For this, simulated data was used, with traits of different levels of heritability (0.30 and 0.50), and controlled by 3 and 100 QTLs. Populations of 1,000 to 200 individuals were defined, with a random reduction of 100 individuals for each population. The power of detection of QTLs and the false positive rate were obtained by means of QR considering three different quantiles  and also by means of the General Linear Model (GLM). In general, it was observed that the QR models showed greater power of detection of QTLs in all scenarios evaluated and a relatively low false positive rate in scenarios with a greater number of individuals. The models with the highest detection power of true QTLs at the extreme quantils (0.10 and 0.90) were the ones with the highest detection power of true QTLs. In contrast, the analysis based on the GLM detected few (scenarios with larger population size) or no QTLs in the evaluated scenarios. In the scenarios with low heritability, QR obtained a high detection power. Thus, it was verified that the use of QR in GWAS is effective, allowing the detection of QTLs associated with traits of interest even in scenarios with few genotyped and phenotyped individuals.The aim of this study was to evaluate the performance of Quantile Regression (QR) in Genome-Wide Association Studies (GWAS) regarding the ability to detect QTLs  To the increase in population is added the growing concern about environmental impacts and the limitations of arable areas, which culminates in the demand for increased productivity of agronomic species2. In recent years, it is estimated that about 50% of the increase in productivity of several species was driven by genetic breeding, which has been seeking new strategies to obtain more adapted, resistant, and productive cultivars4.The world's population reached 7.7 billion inhabitants in 2019 and may reach 9.7 billion by 20509. The potentials of GWAS have already been successfully explored in traits of economic interest and in different crops, such as barley11, maize14, soybean16, rice20, wheat23 e arabica coffea26.In this context, genome-wide association studies (GWAS) have been conducted in order to identify genetic variations that may be associated with phenotypic traits of interest27. When the correction for population structure is added to the single markers regression model, this model is called General Linear Model (GLM)28.However, the estimation of parameters via single markers and GLM are based on conditional means, which may be inadequate when the errors do not follow a normal distribution29 and in the presence of heteroscedasticity. An alternative and still little explored methodology for GWAS studies is Quantile Regression (QR)30. This methodology, unlike methods based on means, allows adjusting regression models for different levels (quantiles) of the distribution of the phenotype of interest, does not require assumptions about the error distribution, and is robust to discrepant points31. QR has already been successfully applied in GWAS studies on real data by32 for traits related to the flowering time of common beans. These authors evaluated 80 common bean genotypes and 384 SNP markers (Single Nucleotide Polymorphism) in order to identify genomic regions for three phenological traits. As a result, the authors found no significant associations using the General Linear Model. In contrast, when using QR at the extreme quantile (τ = 0.10), it was possible to detect 7 significant associations between SNPs and the phenological traits studied. In this study, the number of available genotypes was relatively small for GWAS studies, but it was still possible to detect significant associations using QR in this setting.In GWAS, a classic and widely used statistical method is single markers regression. This method estimates the individual effect of each marker on the phenotype of interest, and, subsequently, multiple hypothesis tests are performed in order to detect which marker effects are statistically significant(Quantitative Trait Locus) has not yet been evaluated. To this end, it is possible to use data simulation since this strategy aims to reproduce the conditions of a biological system, facilitating the understanding of its real functioning and allowing prediction of the performance and recommendations before starting field studies34. In addition, simulation studies are especially convenient for testing and comparing methodologies because they demand fewer resources, time, human efforts, and the possibility of replication, thus generating greater efficiency in inferences35.Although QR has already been applied to real data sets and has obtained interesting and promising results, the effect of population size on the ability to detect QTLs In view of the above, this study evaluated the use of QR in GWAS regarding the power of QTL detection through SNP markers for simulated data with different levels of heritabilities, trait loci, and population sizes. The results of QR were compared with those obtained by GLM.Aiming to access the power of QTL detection and false positives rates in a genome-wide association study was performed a simulation study.An advanced generation composite was obtained from two random mating populations in linkage equilibrium, which were crossed to generate a population of 5,000 elements from 100 families using linkage disequilibrium (LD), subjected to five generations of random mating without mutation, selection, or migration.36.From the advanced generation of the composite, 1000 individuals from the same generation and from 20 families of full siblings, each consisting of 50 individuals, were simulated. The simulated genome was composed of ten chromosomes with a size of 200 centimorgans (cM) each and comprised 2000 bi-allelic single nucleotide polymorphisms (SNPs) separated by 0.1 cM across the ten chromosomes. The LD value in a composite population is Two genetic architectures were simulated, representing different scenarios, with heritabilities of 0.30 and 0.50 and with 100 and 3 numbers of quantitative trait loci (QTLs), distributed randomly in the regions covered by the SNPs. The first scenario follows the infinitesimal model and the other (second scenario) with three major effects genes accounting for 50% of the genetic variability. For the former, to each of 100 QTLs one additive effect of small magnitude on the phenotype was assigned . For the latter, small additive effects were assigned to the remaining 97 loci. The effects were normally distributed with zero mean and variance, allowing the desired heritability level. The phenotypic value was obtained by adding to the genotypic value a random deviate from a normal distribution 37. More information can be found detailed in38.The data set was simulated using the Real Breeding program39, 200 individuals are considered as being sufficient for the construction of reasonably accurate genetic maps. A random reduction of 100 individuals was defined in each scenario, respecting the proportionality of individuals removed from each family. Thus, in all, thirty-six distinct scenarios were evaluated. These scenarios correspond to the combination of two levels of heritability, two genetic architectures, and nine variations in population size.Subsequently, in order to evaluate the effect of population size reduction, populations were defined with numbers of individuals ranging from 1,000 to 200 individuals. According to2 were plotted against the genetic distance between markers (in cM). Subsequently, a local polynomial regression (LOESS)42 was fitted to the data and a horizontal straight line was plotted with a critical value of r2 = 0.2044. The window distance, defined as the intersection of the fitted LOESS curve and the horizontal straight line, will be used to determine which markers are associated with QTLs. Thus, all markers that distance the value of the window obtained  in relation to each QTL are considered as markers associated with the QTLs. The square of the correlation coefficient LD.decay function of the sommer package45 and the fit of the polynomial regression model using the loess function, both from the R software46.A linkage disequilibrium (LD) analysis was performed to determine the markers associated with QTLs. Specifically, the LD decay pattern between marker pairs across the genome was obtained using a figure in which the square values of the correlation coefficient r48. The number of principal components adopted was obtained using STRUCTURE 2.3.4 software49, selecting 300 markers in linkage equilibrium, aiming to ensure that these markers are not associated. A cluster