the familial environment (f2), the environment shared by couples (c2) and siblings (s2), and the shared geographic location of residence (p2). We fit the models in a Markov chain Monte Carlo procedure with a Bayesian framework see  for the First, interaction models (IM1 and IM2) fit the data better than their linear counterparts (LM1 and LM2) in 17 out of 20 comparisons. The three exceptions are LM2 versus IM2 in adjustment disorder and substance abuse, and LM1 versus IM1 in bipolar disorder. The lower WAIC estimates suggest the interaction models fit the data better than the linear model, with smaller information loss.Correspondingly, gene-environment interactions seem to explain a significant portion of the total phenotypic variance. For example, gene-environment interactions under the best-fitting IM1 model explain over 29% of the total anxiety/phobic disorder phenotypic variance  model corresponds to an extremely high heritability estimate (95%). However, the best (in terms of the WAIC model), IM2, incorporating all environmental and interaction effects, corresponds to a much lower heritability of 55%. Similarly, for bipolar disorder, heritability is as high as 80% for LM0, while for the WAIC-best model, IM2, it drops to 53%. This pattern is common across all of the neuropsychiatric disorders that we studied: The simpler models  tend to provide higher heritability estimates compared with the more complex models (LM2 and IM2).If we apply a different model selection criterion, called PSIS-LOO-CV,p2, the proportion of variance contributed by each family’s geographic position, are remarkably variable across disorders. For anxiety/phobic disorder, migraine, substance abuse, and bipolar disorder, the geographic position does not explain much of the variance . By contrast, for ADHD and PTSD, the geographic variation contributes more profoundly to the overall variance. The p2 estimates for ADHD and PTSD are close to 6%, according to their WAIC-best model LM2. Besides the findings regarding the G-by-E effects and heritabilities, estimates of For both ADHD and PTSD, all models across the complexity spectrum  give nearly identical patterns of l US see . This suWe also inspected the fixed-effect estimates of demographic (sex and age) and environmental factors  in our data for these ten most common neuropsychiatric diseases. We then analyzed how the fixed-effect environmental qualities affect our neuropsychiatric diseases’ log-odds. For selectionists working with domesticated species the notion of heritability is an instrument, while the remaining environmental variability is a nuisance. In the case of human disease, the situation may be quite the opposite. Associations between genetic variation and disease may lead to genetic tests and indicate molecular pathways that should be targeted for treatment. However, for most complex diseases, genetic variation is not very instrumental in disease treatment; predicted genetic predisposition to complex disease is often seen as a verdict rather than an actionable warning or advice.This is not so with environmental predisposition to disease. If we knew a certain environmental stimulus might trigger a particular disease, we could take preventive measures or design life strategies aimed at avoiding dangerous triggers. Similarly, with interactions of genetic and environmental signals, information can become practical and clinically actionable. If we were able to ascertain a catalog of genetic variants interacting with specific environmental stimuli, we could design personalized environmental plans for patients at risk.For the ten most frequently diagnosed neuropsychiatric conditions in our data, we designed a group of Bayesian regression models incorporating various genetic, environmental, and demographic effects. By comparing models with G-by-E interactions with their linear counterparts, we established the existence of interactions with considerable strength between the genetic variations and environmental stimuli affecting the manifestation of neuropsychiatric disorders. We also estimated a set of model parameters measuring the strength of association between the patient’s geographic location, sex, age, and the local environment’s quality with the likelihood of disease manifestation.,23Unexplained geographic variations see  and S1 cFixed effects estimated for EQIs see  indicateOur analyses open additional research opportunities. One possible step forward would be to validate these findings in large population biobanks with genetic data (such as UK Biobank or FinnGen). The present work has demonstrated that much is waiting for investigation. We can compute the interactions between genetics and concrete environmental indices, such as geographic locations, pollutants, and socioeconomic factors. This analysis could produce more easily interpretable results than ours; we only considered interactions between random genetic and environmental effects that are more difficult to interpret. Moreover, we can exploit experiments and sequencing data to dig deeper into interactions between particular genetic variants and exterior conditions. By designing specific assays and methods, it is also possible to determine these interactions’ directions and mechanisms. Does the G act as a modifier of the environmental effects, E? Does the E act as a modifier of the G? Are genetic epistasis (G-by-G) and E-by-E effects involved in disease etiology? Future efforts could answer these questions and allow us to map out strategic plans for preventive and precision medicine.Our study finds substantial gene-environment interactions in common neuropsychiatric diseases through elegant methods. However, there remain many unsolved puzzles.Our estimation method relies on the presumption that the pedigree and residency information truthfully reflect the real situation. In the current version of IBM’s Health MarketScan database, demographic and family information is limited to age, sex, area of residence, and information about family members enrolled under the same health insurance policy. The data only label if a family member is a “parent” or a “child”—adoption or biological relation has not been meticulously documented. We also do not know how the residency information truthfully reflects the actual environmental exposure. This inconsistency between our assumptions and the information in data (or lack thereof) might compromise our estimation accuracy, even with the large scale of our data and the quality control steps we have performed. Our analysis and corresponding results are based on populations that consistently lived in the same geographic location during the study period. We excluded from our analysis a relatively small subset of families who lived in more than one place during the study period. Environmental exposures for such populations were more difficult to estimate and incorporate into our model. Therefore, caution should be exercised when interpreting and generalizing the results reported in this study.On the methodology side, we relied on a fully Bayesian approach that provided merits such as a model-centered inference process, intuitive uncertainty quantification, and the availability of versatile model comparisons and regularization tools. However, a Bayesian method also entails many disadvantages. A Bayesian sampling only guarantees convergence to the posterior distribution, as its iteration time continues to infinity. For real-world complex models, various advanced tools such as multiple independent samplings, variational inference initialization, and No-U-Turn samplers,It is not definite what, precisely, the G-by-E effects represent. One well-liked interpretation reads the gene-environmental interaction as heterogeneous genetic effects conditioned on different environments or exterior exposures.hc2 for bipolar disorder, PTSD, and ADHD, coupled with reduced