The exploitation of the genetic diversity of crops is essential for breeding purposes, as the identification of useful/beneficial alleles for target traits within plant genetic resources allows the development of new varieties capable of responding to the challenges of global agriculture .Whole genome re-sequencing, genome skimming, fractional genome sequencing strategies, and high-density genotyping arrays enable large-scale assessment of genetic diversity for a wide range of species, including major and “orphan” crops . This isFor this Research Topic we sought high-quality contributions, covering various aspects of genomics-assisted-breeding: increase in yield, improvement of nutritional content and end-use quality of crops, climate-smart agriculture, cropping systems in agriculture. We did not miss to ask for contributions on technical challenges related to the design of GWAS and GS experiments and data analysis.Enhancing knowledge on (a)biotic stress tolerance of plants has a major impact on crop improvement strategies that aim to develop high yielding varieties in suboptimal environmental conditions.Odilbekov et al. performed GWAS on a collection of nearly 200 winter wheat accessions to identify loci associated with seedling-stage resistance to Septoria tritici blotch (STB) disease, which is responsible for severe yield losses worldwide. Association tests with different statistical models returned a strong signal on chromosome 1B. Seven genes were identified as the most probable candidate genes for this QTL, as they play a key role in plant immunity and modulate the defense response. Finally, the authors demonstrated that the accuracy of the GS model for STB resistance can be improved when modeling GWAS associated variants as fixed effects.Thapa et al. performed GWAS on a panel of 257 rice accessions to identify the QTLs and the underlying candidate genes responsible for cold tolerance and cold recovery during the germination phase. Their findings enrich the toolbox available to breeders for the development of new varieties with tolerance to low temperatures.Hernández and Cortés subjected 78 geo-referenced wild common bean accessions to genotyping-by-sequencing (GBS) and derived three heat stress indices from phenotypic data points. Then, they applied the latest-generation GWAS models under a genome–environment association framework to identify putative loci underlying heat stress adaptation. The goal was to identify new sources of tolerance in the wild gene pool for use in breeding programs.Zaïm et al., tested in the open field and in different environments four recombinant inbred line populations of durum wheat. GBS and the construction of a consensus linkage map led to the identification of over 30 QTLs for key agronomic traits. Six QTLs were found to be associated with grain yield and thousand kernel weight. The SNP markers anchored to these QTLs were then included as fixed effects into GS models, improving overall accuracy.Increasing of crop yield potential is one of the main goals of breeding. Indeed, producing more with less is the key to feeding the growing world population. Within this motivating context, Sidhu et al. performed GWAS on a collection of almost 300 winter wheat accessions to determine SNP markers associated with coleoptile length. As a result, the authors identified eight candidate regions within which they found genes possibly involved in determining the target phenotype.Many articles aimed to improve the predictive accuracy of GS models by considering some variables that influence traits or by proposing innovative technological solutions to fully exploit the genetic variability of plant genetic resources.Crossa et al. is about the comparison of the genome-based prediction accuracy of four methods: the additive genomic best linear unbiased predictor (GB), non-additive Gaussian kernel (GK), arc-cosine kernel (AK), and Deep Learning (DL). Single-environment and multi-environment G × E models on two real wheat datasets were used for benchmarking. Comparative analysis showed that AK outperformed the remaining methods, as it ensures competitive predictions at low costs in the tuning process.The article by Olatoye et al. identified main effect and epistatic effect loci of flowering time, maturity, and seed size in cowpea using a MAGIC population. Then, they used the identified quantitative trait nucleotides as fixed effects in parametric, semi-parametric, and non-parametric GS models and demonstrated that a priori knowledge of the genetic architecture of a trait improves prediction accuracy.Allier et al. proposed adjustments to two parameters, namely the expected genetic value in the progeny (V) under a certain constraint on inbreeding (D), of the cross-selection strategy they published earlier. This arises from the need to consider within-family selection in recurrent genomic selection programs. The authors compared their UCPC-based optimal cross-selection strategy with the existing ones and proved that it was more efficient for converting genetic diversity into short- and long-term genetic gains.Klápště et al. improved genomic predictions for traits with relatively low heritability and poor prediction accuracy by implementing multi-trait models based on the use of a marker-based relationship matrix, instead of classic pedigrees. The models applied to the diameter at breast height (target trait) did not outperform the multivariate model using all genetic markers in the case of the Pinus radiata population; conversely the strategy was advantageous in the case of the Eucalyptus nitens population, where the target trait had a low/moderate correlation with other heritable traits.Kehel et al., 789 bread wheat landraces held in-trust at the gene bank of the International Center for Agricultural Research in the Dry Areas were scanned for seed traits and genetically evaluated using 12k DArTSeq SNP markers. Based on cross-validation, predicting untyped seed traits can be as accurate as 74% for seed width. Moreover, when incorporating climatic and environmental variables based on passport data, the prediction accuracy improved by an additional 8%. These findings advocate the advancement in predictive analytics and genomic technologies for identifying potential donors of desirable alleles for genetic introgression.The untapped genetic variation preserved in germplasm banks serves as a source for future food and nutritional security for the globe. However, a major obstacle that prevents the use of bank accessions is the lack of adequate characterization and performance evaluation. In Lstibůrek et al. conducted a multi-trait and multi-site large-scale genetic analysis with 4,625 25–35 years old European larch trees grown over 21 reforestation sites across four distinct climatic regions. In this study, the capacity of the marker-based pedigree information was demonstrated by comparing in situ heritability estimates. Furthermore, using this approach, a higher genetic response of the selected individuals can be expected for fitness and productivity attributes, suggesting that broad-spectrum climatic genetic evaluation can be an effective guiding principle for reforestation and genetic resource management without the reliance on structured tree breeding methods.Considering the long reaction time and the expensive cost in conservation and sustainability of forest resources, Finally, the last series of articles describes some data resources available for future studies or technical challenges related to the design of GWAS experiments.Piot et al. analyzed over 1,000 Populus trichocarpa genomes to assess genomic diversity and identify rare and common alleles with high confidence for subsequent use in GWAS. Approximately 5% of the variants identified were non-synonymous and could represent rare defective genetic variants hypothetically associated with poplar phenotypic plasticity.Srivastava et al. is quite different in content, as it provides an overview of the latest development of genetic and genomic resources in pearl millet and their use in GWAS and in the development of GS models for the estimation of GBEVs .The mini-review by Pavan et al. provides advice on how to plan the experiments and choose the most appropriate and cost-effective genotyping method for crop GWAS. It also describes which quality control procedures should be applied on genotypic data points to avoid bias and false signals in genotype-phenotype association tests.The review by As genomics-driven knowledge advances rapidly and data science techniques for omics data continue to evolve and improve, the combination of the huge amount of genetic and phenotypic data points becomes more and more reachable. We looked at innovative examples whose purpose was to describe the genome-to-phenome connection and causation and to highlight the strengths and weaknesses of popular data mining strategies. We hope that the articles in this Research Topic can give further impetus to this area of research and can help expand the tools available to breeders.