number (K) ranging from 1 to 21 was tested, with ten independent replicates for each K value. In order to identify the optimal number of K, 10,000 iterations were run, with 1,000 burn-in. Then, the ∆K index50 implemented in Structure Harvester software51 was calculated to determine the choice of the most likely value of K. Subsequently, the K first principal components (CP) were used as fixed effect covariates in the GWAS model.To perform the genome-wide association analysis, first, the correction for population structure was performed through principal component analysis (PCA) of the genomic relatedness matrix (G)Y is the vector of phenotypic information; μ is the population mean; The GWAS model was defined by:32. This methodology consists of estimating the parameters at the τ (·), denoted check function by30, is defined by:The methods estimate the individual effect of each marker on the phenotype of interest and then perform multiple hypothesis tests in order to detect which marker effects are statistically significant. The parameters were estimated via QR for different levels (quantiles) of the distribution of the phenotype of interestrq function from the quantreg package52 of the R software was used. The individual coefficients (effects) of each marker are estimated by summing the weighted absolute errors. For estimation, it is necessary to use linear programming algorithms. One of the methods used is the Simplex Method53.In this study, three quantiles  were evaluated. For model fitting, the The parameters were also estimated using GLM. This methodology consists of estimating the parameters in average terms and solving the following optimization problem:54 of the R software46.For model fitting, the individual coefficients (effects) of each marker were estimated by minimizing the sum of squared errors by the ordinary least squares method using the GAPIT R packaget-student tests were performed according to the methodology used, in order to analyze the existence of significant associations between the marker and the phenotype of interest. In the general linear model, the standard error estimate used was the usual, while in the quantile regression it was based on rank56. However, due to the high density of markers, performing multiple tests can lead to an increase in false positive associations27. An alternative to controlling this rate is the False Discovery Rate (FDR)58. One way to consider the FDR in hypothesis testing is through a correction in the p-value associated with the test, called the q-value59. In this study, a significance level of 0.01  The power of QTL detection corresponds to the proportion of pre-established windows   that contain at least one marker considered significant by means of the statistical methods evaluated. ii) The false positive rate corresponds to the ratio between the number of markers that were significant by the evaluated statistical methods and are not associated with QTLs and the number of markers that are not associated with QTLs.50, ∆K was plotted against the number of clusters (k). The maximum value of ∆K occurred at K = 19 and K = 18 for the scenarios of 3 QTLs and 100 QTLs, respectively  from each QTL are considered as markers associated with the QTLs.60, in which the authors evaluated the effect of population size in GWAS, considering data from barley germplasm. In this study, the authors used a base population consisting of 766 individuals, and population size reduction was achieved by random resampling without replacement, forming populations with 96, 192, 288, 384, 480, 576, and 672 individuals, and observed that the detection power of QTLs decreased according to population size reduction61. Also evaluated the power of GWAS to identify true significant associations using simulated Arabidopsis data set with 200, 400, and 800 individuals. As a result, the authors observed that the power of identifying true associations decreased as the number of individuals decreased. In addition to these,62evaluated the influence of sample size in GWAS using simulated data from a Chinese soybean germplasm population consisting of 200, 400, 600, and 800 individuals randomly sampled from an ideal base population. As a result, the authors observed that the detection power of true significant associations decreased, and the false positive rate increased with decreasing sample size. Furthermore, according to63 and64, the efficiency of GWAS requires large population sizes.The general linear model obtained a low power of detection of QTLs in all scenarios evaluated Table . In the 55. Thus, the statistic of the test used generally presents higher values and, therefore, a greater number of QTLs being considered significant.However, the pattern reported by the authors mentioned above and those observed here for the GLM was not observed when using the QR models. In general, the QR, in all scenarios evaluated, obtained high detection power Table . AdditioIn scenarios with 3 QTLs, at quantiles of 0.10 and 0.90, regardless of heritability and population size variation, QR detected almost all simulated QTLs . As a result, the authors found no significant associations using GLM. On the other hand, when using QR at the 0.10 quantile, one and six significant SNPs were found for DPF and DTF, respectively. Although the work of66 and67 was not conducted in the context of genome-wide association, the authors also evaluated the performance of QR on simulated data set with small population sizes and concluded that QR is a robust technique in these situations. This result is very promising in breeding programs that have a reduced number of available genotypes.The detection of significant SNPs with a small population size and at the extreme quantile has already been observed byRegarding the rate of false positives, we have found that the GLM, in all scenarios evaluated, presented low values for this rate. This result may be related to the low detection power of QTls by this methodology Table . The fal62, in which the authors compared the detection power of true significant associations using five GWAS methods. This was done using simulated data from a Chinese soybean germplasm population with different levels of heritability  and two genetic architectures with 10 and 100 QTls. As a result, the authors observed that the detection power was dramatically reduced for all methods and scenarios evaluated when the heritability of the trait was reduced. On the other hand, this behavior was not observed when using the QR methodology. The QR obtained greater or equal powers of detection of true significant associations in scenarios with lower heritability (h2 = 0.30) regardless of the number of QTLs and sample size  were the most efficient models in the simulated conditions because they were the ones that obtained the highest QTL detection powers. In the scenario where the detection power of the QR in the three evaluated quantiles was equal, the QR (0.50) was more efficient, as the false positive rate was lower. In the low heritability scenarios, QR obtained a high detection power of QTLs. The false positive rate obtained by the QR methodology in the scenarios with many individuals is relatively low. QR proved to be efficient both in scenarios with many individuals and in scenarios with a small population size.


Brassica napus L.), the third largest oil crop, is an important source of vegetable oil and biofuel for the world. Although the breeding and yield has been improved, rapeseed still has the lowest yield compared with other major crops. Thus, increasing rapeseed yield is essential for the high demand of vegetable oil and high-quality protein for live stocks. Silique number per plant (SN), seed per pod (SP), and 1000-seed weight (SW) are the three important factors for seed yield in rapeseed. Some yield-related traits, including plant height (PH), flowering time (FT), primary branch number (BN) and silique number per inflorescence (SI) also affect the yield per plant (YP). Using six multi-locus genome-wide association study (ML-GWAS) approaches, a total of 908 yield-related quantitative trait nucleotides (QTNs) were identified in a panel consisting of 403 rapeseed core accessions based on whole-genome sequencing. Integration of ML-GWAS with transcriptome analysis, 79 candidate genes, including BnaA09g39790D (RNA helicase), BnaA09g39950D (Lipase) and BnaC09g25980D (SWEET7), were further identified and twelve genes were validated by qRT-PCRs to affect the SW or SP in rapeseed. The distribution of superior alleles from nineteen stable QTNs in 20 elite rapeseed accessions suggested that the high-yielding accessions