Teacher expectations of pupil ability can influence educational progression, impacting subsequent streaming and exam level. Systematic discrepancies between teacher expectations of pupil achievement may therefore have a detrimental effect on children’s education. Associations between socioeconomic and demographic factors with teacher expectation accuracy have been demonstrated, but it is not known how teacher expectations of achievement may relate to genetic factors. We investigated these relationships using nationally standardized exam results at ages 11 and 14 from a UK longitudinal cohort study. We found that teacher expectation of achievement was strongly correlated with educational test scores. Furthermore, the accuracy of teacher expectation was patterned by pupil socioeconomic background but not teacher characteristics. The accuracy of teacher expectation related to pupil’s genetic liability to education as captured by a polygenic score for educational attainment. Despite correlation with the polygenic score, we found no strong evidence for genomewide SNP heritability in teacher reporting accuracy. They can influence the subjects that pupils take, whether they are entered into an advanced stream, the level of exam they are entered to, how long they remain in education and ultimately their educational attainment10. These expectations are based on a teacher’s understanding and experience with pupils over an extended period and can have advantages over pupil achievement measured by test performance12. For example, expectations may avoid a misleading representation of a pupil’s ability if they tested on a particularly good or bad day, they avoid incentives to “teach to the test”, they may remove the stress of formalised testing, and they can ensure that ability is measured using a broader range of factors than test performance alone15.Teachers’ expectations of ability can affect pupils’ academic achievement throughout their educational career from initial enrolment through to the end of compulsory schooling20. Teacher expectation theory posits that while teachers form inferences about their student’s future academic achievement for individuals and groups of students, their expectations of pupils may be biased by students’ backgrounds23. Second, variation in teacher and classroom characteristics may result in systematic differences in the accuracy of teacher expectations. Teachers with larger class sizes have less individual contact time with each pupil, meaning that their expectations may be less reliable than teachers with smaller classes24. Third, teachers may only have a small sample of previous students to draw upon so the accuracy of their expectations of future pupil performance may be dependent on their level of experience25. Given these advantages and disadvantages, teacher expectations can be used for early assessment and streaming before being replaced by formalised testing and assessment later in schooling. However, recent policy updates highlight how this is not always the case. The Covid-19 pandemic led to the use of assessments from teacher expectations for determining academic performance in the UK, following heavy criticism of the UK Government’s initial statistical model for exam results which was reported to have widespread inconsistencies.However, disadvantages also exist with teacher expectations. First, there is potential for either conscious or unconscious bias against specific pupils or groups, such as by gender, socioeconomic background, ethnicity or special educational needs status28. For example, a meta-analysis of 39 studies demonstrated that teacher’s expectations of pupils was linked to pupils’ ethnicity, with higher expectations being held for European-American pupils than for ethnic-minority pupils29. These systematic differences can be detrimental to pupils who are under or overestimated by their teachers. For example, pupils who felt undervalued by teachers may be less likely to be engaged in school and have lower achievement than expected30. Conversely, pupils whose ability is overestimated may be overlooked by teachers or placed into streams that are too advanced for them and they therefore may not receive adequate support to accomplish their academic potential16.Previous studies have shown that systematic differences exist in the accuracy of teacher expectations of subsequent achievement across groups of pupils. On average teachers underestimate outcome for students with special educational needs, those of black-African and black-Caribbean ethnic origin, and those of a lower socioeconomic position, and boys33. The largest genome-wide association study of education to date identified over 1000 SNPs which combined into a polygenic score (PGS) explain around 12% of the variation in educational attainment. Because genetic variation is set at birth and cannot be affected by environmental factors post-conception, associations between genetic factors and individual characteristics are robust to confounding and reverse causation that pervade much educational research34. While genetic variation is not directly observable, its effects on education are.New data and methods offer the opportunity to examine the accuracy of teacher expectations in novel ways. The use of genetic