Tamarix), a notorious invasive shrub in the western US introduced from Eurasia may have adapted to low rainfall as the species widely occupies the arid land throughout the southwestern US. We investigated variation of quantitative traits in saltcedar between two regions exhibiting opposing average annual precipitations under experimentally manipulated water treatments to test local adaptation. We measured eight quantitative traits, proxies for fitness and genotyped 64 individual samples using genotype by sequencing technique. To test local adaptation, we applied CTQ - CTF test based on null distribution of CTF estimated from 2,697 genome-wide SNPs and CTQ estimated for the eight phenotypic traits measured. Saltcedar in the southwestern US exhibited a significant interaction between the degree of leaf loss  under simulated drought conditions and the origins from which the genotypes were collected, either relatively high or low rainfall regimes. The divergence found in leaf loss was significantly greater among regions than the expected given the genetic divergence on neutral loci suggesting signature of local adaptation responding to drought. The results demonstrate adaptive potential of saltcedar populations to extreme drought. As extreme aridity is often predicted in climate models across the southwestern US, the western saltcedar genotypes locally adapted to drought may further expand their ranges in this region.Biological invasion poses several biotic and abiotic challenges due to abrupt distribution shifts. Invasive species may benefit from local adaptation responding to environmental stresses during colonization. Saltcedar ( A key to understanding invasion success is to determine what mechanisms enable some colonists to deal with environmental stresses and become successful invaders while many colonists fail to survive in a novel range. Invasive species may cope with the limiting factors in several ways including the following; first, general purpose genotypes  and secoLythrum salicaria L. (Lythraceae) evolved earlier flowering time at its northern invasion front suggesting adaptive evolution of phenology in the northern genotypes. Adaptation may contribute to ecological range expansion of colonists and increase overall invasiveness, but further empirical studies are in need to prove the role of adaptation.Alternatively, the invasive species may benefit from adaptation to cope with the novel environmental challenges in a new location . AdaptatAvena barbata Pott ex Link (Poaceae) and Bromus madritensis L. (Poaceae)] and found regional phenotypic trait divergence responding to the water treatment  is expected to be the same as STF for neutral loci  are widespread invasive species in the Western US , and New Mexico with an average annual precipitation about 200 mm  with mixture of coarse peat moss, vermiculite and perlite (1:1:1 ratio) in the Texas Tech Biology greenhouse. After several attempts, 10 of 90 genotypes failed to develop roots from any replicated stem cutting and were eliminated from the experiment. After 4 weeks, I transplanted two replicates from each of the 80 genotypes into 8 ℓ plastic pots  with field collected soil  and cultivated them for 4 weeks prior to experimental manipulation. I sampled the soil from about 30 cm below the surface for each population and used the collected soil for cultivating the genotypes of the same population. I watered the plants daily using tap water and fertilized once per week with commercial water-soluble fertilizer . Due to mortality during cultivation, total of 64 genotypes were successfully grown and used in the drought experiment Table 1.Phenotypic traits  that are significantly correlated with the initial size of the plants P< 0.05; Table 2 Genotyping-By–Sequencing GBS;  approachP< 10e-6) to screen out SNPs with extremely high heterozygosity likely resulted from false SNP call or mis-assembly ensuring to keep loci with true structure that exhibit decreased expected heterozygosity.I called SNPs for 64 genotypes using the UNEAK pipeline in TASSEL 3.0 . I firstHe) and mean number of alleles (Na) over 2,697 SNPs in GENALEX v. 6.5 (CTF), among populations within regions (SCF), and among populations overall (STF) using Arlequin version 3.5 (CTF (genetic differentiation among region) using locus-by-locus AMOVA in Arlequin version 3.5  was estimated as in Hierarchical genetic divergence among regions and among populations within each region were both used to estimate 2r > 0.2) were purged for marker inferred relatedness estimation using Plink 1.9 (2h) based on the covariance of phenotype similarity and marker inferred relatedness estimated from a set of 422 unlinked SNPs using Ritland’s MARK ver. 3.1 (available at http://genetics.forestry.ubc.ca/ritland/programs.html). I estimated 95% confidence intervals of 2h by randomly resampling 422 SNP data set with 1,000 bootstrap replicates in R 3.3.0  as random effects using linear model in R 3.3.0 package ‘varComp’ . To ensulink 1.9  . I calc R 3.3.0  .CTQ for the trait against the distribution of CTF distribution. The significance threshold for CTQ to be outlier against the CTF distribution was set to α = 0.05.To determine whether the regional level divergence on leaf loss is excessive to neutral expectation, I compared He=0.27-0.33; Na=1.76-1.95 He=0.33; Na=1.95), whereas the Seymour population (moderate environment region) showed the lowest genetic variation , whereas the variance among populations within each region was 3% . Except for 2h of leaf loss, the 2h of the remaining 7 phenotypic traits were low and did not significantly differ from zero . The estimate of region-level quantitative trait divergence on leaf loss (CTQ) was 0.77. CTQ of leaf loss fell far above 95% of the estimated regional variance for neutral genetic markers  among the two extreme aridity conditions was significantly greater than the estimated null divergence  to divergence of random samples from molecular markers . To avoid biases of using point estimates i.e. mean of STF from a few loci, I generated an empirical STF distribution based on large number of SNPs collected across the whole genome  under the title: "Quantitative trait divergence and local adaptation to drought in the invasive Saltcedar (Tamarix)". Phenotypic data are provided as The author confirms being the sole contributor of this work and has approved it for publication.This study was supported by research fund from Chosun University, 2022.I am grateful to Texas Tech Biology Department and Texas Tech University Association of Biologists for providing travel funds and greenhouse equipment. Greenhouse manager Jenifer Smith and staff William Barnes have helped with experiment settings and given advices for cultivating. Dr. Yeong-Seok Jo gave great help with collecting samples and greenhouse cultivation. Finally, I give my special thanks to Dr. Olson at Texas Tech, Dr. Jonathan Friedman from USGS for invaluable comments and for the help of revising the manuscript.The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Here, we present a memory-efficient, visualization-enhanced, and parallel-accelerated R package called “rMVP” to address the need for improved GWAS computation. rMVP can 1) effectively process large GWAS data, 2) rapidly evaluate population structure, 3) efficiently estimate variance components by Efficient Mixed-Model Association eXpedited (EMMAX), Factored Spectrally Transformed Linear Mixed Models (FaST-LMM), and Haseman-Elston (HE) regression algorithms, 4) implement parallel-accelerated association tests of markers using general linear model (GLM), mixed linear model (MLM), and fixed and random model circulating probability unification (FarmCPU) methods, 5) compute fast with a globally efficient design in the GWAS processes, and 6) generate various visualizations of GWAS-related information. Accelerated by block matrix multiplication strategy and multiple threads, the association test methods embedded in rMVP are significantly faster than PLINK, GEMMA, and FarmCPU_pkg. rMVP is freely available at  The computation burden of genome-wide association studies (GWAS) is partially caused by the increasing sample size and marker density applied for these studies. As a result, how to efficiently analyze the big data is a big challenge. Additionally, GWAS have been widely used for detecting candidate genes that control human diseases and agricultural economic traits, where the accuracy of the results is of significant implication. Thus, how to achieve higher statistical power under a reasonable level of type I error is another challenge Introducing the population structure concept into GWAS has dramatically improved the accuracy of detection. For example, incorporating the fractions of individuals belonging to subpopulations, namely Q matrix, reduces both false positive and false negative signals False positives also stem from individuals that exhibit high variability in pairwise relatedness presumptively classified into different subpopulations. In addition to integrating population structure, statistical power can be substantially improved by the incorporation of hidden relationships in a mixed linear model (MLM) — particularly when population structure is less dominant than the cryptic relatedness Besides the difference in computing time, MLM does not provide high statistical power compared to GLM. The difference in statistical power between GLM and MLM is negligible in some scenarios, such as mapping genes under the same false discovery rate (FDR) in populations with strong population structure Although recently developed methods have improved statistical power under certain assumptions, determining the most appropriate method for a given dataset is still convoluted. Human genetic studies often use large datasets with simple models, while plant and animal genetic studies prefer complex models with limited sample sizes. For a specific trait, it is usually difficult to identify the real genetic architecture and the most appropriate method to be used. Researchers have to try out multiple methods and identify candidate genes based on both statistical and biological evidence. Additionally, existing GWAS software rarely focus on providing a flexible plotting function to display GWAS-related information in a way that satisfies the personal aesthetic requirements of the researchers. Furthermore, with the development of multi-trait methods, such as GSA-SNP2 We split the entire GWAS procedure into six sections: data preparation, evaluation of population structure, estimation of variance components, association tests, globally efficient design on GWAS process computing, and result visualization. Abundant functions have been implemented in rMVP for each section.e.g., genotype data coded as integer  or dosage/probability ]. All aforementioned formats will be converted to the ‘big.matrix’ format. The advantage of converting genotype files into ‘big.matrix’ is that the size of the file is only limited by the storage capacity of the hard disk but not the processing capacity of random access memory  rMVP accepts multiple popular formats for genotype files, such as PLINK binary, Hapmap, VCF, and Numeric [For population structure analysis, PCs can be calculated using all available markers. An ideal population for GWAS assumes that the individuals are randomly selected from a big population, but the population could always be classified to multiple subpopulations in fact. As the alleles with different frequencies in different subpopulations would generate false positives, we recommend to integrate the top 3–5 top PCs as covariates into model to control false positives caused by population structure following previous studies Four algorithms are implemented for estimating variance components in rMVP: Brent (default method in rMVP) e.g., PCs) added to association test models, the inverse of the design matrix corresponding to the covariates will be calculated n times, where n is marker size. Block matrix multiplication strategy can be used to speed up the processes including inverse of the design matrix corresponding to the covariates and the testing markers. This strategy is used in all available association test methods in rMVP. Take GLM as an example, the FEM function can be written as:k fixed effect vectors added as covariates in the model, k fixed effect vectors and GLM, MLM, and FarmCPU methods are implemented in rMVP for association tests. When there are more than one covariate . The Eigen decomposition analysis is conducted on the correlation matrix m by m, and this would lead to high requirements of both memory and computing time with the increasing number of SNPs. 2) The SVD analysis could be conducted on the n by m matrix. 