contained more superior alleles. These results would contribute to a further understanding of the genetic basis of yield-related traits and could be used for crop improvement in B. napus.Rapeseed ( Brassica napus  is one of the most important oilseed crops worldwide as vegetable oil, animal feed and biofuel , genome wide association study (GWAS) has become a powerful tool for deciphering the genetic architecture of complex quantitative traits  mapping and map-based cloning . Zhou ete traits . Based oentified . IntegraB. napus . And staB. napus . With thin crops . Using 1B. napus . Based oB. napus . Using aB. napus . FurtherB. napus . Most ofB. napus . HoweverB. napus .Recently, multi-locus GWAS (ML-GWAS) methodologies, including FASTmrEMMA, ISIS EM-BLASSO, mrMLM, FASTmrMLM, pLARmEB, pKWmEB, were developed as an effective approach for association analysis . And varIn the present study, we aimed to identify novel loci for seed yield and yield-related traits in rapeseed. Six ML-GWAS approaches were used to determine novel QTNs based on high-quality SNPs in 403 rapeseed accessions for eight yield traits in three environments. And we also analyzed the significant QTNs and pinpointed multiple candidate causal genes for the QTNs. The candidate genes and elite alleles identified with yield traits will provide an insight into further exploration of the genetic architecture of yield traits in rapeseed and genetic improvement of rapeseed.https://www.cgris.net/rapedata/ or http://brassicanapusdata.cn/. The yield traits including SI, SN, SP, SW, and YP as well as three yield-related traits, such as PH, BN, and FT were measured according to the measurement standards  . GATK v. These Shttps://cran.r-project.org/web/packages/mrMLM/index.html) (P ≤ 0.0002) was chosen to examine the association between markers and yield-related traits (https://github.com/yinliLin/R-CMplot) was employed to visualize Manhattan and QQ plots of GWAS. Using the Tassel 5.2 tool (R2) of alleles, and R2 values were calculated within a 0 to 10 cM window. The phenotypic-effect value of allelic variation for each trait was calculated by the phenotypic data across the 403 accessions. The relative phenotypic data were visualized with box plots using the R 4.2.1 software.Six ML-GWAS methods, including the mrMLM, FASTmrMLM, FASTmrEMMA, pLARmEB, pKWmEB, and ISIS EM-BLASSO, were used to identify significant QTN. All six ML-GWAS approaches are implemented in R package “mrMLM” (ex.html) . Defaultd traits . Princip5.2 tool , LDs betbzh’ reference genome (https://www.genoscope.cns.fr/brassicanapus) (https://www.ncbi.nlm.nih.gov/) and annotated for Arabidopsis homologous genes by BLAST analysis (The putative candidate loci were identified by at least two different GWAS methods. Candidate genes were predicted from the upstream or downstream 200 kb region of stable QTL loci using the ‘Darmor-canapus) . Then thanalysis . Haplotyanalysis .® UltraTM RNA Library Preparation Kit was used to construct libraries and quality control was checked by Agilent 2100 Bioanalyzer System. Clean reads after filtering the raw reads were mapped to the “Darmor-bzh” reference genome (https://www.genoscope.cns.fr/brassicanapus) using HISAT2 software  of two extremely SW accessions R01 (large seed) and R56  for RNA-seq at two weeks after pollination (2 WAP), three weeks after pollination (3 WAP), and four weeks after pollination (4 WAP). Illumina’s NEBNextsoftware . Gene exsoftware . Differesoftware . Differesoftware .®Q RT SuperMix . Data collection was performed in QuantStudio™ real-time PCR software . All the primers are listed in BnACTIN (BnaA03g55890D) and relative expression levels were calculated using a 2-ΔΔCT analysis method . Briefly, 1μg of total RNA was used for RNA-seq and cDNA synthesis was performed using HiScripts method .Phenotypic values for eight yield traits of rapeseed in three environments, including PH, FT, BN, SI, SN, SP, SW, and YP were used to determine whether significant phenotypic differences existed in these traits Figure 1To uncover the relationships of the different yield traits, Pearson correlation coefficient (PCC) was used to assess correlations between pairs of traits in the eight yield-related traits Figure 1A total of 908 QTNs for eight yield traits were identified using at least two of the six ML-GWAS methods, namely FASTmrEMMA, FASTmrMLM, ISIS EM-BLASSO, mrMLM, pKWmEB, and pLARmEB , followed by FT (1.78 ~ 16.40). The number of these QTNs varied considerably in the A and C subgenomes, 23 and 44 respectively, and were more numerous on chromosomes C03, C08, and C09, with 10, 7, and 8, respectively.In order to obtain reliable results, we further analyzed QTNs shared by at least two models in different environments within the 1 Mb region. A total of 75 significant stable QTNs (or QTN clusters) controlling eight yield-related traits were obtained Table 1.Forty QTNs shared by ML-GWAS and SL-GWAS within the 1 Mb region were found to associate with the eight yield traits, with the highest number of QTNs associated with SW (10) and the lowest with SI (2) . Among tSince SW is the important component of yield traits, and is relatively stable in different environments in this study, we further analyzed the QTNs associated with SW. A total of 21 significant QTNs were identified simultaneously in at least 2 environments as well as in three models Table 2.BnaA09g39950D may increase seed weight.To identify the favorable alleles of QTNs for the eight yield traits in rapeseed, we analyzed the significant phenotypic differences between the elite and alternative alleles of 21 QTNs , which is involved in maintaining the embryonic hormone gradient, and also involved in shoot and root development. The genes BnaA07g30180D (SAUR protein), BnaA09g39680D (AUX/IAA protein), BnaA09g40340D  and BnaC03g46450D (SAUR protein) have all been implicated in the regulation of plant growth , BnaA09g39790D (RNA helicase), and BnaA09g39950D (Lipase) were identified to associate with SW   . We foun= 20.56) Table S6BnaC09g25980D (SWEET7) is a candidate gene for SP, which is extremely highly expressed in R56 plants and lowly expressed in R01  was more highly expressed in R01, and expression levels increased progressively with developmental time  and gibberellin (GA), cyclin-related genes, and TFs in the 2572 DEGs , BnaA09g39790D (RNA helicase), and BnaA09g39950D (Lipase) were identified to affect seed size  genes have been identified to associate with SW or YP and the favorable haplotype of BnNPC6.C01 could increase seed oil content and seed yield (Arabidopsis and B. napus (via the phloem to developing seeds during seed filling (BnaC09g25980D (SWEET7) was validated to be highly expressed in R56  was highly expressed in R56, which may affect the seed size  and JAZ 9 (BnaA07g28810D) were up-regulated in R01, while another candidate gene JAZ10 (BnaC09g43860D) was highly expressed in R56  were up-regulated in R56 (BnaC09g43890D (NAC083) was validated highly expressed in R01  signaling . In thisongation . In prevB. napus . In our B. napus Table S6pression . A numbed weight . In thisd in R56 . In addie/weight . And VvNrapevine . Therefovia a combinatory approach of ML-GWAS methods to facilitate the detection of yield-related QTNs in rapeseed. These findings will provide valuable information for understanding the mechanism underlying seed yield and yield-related traits and accelerate the crop improvement of rapeseed.In this study, a total of 908 QTNs were detected for eight yield traits using two or more ML-GWAS methods. Of them, 75 stable QTNs (or QTN clusters) controlling yield traits were obtained with a significant QTN cluster on chromosome A09 for SW, which was also identified by SL-GWAS. Twenty elite rapeseed accessions had a diverse distribution of superior alleles, and the high-yielding accessions contained more superior alleles. Integrated ML-GWAS with transcriptome analysis, 79 candidate genes were found to associate with SW or SP. Some genes related to plant hormones such as auxin, JA, and GA, were involved in the regulation of rapeseed yield. Thus, many robust QTLs with candidate genes were identified to regulate seed size and yield traits in rapeseed. This study made a beneficial attempt The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found in the article/JH and SL designed and supervised the research. SL, HZ, JH, YL and CD performed multi-locus GWAS and bioinformatics analysis. CZ, RG, RZ, JD and JH performed the experiments and data analysis. CZ, RZ, JH and HZ wrote and revised the manuscript. All authors contributed to the article and approved the submitted version.