estimates of heritability. Essentially, the model and data “tell us” that, in nuclear families, parents  are more similar genetically and environmentally than randomly expected for specific disorders, such as PTSD and ADHD. For PTSD this may mean that both parents, but not offspring, might have been exposed to similar stressors, resulting in PTSD. Another reason for high hc2 could be assortative mating: data suggest that couples tend to have similar psychological trends, such as ADHD. They are also possibly more genetically similar with each other than a randomly drawn couple. Because heritability is an additive genetics’ portion of the overall phenotypic variance, increase in hc2 necessarily reduces estimates in h2 (heritability).The reader might wonder how to interpret high values of In this study, we estimated only the linear G-by-E effects with a most simplified model , estimating their total input into the phenotypic variation, without the ability to identify specific genetic variants and environmental factors. It is plausible—and even likely—that higher orders of factor interactions may play a role in phenotypic variations. For example, genetic epistasis and environment-environmental effects could “collaborate” to produce G-by-G-by-E or G-by-E-by-E interaction effects. The next important target would be to map specific genetic variant-environmental stimulus pairs for each disorder and ascertain the mechanism(s) of these interactions. Achieving this goal is likely to require the construction of new datasets approaching the “ideal” dataset described in this article’s As possibly the most famous saying among statisticians goes, “all models are wrong, but some are useful;”andrey.rzhetsky@uchicago.edu).A.R. , we then estimated how much of the phenotypic variation came from genetic factors, different environmental factors, or interactions between them, using the insurance claim data from 138 thousand US families. Our results suggest that gene-environment interactions account for substantial common neuropsychiatric disorder risk variability.Our main data resource is the IBM Health MarketScan dataset,,We used a comprehensive collection of raw environmental measurements, deriving from them environmental quality indices (EQIs) developed by the US Environmental Protection Agency (EPA) to quantify the fixed environmental factor in our mixed-effects models.We employed a mixed-effects generalized linear regression modeling methodology, using logit-link for binary disease outcome. The fixed-effects included basic demographic factors (such as sex and age groups) and we split the environmental quality indices by categories: air, water, land, sociodemographic, and built-environmental . For the random effects, we designed specific relationship matrices which determined correlation structures across individuals. For example, we specified genetic random effects with a multivariate normal distribution using the genetic relationship matrix (GRM), which indicated the relatedness between individuals. Similarly, environmental random effects shared by family members, couples, or siblings also followed distributions controlled by corresponding relationship matrices see the . In addiWe also considered the interaction between genetic and environmental random effects. By forwardly adding variables, we constructed a group of models from the simple to the more complex. h2) corresponds to the genetic random effect. In p2, h2, f2, c2, s2, e2, hf2, hc2, hs2, and he2, which represent how much outcome variation can be attributed to the geographic factors, genetic factors, familial environments, couple-shared environments, sibling-shared environments, individually-independent environments, interactions between genetics and familial environments, interactions between genetics and couple-shared environments, interactions between genetics and sibling-shared environments, and interactions between genetics and individual environments, correspondingly. Note that the individually independent environment effects E may include personal experiences in school or the workplace that are not shared with family members, and it could also encompass noises in the clinical assessment or other errors. Please refer to the Finally, it was possible for us to define statistics that quantified how much outcome variation (logit-probability of disease) could be explained by these additive random effects. For example, heritability  and environmental quality, we acknowledged that geographic position might also play a part in disease etiology.Given a patient’s dwelling’s latitude and longitude (coordinates) The Gaussian process model constrains the distribution of Therefore, if we chose the kernel function Here, we used the exponentiated quadratic kernel function, which is commonly used in geo-statistics and applications describing quantities distributed in a smooth metric space:In all, as a forward addition to the simplest linear model 0 (LM0), we expressed the logit-probability of a disease presenting for an individual as:The variance-covariance of This can be derived from the kernel function, Expression (10), as we did in Expression (9).Consequently, the geographic position factor We then considered the interaction between the genetic effect and the environmental effect. The logit-probability of having a disease can be expressed asThe scale factor The variance-covariance of Note that the above expression, demonstrates the method by which we fit the model specified in Expression (14), not (15). Expression (15) functioned as an intermediate step for calculating the total variance based on the estimates of We assumed that the genetic effect and the environmental effects are statistically independent. The operator Furthermore, interactions between genetics and the environment can also explain the variance of the logit-probability. We defined a new interaction factorThe linear models 0 and 1 incorporate the individually-independent environmental effect These additional environmental effects were assumed to follow multivariate normal distributions:We determined the relationship matrices The variance-covariance of We defined the heritability Similar to our process in the experimental models 1 and 2, we added interaction terms to the above-defined linear model 2. Thus, in this model, the logit-probability of having a disease is:The variance-covariance of We defined the heritability The models specified in Expressions (1), (11), (14), (18), and (23) are nonlinear mixed-effects models, which we can represent in a general form:However, this likelihood was not computable because of the unobserved random effects ,We were then free to apply suitable methods, such as stochastic gradient decant (SGD) or the expectation-maximization algorithm (EM) to approximate the maximum likelihood estimates – with one caveat: The ML approaches are known to underestimate the variances.,,We chose to use a fully Bayesian framework to avoid the drawbacks of ML and other related Frequentist methods. Solving the model with a Bayesian’s view provided several advantages towards solving our problem. First, for any statistical model, the Bayesian method follows an intuitive, easy-to-construct flow – model and prior specification first, and all the inferences would be automated on the computer’s side. The model-centered, uniform flow allowed us to focus our attention on exploring various models (LM0 to IM2) and their biological interpretations – with no liability to solve a novel nonlinear model. Additionally, Bayesian methods allowed us to quantify the statistical uncertainty in a natural manner because the inference would be done in a sampling process (MCMC). In a fully Bayesian framework, mean, credible intervals, or other distribution statistics are computable upon obtaining the samplings. By contrast, the ML and other related Frequentist methods do not provide an integrated