3) The PCs could be also derived by performing the Eigen decomposition of the GRM, which could be calculated by n by n. In the majority of cases, the number of markers (m) is far more than the number of individuals (n), and thus this method has the smallest computational complexity compared with the other two. Moreover, the construction of GRM is always a key part in a commonly used GWAS procedure, which has been precomputed already. Not only that, as shown in m by n matrix , which can be derived from cantering the additive genotype matrix that was coded as 0, 1, and 2 for genotypes AA, AB, and BB, respectively; A standard GWAS pipeline generally includes PC derivation, GRM construction, variance component estimation, and association tests. There are three commonly used strategies for deriving the PCs. 1) The Eigen decomposition results of the matrix that represents the correlation coefficients between pairs of markers could be derived by High-quality figures are generated to display data information, population structure, and GWAS results, including marker density plot, phenotype distribution plot, principal component analysis (PCA) plot, Manhattan plot, and Quantile-Quantile (Q-Q) plot.Genotype matrices are the biggest datasets for GWAS. In rMVP, genotype data in multiple formats are converted to ‘big.matrix’, which can minimize RAM usage through generating a bridge that facilitates RAM accessing the data on the hard disk instead of loading it to RAM directly as the most software tools do. rMVP achieves this goal by using the ‘bigmemory’ package to build data mirrors that are accessible to RAM, while the actual data remain on the hard drive. In this way, very little RAM capacity is needed for the temporary storage of the data. Once the data mirrors are built, users will never need to re-build them again and the time of loading input data is negligible. When multiple threads are used to accelerate the association tests, no additional data mirrors will be copied for each thread as all threads will share the same data mirrors.r × c × t × 8 bytes, where r and c are the number of rows and columns of a matrix, respectively, and t is the number of threads. From the results shown in Here, we made a rough illustration of ‘big.matrix’-based memory storage of one and multiple threads for rMVP. The complete GWAS procedure of three methods was recorded for RAM usage test in a Linux server (‘RES’–‘SHR’). In this test, the product of genotype data size was measured in standard R matrix format, and ‘theoretical RAM cost’ for multiple threads in ‘fork’ mode is defined as For MLM in e.g., GEMMA, GCTA, and GAPIT). For the “memory” mode, all the matrices that are required for constructing the GRM are stored in the ‘big.matrix’ format and the matrix multiplication of ‘big.matrix’ is implemented by our newly developed C++ function, which could be parallel accelerated by using the OpenMP technology. Although it can significantly decrease the memory cost, more computing time is required , GEMMA , and FarmCPU_pkg , respectively, rMVP (written in R and C++) was compared with these software packages for speed performance; the computing time was recorded for each software from loading data to generating result files  and thread level parallel (TLP). For DLP, based on the Microsoft R Open platform, multi-threads have been automatically assigned to speed up the mathematical calculation, such as matrix manipulation. For TLP, association tests on millions of markers are allocated to a group of threads and calculated simultaneously. rMVP switches between the two levels of parallel computation to achieve the highest speed based on the biggest computation requirements in different GWAS procedures. Since three association test methods  in rMVP nearly generated consistent association results  with andlt files . DetaileBenefiting from the block matrix multiplication and parallel computation strategies, rMVP is several times or even dozens of times faster than PLINK (v1.9), GEMMA, and FarmCPU_pkg at single-thread level, and the gap increases significantly for multiple-thread computing.‘MVP.report’ function provides a pack of high-quality figures for visualizing GWAS-related information, including data information, population structure, and GWAS results.A) and marker density  can distribute the tasks to 1000 threads on multiple nodes. DPS is also better at dealing with hundreds or thousands of phenotypes and large computing tasks that need to be split, but its performance is limited by the efficiency of data transfer among multi nodes through the local network. However, association tests in rMVP can be accomplished within 10 h for a dataset that includes 500,000 samples and 5,000,000 markers for each sample using FarmCPU model, suggesting that our rMVP can meet most users’ requirements.rMVP currently only supports DLP and TLP for parallel computation, lacking the implementation of distributed parallel system (DPS). Compared with TLP that can speed up the computation using 100 threads on a single node, DPS . With the development of graphic processing unit (GPU) technology, we can get thousands of cores and higher memory bandwidth at a low price. Most of the processes in the GWAS analysis have good independence and can give full play to the advantages of GPU parallel computing. However, the bottleneck of limited GPU memory makes it difficult to perform GPU-based GWAS analysis on a large population. In the future, we plan to extend rMVP to support parallel computing on multiple machines with each machine containing multiple GPUs, and explore new memory optimization methods. Incorporating the aforementioned methods will greatly improve the versatility of rMVP.https://cran.r-project.org/web/packages/rMVP) and GitHub (https://github.com/xiaolei-lab/rMVP).The rMVP package is available on both CRAN (The authors have declared no competing interests.Lilin Yin: Data curation, Writing – original draft, Visualization, Software. Haohao Zhang: Writing – original draft, Software. Zhenshuang Tang: Validation. Jingya Xu: Validation. Dong Yin: Validation. Zhiwu Zhang: Software. Xiaohui Yuan: Resources, Writing – review & editing. Mengjin Zhu: Writing – review & editing. Shuhong Zhao: Writing – review & editing. Xinyun Li: Supervision, Writing – review & editing. Xiaolei Liu: Supervision, Methodology, Software, Writing – original draft.


Several studies demonstrate genetic variation in response to dietary restriction (DR) by replicating treatments across isogenic lines/strains from genetic reference panels. These studies typically quantify the response to DR as an effect size, estimated for each strain separately . Such “no-pooling” analyses are expected to systematically overestimate variation in response DR, principally by overlooking sampling variance. In contrast, “partial-pooling” analyses using mixed-effects models are less prone to this bias. I demonstrate these issues using simulations, which also show that partial-pooling analyses can improve replicability among studies. Regardless of the analyses used, estimates of among-strain variation will have low precision when sample sizes are small. A worked example using survival data in mice is given. Life-span studies using genetic reference panels always have to trade-off within- and among-strain replication owing to logistical challenges. The simulation presented can also be used to help design such studies through power analysis. Dietary restriction  involves a reduction in the calories consumed while avoiding malnutrition. Relative to ad libitum (AL) feeding, DR extends life in numerous organisms ,2. HowevGenetic reference panels constitute dozens of lines of a model organism, where the genetic variation within each line has been minimized, usually through inbreeding eg, ,6). Coll. Coll6))Several studies have reported among-strain variance in response to DR using genetic reference panels (see ref. ). Such cHere, I use statistical simulation to show how calculating individual pairwise effect sizes, also known as a “no-pooling” analysis , risks ohttps://github.com/AlistairMcNairSenior/GenRefPanelSimulation.All analyses were implemented in R. Code is available at simsurv package . In these simulations, I use a Gompertz distribution, a popular distribution that assumes that the hazard of mortality increases exponentially with age as:h(t) is the hazard of death at time t, a is the baseline hazard, and b is the time-dependent change in the hazard. The Gompertz distribution has been widely used to model mortality in rodents, meaning the literature can be used to parameterize this simulation. Based on Simons et al. (a and b in AL-fed rodents are log(a) = −11.57 and log(b) = −4.9. Assuming these parameters gives a slightly skewed distribution, with a heavy negative tail and the bulk of mortality beyond 100 weeks  is the base hazard coming from eqn (1), Xi is a dummy predictor stating whether animal i is under DR or not , μ is the overall natural logarithm of the hazard ratio (lnHR) for the effect of DR, and δj is the deviation of strain j from the overall μ. Strain-specific effects were drawn from a normal distribution with a mean of 0 and standard deviation (SD) σδ (eqn (3)).where σδ . A useful metric for the degree of variation in response is the coefficient of genetic variation in response, CVG:In this model, the parameter for the among-strain (genetic) variation in the effect of DR on survival is G is useful because it is unitless and thus facilitates comparisons among estimators.CVμ, is −0.5 . The meThis simulation assumes homogenous survival among strains under AL. In the G, I estimated the SD among strains (σδ in eqn (4)) in MD using 2 approaches.I began by quantifying the effect of DR using the difference in mean life span between DR and AL (mean difference [MD]) as an effect size; MD has been widely used . To calSD among these estimates. As a visualization of the estimated variation among MDs, I used the waterfall plots that have been routinely presented and interpreted as evidence of genetic variability elsewhere  analysis, where the effect sizes were estimated by applying a linear model (LM) to data stratified by strain, before calculating the tuted in ). The noSecond, I applied a “partial-pooling” (or “random-effect”) analysis using a single linear mixed model (LMM). Internally, the LMM uses random regression, where the MD for each specific strain is approximated as the weighted average of the MD estimated from strain-specific data and the MD from the data for all strains pooled . BecauseLMs and LMMs assume that  life-span data are normally distributed. While larger sample sizes can provide some protection, violating the assumption of normality can be particularly problematic when sample sizes are small as is often the case for life-span studies on rodents. An alternative approach based on time-to-event principles is to estimate the lnHR. To estimate variation in lnHR, I used a Cox proportional-hazards model (CM) applied to each strain and a Cox proportional-hazards mixed-effects model . Here, the CM represents a no-pooling analysis, while the CMM is the partial pooling equivalent.base and CMs using the “coxph” function in the survival package. LMMs and CMMs were implemented using the “lmer” and “coxme” functions in the lme4 (coxme (LMs were implemented using the “lm” function in the lme4  and coxm4 (coxme  packagesG = 0). The no-pooling MD effect sizes for the different strains range from life-span extension of 200 days to a reduction of 271 days. There are statistically significant increases in 3 strains, and a significant reduction in one. A crude visual interpretation of the range of effect sizes in SD among effects is 106.1 days. Hence the estimated CVG is 1.17, despite the true value being 0. This analysis again suggests genetic variation in response. However, it is notable that the rank order of strains has changed from that in Demonstrating the sensitivity of the analysis to sampling, in SD among strains is just 42.7, making the CVG 0.47 . For a visual comparison of the estimated strain-specific effects from the pooling analysis , I have overlaid the “strain-specific” estimates from the LMM in Re-analyzing the same data in SD among strains is 0.008 and the CVG is 0.014 .G from no-pooling methods become less extreme but are still present .No-pooling methods become less biased as the sample size increases regardless of the degree of true variation . However present . It is nI estimated the replicability of strain-specific effects of DR . The simulation presented can be used as a powerful analysis tool to help navigate these issues in study design .glac172_suppl_Supplementary_MaterialClick here for additional data file.