The identified MTAs and rice lines having high SVI traits , high yield under aerobic , irrigated conditions , robust root traits like root length , root volume  can be further employed in breeding programs for the targeted environments aimed at improving seedling vigour, yield-related traits under irrigated condition, aerobic condition as adaptability to water-saving technology.The development of nutrient-use efficient rice lines is a priority amidst the changing climate and depleting resources viz., water, land, and labor for achieving sustainability in rice cultivation. Along with the traditional transplanted irrigated system of cultivation, the dry direct-seeded aerobic system is gaining ground nationwide. The root-related traits play a crucial role in nutrient acquisition, adaptation and need to be concentrated along with the yield-attributing traits. We phenotyped an association panel of 118 rice lines for seedling vigour index (SVI) traits at 14 and 21 days after sowing (DAS), root-related traits at panicle initiation (PI) stage in polythene bags under controlled aerobic condition, yield and yield-related traits under the irrigated condition at ICAR-IIRR, Hyderabad, Telangana; irrigated and aerobic conditions at ARS, Dhadesugur, Raichur, Karnataka. The panel was genotyped using simple sequence repeats (SSR) markers and genome-wide association studies were conducted for identifying marker–trait associations (MTAs). Significant correlations were recorded for root length, root dry weight with SVI, root volume at the PI stage, number of productive tillers per plant, spikelet fertility, the total number of grains per panicle with grain yield per plant under irrigated conditions, and the total number of grains per panicle with grain yield per plant under aerobic condition. The panel was divided into three sub-groups (K = 3) and correlated with the principal component analysis. The maximum number of MTAs were found on chromosomes 2, 3, and 12 with considerable phenotypic variability. Consistent MTAs were recorded for SVI traits at 14 and 21 DAS , yield traits under irrigated conditions  across years at ICAR-IIRR, grain yield per plant  under the aerobic condition, grain yield per plant at irrigated ICAR-IIRR and SVI (RM5501), root traits at PI stage . Functionally relevant genes near the MTAs through  The dry-direct seeded aerobic system of rice cultivation has been identified as an alternative system to the traditional transplanted irrigated system of rice cultivation  and dry season (Rabi).Association mapping (AM) also known as linkage disequilibrium (LD) mapping is a rapid approach for the identification of quantitative trait loci (QTL), genes/alleles associated with agronomically economic traits. The LD is defined as non-random association of alleles at two or more different loci. This mapping is based on historic recombination events and LD by the strength of the correlation between a trait and a marker in natural populations or panels with diverse lines to identify marker–trait associations (MTAs) . It has 22.1tropical japonica accessions, Oryza glaberrima accessions. This panel was formed based on the genetic diversity among the lines and, prior information on yield-related traits and will be hereafter referred to as an association panel (AP). These lines were collected from the breeders of ICAR-Indian Institute of Rice Research (IIRR), Hyderabad  mutants of BPT-5204, and Nagina 22 (N22), wild introgression lines, 2.2Experiment 1: Evaluation of rice association panel for root-related traits in polyhouse under aerobic conditiona) At the seedling stage for seedling vigour traits (SVI_P)th, 21st DAS), to record seedling vigour traits viz., germination per cent (G %), shoot length (SL), root length (RL), total seedling length (TSL). The SL, RL, TSL were recorded manually using a centimeter scale. The shoot fresh weight (SFW), root fresh weight (RFW), total fresh weight (TFW), shoot dry weight (SDW), root dry weight (RDW), and total dry weight (TDW) were recorded using an electronic balance . The root to shoot length ratio (RSLR), root to shoot fresh weight and dry weight ratios (RSFWR and RSDWR) were derivative parameters calculated by division. The root surface area (RSA), root average diameter (RAD), root length per volume (RLPV) and root volume (RV) were recorded using WinRHIZO Pro software (version 4) (Phenotyping of seedling vigour traits at 14 and 21 days after sowing (DAS) was carried out in polyhouse under aerobic condition at ICAR-IIRR Hyderabad for two years 2018 and 2019 (rsion 4) . The Seeb) At the panicle initiation (PI) stage for root architecture traits (Root_PI)version 4)   (Supplemrsion 4) .Experiment 2Field evaluation under the irrigated condition at ICAR-IIRR, Rajendranagar Hyderabad for yield and yield-related traits (Irri_RJN))The seeds of the association panel were grown under irrigated conditions during the wet season 2019 and 2020 and dry season 2020 at ICAR-IIRR, Rajendranagar, Hyderabad. The experiment was laid out in Augmented Randomized Complete Block Design (RCBD) wherein, each block comprised of 23 rice lines along with checks  under irrigated conditions. The seeds were sown on the nursery beds and 30 days after sowing, the plants were transplanted under irrigated conditions Irrigated, DhadesugurThe rice association panel was evaluated for yield and yield-related traits under irrigated and aerobic conditions in the wet season 2020 at the Agricultural Research Station (ARS), Dhadesugur, University of Agricultural Sciences, Raichur. The irrigated field design and maintenance were similar to experiment 2 with a recommended package of practices.Aerobic, DhadesugurFor the aerobic condition, the experiment was laid out in Augmented Randomized Complete Block Design with five blocks; each block consisting of 30 diverse rice lines along with checks . The seeds were dry directly sown (each line was sown in two rows of two-meter length at a spacing of 20 cm x 15 cm) and 15 days after sowing extra seedlings were thinned manually and a single plant per hill was maintained . The tra2.3version 4.0.2) (https://cloud.r-project.org/package=augmented RCBD) using the R script. This package also provided histograms and box plots for each trait. Correlation analysis and correlation plots were plotted using past3 V 3.22 (https://past.en.lo4d.com/windows).The augmented analysis of variance (ANOVA) for yield-related traits and completely randomized design (CRD) ANOVA for root-related traits, estimation of the genotypic coefficient of variability, phenotypic coefficient of variability, broad-sense heritability and genetic advance as per cent mean were executed in R Studio (2.4Genomic DNA was isolated from the leaves at 21 days old seedlings using the CTAB method of the association panel . The quahttps://darwin.cirad.frunweightedeighted) Neighbor-joining (NJ) tree was constructed based on a dissimilarity matrix for a distance-based approach. The principal component analysis (PCA) bi-plot was generated based on the principal components and Eigen values in DARwin. The polymorphic information content (PIC) of each marker was calculated  for seedling vigour traits at 14 and 21 DAS under polyhouse conditions, for root traits at PI stage, yield and yield-related traits under aerobic and irrigated conditions. The allelic data of the polymorphic SSR markers along with the phenotyping data were used as input in the TASSEL 4. The statistical models mixed linear model (MLM) that considers the kinship K and population structure Q (K+Q) and generalized linear model (GLM) were used for assessing the marker-trait associations. The corresponding p-values were corrected based on the marker F test; a false discovery rate (FDR) of 0.05 was selected as a threshold for significant associations, according to 2 value of >0.1. The corresponding markers pair-wise LD plots were plotted. The Manhattan plots were plotted for phenotypic traits based on the negative log value of p. The rooted tree diagram was plotted based on the genetic distance PCA in TASSEL 4 function. The markers having significant associations with the traits under both MLM and GLM were considered. A stringent criterion was followed for filtering the significant MTAs (R2>0.1 and p<0.05) by considering only the markers having significant association with more than two traits in all the data using Microsoft excel.Association between the recorded phenotypic traits and SSR-derived genotypic data was carried out using TASSEL 4 (2.7http://rice.plantbiology.msu.edu/cgi-bin/gbrowse/rice/#search). The genes were selected and thoroughly checked for their function, expression using the locus search and gene information available at the Rice Annotation Project Database (RAP-DB) (https://rapdb.dna.affrc.go.jp/) and Rice Genome Annotation Project (RGAP) (http://rice.plantbiology.msu.edu/cgi-bin/) data putative functions and gene annotation assignments (GO assignments). In depth in silico analysis of the genes associated with the marker was executed using the available expression databases viz., Rice Expression Database (RED) IC4R (http://expression.ic4r.org/), RiceXpro (https://ricexpro.dna.affrc.go.jp/), RGI Rice Gene Index (https://riceome.hzau.edu.cn), NetREx Network-based Rice Expression Analysis (https://bioinf.iiit.ac.in/netrex/index.html). The expression of the genes was checked in the specific databases based on the respective database’s specifications, tissues, experimental conditions, etc. The expression of genes was recorded specifically in the roots, and panicles at the seedling and reproductive stage according to the available information in the database. A set of specific genes expressed in the roots and panicles were further considered and an apparent score was given to each gene on the basis of the expression values in all the databases. The scores were represented as a heat map using Microsoft Excel.The significantly linked SSR markers associated with more than two phenotypic traits were selected for mining the nearby genes in the 1Mb spanning region using MSU v.7 rice genome browser (33.1At the