method for estimate inferences and their uncertainties – the ML estimations may involve first-order approaches like SGD, while approximating the confidence intervals involved typically require a separated calculation of the likelihood’s higher-order derivative.To find the posterior distribution of a parameter After specifying the hierarchical models with priors and likelihood functions, Bayesian inference methods rely on a sampling algorithm (sampler) to draw from the posterior distribution and approximate the posterior efficiently. In the present study, we used Hoffman and Gelman’s No-U-Turn sampler (NUTS)Compared to prior research in heritability estimation, our model incorporates additional effects of gene-environment interactions. The identifiability and performance might appear questionable for estimation under the new model. Therefore, we conducted statistical simulations to assess whether the inference under the model can untangle effects of genetics, environmental factors, and gene-environment interactions from appropriately simulated data, see We considered a simplified interaction model. The logit-probability of having a disease can be expressed asWe assigned five sets of genetic variance scale Bayesian Inference section of the For each experimental set, we sampled 1,000 families from our data, and generated corresponding binary phenotype with the logit-probability defined in Expression 29. Given the simulated phenotypic data, family relationship information, and the model, we then conducted the Bayesian inference using the method we descried in the We repeated this sampling and inference process 100 times for each experimental set and computed the corresponding 95 percent credible intervals for


Multi-population cohorts offer unprecedented opportunities for profiling disease risk in large samples, however, heterogeneous risk effects underlying complex traits across populations make integrative prediction challenging. In this study, we propose a novel Bayesian probability framework, the Prism Vote (PV), to construct risk predictions in heterogeneous genetic data. The PV views the trait of an individual as a composite risk from subpopulations, in which stratum-specific predictors can be formed in data of more homogeneous genetic structure. Since each individual is described by a composition of subpopulation memberships, the framework enables individualized risk characterization. Simulations demonstrated that the PV framework applied with alternative prediction methods significantly improved prediction accuracy in mixed and admixed populations. The advantage of PV enlarges as genetic heterogeneity and sample size increase. In two real genome-wide association data consists of multiple populations, we showed that the framework considerably enhanced prediction accuracy of the linear mixed model in five-group cross validations. The proposed method offers a new aspect to analyze individual’s disease risk and improve accuracy for predicting complex traits in genotype data. In this study, we developed a statistical approach to dissect and predict human complex traits using genotype data. Distinct from existing methods that focus on refining effect size of genetic factors, the proposed method, Prism Vote, improves risk prediction from the dimension of individual, such that disease probability of a subject is regarded as a composite risk shaded from multiple subpopulations, thereby drawing information from both stratum-specific estimation and individualized risk composition. We showed in simulation studies that the PV enhanced prediction performance of several base prediction models significantly, particularly when genetic heterogeneity in the data is high. We also demonstrated in real genome-wide association study data of mixed populations that the PV considerably enhanced prediction accuracy of linear mixed models for traits including body-mass index, height, hypertension, and others. The PV framework offers an effective and scalable approach to leverage subpopulation information to perform risk prediction in mixed populations. One attpulation . Coram eel (LMM) . On the el (LMM) ,13. As tAlternatively, we consider prediction in multiple populations by leveraging the dimension of individual identity, which can be incorporated together with the SNP-centered methods to improve risk prediction. Under the proposed framework, named the Prism Vote (PV), the disease risk of a subject can be considered as a composite risk shaded from multiple subpopulation strata, in which stratum-specific genetic risk are characterized, while overall risk of the subject is integrated using Bayesian probability according to one’s propensity to subpopulations. Therefore, subjects with identical alleles at risk loci may be predicted with non-identical disease probability as subpopulation propensity varies. In the PV framework, subpopulation can be regarded as strata of more homogeneous genetic architecture compared to the non-stratified data, which might be shaped by ancestral difference or implying subject groups experiencing similar exposures altering gene-environmental interactions. The prediction utility of PV is demonstrated in three simulation studies and two genome-wide association datasets of mixed populations.The PV leverages on the genetic heterogeneity and polygenicity nature of complex traits. The detection of trait-associated markers, thousands of variants with modest effect size, are sensitive to the underlying genetic architecture of data. Stratification of samples may lead to the identification of stratum-specific risk loci and effects. The framework obtains stratum-wise risk estimates and delivers the individualized risk probability of traits through modelling the disease of a subject as a composite risk outcome from multi-layer subpopulations.i is attributed from multiple risk strata. Let Y denote a phenotype of binary outcome, and xi is the genotype matrix of subject i. Disease probability of the subject can be written as,Suppose risk of a trait for subject Eq 1 is referred to as the PV probability of a trait for a subject. It could be generalized to Y. In the equation, k, to be obtained by a base prediction model; and Pr (i∈k|xi) is the propensity of subject i belonging to stratum k, calculated by the Bayes theorem:xi|i∈k) is the probability of observing xi given subject i belongs to stratum k∈{1,⋯,K}; and Pr(i∈k) is estimated by the proportion of kth stratum out of all samples. Fig 1 shows a schematic diagram of the PV framework. The term “prism” reflects the interpretation that a subject’s disease risk is decomposed into a spectrum of risk distributions by population strata.ij be genotype of subject i for SNP j, coded by minor allele counts , i = 1,⋯,N, and j = 1,⋯,P. The genetic matrix GN×P is normalized to X, by letting j, and j (11). Compute N×N covariance matrix Ψ. Principal component analysis on X for subjects of both the training and testing data is used to obtain the eigenvectors, denoted as vr, r = 1,⋯,N, and vΨr = λrvr. Each vector vr∈ℝN corresponds to the rth largest eigenvalue λr. ith loading of the eigenvector and carries the interpretation of ith subject’s variation along the rth ancestry axis. Suppose the top q eigenvectors contain a good amount of variation; wi indicates the ith subject’s variation summarized in the top q eigenvectors’  directions. By dividing w into K quantiles, the training subjects can be assigned to the K strata according to their quantile location in w. The eigenvectors were obtained using the PLINK [K and q can be determined from cross-validations excluding the independent test data (S1 Appendix).A PC-based approach is adopted to cluster subpopulations as the PCA requires less assumptions and could be applied in various data types. Let ghe PLINK . The K ak is Nk is the number of subjects in the stratum. Position of a new subject i in