We conduct a genome-wide association study (GWAS) of educational attainment (EA) in a sample of ~3 million individuals and identify 3,952 approximately uncorrelated genome-wide-significant single-nucleotide polymorphisms (SNPs). A genome-wide polygenic predictor, or polygenic index (PGI), explains 12–16% of EA variance and contributes to risk prediction for ten diseases. Direct effects  explain roughly half the PGI’s magnitude of association with EA and other phenotypes. The correlation between mate-pair PGIs is far too large to be consistent with phenotypic assortment alone, implying additional assortment on PGI-associated factors. In an additional GWAS of dominance deviations from the additive model, we identify no genome-wide-significant SNPs, and a separate X-chromosome additive GWAS identifies 57. A genome-wide association study in ~3 million individuals identifies 3,952 independent variants associated with educational attainment. A polygenic index explains 12–16% of variance for this trait and contributes to risk prediction for ten diseases. For this reason, and because EA can be measured accurately at low cost, cohort studies used in genetic epidemiology and medical research routinely measure participants’ EA.EA is an important dimension of socioeconomic status that features prominently in research by social scientists, epidemiologists and other medical researchers. EA is strongly related to a range of health behaviors and outcomes, including mortality2. Here we report and analyze results from an updated meta-analysis of EA in a combined sample nearly three times larger . The increase comes from expanding the sample for the association analyses from 23andMe from ~365,000 to ~2.3 million genotyped research participants. As before, our core analysis is a GWAS of autosomal SNPs. Our updated meta-analysis identifies 3,952 approximately uncorrelated SNPs at genome-wide significance compared to 1,271 in the previous study. The larger sample size yields more accurate effect-size estimates that allow us to construct a genome-wide PGI  that has greater prediction accuracy, increasing the percentage of variance in EA explained from 11–13% to 12–16%, depending on the validation sample, an increase of approximately 20%. In meta-analyses of the expanded 23andMe sample and the UK Biobank (UKB)3, we also conduct an updated GWAS of the X chromosome  and the first large-scale ‘dominance GWAS’  of EA on the autosomes . In our updated X-chromosome GWAS, we increase the number of approximately uncorrelated genome-wide-significant SNPs from 10 to 57. Our dominance GWAS identifies no genome-wide-significant SNPs. Moreover, with high confidence, we can rule out the existence of any common SNPs whose dominance effects explain more than a negligible fraction of the variance in EA. Table The most recent GWAS meta-analysis of EA had a combined sample size of ~1.1 million individuals4, but also adds nontrivial predictive power for ten diseases we examine, even after controlling for disease-specific PGIs. Next, using a combined sample of ~53,000 individuals with genotyped siblings and ~3,500 individuals with both parents genotyped, we examine the predictive power of the EA PGI controlling for parental EA PGIs. By controlling for parental EA PGIs, we isolate the component of predictive power that is due to direct effects5, or the causal effects of an individual’s genetic material on that individual6. For EA and 22 other phenotypes, controlling for the parental EA PGIs roughly halves the EA PGI’s association with the phenotype. In contrast, when we examine PGIs for height, body mass index (BMI) and cognitive performance, controlling for parental PGIs has far less impact on their associations with their corresponding phenotype. Thus, the EA PGI stands out as unusual in terms of how much of its predictive power is not due to direct effects.The rest of the paper investigates the scope and sources of the PGI’s predictive power. We first document that the EA PGI not only predicts a range of cognitive phenotypes, as has been found in previous work7, we estimate the correlation between mate-pair PGIs for EA, as well as for height. For height, the correlation between mate-pair PGIs is close to that expected under phenotypic assortment . Once again, EA is different; the correlation between mate-pair PGIs for EA is much larger than one would expect from phenotypic assortment on EA. We find evidence that population structure captured by principal components (PCs) and assortment on cognitive performance explain some, but not all, of the excess mate-pair PGI correlation. These findings shed further light on the EA PGI’s predictive power for EA and other phenotypes; the factors on which mate pairs assort that are not EA but are correlated with the EA PGI ) likely also contribute to the PGI’s predictive power.Finally, we use PGIs to study assortative mating. Using 862 genotyped mate pairs in the UKB and 1,603 pairs in Generation Scotland (GS)For a less technical description of the paper and of how it should—and should not—be interpreted, see the frequently asked questions in Supplementary Data N = 324,162, excluding UKB and 23andMe), new association results from 23andMe  and new association results from a GWAS we conducted in UKB with an improved coding of the EA measure  score regression8 intercept (1.66), confounding accounts for 7% of the inflation, similar to previous GWAS of EA (ref. 2) , by combining three sets of summary statistics: public results from our previous meta-analysis of 69 cohorts (r2 < 0.1) variants with an association P value below 5 × 10−8. At the stricter threshold9 of P < 1 × 10−8, the number declines to 3,277  with other COJO lead SNPs and may represent secondary associations within a locus. Adjusted for the winner’s curse, we find that the effects of our lead SNPs are consistently quite small. On average, an additional copy of the reference allele of the median SNP is associated with 1.4 weeks more schooling: the effects at the 5th and 95th percentiles  are 0.9 and 3.5 weeks, respectively  for ~200,000 SNPs on the X chromosome . Theory and evidence from the quantitative genetics literature, including findings from two recent papers14 that estimated dominance SNP heritability across dozens of phenotypes (but not EA), suggest that dominance effects explain at most a very small share of the variance in polygenic phenotypes15. Nevertheless, in the behavior genetics literature, when the phenotypic correlation between monozygotic twins is more than twice as large as the phenotypic correlation between dizygotic twins, it remains common practice to attribute the violation of the additive model to dominance variance.We conducted a GWAS of dominance deviations from the additive model  by meta-R2 of 0.0015% (R2 ≅ 0.04%). Therefore, the absence of genome-wide-significant SNPs suggests that dominance effects of common SNPs, taken individually, are negligibly small.The Manhattan plot from our dominance GWAS is shown in red in the bottom panel of Fig.  0.0015% . Such efP = 0.54). In the Next, we turn to the combined dominance effects of common SNPs. Applying an adapted version of LD Score regression to the summary statistics, we estimate a SNP heritability of 0.00015 (s.e. = 0.00024), which is statistically indistinguishable from zero . We applied a recently developed method that uses dominance GWAS summary statistics to estimate ID17. Our estimate implies the offspring of first cousins have on average ~1.0 fewer months of EA (P = 0.04) than the offspring of unrelated individuals.Even when the phenotypic variance across individuals explained by dominance is negligible, the combined dominance effects on an individual can be substantial when homozygosity (which is deleterious on average) is increased genome-wide due to inbreeding18, a representative sample of American adolescents followed into adulthood; the Health and Retirement Study (HRS)19, a representative sample of Americans over age 50 years; and the Wisconsin Longitudinal Study (WLS)20, a sample of individuals who graduated from high school in Wisconsin in 1957. Because of the range restriction for EduYears in WLS, we do not use it to evaluate predictive power for EA. Our measure of prediction accuracy is the ‘incremental R2’, or the gain in coefficient of determination (R2) when the PGI is added as a covariate to a regression of the phenotype on a set of baseline controls . All PGIs that we analyze are based on a meta-analysis that excluded Add Health, HRS and WLS.We assessed empirically how well a PGI derived from the autosomal GWAS of additive variation predicts a host of phenotypes related to EA, academic achievement and cognition. We used three European genetic-ancestry holdout samples from the National Longitudinal Study of Adolescent to Adult Health R2 of 9.1% in Add Health and 7.0% in HRS . This PGI explains 15.8% of the variance in EduYears in Add Health and 12.0% in HRS  is more predictive than our LDpred PGI. It explains 17.0% of the variance in EduYears in Add Health and 12.9% in HRS, with a sample-size-weighted mean of 14.3%  in African-genetic-ancestry to European-genetic-ancestry samples have been 22% (ref. 23) and 36% (ref. 24). When we used our PGI to predict EduYears in samples with African genetic ancestries from the HRS  and Add Health , the incremental R2 was 1.3% , 0.6% to 2.2%) and 2.3% , implying that the relative accuracies for EA in the HRS and Add Health are only 11% and 15%, respectively. Using the UKB, we find that the relative accuracy is smaller than would be predicted based on population differences in allele frequencies and LD alone (Online Methods), and this discrepancy is greater for EA than has been found in prior work25 for height, BMI and six other phenotypes , gene–environment interactions and differences between populations in gene–environment correlations, assortative mating and environmental variance.PGIs like ours that are constructed from GWAS in samples of European genetic ancestries are generally found to have much lower predictive power in samples with other genetic ancestries; for example, on average across phenotypes, estimates of relative accuracy , GS (ref. 7) and the Swedish Twin Registry (STR)38. We did not have sufficient power to study the diseases from Fig. For this analysis, we used a combined sample of ~53,000 individuals with genotyped siblings and ~3,500 individuals with both parents genotyped  is due to direct effects. Fig. 40—the mate-pair PGI correlation should equal the product of the mate-pair phenotypic correlation, the correlation between the father’s phenotype and PGI and the correlation between the mother’s phenotype and PGI. We examined whether correlations between mate-pair EA PGIs fit this model  and GS . Under the (commonly assumed) hypothesis of phenotypic assortment—according to which the mate-pair genetic components are independent conditional on the mate-pair phenotypesdel Fig. , and we del Fig. . Height For height, phenotypic assortment predicts a mate-pair PGI correlation of 0.087 (s.e. = 0.007) (the gray point in the figure), which is only somewhat smaller than the observed estimate of 0.106 and is contained within the 95% CI. In contrast, for EA, the predicted value of 0.031 (s.e. = 0.004) is much smaller than, and statistically distinguishable from, the mate-pair PGI correlation of 0.175. Phenotypic assortment on EA would also imply that after residualizing the PGI on EA, the mate-pair PGI correlation should fall to zero. In fact, the correlation falls by only 37%, to 0.110 (s.e. = 0.021).41, but social homogamy that is related to genetic ancestry  will do so if there are components of genetic ancestry correlated with the PGI. After residualizing the EA PGI on 40 PCs of the genomic relatedness matrix in addition to EA, we find that the mate-pair PGI correlation falls to 0.091 (s.e. = 0.021). This implies that some, but not most, of the mate-pair PGI correlation is due to assortment on genetic ancestry captured by the PCs (or some factor correlated with the PCs). In the UKB, further adjustment for birth