seedling stage for seedling vigour traits (SVI_P)Analysis of variance for SVI traits viz., G (%), SL, RL, TSL, SFW, RFW, TFW, SDW, RDW, TDW, SRLR, RSFWR, RSDWR, RAD, RLPV, SVI-I, SVI-II showed significant variation except for the traits RSA, RV at 14 DAS during 2018 and G (%) at 14 DAS during 2019 respectively (At the panicle initiation stage for root architecture traits3) showed the highest GCV and PCV coupled with high heritability and high GAM, followed by RAD with the range 1.05 to 15.40 mm  exhibited genetic variations of 2% among the populations and 98% among individuals of the population  of −13,265.40, as per the Evano table output was obtained in Structure harvester (3.62>0.1 with p<0.05) were detected when analyzed by both GLM and MLM, whereas 78 significant MTAs were detected when analyzed only in MLM, in all seedling traits, root- related traits, yield and yield related traits. For SVI with 19 seedling vigour traits at 14 and 21 DAS R2 and p-values are given in 2 (0.336), with the corresponding p-value of 2.83E-07 followed by RM80 with RSA  and RM22961 with SL  at 14 DAS. At 21DAS, RM25310 associated with TDW exhibited the highest R2 (0.224) and p (0.010), followed by RM25310 with SDW  and RM13962 with RL . Three common significant MTAs were observed viz. RM22961 with SL and TSL, RM28157 with RLPV and RM1385 with SL consistently at both 14 and 21 DAS during 2018 and 2019.A total of 59 common significant marker–trait associations (MTAs) ,  for the years 2019 and 2020 respectively, followed by PL with the R2 = 0.177 and p = 0.009, the markers RM13962 associated with PH and TNG also showed high R2 values 0.167 and 0.157, p-values of 0.025 and 0.038 respectively.The associations of molecular markers with yield and yield-related traits in rice under irrigated conditions at ICAR-IIRR , RM18472  and RM2584  respectively. The association of molecular markers with yield and yield-related traits in rice under aerobic conditions at Dhadesugur is given in 2 = 0.101, 0.128 and p-value = 0.042, 0.025 respectively), RM4455 with PL  and RM3188 with SF . The marker RM1146 showed the highest R2 value of (0.128) with GYP. The Q-Q plot, Manhattan plot and LD plots obtained from TASSEL 4 also confirmed the significant association of markers with the traits. The Q-Q plot distribution depicted that the data is symmetric and the distributions of p-values according to the traits were normally distributed and also considered the type of error (Type I and II) in deciphering the MTAs.The association of molecular markers with yield and yield-related traits in rice under irrigated conditions at Dhadesugur  after drought induction. The gene, LOC_Os01g61044 encoding the amino acid transporter has been associated with the number of spikelets per panicle under direct seeding (in silico databases showed upregulation of the gene in root under abiotic stress. The pumilio-family RNA binding repeat-containing protein (RM18472(5_16.64), SFW, TFW_14SVI_P, SF_Irri_DSG), OsSCP42 serine carboxypeptidase (RM410(9_18), RL_Root_PI, TNG, GYP_Irri_RJN), patatin (RM1015(12_22)  have been reported to be upregulated upon ABA treatment, drought, cold, and osmotic stresses. These genes are associated with the root traits at seedling and reproductive stages and can be further explored for gene expression in roots. The amino acid transporter (GYP_Irri_RJN) has been recorded to be expressed in roots, panicle tissues, and upon induction of abiotic stresses. The OsWD40-37 WD domain-containing protein (RM3188(2_3.45)) is proposed to be a promising candidate for further studies related to yield under aerobic conditions.The marker RM5501(1_35) had six functionally significant genes encoding,  seeding . This ge42hbs) was divided into three categories: high (above 60%), medium (30%–60%), and low (less than 10%). . . GAM is an 10%). . Estimatan 10%). . Broad san 10%). . High GCan 10%). . The narBreeding for seedling vigour has been a major breeding target in rice and other crops under DSR . RelativBased on our findings, the lines viz., Langphou, Mouli, TI-128, JBB-631-1, Ratnachudi and Tellahamsa showed promising performance for seedling vigour traits. Lines namely, NPK-45, Moirangphou-Angouba, JBB-661, Wangoo-Phou, GNV-1109, NPK-13 and Dissi showed promising performance for root-related traits. Similarly, lines viz., KR-209, Pat-Phou, JBB-631-1, SM-363, Wangoo-Phou, PB-3 and MTU1010 showed promising performance for yield and yield-related traits under irrigated conditions. The lines Phouren, Ratnamudi, NPK-43, TI-112, TI-87, JBB-631-1 and JBB-684 showed promising performance for yield traits under aerobic conditions. From the overall field experiments considering all the environments and all the locations the lines Langphou, KR-209, JBB-631-1, Akut-Phou, TI-36, GNV-14-96-1 and NPK-43 exhibited consistent performance for yield and yield-related traits like GYP, TW, SF and NPP over the checks.Genetic diversity is the key determinant of germplasm utilization in crop improvement. Population with a high level of genetic variation is a valuable resource for broadening the genetic base in any breeding program. The lines used in this study should have a complex breeding history, from diverse genetic backgrounds . In this2 of >0.1 and p-value < 0.05) with more than two phenotypic traits were selected for searching the nearby genes in 1Mb spanning region. The genes identified were consistent with the associated phenotypes. Among the significant MTAs, six hypervariable markers viz., RM1385, RM18472, RM18939, RM22961, RM25310 and RM28157 on the chromosome numbers 2, 5, 5, 8, 10 and 12 respectively were found to be novel for the identified genes. Our results correlate with earlier report by LOC_Os03g08880 and LOC_Os06g13060) were linked to maximum root length and two were related to total root weight. The marker RM22961 associated with traits TSL and SL at the seedling stage at 14 and 21 DAS and also associated with TPL and SL at the PI stage and with grain yield per plant under aerobic conditions. in-silico analysis identified abiotic stress-related genes viz., NAM, LEA, MADS, NAC, bZIP, WRKY, RING finger, spanning the nearby regions of the markers implying high co-relation of the marker with the root and yield traits contributing to aerobic adaptation, whereas OsbHLH120 for root thickness, OsNAC10 for root thickness and drought tolerance, OsPHR3 for LR development, PIP1;3/RWC3 for root length and water stress avoidance, OsMADS18 for root elongation, and OsNLA1 for root length and growth through transcriptome study. NECKLEAF1 (nl1) associated with NSPexp1. OsMADS6-5 was present within the LD block of q-25 which controls the floral organ identity and flowering time. Further linked markers can be utilized for aerobic breeding programs for the selection of SVI, root yield and yield-related traits under aerobic and irrigated conditions. The shortlisted promising candidates genes associated with the yield and root-related traits can be further analysed for quantitative gene expression and functional cloning.The mutant lines, and introgression lines identified for yield (based on earlier reports) were selected for exploring the traits desirable for the aerobic system of cultivation, those lines also had desirable traits as well as co-relation with yield. The marker–trait associations reveal that robust MTAs identified could serve as a valuable resource for enhancing seedling vigour, root traits and yield-related traits indicating their feasibility to use in the marker-assisted breeding programme. We considered majorly the associations identified by the MLM over the associations identified by the GLM . The MLM5The present study is novel and the first of its kind in India wherein the association panel has been studied concomitantly for seedling vigour, root traits, as well as yield and yield-related traits under aerobic conditions. The conglomeration of these traits at the seedling stage, panicle stage as well as reproductive stages in different environments have given key insights on the association of SSR markers with highly variable and correlated phenotypic traits and the identification of novel MTAs and regions. Consistent MTAs were identified for RM25310 (GP and TDW), RM2584 (GP), RM14753 and RM80 (RFW), RM22961 , RM18472 , RM1385 , RM25310 , RM80 , RM22961 , RM1385 , RM410 (GYP), RM20698 (PH), RM2584 (SF), RM5179 (TNG), RM2584 (SW and GYP) under aerobic conditions. Rice lines having better early seedling vigour, robust root traits, yield and yield-related traits can be utilized for improving early seedling vigour, root, yield and yield related traits in breeding programmes as a pre-breeding material and donor lines for the aerobic system of rice cultivation. The stable introgression lines and mutant lines identified for robust root traits, and can be proposed for further evaluation in the multi-location rice trials of All India Coordinated Research Project on Rice (AICRPR) trials. The novel marker traits associations identified in this study can be validated in mapping populations to deploy in the marker-assisted breeding programs. Identification of candidate genes in the MTA region needs to be validated using gene expression studies and can be functionally validated through over-expression or new breeding technologies like gene. The association panel used in this study can be a basis for haplotype breeding for developing climate-resilient rice lines. The development of high yield potential, seedling vigor lines suitable for the aerobic system of cultivation is a need of the hour and will be in line with the government policy to double farmer’s income and livelihood with low input costs and maximum yield.The original contributions presented in this study are included in the article/The study was conceptualized and planned by KB; phenotyping of the panel was executed by RP, H, NM, AP; phenotypic and genotypic data analysis were done by RP, MB, DB, KB, GC, AS, YR, PS, JD; supervision and critical editing were done by KB, MM, LR, DS and RS. All authors contributed to the article and approved the submitted version.