the ancestral space can be calculated by i belongs to stratum k can be estimated by,wi in the kth stratum, i∈k.The probability of observing a subject belonging to a particular stratum can be approximated based on the distance of a subject to the stratum center. The center of stratum K strata; (3) obtain stratum-wise predictors by a base prediction model in the training data, resulting K sets of predicted Y for the test data; (4) calculate the propensity of a test subject i to stratum k using Eq 3; (5) obtain the final predicted Y for the test set by Eq 1.In sum, the procedure of applying the PV is as follows: (1) Obtain eigenvectors and eigenvalues of all subjects genotypes (training and testing data) calculated in the ancestral direction; (2) divide the training set into xi,j for subject i at locus j from a binomial distribution, j in the EA and AA data, respectively; i in the two populations; S1 Fig). Three thousand causal variants were selected for the AA and EA population, respectively, among which 75% was common to both populations and 25% was unique to a single population [β~N, 300 SNPs of moderate effects with β~N, and the remaining variants from β~N [j in EA and AA, respectively. A linear model was used to obtain phenotype of subjects from the causal variants and effect sizes, in which the residual term follows a normal distribution of variance satisfying alternative heritability scenarios . In the mixed data consisted of the EA, AA, and admixed populations, PV was implemented with base prediction models controlling for the top ten PCs, and by the reference methods that are the base models controlling for PCs only. For the base models, we considered the linear regression model (LM), BayesR [K and q can be found in S1 Appendix. Throughout the simulation and real data application in this study, prediction accuracy is measured by Pearson correlation coefficient between the observed and predicted outcome for continuous phenotypes, and by area-under-the-curve (AUC) for binary outcomes. Averaged prediction accuracy on independent test sets in the five-group cross-validation (5GCV) was reported.Simulation study I aims to investigate the effect of incorporating PV with an LMM base prediction model in dataset consists of multiple populations. The genotype data was obtained from two real GWAS of African and European populations from the GAIN project (dbGaP accession number: phs000021.v3.p2). We extracted data including 1,932 subjects of African ancestry (AA), 2,657 subjects of European ancestry (EA), and 9,242 common (MAF>1%) genetic variants of chromosome 22. The admixed population genotype data of 2,000 subjects was simulated by sampling a genetic variant pulation . Effect 0, 10−4) . Risk ef, BayesR , and Dir, BayesR . The BayFig 2 showed that the PV generally improved prediction accuracy of the base models comparing to the reference methods in 5GCV. Under the high heritability scenario, the PV improved the mean prediction correlation coefficient of the BayesR from 0.49 to 0.54 by 10.2%, and improved the DPR from 0.46 to 0.58 by 26.5% . PV improved the LM and DPR in all heritability scenarios, while it only enhanced BayesR under the high heritability setting. This might be due to the sparse effect model assumption made by the BayesR, from which modest causal effects were prevailingly estimated as zero in genetic data of low heritability.βk∈ℝm denote effect of m causal SNPs in population k, which follows a multivariate normal distribution [k and k′, k≠k′∈{1,⋯,K}. The covariance ρk,k′ approximates the “shared heritability”. Thus, genetic similarity of two populations can be measured by the ratio η = ρk,k′/(σkσk′). When η = 0, the populations share no effect similarity; and as η approaches one, the traits are influenced by similar genetic effects in the mixed populations. As shown in Fig 3, the reference group (DPR + PCs)’s prediction accuracy observes substantial reduction as genetic similarity in populations decreases, while DPR implemented in the PV framework produces stable prediction accuracies in all scenarios. For instance, under the high heritability scenario , as effect similarity decreases from 80% to 20%, mean prediction accuracy by the base model in the reference group reduces from 0.52 to 0.40 by 23.1%, while the accuracy with PV only slightly drops from 0.48 to 0.47 by 2.1%. Under the medium and high heritability settings  and genetic similarity  category, eight datasets were simulated at different sample sizes . As sample size of data steadily increases, implementing PV results in prediction accuracy gain in all nine scenarios . Particularly, when N = 40,000, h2 = 0.8 and η = 0.1, PV improved the prediction accuracy of DPR from 0.59 to 0.80 by 26.3% .This simulation considers influence of sample size on prediction accuracy. In each combination of heritability . Quality control (QC) was performed by removing SNPs with genotype call rate < 95%, Hardy-Weinberg equilibrium (HWE) p-value < 5×10−8 or MAF < 0.01. After QC, 560,899 autosomal SNPs were available for analysis. The second GWAS is a subset of the non-European population in the UK Biobank [). After QC, 26,506 subjects and 524,557 SNPs were available for analysis. In the PAGE data, traits including the body mass index (BMI), height, diabetes, and hypertension were analyzed; and in the UK biobank data, BMI, height, cardiovascular disease (CVD), and diabetes diagnosed by doctor (diabetes) were analyzed. For both datasets, the optimal stratum number was estimated to be two, and q was set to ten.The first real GWAS data for application is from the Population Architecture through Genomics and Environment (PAGE) project (dbGap accession number phs000220.v2.p2). A total number of 9,075 subjects were extracted, consisted of 3,520 self-identified African, 2,104 Hawaiians, and 3,451 Japanese . Comparing to the reference method (DPR+PCs), PV enhanced the prediction accuracy of base model by 12.1% (SD 4.7%) for BMI, 2.0% (1.5%) for height, 5.2% (SD 2.1%) for hypertension, and 5.4% (SD 2.2%) for diabetes. For easier interpretation of the results, we also displayed the prediction outcome achieved in single populations (S1 Table). In general, by the reference method, prediction accuracy in the joint cohort is in between the highest and lowest performance achieved in single populations , while the PV elevates the prediction outcome in mixed population data close to the best accuracy reached in single populations. For example, in Fig 5D, the prediction for diabetes by the reference method is in-between its performance in the Japanese population that is observed with the lowest accuracy and the African population the second lowest; while the PV improves the joint cohort prediction to an accuracy achieved in the Hawaiian population with the highest performance. Furthermore, as shown in Fig 5A, PV increases prediction accuracy for BMI to 0.374 (SD 0.004) in the mixed population, a level unreached in single populations, among which the best performance is only 0.299 (SD 0.022).In the PAGE data, PV was implemented with DPR controlling PCs for predicting BMI, height, diabetes, and hypertension (S2 Table), applying PV with the DPR base significantly improves the prediction accuracy for the BMI by 12.0% (SD 5.6%), for the height by 1.44% (SD 0.38%), for the CVD by 5.9% (SD 1.0%), and for the diabetes by 3.7% (SD 2.2%) (S3 Table). Prediction standard deviations also considerably reduce in the joint data analysis, benefited from the larger sample size. Finally, we compared the estimated effect size of the top 5,000 SNPs in the two real GWAS datasets ; the effect sizes are vastly different between stratum, suggesting prevailing genetic heterogeneity in these data.In UK Biobank data composed of five minority populations and subjects of 12 vague self-reported ancestries . Individuals’ group membership probabilities obtained by the PC-based