coordinates and the center where participants were assessed (Online Methods) resulted in a slight reduction of the correlation between mate-pair PGIs  that identify just a few SNPs to well-powered analyses of most of the variation from common SNPs, it has become possible to address an ever-increasing set of questions. For example, we find that the EA PGI has predictive power across a broad range of educational, cognitive and health-related phenotypes and diseases. Our results show that this predictive power derives both from direct genetic effects and from gene–environment correlation (likely including indirect genetic effects from relatives), with assortative mating amplifying the predictive power over what would be expected under random mating.The results of previous large-scale GWAS of EA have proven useful across many different areas of research, including medicine56, researchers from the Hawaii School58 and the sociologist Sandy Jencks famously came up with strikingly different explanations for a set of kinship correlations on cognitive test scores assembled by Jencks et al.59. A careful analysis by Loehlin60 showed that the three sets of researchers arrived at different explanations for the same data primarily due to their divergent assumptions about dominance, assortative mating, and special twin environments.Our findings are also relevant for informing some decades-old debates in the behavior genetics literature. Because the parameters of a general biometric model cannot be separately identified from a small number of phenotypic correlations among different types of relatives, researchers typically have to assume that some of the parameters equal zero in order to estimate other parameters. In the 1970s, for example, researchers from the Birmingham SchoolAlthough our results concern EA rather than cognitive test scores, we believe they are relevant for evaluating the plausibility of some of the assumptions underlying the modeling approaches that have been used to explain familial resemblance in EA and cognitive phenotypes. Three of our findings are especially relevant: (1) dominance variance due to common variants is negligible, (2) much of the predictive power of the EA PGI is not explained by direct effects and (3) the mate-pair PGI correlation is far too strong to be consistent with assortative mating purely on phenotype. Overall, these findings suggest that any model of EA that requires substantial dominance to fit the data, restricts gene–environment correlations to zero or assumes assortative mating is purely based on phenotype is likely to be misspecified. Thus, our analyses demonstrate how results from large-scale GWAS and the resulting PGIs can be used to improve the identifiability of behavior–genetic models.13.The sample size of the GWAS of EA reported in this paper is the largest published to date. For some purposes, such as attaining greater predictive power for the PGI, there are clearly diminishing returns. However, even larger samples will enable other analyses that have not yet been adequately powered, such as estimating differences in SNP effect sizes across phenotypes or populations and estimating the fraction of variance explained by epistatic interactionsThis article is accompanied by a 62, the EduYears phenotype was coded by mapping the highest level of education that a respondent achieved to an International Standard Classification of Education 1997 category and then imputing a years-of-education equivalent for each International Standard Classification of Education 1997 category. Details on cohort-level phenotype measures, genotyping and imputation are in Supplementary Table As in previous GWAS62, but this classification overstates their average years of schooling  but no college or university degree were previously coded as having 19 years of educationchooling . We therIn previous GWAS, individuals younger than 30 years when EA was measured were excluded to ensure that almost everyone had completed formal schooling. In the 23andMe GWAS for the current paper, ~16% of the individuals are aged 16–29 years. To explore the effect of including these individuals, we conducted a simulation using the UKB data , new association results from 23andMe  and new association results from a GWAS we conducted in UKB with the identical methodology as in Lee et al. but with the improved coding of EduYears described above . All cohort-level analyses were restricted to European-genetic-ancestry individuals who passed the cohort’s quality-control filters and, except in 23andMe as described above, whose EA was measured at an age of at least 30 years. We did not run sex-stratified analyses for the autosomal meta-analysis, because there is compelling evidence from our prior work that the male–female genetic correlation for EduYears is close to one. For example, the Okbay et al.62 data yield an estimate of 0.98 (s.e. = 0.029).For our additive GWAS of EduYears, we meta-analyzed three sets of summary statistics: publicly available results from Lee et al.62 and implemented in the EasyQC R package but updated to a more recent reference panel and adjusted to account for the large GWAS sample sizes (63), for all SNPs that passed the quality-control thresholds in the new 23andMe and UKB results, we conducted a sample-size-weighted meta-analysis of these new results with the 69 results files from Lee et al.2 . After the meta-analysis, we inflated the standard errors by the square root of the intercept 8 estimated from the meta-analysis summary statistics.To the new 23andMe and UKB results, we applied a quality-control protocol similar to the one described previouslyle sizes . Using t2 and implemented in Plink (ref. 64), with a pairwise r2 cutoff of 0.1 and no physical distance cutoff  was conducted in a pooled male–female sample using a 0/2 genotype coding for males. The UKB analysis  was an inverse-variance-weighted meta-analysis  of sex-stratified association analyses conducted using BOLT-LMM v2.3.4 (ref. 66). Following Supplementary Note section 4.1 of Lee et al., we used the sex-stratified UKB analyses to estimate the X-chromosome SNP heritability for males and females, as well as the male–female genetic correlation  and UKB  summary statistics. Similar to the additive GWAS, after the meta-analysis, we inflated the standard errors by the square root of the intercept from an LD score regression. We used LD scores that account for the faster decay of information from tagged SNPs as a function of LD for dominance effects . The LD score regression was restricted to the set of HapMap3 SNPs, and the dominance LD scores were estimated using the 1000 Genomes phase 1 reference sample67.We conducted a sample-size-weighted meta-analysis for 5,870,596 autosomal SNPs that passed quality control filters and were available in both the 23andMe (https://osf.io/uegqv/) to assess whether the estimates of the dominance effects for various subsets of SNPs are consistent across UKB and 23andMe  on the inbreeding coefficient across individuals. To estimate ID for EA, we used ldscdom software, which implements a recently developed method21, assuming a Gaussian prior for the distribution of effect sizes and restricting to HapMap3 SNPs. LD patterns were estimated in a sample of 14,028 individuals and 1,214,408 HapMap3 SNPs from the public release of the Haplotype Reference Consortium reference panel68. The PGIs were obtained in Plink2 (ref. 69) by multiplying the genotype probabilities at each SNP by the corresponding estimated posterior mean calculated by LDpred and then summing over all included SNPs P value cutoffs of 5 × 10−8, 5 × 10−5, 5 × 10−3 and 1  were made in Plink2 (ref. 69) using the clumping algorithm described in the section ‘Additive genome-wide-association study meta-analysis’ and the procedure described above. The SNP weights were set equal to the coefficient estimates from the meta-analysis (Supplementary Table The ‘clumping and thresholding’ PGIs with 22) PGI were obtained using GCTB software70. We assume four components in the finite mixture model, with initial mixture probabilities π =  and fixed γ = , where γ is a parameter that constrains how the SNP-effect-size variance scales in each of the four distributions. LD was estimated using 2,865,810 pruned common variants from the full UKB European-genetic-ancestry  dataset from Lloyd-Jones et al.22. Weights were obtained for 2,548,339 of these SNPs that overlapped with the summary statistics after excluding the major histocompatibility complex region. PGIs were constructed in Plink2 (ref. 69) by multiplying the genotype probabilities at each SNP by the corresponding estimated posterior mean calculated by SBayesR and then summing over all included SNPs  R2 values by performing a bootstrap with 1,000 repetitions.To evaluate prediction accuracy, we first regress the phenotype on the controls listed above without the PGI. Next, we rerun the regression but with the PGI included. For quantitative phenotypes, our measure of predictive power is the incremental 71. The expected coefficient of determination, R2, can be expressed as the following function of the discovery sample size, N:We calculate the expected prediction accuracy of the EA PGI using a generalization of de Vlaming et al.A may vary by prediction sample, B does not. We estimate A and B by nonlinear least squares using data from Add Health and HRS. More details of this calculation can be found in Although 25 to investigate the factors contributing to the substantial loss of prediction accuracy of the EduYears PGI in samples of African genetic ancestries. We define the European genetic ancestries to African genetic ancestries relative accuracy (RA) asN = 425,231). We identified 507 approximately independent genome-wide-significant SNPs , setting the window size equal to 1 Mb and the LD r2 threshold to 0.1). We then used these 507 SNPs to generate PGIs and evaluate their accuracy in UKB holdout samples of African-genetic-ancestry individuals  and European-genetic-ancestry individuals . To compare our empirical estimate of RA to the RA predicted by the model, we used genotypes from 503 European-genetic-ancestry and 504 African-genetic-ancestry participants in the 1000 Genomes Project to estimate genetic-ancestry-specific MAF and LD correlations between all candidate causal variants (defined as any SNP within a 100-kb window of a genome-wide-significant SNP whose squared correlation with the genome-wide-significant SNP is above 0.45). Following Wang et al., we then substituted these estimates into their equation (2)  as described above but using the summary statistics of a meta-analysis of EA that excludes UKB. Disease-specific PGIs were constructed using summary statistics from GWAS conducted among participants of European genetic ancestries for nine phenotypes  (ref. ld 41270  and 24.R2 of adding the variable(s) to a logistic regression of the disease phenotype on sex, a third-degree polynomial in birth year and interactions with sex, the first 40 PCs and batch dummies. 95% CIs around the incremental Nagelkerke’s R2 were obtained by performing a bootstrap with 1,000 repetitions.For the various diseases, we computed the predictive power of (1) the EA PGI, (2) the disease-specific PGI and (3) these two PGIs together with their interaction , GS (ref. 7) and STR (ref. 38). In both UKB and GS, first-degree relatives were identified using KING with the “–related–degree 1” option72. For parent–offspring relations, the parent was identified as the older individual in the pair. We removed 621 individuals from GS that had been previously identified by GS as being also present in UKB  and GS (1603 mate pairs) by identifying genotyped parents of genotyped individuals within each sample. Let Further information on research design is available in the Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at 10.1038/s41588-022-01016-z.Supplementary InformationSupplementary Note and Supplementary Figures 1–5.Reporting SummaryPeer Review FileSupplementary TablesSupplementary Tables 1–30.Supplementary Data 1Frequently asked questions.