M, of underlying loci tends to infinity. As in the additive case, the multivariate normal distribution of trait values across the pedigree can be expressed in terms of variance components in an ancestral population and probabilities of identity by descent determined by the pedigree. Now, with just first-order dominance effects, we require two-, three-, and four-way identities. We also show that, even if we condition on parental trait values, the “shared” and “residual” components of trait values within each family will be asymptotically normally distributed as the number of loci tends to infinity, with an error of order The classical infinitesimal model is a simple and robust model for the inheritance of quantitative traits. In this model, a quantitative trait is expressed as the sum of a genetic and an environmental component, and the genetic component of offspring traits within a family follows a normal distribution around the average of the parents’ trait values, and has a variance that is independent of the parental traits. In previous work, we showed that when trait values are determined by the sum of a large number of additive Mendelian factors, each of small effect, one can justify the infinitesimal model as a limit of Mendelian inheritance. In this paper, we show that this result extends to include dominance. We define the model in terms of classical quantities of quantitative genetics, before justifying it as a limit of Mendelian inheritance as the number,  The classical infinitesimal model is a simple and robust model for the inheritance of quantitative traits. In previous work, Barton, Etheridge, and Véber showed that—when trait values are determined by the sum of a large number of Mendelian factors, each of small effect—one can justify the infinitesimal model as limit of Mendelian inheritance. Here, the authors extend these results to include a nonlinear dominance effect. In the classical infinitesimal model, a quantitative trait is expressed as the sum of a genetic and a nongenetic  component, and the genetic component of offspring traits within a family follows a normal distribution around the average of the parents’ trait values, and has a variance that is independent of the trait values of the parents. With inbreeding, the variance decreases in proportion to relatedness. When trait values are determined by the sum of a large number of Mendelian factors, each of small effect, as we show in across the population can be far from normal; the infinitesimal model as we define it only asserts that the within-family distributions of the genetic component of the trait are Gaussian, with a variance–covariance matrix that is determined entirely by that in an ancestral population and the probabilities of identity determined by the pedigree. Moreover, as a result of the multivariate normality, conditioning on some of the trait values within that pedigree has predictable effects on the mean and variance within and between families. In other words, knowing the trait values for some individuals in the population does not distort the multivariate normality of the distribution of the unobserved traits, and the mean and covariances of these traits may be derived explicitly .We emphasize that as a result of selection, population structure, and so on, the trait distribution In this paper, we show that this extraordinary robustness of the infinitesimal model extends to include dominance. The distribution of the genetic part of the trait will once again be a multivariate normal distribution whose mean and variance is expressed in terms of the variance components in an ancestral population and probabilities of identity by descent determined by the pedigree, but now, with just first-order dominance effects, the identities required will involve up to four genes. As with the case of epistasis, the mean is not a simple function of the trait values in the parents, and there is nontrivial covariance between families. One can think of the genetic component of the trait values within a family as consisting of two parts. Both are normally distributed. In the additive case, the first reduces to the mean of the trait values of the parents; with dominance it will be random , but the same for all individuals in the family. What is at first sight surprising is that even if we condition on knowing the trait values of the parents, this shared quantity is normally distributed. Assuming there is no mutation to ease the presentation  We now define the infinitesimal model in terms of classical quantities of quantitative genetics that can be expressed in terms of expectations in the ancestral population and identities determined by the pedigree. We use the notation of To simplify notation, we shall use 1 and 2 in place of andi and j, respectively,In this expression, the term proportional to Equation . The comi and j in the identities refer to the individuals themselves, not their parents; for example, the expression i and one sampled at random from individual j. We reserve letters for individuals in the current generation, and numbers for their parents.Note that, in contrast to our expression for the variance of If we combine the components Here again, the term proportional to andi. We see how to recover this term in Remark For a single individual, its trait value can only depend on the two alleles that it carries at each locus, so it is no surprise that this expression depends only on pairwise identities between those two genes. We remark that Equation  differs We emphasize again that our partition of the trait values into a contribution that is shared by all individuals in a family and residuals differs from the conventional split into an additive part and a dominance deviation. The additive part of the trait is andRemark 2Notice that the purely additive case can be simply recovered by taking Under the infinitesimal model, the trait values of individuals across the pedigree are given by a multivariate normal. Therefore, standard results on conditioning multivariate normal random vectors on their marginal values, which for ease of reference we record in Just as in the classical infinitesimal model, the mean and variance of the residuals quations –27)]. F]. FRAi+Rwith a corresponding definition for with andAi+Di is Although in the presence of dominance the expressions  and 18)18) are rIn this section, we present numerical examples to illustrate the accuracy of the predictions of the infinitesimal model, again disregarding the environmental component of the trait.t is close to We first generated a pedigree for a population of constant size of Z, which depends on H; that is, the probability that the effects across the three genotypes at locus l is We define a trait, In the ancestral population, the allele frequencies were generated to mimic neutral allele frequencies with very low mutation rates, but conditioned to segregate at each locus. Thus, allele frequencies at every locus were sampled independently and according to a distribution with density proportional to Variance components are defined with respect to this reference set of allele frequencies. For the population generated for the examples presented here, these values were A and D and then in each generation we calculate the mean and variance of these quantities across the 30 individuals in the population. This is only intended to give some feeling for the ways in which the components fluctuate through time. Of course the infinitesimal model is only providing a prediction for the distribution of trait values within families; a single realization will see substantial contributions to trait values from linkage disequilibrium  variance of the shared component, and for this we shall see that we need to control the build up of linkage disequilibrium between pairs of loci. It will turn out that since all pairs of loci are in linkage equilibrium in the ancestral population, any This does not mean that the linkage disequilibria do not affect the trait values, but because of the very many different combinations of alleles in an individual that are consistent with a given trait, observing the trait tells us very little about the allelic state at a particular locus. The allele at that locus can only ever contribute As the population evolves, and we are able to observe more and more traits on the pedigree, we gain more and more information about the allele that an individual carries at a particular locus. In Our derivations will depend on two approaches to proving asymptotic normality. The first, which we apply to the portion observed traits; i.e. traits distorted by a small environmental noise, c.f. Remark If the environmental component is taken to be normally distributed, then exactly as in l on the two chromosomes drawn from the ancestral population will be denoted Recall that we assume that in generation zero, the individuals that found the pedigree are unrelated and sampled from an ancestral population in which all loci are assumed to be in linkage equilibrium. The allelic states at locus l, the conditional expectationand observing that the second and third terms on the right-hand side are functions of As a consequence, partitioning over the possible values of