data in educational research is growing and there is now evidence that many genetic variants  associate with educational attainment, achievement and progressIf teachers’ expectations of their students’ achievement are unbiased, then the accuracy of their expectations of student attainment should not be related to the students’ polygenic scores for educational attainment. Alternatively, an associations between the teachers’ expectations of achievement may suggest bias towards other unmeasured characteristics. For example, if teachers overestimate the achievement of a given group (for example girls from high socioeconomic position (SEP) backgrounds) and underestimate the achievement of another group (for example boys from low SEP backgrounds) then we might expect the difference between teacher expectations and exam results to be partially explained by the educational attainment polygenic score. To investigate this, we estimated the association of teacher expectation accuracy with socioeconomic, demographic and genetic factors in the Avon Longitudinal Study of Parents and Children (ALSPAC), a UK longitudinal cohort.We investigated the following three hypotheses: (1) do teacher expectations accurately associate with realised achievement?, (2) do teacher expectations associate with teacher characteristics and pupil socioeconomic and demographic factors? and (3) Do pupils’ common genetic variation explain differences in the accuracy of teacher expectations?Due to attrition and item non-response in the ALSPAC cohort, the complete case samples of ALSPAC participants available for analyses are 2341 at Key Stage 2 (age 11) and 3696 at Key Stage 3 (age 14). We therefore ran multiple imputation to recover missing data and increase the statistical power of our analyses. Our multiple imputation sample was 7465, with imputations run over 100 iterations. Teacher expectation accuracy was obtained by regressing realised achievement in standardised national examinations for Mathematics, English and Science on teacher expectations of performance in these subjects.2 values of 0.78 and 0.85 at Key Stages 2 and 3 respectively.Each one standard deviation (SD) increase in teacher expectation was associated with a 0.88  and 0.92  SD increase in realised achievement at Key Stages 2 and 3 respectively in the imputed data , teacher experience , or class size  associated with teacher expectation accuracy. Results were consistent across the imputed and complete case analyses  and Key Stage 3   for Key Stage 2 and 14% for Key Stage 3  after adjustment for principal components of ancestry. Like the PGS results, this suggests that pupil’s under or over-performance relative to their teacher’s expectations may relate to their genome-wide genetic variation . We found evidence that teacher expectation accuracy was related to some socioeconomic or demographic factors, principally pupil’s maternal education and age in year at both Key Stages, and parental social class and household income at Key Stage 2 and 3 respectively. These patterns were consistently in the same direction, whereby pupil’s from more disadvantaged backgrounds underperformed compared to their advantaged peers. Our findings conform to those from previous studies which have found differential teacher expectation accuracy towards certain groups of pupils such as those from lower socioeconomic position backgrounds32 were more likely to outperform their teachers’ expectations compared to children with lower polygenic scores. Using all genomewide data within a GREML-GCTA framework we found only weak evidence for SNP heritability at both ages, though these results should be interpreted with caution due to their imprecision. These results suggest that some of the variation in teacher reporting accuracy can be explained by genetic variation at the pupil level. Conversely, they suggest that most of the variation in teacher expectation accuracy can be explained by non-genetic  factors. Genetic liability towards educational performance could operate through a range of mediating mechanisms, such as personality characteristics or attitudes to learning and schoolwork36. In this way, ‘invisible’ genetic variation may become visible to teachers, influencing their expectations of a pupil’s future performance. Future studies with larger sample sizes are required to verify these findings, however our results build upon previous studies demonstrating robust associations between genetic factors and achievement throughout schooling40.We found mixed evidence for associations between genetic factors and teacher expectation accuracy. Pupils with a higher value of the polygenic score from a large GWAS of educational attainment41. Prejudice on the teachers part however may have been more likely to result in pupils over performing their teachers (unfairly negative) expectations. Similarly, pupil behavioural change due to self-fulfilling prophecies from inaccurate teacher forecasts may be expected to result in accurate teacher expectations, even if they are prejudiced42. Regardless, our findings highlight that some groups of students systematically underperform their teachers’ expectations. We were unable to reliably investigate how ethnicity related to teacher expectations because the ALSPAC cohort had