The markers detected by genome-wide association study (GWAS) make it possible to dissect genetic structure and diversity at many loci. This can enable a wheat breeder to reveal and used genomic loci controlling drought tolerance. This study was focused on determining the population structure of Iranian 208 wheat landraces and 90 cultivars via genotyping-by-sequencing (GBS) and also on detecting marker-trait associations (MTAs) by GWAS and genomic prediction (GS) of wheat agronomic traits for drought-tolerance breeding. GWASs were conducted using both the original phenotypes (pGWAS) and estimated breeding values (eGWAS). The bayesian ridge regression (BRR), genomic best linear unbiased prediction (gBLUP), and ridge regression-best linear unbiased prediction (rrBLUP) approaches were used to estimate breeding values and estimate prediction accuracies in genomic selection.Population structure analysis using 2,174,975 SNPs revealed four genetically distinct sub-populations from wheat accessions. D-Genome harbored the lowest number of significant marker pairs and the highest linkage disequilibrium (LD), reflecting different evolutionary histories of wheat genomes. From pGWAS, BRR, gBLUP, and rrBLUP, 284, 363, 359 and 295 significant MTAs were found under normal and 195, 365, 362 and 302 under stress conditions, respectively. The gBLUP with the most similarity  with the pGWAS method in the terms of discovered significant SNPs, suggesting the potential of gBLUP in uncovering SNPs. Results from gene ontology revealed that 29 and 30 SNPs in the imputed dataset were located in protein-coding regions for well-watered and rain-fed conditions, respectively. gBLUP model revealed genetic effects better than other models, suggesting a suitable tool for genome selection in wheat.We illustrate that Iranian landraces of bread wheat contain novel alleles that are adaptive to drought stress environments. gBLUP model can be helpful for fine mapping and cloning of the relevant QTLs and genes, and for carrying out trait introgression and marker-assisted selection in both normal and drought environments in wheat collections.The online version contains supplementary material available at 10.1186/s12864-022-08968-w. Triticum aestivum L., AABBDD, 2n = 6x = 42), as an economically important crop, provides iron, calcium, zinc, vitamin B, starch, fiber, fats, and dietary proteins  and crop coefficient [KC] were estimated to measure evapotranspiration (ETC = KC × ET0) . Furthermore, the significant SNPs were analyzed via KOBAS version 2.0 for gene ontology enrichment analysis in KEGG [https://www.genome.jp/kegg/].The ensemble-gramene database was employed to extract the molecular and biological functions of SNPs in the gene ontology by using the IWGSC RefSeq V.2.0, which has been provided for the Chinese Spring [GP was calculated by various approaches: BRR , 73, gBLThe descriptive statistics and correlation analysis were implemented by R V.4.1 using the dplyr, ggpubr, psych, and ggplot2 packages. Heatmap analysis was carried out using heatmap.2 function in gplots R package to classify wheat accessions.Additional file 1: Supplementary Table 1. Mean, coefficient of variation (CV), broad senseheritability (H2), and combined analysis of variance based onstudied traits in 298 Iranian wheat landraces and cultivars. Supplementary Table 2. Overview on the landraces and cultivars of Iranian wheat studied. Supplementary Table 3. Pattern of total monthly precipitation andirrigation for the 2018-19 and 2019-20 cropping seasons. Supplementary Fig. 1. Correlation coefficients between the studied agronomic traits for Iranian wheat landraces and cultivars. . Abbreviations: PH, Plant height; GY, Grain yield; GN, Grain number per spike; TKW, Thousand kernel weight; SW, Spike weight; SA, Spike area; SH, Spike harvest index; SF, Spike fertility. Supplementary Fig. 2. GWAS results for agronomic traits andbreeding Values of Iranianlandraces and cultivars in well-watered environments. Agronomic traits (A), BRR (B), gBLUP (C), and rrBLUP (D). Abbreviations: PH, Plant height; GY, Grain yield; GN, Grain number per spike; TKW, Thousand kernel weight; SW, Spike weight; SA, Spike area; SH, Spike harvestindex; SF, Spike fertility. Supplementary Fig. 3. Manhattan and QQ-plots of highly associatedhaplotypes for and MLM in Iranian wheat landraces and cultivars in well-wateredenvironments. X axis represents chromosomes: 1) 1A, 2) 1B, 3) 1D, 4) 2A, 5) 2B, 6) 2D, 7) 3A, 8) 3B, 9) 3D, 10) 4A, 11) 4B, 12) 4D, 13) 5A, 14) 5B, 15) 5D, 16) 6A, 17) 6B, 18) 6D, 19) 7A, 20) 7B, 21) 7D. Supplementary Fig. 4. GWAS results foragronomic traits and breeding Values of Iranian landraces and cultivars inrain-fed environments. Agronomictraits (A), BRR (B), gBLUP (C), and rrBLUP (D). Abbreviations: PH, Plant height; GY, Grain yield; GN, Grain number per spike; TKW, Thousand kernel weight; SW, Spike weight; SA, Spike area; SH, Spike harvest index; SF, Spike fertility. Supplementary Fig. 5. Manhattan and QQ-plots of highly associatedhaplotypes for and MLM in Iranian wheat landraces and cultivars in rain-fed environments. X axis represents chromosomes: 1) 1A, 2) 1B, 3) 1D, 4) 2A, 5) 2B, 6) 2D, 7) 3A, 8) 3B, 9) 3D, 10) 4A, 11) 4B, 12) 4D, 13) 5A, 14) 5B, 15) 5D, 16) 6A, 17) 6B, 18) 6D, 19) 7A, 20) 7B, 21) 7D. Supplementary Fig 6. The KEGG pathway of metabolic pathways. Supplementary Fig 7. The KEGG pathway of oxidativephosphorylation. Supplementary Fig 8. The KEGG pathway of biosynthesis of amino acids. Supplementary Fig 9. The KEGG pathway of ascorbate and aldarate metabolism. Supplementary Fig 10. The KEGG pathway of sulfur metabolism. Supplementary Fig 11. The KEGG pathway of fatty acid elongation.