With this modification of Moreover, still without loss of generality, by absorbing the mean into In this notation, the genetic component of the trait of an individual in the ancestral population (which we denote by and by Equations  and 23)23), we hl. We also assume that all the quantities in the top part of We assume that the scaled allelic effects i in our pedigree, each of which contributes exactly one gene at each locus in a given offspring. Mendelian inheritance translates into the property that the gene passed on by parent i as being labeled 1 and 2, according to whether they are inherited from l in parent l in individual i. Thus, l in individual i is inherited from gene 1 in l in individual i is inherited from gene 1 in We now need some notation for Mendelian inheritance. Recall that i in generation t is given byIn this notation, the trait of individual whereandThe terms The sums +25) and andAi anThe sums +27) com comAi ant . Our main result extends this to include dominance, at least under the assumption that the ancestral population was in linkage equilibrium.In t and some collection of the observed trait values of individuals in that pedigree up to generation With dominance, the expression for the distribution of the mean and variance–covariance matrix of the multivariate normal i and the pedigree, the components We will focus on proving that conditional on knowing just the trait values of the parents of individual The extra challenge compared to the additive case is that, in contrast to the part Recall that the trait values that we observe, and therefore on which we condition, are the sum of a genetic component and an independent environmental component; that is, the observed trait value iswhere, for convenience, the t, t. A simple application of the Central Limit Theorem gives thatWe write is asymptotically distributed as a multivariate normal random variable as for suitable constants quations , 10), a, aC,C~ . Since Mendelian inheritance ensures that  the allelic states at different loci are independent, this is a straightforward application of a generalized Central Limit Theorem . Just as in Our first task will be to show that conditional on the pedigree, the distribution of the trait values in generation The same Central Limit Theorem guarantees that the joint distribution of To verify that the conditional distribution is asymptotically normal, we shall show that observing the trait value of an individual provides very little information about their allelic state at any particular locus, or any particular pair of loci, and consequently conditioning on parental trait values provides very little information about allelic states in their offspring. This is  achieved through an application of Bayes’ rule, although some care is needed to control the cumulative error across loci. We use this to calculate the first and second moments of Of course checking that the first two moments of the conditional distribution of t. Just as in the additive case, this can be extended to conditioning on any combination of traits in the pedigree up to generation t to destroy the asymptotic normality of its trait value. This is justified in i from looking at the trait value of one its relatives, is proportional to the probability of identity with that individual as dictated by the pedigree.We only present our results in the case in which we condition on the parental traits of a single individual in generation We first illustrate the application of the generalized Central Limit Theorem by showing that in the ancestral population, the distribution of To prove this, it is enough to show that for any choice of where nce σA2+σ∑j=1N0βj2jth individual in generation zero. Set B, so that the sum of the scaled effects at each locus is bounded by l. Moreover, since the individuals that found the pedigree are assumed to be unrelated and sampled from an ancestral population in which all loci are in linkage equilibrium, using Equations (and we abuse notation by writing quations  and 23)Ψlj for tTheorem Here, C. In particular, taking for a suitable constant t converges to that of a multivariate normal, with mean vector Exactly the same argument shows that the distribution of quations  and 11), there can be an arbitrary distortion away from Gaussian Our work provides some mathematical justification for the ubiquity of the Gaussian, and the empirical success of quantitative genetics—a success which is remarkable, given the complex interactions that underlie most traits. The limit is not universal: a nonlinear transformation of a Gaussian trait leads to a non-Gaussian distribution, and failure of the infinitesimal model. This is because epistatic and dominance interactions then have a systematic direction, which violates the terms of the Central Limit Theorem. (Recall that in our toy example in the section on modeling Mendelian inheritance, we needed a “balance” in the dominance component, which we see reflected in our main results in the requirement that he trait .If traits truly evolve in this infinitesimal regime, then it will be impossible to find any genomic trace of their response to selection. This extreme view is contradicted by finding an excess of “signatures” of selection in candidate genes, though it might nevertheless be that these signals are generated by alleles with modest In principle, we can simulate the infinitesimal model exactly, by generating offspring from the appropriate Gaussian distributions. For the additive case, this is straightforward, since we only need follow the breeding value of each individual, and the matrix of relationships amongst individuals e.g. , 2018. HWe have not set out the extension of the infinitesimal model to structured populations in detail. In principle, this just requires that we track the identities within and between the various classes of individual. One motivation for the present theoretical work was to extend our infinitesimal model of “evolutionary rescue”  to incluOne of the most obviously unreasonable assumptions of the classical infinitesimal model, and the extension described here, is that there are an infinite number of unlinked loci. The main value of the infinitesimal model may be to show that trait evolution depends on only a few macroscopic parameters; even if we still make explicit multilocus simulations, this focuses attention on those key parameters, and gives confidence in the generality of our results. Quantitative genetics has developed quite separately from population genetics. Although the theoretical synthesis half a century ago  stimulat


No significant genetic correlations or causal relationships with BAG were found for Parkinson’s disease, major depressive disorder, or schizophrenia, but two-sample Mendelian randomization indicated a causal influence of AD (p = 7.9 × 10−4) and bipolar disorder (p = 1.35 × 10−2) on BAG. These results emphasize the polygenic architecture of brain age and provide insights into the causal relationship between selected neurological and neuropsychiatric disorders and BAG.The difference between chronological age and the apparent age of the brain estimated from brain imaging data—the brain age gap (BAG)—is widely considered a general indicator of brain health. Converging evidence supports that BAG is sensitive to an array of genetic and nongenetic traits and diseases, yet few studies have examined the genetic architecture and its corresponding causal relationships with common brain disorders. Here, we estimate BAG using state-of-the-art neural networks trained on brain scans from 53,542 individuals (age range 3–95 years). A genome-wide association analysis across 28,104 individuals (40–84 years) from the UK Biobank revealed eight independent genomic regions significantly associated with BAG ( Over the last decade, brain age has emerged as a promising measure of overall brain health , 2. To eKCNK2, and one in the chromosome 17 inversion region (17q21.31) [Genetic differences have been shown to explain a sizeable portion of interindividual variation in BAG. Twin-based heritability for BAG has been estimated to be as high as 0.66 , and sin7q21.31) , 19. Gen7q21.31) . These r7q21.31)  found a Although BAG has been frequently associated with clinical conditions and health-related phenotypes and behaviors, the underlying genetic basis for the observed associations has seldom been investigated, possibly due to incomplete knowledge of the genetic architecture of the former. Furthermore, the causal relationships between BAG and brain disorders remain untapped. Mendelian randomization (MR) has become an attractive tool to interrogate cause-effect relationships between risk factors and disorders . Two-samIn the present work, we improve the yield of genetic associations for BAG using three strategies: First, we estimate brain age using a state-of-the-art deep neural network architecture (SFCN-reg) trained on one of the largest samples assembled to date . Then weAll datasets used in the present study have been obtained from previously published studies that have been approved by their respective institutional review boards, research ethic committees, or other relevant ethic organizations.We used UK Biobank imaging data  