method described in this study gave concordant estimates as the outcome obtained from the Bayesian maximum likelihood approach implemented in the ADMIXTURE software [S6 Appendix).The component steps of the framework can be substituted with alternative methods according to data attributes. In the population stratification step, either a model-based or model-free model may be incorporated –22. The S7 Appendix), PV significantly improved the prediction correlation coefficient from 0.372 (SD 0.013) to 0.389 (SD 0.015) in 5GCV comparing to using the base model with PCs. Nevertheless, no significant difference was observed in the prediction for the other traits .For the prediction step, linear mixed model is pertinent for this study design for its good property of simultaneous estimation of whole genome SNPs effects and prediction. Other approaches, such as the machine learning methods, or the PRS, may be applied to construct predictors in stratum. To apply the PRS, the following issues shall be considered. The PRS draws summary statistics from well-powered external datasets, however, these external populations were predominantly of the European ancestries. Therefore, although coefficient of the aggregated PRS can be evaluated in stratum, to differentiate SNP-effects across stratum, one need to estimate the transferrable part of the effect size from auxiliary data to strata ,23, or tThe PV framework leverages on data’s genetic architecture to form homogeneous genetic strata. The grouping of subjects is a complicated issue as it is simultaneously influenced by the sample size, underlying genetic models of the trait, and genetic architecture in strata. In either model-based or model-free approach, the number of population clusters was often determined empirically ,20,21. IS8 Appendix). Another advantage of the PV is that it allows distributed programing of large genomic datasets in the dimension of subjects. Traditionally, SNPs are assigned to multiple clusters to increase computation efficiency, yet distributed computing is difficult to be carried out for the prediction models requiring simultaneous evaluation of biomarkers, such as the LMM or penalized regression. Markedly, the PV framework enables the simultaneous evaluation and prediction incorporating all SNPs in distributed calculations, by applying the prism filter on individuals and estimating disease risk from genetic background of the subpopulations that are assigned to CPU-clusters. Meanwhile, the PV’s Bayesian probability framework maintains total information gain from the subpopulations, producing a balanced and potentially improved prediction outcome.One notable advantage of the PV framework is that it enables prediction for subjects with unknown or admixed ancestries by decomposing subject’s propensity to more homogeneous subpopulation stratum, thereby allowing the extraction of information from other populations to inform prediction of admixed samples Click here for additional data file.S2 AppendixS2 Appendix. Table. The Pearson correlation of predicted phenotype and true phenotype using different methods (Simulation Study I). S2 Appendix. Fig. Compare prediction accuracy in single and mixed populations (Simulation study I).(DOCX)Click here for additional data file.S3 AppendixS3 Appendix. Fig A. Prediction performance of PV with increasing sample size, heritability = 0.2 (Simulation Study III). S3 Appendix. Fig B. Prediction performance of PV with increasing sample size, heritability = 0.5 (Simulation Study III).(DOCX)Click here for additional data file.S4 AppendixS4 Appendix. Fig A. PAGE data. S4 Appendix. Fig B. The genetic ancestry of minority populations in UK Biobank.(DOCX)Click here for additional data file.S5 AppendixS5 Appendix. Fig A. Effect size stratification by subpopulations—PAGE data. S5 Appendix. Fig B. Effect size stratification by subpopulations—UK Biobank data.(DOCX)Click here for additional data file.S6 AppendixS6 Appendix. Fig A. genetic ancestries in simulation study IV. S6 Appendix. Fig B. Comparing genetic ancestry fraction estimated by PV and ADMIXTURE.(DOCX)Click here for additional data file.S7 AppendixS7 Appendix. Fig A. PCA projections of the subjects from UK Biobank colored by inferred ancestry. S7 Appendix. Table A. Sample size of inferred ancestry populations in the UK Biobank data. S7 Appendix. Table B. Implementation of PV using LDpred2 as base model in the PAGE data.(DOCX)Click here for additional data file.S8 AppendixS8 Appendix. Table A. PAGE data. S8 Appendix. Table B. UK Biobank data.(DOCX)Click here for additional data file.S1 Fig(DOCX)Click here for additional data file.S1 Table(DOCX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.


Quantification of ancient human intelligence has become possible with recent advances in polygenic prediction. Intelligence is a complex trait that has both environmental and genetic components and high heritability. Large-scale genome-wide association studies based on ~270,000 individuals have demonstrated highly significant single-nucleotide polymorphisms (SNPs) associated with intelligence in present-day humans. We utilized those previously reported 12,037 SNPs to estimate a genetic component of intelligence in ancient Funadomari Jomon individual from 3700 years BP as well as four individuals of Afanasievo nuclear family from about 4100 years BP and who are considered anatomically modern humans. We have demonstrated that ancient individuals could have been not inferior in intelligence compared to present-day humans through assessment of the genetic component of intelligence. We have also confirmed that alleles associated with intelligence tend to spread equally between ancestral and derived origin suggesting that intelligence may be a neutral trait in human evolution. Z-score obtained through METAL software ) based on Fisher exact test .We have demonstrated first ever insight into genetic component of intelligence through PGS in ancient individuals from around 3700–4100 BP. The performed calculations indicate a possibility that people living on the territory of modern Hokkaido and Russia in that period being not less intelligent than modern humans. Absolute IQ values inferred from PGS in Afanasievo individuals and Funadomari Jomon individual tends to be within the 95% range of mean general human population suggesting similarity of intelligence of humans living 3700 BP and modern humans. Although intelligence PGS of Afanasievo family tend to fluctuate on the lower tail of normal distribution of the scores of 1000 Genome project these scores translate to absolute IQ values within mean of general population given the low variance explained by intelligence PGS  forming essential cognitive functions. IQ measures have been implicated with survival, adaptation to environment, and mental functioning . DigitalDNA.Land platform has previously demonstrated evaluation of intelligence PGS using GWAS findings based on 72 SNPs . Likely A common approach in studying quantitative traits like intelligence in humans has been based on monozygotic and dizygotic twins . PreviouIntelligence as a phenotypic trait with underlying effects of DNA polymorphism has been likely shaped by evolutionary processes. Majority of mutations in genes affecting underlying cognition used in this study tend to interact in extremely complex networks with higher activity in hippocampal as well as somatosensory neurons . Since nWe demonstrated that genomic data from ancient individuals can be used to evaluate a genetic component of intelligence. Funadomari Jomon as well as Afanasievo family individuals demonstrated intelligence PGS as well as IQ scores in line with modern humans. DNA evidence may indicate a possibility of intelligence being a neutral trait in human evolution suggesting that ancient individuals living 3700–4100 years BP could have been as intelligent as modern humans.