Heat stress negatively influences cattle welfare, health and productivity. To cope with the forecasted increases in temperature and heat waves frequency, identifying high-producing animals that are tolerant to heat is of capital importance to maintain milk production. This study, based on the joint analysis of on-farm performance and weather data, had two objectives: (1) to determine the response in production performances  and udder health (somatic cell score) to temperature-humidity index (THI) variations in Montbeliarde cows, and (2) to estimate the interactions between genotype and THI, to enable the identification of the most adapted animals for facing the expected increases in temperature.Test-day records from first and second lactations from 2016 to 2020 were associated with the average THI during the three days before the test-day record. In total, 446,717 test-day records from 55,650 cows in first lactation and 457,516 test-day records from 58,229 cows in second lactation were analysed. The optimal THI was below 55 (i.e. ~ 12–13 °C) for all traits. Individual responses to THI were estimated by random regression models, which also included individual responses to days in milk. Regardless of the stage of lactation, genetic correlations along the THI gradient were above 0.80, which suggests that genotype-by-THI interactions were weak for production and udder health traits. Nevertheless, a variability in the individual slope of decay could be highlighted at high THI. The genetic correlation between production level at moderate THI and the slope at high THI was negative, while for somatic cell score, it was positive, indicating that heat stress amplifies the susceptibility to mastitis.The optimal THI for French Montbeliarde cows is below 55 for production and udder health traits. Genetic-by-THI interactions are weak in French Montbeliarde cows for production and udder health traits, but not all animals react in the same way to high temperatures. Even if there is little room for improvement, using a heat tolerance index in cattle selection would be relevant to anticipate the expected increases in temperature. Further investigations are needed to interpret this variability on production traits. However, the current selection for mastitis resistance seems appropriate to adapt cattle to rising temperatures.The online version contains supplementary material available at 10.1186/s12711-023-00779-1. Global warming has and will have major negative consequences for livestock production, in particular the increase in the frequency and intensity of heat waves . Indeed,The Montbeliarde breed is raised throughout France, with a stronger presence in the mid-mountain regions of eastern and central France , where aTo perform selection for heat tolerance, indicators of heat stress are needed. There are two main approaches to quantify heat stress. The first one consists in measuring the body temperature or other physiological parameters, such as hormonal response to heat, or measuring behavioral indicators, such as the respiration rate, panting or sweating, which are commonly observed in heat stress events (see –11 and rThis study had two objectives: (1) to identify the values of THI associated with the onset of heat stress and quantify the magnitude of the loss in production and in health performances for Montbeliarde cows; and (2) to estimate genetic-by-THI interactions, which will enable the identification of the animals that are most adapted for coping with the expected rises in temperatures.The performance and pedigree information used in this study are from the French national database. Data from first L1) and second (L2) lactation test-day records on Montbeliarde cows were selected from five French regions  over a period of four years (August 2016 to June 2020). Six phenotypes were analyzed: milk yield (MY), fat content (FC), protein content (PC), fat yield (FY), protein yield (PY), and somatic cell score (SCS). SCS was obtained as a log- transformation of somatic cell concentration  + 3) . All the and seco2 squares covering the whole French territory. The use of modeled data instead of observed data was proposed by Mbuthia et al. [2 squares that covered the location, with the weights equal to the proportion of the surface of the village in each square. The daily THI was calculated as THI = (1.8 × T + 32)-(0.55–0.0055 × RH) × (1.8 × T-26) [The meteorological SAFRAN data provided by the French national meteorological agency (Météo-France) included daily estimates of various indicators for each of the 9892 8 × 8-kma et al. . These d × T-26) , where T × T-26)  and Brüg × T-26) .In a preliminary investigation, different lengths of THI were tested by considering either only the date of the test-day or the average of the THI at the test-day and from one to six days before, totalizing a range of one to seven days of potential heat stress. It was concluded that the average THI over three days (i.e. at the date of the test-day and the two previous days), was optimal to observe the most marked effects of heat stress. Similar results were obtained by Carabaño et al.  and SantThe estimate of the average THI effect on milk production performances was obtained with the following model including THI as a fixed effect:It should be noted that, in this model, the contemporary groups were not defined by HTD, to avoid capturing all the effects of the THI. For this reason, the HY effect was preferred as a contemporary group. Although it may be argued that the effects of month of calving probably capture some of the THI effects, ignoring seasonal variations  are more likely to inflate the estimates of THI effects, and therefore month of calving was also kept as a fixed effect.To estimate genetic-by-THI interactions, random regression models were fitted. Random regression models allow to predict the performance of each genotype under a given environmental condition. HTD was considered as the contemporary group in this model because although it captures the average THI effect, it does not affect the comparison between cows. Since the six traits that were evaluated in this study are known to vary with DIM, the model included random regressions on both THI and DIM as follows:mentclass2pt{minimThe genetic random regression variance matrix The genetic variances and covariances at each DIM and each THI were estimated by pre- and post-multiplying the variance matrix The permanent environmental random regression variance matrix and the permanent environmental variances were defined similarly as follows:The residual variance All these variances allowed to calculate the heritabilities at DIM Finally, this random regression model defined in Eq.  allows tThe slope of the regression on (standardized) THI for animal The genetic correlation between breeding value at DIM In all the analyses, the six traits  were evaluated separately. All fixed effects and variance components were estimated using the WOMBAT software .Figure −1 and − 0.09 kg.d−1 per unit of additional THI in L1 and L2, respectively) for MY, and was highest  for FY and PY. The effect of heat stress on SCS was stronger in L1 (average increase of 10.3%) than in L2 (average increase of 4.8%).The average effect of THI on performances, according to the model in Eq.  is shownWith the random regression models used, different variances across all combinations of DIM and THI were obtained for each trait. Since the main objective of this study was to investigate tolerance to heat stress in dairy cows, all the estimates of variance components, heritabilities, and correlations or breeding values are illustrated along the THI gradient, and at three key stages of lactation: 1) at 60d, just after the peak of lactation; (2) at 150d, in the middle of the lactation curve; and 3) at 240d, when production is also affected by persistency. Even if the shapes of the curves were not identical, for all production traits and in both lactations, Fig.  at 240d, at 60d, For production traits, the patterns of the change in heritability with THI see Fig.  reflecteMost of the estimated genetic correlations between different THI values, within trait, parity and DIM, were higher than 0.90, as shown in Fig. −1/unit of additional THI and the slopes of the sires S4 and S6 were − 0.050 and − 0.046 kg.d−1/unit of additional THI, respectively. The estimates of the genetic standard deviation of the slopes at THI 70 and the total genetic standard deviation of the trait at THI 70 are in Table Although the genetic correlations suggested that the genetic-by-THI interactions were weak, they were not equal to 1, thus we examined the evolution of individual estimated breeding values (EBV) along the THI gradient. Figure The aim of our study was to estimate the effect of THI on production and udder health traits in Montbeliarde dairy cattle, and to identify THI values associated with the onset of heat stress for the aforementioned traits. To our knowledge, this is the first study of heat stress in this breed, as well as the first one to account for daily THI information on French bovine data, regardless of the breed. Therefore, we compared our results to those obtained on other high yielding breeds that are known to be less adapted to heat than tropical breeds  and by Bohmanova et al. [−1 per unit of additional THI, depending on the USA region investigated).The rates of the decline in performances that we report here are of the same order of magnitude as those estimated in Carabaño et al. . These an et al. , but arei et al.  in Luxema et al.  for milkWe estimated the trajectory of genetic parameters of production and SCS traits along the THI gradient in Montbeliarde dairy cattle using random regressions and Legendre polynomials. Ravagnolo and Misztal  proposedAll the traits studied here have previously been shown to vary genetically with DIM. Time-dependent random regressions allow modelling different lactation curves for each cow , thus acAlthough the present random regression model takes the individual variations in the shape of the lactation curve into account, these variations are only briefly addressed in the “In agreement with the results of Brügemann et al.  on PY, BAmong the results for SCS, Bohlouli et al. , HammamiIn agreement with our results, Aguilar et al.  for MY, Some trajectories of variances and heritabilities showed a rebound at the highest THI values. It can be hypothesized that these upward bounces are due to a difference in the genetic determinism of the traits at the highest THI, and to a higher genetic variability at THI above 70 as in Aguilar et al. , CheruiyWithin DIM, our estimates of genetic correlations between THI conditions are very high and in line with Brügemann et al.  and CherWithin-trait and DIM, the permanent environmental correlations between adjacent and between distant THI were also high [minimum estimates of permanent environmental correlations at DIM = 150d were 0.89 for THI ranging from 50 to 70, for FC in L1,  and the slope of decay above the heat tolerance threshold were all negative for production traits, ranging from − 0.16 to − 0.56 on MY, PY and FY in various Holstein populations , 42, 44,Considering the slope as a heat tolerance trait, many authors conclude that there is an antagonistic correlation between production traits currently under selection and heat tolerance , 33, 35.Heat stress induces a decline in the performance of all traits , but they behave differently regarding the definition of neutral temperature. Although there is a systematic decline, the relative effect remains limited, i.e. close to -10%. The climatic conditions encountered in France are not, or not yet sufficiently extreme to observe a very large drop in performances. Within the range of THI observed in this study, interactions between genotype and THI remain limited, with genetic correlations higher than 0.8 and frequently above 0.9 across conditions. These results suggest that the ranking of animals is not severely affected in warmer conditions, but they can also be interpreted as a limited flexibility of the animals to adapt to even more severe conditions. Nevertheless, a number of outlier bulls show strong slopes for THI sensitivity and, thus, it would be interesting to examine their high sensitivity or, even more relevant, their capacity to adapt and cope with heat.Additional file 1: Figure S1. Evolution of additive genetic variances for PY in first (L1) and second (L2) lactation, between 30 and 300 days-in-milk.Additional file 2: Figure S2. Estimates of permanent environmental correlations within trait at different THI for milk yield (MY), somatic cell score (SCS), fat and protein contents (FC and PC) and fat and protein yields (FY and PY) in first (L1) and second lactation (L2). Results are given at 150 days-in-milk.