released in 2019 in combination with a pre-compiled dataset from various sources  and minor allele frequency . In total, ≈8.6 million SNPs were analyzed. Since we have observed apparent differences in predicted brain age across folds . We exc–clump-p 5e-8 –clump-2 1e-6 –clump-r2 0.1. The standard 250 kilo-bases (kb) were used as the inter-region distance threshold. Genes whose genomic coordinates located within the boundaries of each region were assigned to the corresponding region. SNPs with the smallest association p values were taken as the lead SNPs for the corresponding regions. In addition, the gene that is closest to each lead SNP by genomic position was annotated using the Ensembl tool VEP [Association results were ‘clumped’ by the FUMA  web-servtool VEP  . For each GWAS, the association results for European ancestral samples excluding samples from 23andMe were used . The PD GWAS results were obtained from the fixed-effect meta-analysis performed by the International Parkinson Disease Genomics Consortium  [GWAS summary data for four disorders  .Before post-GWAS analysis we processed the results from all GWAS using a standard protocol. Specifically, SNPs having a MAF < 0.05, or imputation INFO < 0.5, or ambiguous allelic coding  were removed from subsequent analyses. The LD score model (ldsc)  was applP values) for BAG were stratified by the corresponding association strength for the conditioned disorder. As the association strength to the conditioned disorder increases, a successive leftward deflation in these curves indicates polygenic enrichment. Similarly, conditional QQ for each disorder versus BAG shows polygenic enrichment in the reverse direction.To visualize polygenic enrichment, conditional QQ plots , 43 werep < 5×10−8) to the exposure traits or disorders were used as potential instruments. The PLINK program and the LD structure of 1KGp3 dataset were used to select instruments with the following parameters, --clump-kb 500 kb, --clump-p1 5×10−8, and --clump-r2 0.01. The TwoSampleMR package [To study the cause-effect relations between BAG and the five disorders, two sets of MR analyses were performed. The first set, using standard models, included the inverse-variance weighted model (IVW) , weighte package  was usedp < 10-3) with exposure to increase statistical power without incurring weak instrument bias in estimation. Although both models control for horizontal pleiotropy, CAUSE directly tests for a shared  versus a causal model for each relation [-3 was taken as the cut-off for selecting instruments, i.e., –clump-p1 10-3.The second set of models included the robust adjusted profile score (RAPS)  and the relation . The samP < 0.05) was such a relation considered causal.As each of the six MR models has different assumptions that are difficult to verify in real data, a majority vote ensemble scheme was used to make conclusions for the existence of cause-effect relations: specifically, only when four or more models indicated a cause-effect relation , for AD diagnosed in a Japanese sample [In addition to applying multiple MR models, GWAS results for height measured for European samples   in each of the five disjoint folds were consistently below 2.5 years . The locus containing the RUNX2 gene , which showed suggestive significance in Jonsson et al. [RUNX2 gene codes for a master transcription factor which plays a critical role in skeletal development [BHMT2, Fig. CAMK2N2 and INPP5A) and metabolism and transcription regulation , both processes are implicated in biological ageing [We identified eight independent genomic loci significantly associated with BAG Fig. . Associareported , 19, altn et al. , was genelopment . Among tl ageing . In SuppMAPT, GFAP, and the Homeobox protein gene NKX6-2. These results suggest that BAG encodes coordinated physiological processes implicating both the brain and the peripheral systems.We further annotated these identified SNPs to nearby genes and regulatory elements (Methods). Most of the associated SNPs are in noncoding regions such as intergenic, intron or untranslated regions , indicating that the true causal variants may be some untyped rare ones not investigated in this study. The clearest signal comes from the regions on chromosome 3 and 5, where the PPIs for the lead SNPs were much larger than that for the second most probable causal SNPs.To nominate causal variants in each locus we performed statistical fine-mapping  for regip < 1.3 × 10−4; Supplementary Figs. We investigate whether the statistically fine-mapped causal variants affect BAG through transcriptional regulatory mechanism using the GETx database . Except rs79107704, the seven SNPs significantly affect the transcription levels of one or more nearby genes  and no significant associations with any other of the four disorders .We observed nominally significant genetic correlation between BAG and AD that did not survive FDR-correction . One year increase in genetically predicted BAG was estimated to reduce the risk of PD by a log odds ratio from 1.4 (by Egger regression) to 0.02 (by MR-RAPS) . Figure p > 0.05)  and Egger-regression . Therefore, the observed negative relations between BAG and PD are less likely to be causal.A close investigation into the scatter plots of instrumental SNPs showed that the causal effect of AD on BAG was primarily driven by a SNP (rs59007384) in the APOE region, which was not identified as a horizontal pleiotropic instrument by MR-PRESSO (outlier test 05) Fig. ; there w05) Fig.  but Egge05) Fig. . SNPs in05) Fig. . Howeverp > 0.05). Therefore, our observed AD and BIP to BAG relations are less likely to be driven by population stratification, i.e., both the exposure and outcome data originating from the same ancestry group. There was also no significant cross-ancestral causal effect detected using AD data from Japanese or African samples , and BIP data from the Japanese sample to BAG .We used the GWAS results for height of European samples and cross-ancestry MR analysis to corroborate the identified causal relations (Methods). We found no causal effect between BAG and height with any of the MR methods employed (all MAPT loci [Combining the advantages of large samples and advanced models for brain age prediction, we confirmed that BAG is a heritable and polygenic trait, and estimated the genetic pleiotropy and causal genetic relations with major brain and mental disorders. We identified seven novel loci associated with BAG, in addition to confirming the previously reported APT loci , 19. AltAP2M1 have been linked to epilepsy, intellectual developmental disorder, and seizures [STH has been associated with frontotemporal dementia and 17q21.31 duplication syndrome [Functional annotation of the genes linked to the identified loci confirms that deviations in BAG are linked to complex processes encompassing multiple biological systems . Althougseizures ; among tsyndrome , 60. MorPrior work has shown higher BAG in patients with a multitude of disorders compared to healthy controls , 9, 11, The causal effect of genetically predicted risk for AD on BAG was small but consistent in directions across the six MR models, four of which were significant after multiple-testing correction. For BIP, although four models showed significant effects, the CAUSE model suggested an opposite direction of effect to the other five models. Thus, we advise careful interpretation of this result. Our attempts of testing causal relations across ancestral groups led to largely null fundings for the AD to BAG relations. We believe these nonsignificant fundings are largely due to the lack of statistical power in the non-European GWAS –53.e.g., medication [The observed causal relations between genetically predicted risk of brain disorders and BAG are intriguing. One possible interpretation is that overt changes in the brain incurred by the disorders contribute to accelerated aging. Another possibility may be that lifestyle and health-related behaviors of patients with clinical conditions such as AD and BIP, dication , may incdication –67 and bdication , 66. Altdication  and psycdication , 69, anddication .MAPT gene region on chromosome 17: After removing chromosome 17 from our analyses, no enrichment was observed in either direction (Supplementary Fig. Our initial results showed weak evidence of a causal relation between BAG and PD, corroborating two recent studies which reported a weak correlation between BAG and PD , 72. StrMAPT gene locus [While the present study advances current knowledge regarding the genetic architecture of and causal contributions to BAG, the results should be interpreted with caution. Although we confirm previously reported genetic associations with BAG, e.g., the ne locus , 19, ourne locus  that reqne locus , may prone locus , and stune locus .In conclusion, the present study increases the yield of genetic associations with brain age to eight genomic loci; implicated genes indicate involvement of calcium signaling, DNA damage repair, protein metabolism, and general innate immune defense. Our analysis did not provide evidence of a causal relationship between BAG and the included clinical conditions, and their interactions remain unclear.Supplementary Information