Early simulations indicated that whole-genome sequence data (WGS) could improve the accuracy of genomic predictions within and across breeds. However, empirical results have been ambiguous so far. Large datasets that capture most of the genomic diversity in a population must be assembled so that allele substitution effects are estimated with high accuracy. The objectives of this study were to use a large pig dataset from seven intensely selected lines to assess the benefits of using WGS for genomic prediction compared to using commercial marker arrays and to identify scenarios in which WGS provides the largest advantage.We sequenced 6931 individuals from seven commercial pig lines with different numerical sizes. Genotypes of 32.8 million variants were imputed for 396,100 individuals . We used BayesR to perform genomic prediction for eight complex traits. Genomic predictions were performed using either data from a standard marker array or variants preselected from WGS based on association tests.The accuracies of genomic predictions based on preselected WGS variants were not robust across traits and lines and the improvements in prediction accuracy that we achieved so far with WGS compared to standard marker arrays were generally small. The most favourable results for WGS were obtained when the largest training sets were available and standard marker arrays were augmented with preselected variants with statistically significant associations to the trait. With this method and training sets of around 80k individuals, the accuracy of within-line genomic predictions was on average improved by 0.025. With multi-line training sets, improvements of 0.04 compared to marker arrays could be expected.Our results showed that WGS has limited potential to improve the accuracy of genomic predictions compared to marker arrays in intensely selected pig lines. Thus, although we expect that larger improvements in accuracy from the use of WGS are possible with a combination of larger training sets and optimised pipelines for generating and analysing such datasets, the use of WGS in the current implementations of genomic prediction should be carefully evaluated against the cost of large-scale WGS data on a case-by-case basis.The online version contains supplementary material available at 10.1186/s12711-022-00756-0. Whole-genome sequence (WGS) data have the potential to empower the identification of causal variants that underlie quantitative traits and diseases –4, increDuring the last few years, there have been several attempts at improving the accuracy of genomic prediction with WGS in the main livestock species. Empirical results have been ambiguous so far. When predicting genomic breeding values within a population, some studies found no relevant improvement in accuracy with WGS data compared to marker arrays –16. OtheOne of the most successful strategies to exploit WGS data consists of augmenting available marker arrays with preselected variants from WGS data based on their association with the trait of interest –31. In sAccurate estimation of allele substitution effects and, ideally, identification of causal variants among millions of other variants are important applications of WGS data in research and breeding. These require large datasets that can capture most of the genome diversity in a population. Low-cost sequencing strategies have been developed, which typically involve sequencing a subset of the individuals in a population at low coverage and then imputing WGS data for the remaining individuals. However, the cost of generating accurate WGS data at such a large scale and the large computational requirements for the analyses of the resulting datasets have limited the population sizes or number of populations that have been tested in previous studies. This hinders the comparison of prediction accuracies across studies, which differ widely in population structures, sequencing strategies, and prediction methodologies used. The largest studies in livestock on the use of WGS for genomic prediction to date have been performed in cattle, for which a large multi-breed reference panel is available from the 1000 Bull Genomes Project , 17, 32.We have previously described our approach to impute WGS data in large pedigreed populations without external reference panels . FollowiWe re-sequenced the whole genome of 6931 individuals from seven commercial pig lines  with a total coverage of approximately 27,243×. Breeds of origin of the nine lines included Large White, Landrace, Pietrain, Hampshire, Duroc, and synthetic lines. The sequencing effort in each of the seven lines was proportional to population size. The number of pigs that were available in the pedigree of each line and the number of sequenced pigs, by coverage, are summarized in Table The sequenced pigs and their coverage were selected following a three-part sequencing strategy that was developed to represent the haplotype diversity in each line. First (1), sires and dams with the largest number of genotyped progeny were sequenced at 2× and 1×, respectively. Sires were sequenced at a greater coverage because they contributed with more progeny than dams. Then (2), the individuals with the greatest genetic footprint on the population  and their immediate ancestors were sequenced at a coverage between 1× and 30× . The seMost sequenced pigs, as well as pedigree relatives, were also genotyped with marker arrays, either at low density (15k markers) using the GGP-Porcine LD BeadChip (GeneSeek) or at high density (50k or 80k markers), using different versions of the GGP-Porcine HD BeadChip (GeneSeek). In our study we only used markers included in the 50k array, which is the latest version of the high-density array. Markers in the 15k array were nested within the 50k array and markers from the 80k array that were not included in the 50k array were discarded. The number of pigs that were genotyped at each density is summarized in Table Tissue samples were collected from ear punches or tail clippings. Genomic DNA was extracted using Qiagen DNeasy 96 Blood & Tissue kits . Paired-end library preparation was conducted using the TruSeq DNA PCR-free protocol . Libraries for resequencing at low coverage (1 to 5×) were produced with an average insert size of 350 bp and sequenced on a HiSeq 4000 instrument (Illumina). Libraries for resequencing at high coverage (15 or 30×) were produced with an average insert size of 550 bp and sequenced on a HiSeq X instrument (Illumina). All libraries were sequenced at Edinburgh Genomics .Sscrofa11.1 (GenBank accession: GCA_000003025.6) using the BWA-MEM algorithm [http://broadinstitute.github.io/picard). Single nucleotide polymorphisms (SNPs) and short insertions and deletions (indels) were identified with the variant caller GATK HaplotypeCaller (GATK 3.8.0) [DNA sequence reads were pre-processed using the Trimmomatic software  to removlgorithm . DuplicaK 3.8.0) , 46, usihttps://github.com/pysam-developers/pysam), which is a wrapper around the htslib program and the samtools package [Read counts supporting each allele were extracted directly from the aligned reads stored in the BAM files, using a pile-up function, to avoid biases towards the reference allele introduced by GATK when applied on low-coverage WGS data . This pi package . Read co package . This pi package .Genotypes were jointly called, phased, and imputed for a total of 483,353 pedigree-related individuals using the ‘hybrid peeling’ method implemented in AlphaPeel , 52. ThiWe analysed phenotypic data on eight complex traits that