Investigating how traits that are important for survival are inherited and influenced by other factors, such as parental quality and physical condition, is crucial for understanding their evolutionary potential, deciphering how they may contribute to local adaptation and taking such capacity into account for conserving threatened species. We studied head shape heritability in the Hungarian meadow viper to investigate the relative importance of inheritance and the maternal and paternal effects in driving the observed morphological variations. Our results show that offspring phenotypes are mainly determined by genetic factors and maternal effects, while paternal effects and residual environmental influences are minimal. This suggests a high evolutionary potential for head shape in the Hungarian meadow viper, which suggests a strong contribution of this ecologically relevant trait in shaping the ability of this endangered species to adapt to changing conditions and/or habitats and which would be useful to consider in captive breeding procedures for conservation efforts.Vipera ursinii rakosiensis). To this end, we used geometric morphometric data from 12 families composed of 8 mothers, 6 fathers and 221 offspring, bred in captivity at the Hungarian Meadow Viper Conservation Centre (Hungary). We separately evaluated maternal and paternal contributions to the offspring phenotype, in addition to additive genetic effects, all determined using a mixed animal model. Our results indicate a strong genetic and maternal contribution to head shape variations. In contrast, the paternal effects—which are rarely evaluated in wild-ranging species—as well as residual environmental variance, were minimal. Overall, our results indicate a high evolutionary potential for head shape in the Hungarian meadow viper, which suggests a strong contribution of this ecologically important trait in shaping the ability of this endangered species to adapt to changing conditions and/or habitats. Furthermore, our results suggest that maternal phenotypes should be carefully considered when designing captive breeding parental pairs for reinforcing the adaptive capacity of threatened populations, whereas the paternal phenotypes seem less relevant.Understanding heritability patterns in functionally relevant traits is a cornerstone for evaluating their evolutionary potential and their role in local adaptation. In this study, we investigated patterns of heritability in the head shape of the Hungarian meadow viper ( Natural selection drives adaptive processes by favoring individual phenotypes that work better, in terms of fitness, in certain environments and conditions Darwin 1859). Traits that display heritable variance have adaptive potential in natural selection, which is crucial to the survival of populations across environmental gradients 859. Trai, as withBiological structures corresponding to different body parts are a remarkable aspect of an organism’s phenotype. They provide a connection between the genotype and the environment, and consequently, they frequently fulfil the aforementioned conditions for being adaptively relevant, exhibit ecologically driven variability and possibly include a strong heritable component . The heaThe lack of limbs in snakes makes them an outstanding system to study the evolutionary and ecological role of the head shape. Snakes frequently exhibit ontogenetic, sexual and phylogenetic variations in the head shape and dimensions relative to their body size ,23,24. TVipera ursinii rakosiensis; family Viperidae) )on range  and Enda Hungary . In thisV. ursinii rakosiensis? (2) What is the relative contribution of the maternal, paternal and environmental effects in generating its head shape diversity? By answering these questions, we aim to elucidate the genetic and external contributions to the head shape variations in vipers, increase our understanding of the evolutionary potential of this important phenotypic trait and contribute towards better practices for the conservation of this endangered viper species.Specifically, in this study, we address the following questions: (1) What is the strength and pattern of head shape heritability in Vipera ursinii rakosiensis) and provide means for habitat and population restoration in Hungary [The Hungarian Meadow Viper Conservation Programme, supported by the European Union’s LIFE fund, was built to protect the Hungarian meadow viper . These landmarks  on high-resolution photographs of a dorsal view of the head. Twenty-eight fixed landmarks and twelve semi-landmarks were modified based on those previously used by  for Vipeandmarks ; Table 1-package ,48. The -package . This pr-package  using thBefore advancing to the heritability analyses, we tested for the presence of sexual dimorphism in adults and offspring separately. For this purpose, we used (M)ANOVA comparisons on the head shape variables and on log(CS) with sex as the predictor variable, as implemented through the function procD.lm of geomorph. The significance was tested using residual permutation procedures with 1000 repetitions ,52. As sV. ursinii, we used restricted maximum likelihood (REML) as implemented in VCE-6 to first estimate the genetic and phenotypic variance components. REML is the preferred method for estimating variance components from mixed effects models in quantitative genetics [To determine whether the head shape is genetically inherited in genetics , and it genetics ,19. One genetics .The particular nature of our data, which originated from captivity breeds of known parents, allowed us to separately evaluate maternal and paternal contributions to offspring phenotypes, in addition to additive genetic effects. As such, we used a complete version of the animal model that included, in addition to offspring identity for evaluating the genetic component of variance, mother and father identities as random effects. This provided the corresponding effects variance–covariance matrices, which allowed us to specifically estimate how much of the phenotypic variance was attributable to maternal and paternal contributions. Note that, here, because breeding was performed in highly controlled conditions, we may expect environmental and clutch effects unrelated to the quality of the parents to have a minimal contribution on the observed phenotypic variations. Finally, we also included log(CS) as a fixed effect to control for any potential allometric effects of size on the shape .G), the maternal (Mat) and the paternal (Pat). Together with residual variance (R) typically attributable to environmental effects [P), i.e., P = G + Mat + Pat + R. Based on the total variance captured by each of these matrices, as represented by their traces, we could assess the relative contribution of each source in explaining the total phenotypic variance. We also examined the properties of these matrices, as expressed through their eigenvectors and eigenvalues, and projected the original shape variables back onto the calculated eigenvectors to visualize the shape variations related to each of them using deformation grids. To examine whether the total shape variation, as well as that explained by additive genetic and maternal effects , were aligned towards similar directions in the shape space, we calculated the angles between pairs of the first eigenvectors of each of them.Once the animal model was fit through REML, we obtained four variance–covariance matrices corresponding to specific model effects of interest: the additive genetic , we used the breeders’ equation as generalized for multivariate data, i.e., 2maxh [To estimate the shape heritability h, we used∆z¯=GP−S , P− beinate data . The privariance ,57, and e [h2max ,59. Simienvalues .Vipera ursinii, cumulatively captured 95.69% of the total shape variance.The PCA conducted on the symmetric portion of the head shape variation provided a total of 38 components with positive eigenvalues, of which the first 2 summarized 56.79% of the total variance. The first 15 components, which were the data dimensions that VCE-6 can handle and were therefore analyzed to estimate the variance sources and heritability in the head shape of −4%, respectively  and additive genetic matrices (G) were fairly aligned with each other (vector angle θ = 29.29°), while the maternal effects (Mat) principal eigenvector exhibited substantially different directionality from both of them . All three variance matrices captured a component strongly associated with the shortening of the snout, both through the posterior displacement of the front border of the head and the anterior displacement of the front edge of the frontal plate, as well as the posterior displacement of the ocular area of the head. However, global phenotypic and additive genetic variances also share a marked change of the shape of the frontal plate, with posterior displacement and narrowing of its posterior border, which translates into visible amplification of the eye entire area. Instead, the maternal effects were related to a forward displacement of the posterior border and a narrowing of the anterior border of the parietal scales.The principal eigenvectors of the phenotypic (Vipera ursinii rakosiensis), and we evaluated the relative contribution of the genetic, maternal, paternal and environmental components for determining the phenotypic variance patterns in this functionally and ecologically important body trait. The combination of geometric morphometrics—to quantify variations across families from a captive breeding program—and quantitative genetic approaches based on a full version of the animal model showed that the viper head shape is mainly determined by additive genetic and maternal effects, while the paternal and residual environmental contributions were negligible. This is the first study providing evidence for a large component of the heritable genetic variation in the head shape of vipers, highlighting the evolutionary potential of this ecologically relevant trait and facilitating the biological interpretation of the adaptive head shape variations in these organisms. Importantly, it suggests that this trait may be highly relevant for the capacity of Vipera ursinii rakosiensis to adapt to changing environments, which is key for the survival of such an endangered species and can be useful for informing and designing captive breeding programs in the context of conservation efforts.In this study, we investigated head shape heritability in the Hungarian meadow viper . Indeed, the heritable component of the global phenotypic variance was shown to be distributed through different directions  with the global phenotypic (P) matrix suggests that the shape variations across individuals, which is the material “visible” to selective processes, is highly aligned with the available genetic variability and, therefore, heritable and potentially subject to selection [P and G are mainly related to a posterior displacement and narrowing of the posterior edge of the frontal plate, which causes the eye area to become proportionally enlarged , and to what extent they are actually also associated with processes such as local adaptation, within-species selective agents  and macroevolutionary differentiation across species remains to be examined. Hypothetically, an amplification of the eye area could be particularly relevant for a grass-dwelling species such as the Hungarian meadow viper, for instance, to increase light reception in environments with reduced luminosity [V. ursinii rakosiensis [Further support towards the idea that the head shape additive genetic variance would probably enhance the head shape adaptability in election . This prelection ,64. The enlarged . Head shon range . Whetherminosity  and to eminosity . The higosiensis  suggestsmaxh2) as captured by the eigenvalue of the first principal component of the −GP matrix was particularly high in salamanders, reaching over 0.8 in some populations. Instead, the heritable portion of the phenotypic variance was rather spread out over different shape directions for wall lizards [h2 values were reported for several head scalation characters studied univariately [h2 estimates higher by definition, though not directly comparable to the multivariate estimates used here). The relatively low heritability values that seem to characterize both the head shape and head scalation in this population of Vipera ursinii rakosiensis may be the outcome of both biological and methodological factors. First, dorsal head scalation has been circumstantially reported to vary ontogenetically in this species [Interestingly, although comparisons across different systems are difficult, due to both biological and methodological reasons, these results are, in some cases, partially consistent but, in others, in contrast with results from previous studies that examined shape heritability in other species. While a high proportion of additive genetic variations for the head shape has been previously reported for both lizards  and sala lizards , in accoariately  (which m species , which cV. ursinii. However, it is important to note that the paternal contributions to offspring phenotypes—difficult as they are to identify with certainty in wild-ranging populations—could be higher in free-breeding animals in the field; this species is known to exhibit a biennial reproductive cycle, and females may mate every year but fecundation takes place when the body conditions are favorable, which usually occurs every second year, a fact that could lead to multiple paternities within a single clutch [From a conservation perspective, our results also highlight that the maternal effects, which usually reflect the maternal qualities and body conditions, have an equally strong and similarly multifaceted effect and should be carefully considered when designing captive breeding programs , as the e clutch . Similare clutch , a fact V. ursinii rakosiensis, since it is a species of high conservation concern, and this study shows that it has the potential to adapt to changing conditions. Studies using the animal model are required, since they are powerful tools to analyze the genetic parameters of the wild and captive breed populations, thus guaranteeing the survival and recovery of this population when reintroduced to the wild.Our study demonstrates that the head shape has major genetic and maternal contributions, with maternal effects being an important external contribution for the head shape diversity in this species. These results are important for the conservation of