low numbers of ethnic minority participants. Previous studies conducted on more ethnically representative cohorts have shown that teacher expectations differ by pupil ethnicity30.Our analyses were unable to determine whether inaccuracies in teacher expectation were due to error or detrimental bias on the teachers part, i.e. whether teachers were prejudiced against specific groups of pupils43, meaning that this demographic are underrepresented and our complete case analyses may be biased. Results from our multiple imputation analyses were broadly consistent with the complete case analyses, suggesting that bias due to attrition may be limited.Several limitations exist with this study. First, generalisability of these findings to the wider UK school population may be limited. Our sample was ethnically homogenous and restricted to those who were recruited from a single geographical area over a three school-year period. This tightly defined sampling frame means that there will likely be reduced environmental and genetic variation in our sample compared to the broader population of the UK. Furthermore, within ALSPAC there is greater attrition for pupils from families of lower socioeconomic position and poorer general healthSecond, the age of the sample may also limit the generalisability of our findings. We examined the accuracy of teacher expectations at ages 11 and 14, but our results may not be transportable to earlier of later stages of education. Additionally, the participants were educated between 2001 and 2006 and teacher expectations may have change since this period.Third, the accuracy of teacher expectations may have differed across Maths, English and Science subjects as many participants will have had subject specific teachers. Our decision to combine across these subjects was taken to provide a more accurate measure of the pupil’s overall academic performance and reflect any general teacher expectation bias. Furthermore, teacher expectations of pupil achievement were provided as categorical levels for each subject, meaning that there was reduced variation in this measure when compared to point scores used for assessment.45. To improve statistical power, we leveraged the larger sample of responses from study mother’s reports of their partners occupation and income, but it is likely that the mother reports will have contained greater measurement error than direct partner reports. Additionally, there was strong correlation between the teacher predicted scores and pupil achieved test scores, even though only a coarse measure of predicted achievement was available. As such, the discrepancies between predicted and actual scores are likely to reflect some measurement error. However, this measurement error may not have differed by the pupils’ other characteristics.Fourth, many variables were subject to potential measurement error. For example, family socioeconomic position is a complex construct encompassing education, income, wealth and other factors, yet we were only able to proxy this using weekly household income, parental social class and the highest level of maternal education48, we were only able to perform the analyses amongst white participants of European ancestry. Previous studies have demonstrated that the direction of teacher expectation accuracy varies by ethnicity4. However, previous work has demonstrated that trait-associated genetic markers do not perform well across ancestral groups49. Larger genotyped samples of ethnic minorities are therefore required to explore this issue further.Finally, because of the ethnic homogeneity of the ALSPAC sample, the European-centric focus of genetic studies, and the need to exclude non-Europeans due to systematic ancestry differences arising from population stratification (which can induce spurious genotype–phenotype associations)In conclusion, this study investigated potential patterns of teacher expectation accuracy by socioeconomic, demographic and genetic factors. We found evidence of systematic socioeconomic and genetic patterning in teacher expectations. Pupils from more disadvantaged backgrounds underperformed their teachers’ expectations compared to their more advantaged peers, and those with higher genetic liability for educational attainment outperformed their teachers’ expectations relative to pupils with lower genetic liability for educational attainment.50. The ALSPAC cohort was representative of the UK population in 1991 on many criteria, but had underrepresentation of ethnic minorities, single parent families and those of lower socio-economic position. Ethical approval for the study was obtained by the ALSPAC Ethics and Law Committee (ALEC) and the Local Research Ethics Committees. Informed consent for the use of data collected via questionnaires and direct assessments was obtained from participants following the recommendations of the ALEC. Informed consent was provided by the study mothers when the participants were minors. All methods were carried out in accordance with relevant guidelines and regulations. Questionnaires were completed by study mothers, the child’s schoolteachers and headteachers to obtain information relating to family background and the school/classroom. The study website contains details of all the data that is available