are commonly included in selection objectives of pig breeding programmes: average daily gain (ADG), backfat thickness (BFT), loin depth (LD), average daily feed intake (ADFI), feed conversion ratio (FCR), total number of piglets born (TNB), litter weight at weaning (LWW), and return to oestrus within 7 days after weaning . Most pigs with records were born during the 2008–2020 period. Breeding values were estimated by line with a linear mixed model that included polygenic and non-genetic (as relevant for each trait) effects. Deregressed breeding values (dEBV) were derived from the estimated breeding values for each trait following the method of VanRaden et al. . Only inWe split the individuals in each line into training and testing sets. The testing sets were defined as individuals from full-sib families from the last generation of the pedigree . Only families with a minimum of five full-sibs were considered. The training set was defined as all individuals that had a pedigree coefficient of relationship lower than 0.5 with any individual in the testing set. This design was chosen to mimic a realistic situation in which breeding programmes evaluate selection candidates that are available in a selection nucleus at any given time.To assess the effect of the size of the training set on prediction accuracy, we created training sets with a reduced number of phenotype records for the three largest lines for the three traits with the largest number of records. We did this by removing the oldest animals, such that approximately the most recent 10, 20, or 35 to 45 thousand phenotype records remained in each of the reduced training sets.Due to the computational requirements of the analyses (mainly for the preselection of the WGS variants to be included in the prediction equations), we could not replicate every analysis to assess the variability of the results. However, we did perform replicated validation analyses in the largest, one intermediate, and the smallest lines for two traits with a large and small number of phenotype records. To do this, we randomly split the testing sets into five subsets, with each full-sib family represented exclusively in one of the subsets. Training sets for each replicate were defined as for the general case.To provide an association-based criterion to preselect variants for genomic prediction, we performed a single-SNP GWAS for each trait and line. This step included only the individuals in the training set. We fitted a univariate linear mixed model that accounted for genomic relationships as:software , 55 to fTop40k: To mimic the number of variants in ‘Chip’, we preselected the variants with the lowest p-value (not necessarily below the significance threshold) in each of consecutive non-overlapping 55-kb windows along the genome. In addition, to test the impact of variant density on prediction accuracy, we preselected the top 10k, 25k, 75k, or 100k variants based on the same criterion.–6) were preselected from the WGS data and merged with those in ‘Chip’. When a 55-kb window contained more than one significant variant, only the variant with the lowest p-value was selected as a proxy to reduce the preselection of multiple significant variants that tag the same causal variant. When a significant variant from WGS data was already included in the marker array, it was considered only once and in the rare cases of genotype discordance between the WGS and marker array data, the genotype was replaced with the mean genotype value in that line. On average, 309 significant variants were identified per trait and line  was set as the benchmark for prediction accuracy. It contained all ~ 40k variants in the marker array. For WGS, we preselected sets of variants because currently available methods for genomic prediction are not yet capable of handling datasets as large as the complete WGS without exorbitant computational resources. We tested different alternative strategies for preselecting variants for the prediction model based on the GWAS results:https://github.com/syntheke/bayesR; accessed on 30 April 2021), with default settings. Prediction accuracy was calculated in the testing set as the correlation between the predicted genomic breeding values and the dEBV. Bias (inflation/deflation) of the prediction accuracy was calculated as the regression coefficient of the dEBV on the predicted genomic breeding values. For ease of comparison between traits and lines, the difference between prediction accuracy based on WGS and marker array data was calculated and analysed by fitting linear models with the size of the training set as a covariate and trait and line as fixed effects when appropriate.Genomic prediction was performed by fitting a univariate model with BayesR , 57, whiWe considered multi-line scenarios in which the training set was formed by merging the training sets that had been defined for each line. All analyses were performed as for the within-line scenarios but with line as an additional effect in the prediction model. In the multi-line scenarios, the benchmark genomic prediction was obtained using all variants from the marker array that passed quality control and were imputed for at least one line (referred to as ‘ML-Chip’). For ease of computation, the strategies for preselection of variants from WGS were applied only to the subset of 9.9 million variants that had been called and imputed in all seven lines. Thus, we defined the variant sets ‘ML-Top40k’ and ‘ML-ChipPlusSign’ by preselecting variants following the same criteria as in the within-line scenarios, but using a multi-line GWAS with line as an additional effect. For ML-ChipPlusSign, 60 to 7247 significant variants were identified per trait Table  and mergWhole-genome sequence data improved genomic prediction accuracy compared to marker array data in some scenarios, especially when there was a sufficiently large training set and when an appropriate set of WGS variants was preselected. Figure –6 per individual (p < 0.001) for Top40k and 0.3·10–6 per individual (p = 0.017) for ChipPlusSign. This was, at least partly, driven by the smaller number of significant associations that were detected with smaller training sets. For ChipPlusSign, with a training set of 20k individuals or less, 118 to 287 significant variants were added to the marker array; with a training set of 35k to 45k individuals, 288 to 709 significant variants were added; and with all available individuals in the training set, 424 to 1083 significant variants were added. Thus, if the marker array was augmented with the significant variants detected with all available individuals  than for Top40k .Figures We observed diminishing increases in accuracy when we increased the density of the variants used in prediction. Increasing the number of variants from 40k in Top40k to 75k yielded small improvements in genomic prediction accuracy compared to Top40k, but increases up to 100k variants provided smaller or null additional gains  the prediction accuracy that we achieved with WGS data compared to the commercial marker array data and the scenarios in which WGS may become beneficial, (2) the potential pitfalls for the effective use of WGS for genomic prediction and the need for optimised pipelines for generating and analysing WGS datasets, and (3) the suitability of WGS data for genomic prediction with current implementations of genomic prediction.We compared the genomic prediction accuracy based on the current marker array (Chip) with that based on sets of preselected WGS variants such that the number of variants remained similar across sets. Improvements in prediction accuracy are expected to be limited if current marker arrays are already sufficiently dense to capture a large proportion of the genetic diversity in intensely selected livestock populations because such populations typically have small effective population sizes , 17. NevUsing ChipPlusSign, we augmented the marker array with 23 to 1083 significant variants preselected from WGS data across the different scenarios. In the most successful scenarios, a minimum of around 200 significant variants were added and prediction accuracy improved by 0.025 on average with training sets of around 80k individuals. Other studies suggested additions of a larger number of variants. In Hanwoo cattle, adding around 12k variants  to a custom 50k marker array increased accuracy by up to ~ 0.06 . In sheeThe only modest increases in accuracy obtained with ChipPlusSign and Top40k compared to the marker array could also be a consequence of the difficulty for fine-mapping causal variants through GWAS on WGS data. Theoretically, inclusion of all causal variants associated with a trait in the marker array should improve genomic prediction accuracy . AlthougThe advantage of using WGS may also be limited by the small effective population size of livestock populations under selection  and by tWe observed that the robustness of genomic prediction with WGS data across traits and lines was low, resulting in a drop in prediction accuracy in some scenarios. Previous studies have shown that using the same data for preselecting variants through GWAS and for training the prediction equation can reduce the accuracy of genomic predictions and bias the resulting predicted genomic breeding values , 64. We We did not directly evaluate the persistence of the accuracy of genomic predictions across generations, but previous studies with empirical data found that the use of WGS data did not increase the persistence of accuracy . We expeEffective use of WGS for genomic prediction can only be achieved when many other steps are completed to produce genotype data at the whole-genome level. Each of these steps has potential pitfalls that can limit the success of using WGS. This includes optimization of the choice of individuals to sequence, of the bioinformatic pipeline to call variants, of the imputation of the WGS, and of filtering of variants. When combined with the multiplicity of strategies to preselect variants for genomic prediction , the whole process includes many variables that can affect the final result and that are not yet well understood. Therefore, a much greater effort for optimising the whole process is required. Here, we tested relatively simple approaches to evaluate how they performed with large WGS datasets. We have previously discussed what, in our opinion, are the main pitfalls of our approach for selection of individuals to sequence  and the Imputation of WGS data is particularly challenging because typically a very large number of variants need to be imputed for a very large number of individuals from few sequenced individuals. As a consequence, genotype uncertainty can be high , 65, 66.We have assessed the accuracy of our imputation approach elsewhere , 52 and Genomic prediction accuracy could be improved by accounting for genotype uncertainty of the imputed WGS. In that case, it could be advantageous to use allele dosages rather than best-guess genotypes , althougUsing WGS data to simply increase the number of variants in the genomic prediction analyses does not improve genomic prediction accuracy , 19, 22.A popular strategy to preselect variants for the prediction model is based on association tests. Genome-wide association studies on WGS data are expected to confirm associations that were already detected with marker arrays but also identify novel associations  between groups of individuals with high and low phenotype values to avoid the negative impact of spurious associations [Several methods to improve variant preselection for genomic prediction have been proposed. VanRaden et al.  suggesteciations .It is also likely that genomic prediction models, estimation methods, and their implementations need to be improved to leverage the potential of WGS data. This is an active area of research and multiple novel methodologies have been proposed over the last years. Some examples are a combination of subsampling and Gibbs sampling  and a moSome of the most promising new methods for genomic prediction incorporate prior biological information into the models. One such method is BayesRC , which eThe small improvements in genomic prediction accuracy that we achieved with WGS data reflect the limited dimensionality of genomic information in intensely selected livestock populations , which tOur results show that the use of WGS data has some potential to improve genomic prediction accuracy compared to marker arrays in intensely selected pig lines. However, the prediction accuracy with a given set of preselected WGS variants was not robust across traits and lines and the improvements in prediction accuracy compared to marker arrays were generally small. The most favourable results for WGS were obtained when the largest training sets were available and used to preselect variants with statistically significant associations to the trait for augmenting the established marker array. With this method and training sets of around 80k individuals, average improvements of genomic prediction accuracy of 0.025 were observed in within-line scenarios. A combination of larger training sets and optimised pipelines for generating and analysing WGS datasets could further improve genomic prediction accuracy with the use of WGS data. The whole strategy for generating WGS data at the population level must be carefully stress-tested and further optimised. However, with the current implementations of genomic prediction, the use of WGS should be carefully evaluated on a case-by-case basis against the cost of generating WGS data on a large scale.Additional file 1: Figure S1. Population structure of the sequenced pigs according to the two first principal components.Additional file 2: Figure S2. Prediction accuracy for all traits and lines.Additional file 3: Figure S3. Genomic prediction accuracy obtained with each set of preselected whole-genome sequence (WGS) variants (either Top40k or ChipPlusSign) against that obtained with the marker array (Chip) in each of the five replicates.Additional file 4: Table S1. Comparison of the results obtained with a single replicate or with five replicates.Additional file 5: Figure S4. Genomic prediction accuracy by density of preselected whole-genome sequence variants in the prediction model.Additional file 6: Figure S5. Genomic prediction accuracy of whole-genome sequence data in multi-line scenarios compared to the marker arrays in within-line scenarios.Additional file 7: Figure S6. Genomic prediction accuracy of ML-Top40k.Additional file 8. Genomic prediction and genome-wide association study using simulated traits.Additional file 9: Figures S7 and S8. Genomic prediction results using simulated traits.Additional file 10: Figure S9. Genomic prediction accuracy and bias when preselection of variants and training of the predictive equation are performed in two mutually exclusive subsets.Additional file 11: Figure S10. Genome-wide association study on backfat thickness with marker array or whole-genome sequence data in line A.Additional file 12: Table S2. Genome-wide association study results using simulated traits.