through a fully searchable data dictionary and variable search tool . Due to low numbers in the minority ethnicity groups and problems with multi-ancestry genetic analyses (below), all non-White participants were excluded.We used data from the Avon Longitudinal Study of Parents and Children (ALSPAC), a longitudinal birth cohort study based in Bristol, UK. ALSPAC initially recruited 14,541 pregnant women with an expected delivery date between April 1991 and December 1992. When the oldest children were approximately seven years of age, an attempt was made to recruit eligible children that were not included in the original sample. This resulted in a total eligible sample size of 15,454 pregnancies of which 14,901 children were alive at one year of age. For full cohort details and study design seeWe used fine graded achievement scores at two of the major “Key Stages” of UK education  obtained from the UK National Pupil Database (NPD) through data linkage to the ALSPAC cohort. Achievement scores were determined from examinations at the end of each Key Stage.Teacher expected achievement was available from the NPD as categorical variables indicating the national curriculum level  that a pupil was expected to achieve for each of Mathematics, English and Science. The average of these three measures was taken and converted to a point score to enable comparability with achievement scores  on teacher expectation scores (the independent variable) at Key Stages 2 and 3. A positive value therefore indicates that a pupil outperformed their teacher’s expectation in their examinations. For ease of interpretation, accuracy scores were standardised to follow a normal distribution with mean zero and standard deviation one. This enabled investigation into systematic inaccuracy of teacher expectations against a variety of demographic and teacher characteristics, and exploration of heterogeneity in the teacher expectations across groups.Information on participant sex at birth and month of birth was obtained from birth records. Month of birth was recoded with September as the first month to represent age in school year (the school year in the UK starts in September). Self-report questionnaires completed by the study mothers during pregnancy provided information on family socioeconomic position. Socioeconomic position was proxied by parental social class based on occupation at cohort member birth, the mother’s highest education qualification at cohort member birth, and family income at cohort member age four. Study mothers reported their own and their partners’ occupation, with responses coded to the Standard Occupational Classification (SOC) codes and converted to social class based on occupation, with the following seven bands: I ; II ; III-NM ; III-M ; IV (Partly-skilled occupations); V (Unskilled occupations); Armed forces. Armed forces responses to social class were recoded to II due to low number of observations. Where both maternal and paternal social class were available, the highest social class was taken. Mothers highest level of education was categorised as follows: Degree; A-level ; O-level ; Vocational qualifications; Certificate of Secondary Education . Family income per week was reported in the following bands: less than £100; £100–199; £200–299; £300–399; £400 or more; Don’t know. Responses of “don’t know” were coded as missing.Teachers provided information through self-report questionnaires at Key Stage 2 (age 11) about their gender , length of service , and the number of pupils per class. School headteachers provided information on the Special Educational Needs (SEN) status of participants, characterised as: (1) Has a statement; (2) Currently being assessed; (3) Not statemented; (4) Has been refused. SEN status of 2, 3 and 4 were re-coded to “Not statemented”.–7) were removed. Cryptic relatedness was measured as a proportion of identity-by-descent (IBD > 0.1), with related participants passing all other quality control thresholds retained in subsequent phasing and imputation, described fully in supporting information. 8237 children passed these quality control filters.DNA of the ALSPAC children was extracted from blood, cell line and mouthwash samples, then genotyped using reference panels and subjected to standard quality control approaches. ALSPAC children were genotyped using the Illumina HumanHap550 quad chip genotyping platforms by 23andme subcontracting the Wellcome Trust Sanger Institute, Cambridge, UK and the Laboratory Corporation of America, Burlington, NC, US. Standard quality control methods were applied to the resulting genome-wise data. Individuals were excluded based on sex-mismatch, minimal or excessive heterozygosity (< 0.320 and > 0.345), individual missingness greater than 3% and insufficient sample reduction (IBD < 0.8). Multidimensional scaling was used to stratify the population, comparing with Hapmap II (release 22) European descent (CEU), Han Chinese, Japanese and Yoruba reference populations; all individuals with non-European ancestry were removed. SNPs with a minor allele frequency (MAF) of less than 1%, a call rate of less than 95% or evidence for violations of Hardy–Weinberg equilibrium ), combining 477,482 SNP genotypes which were in common between the samples. SNPs with genotype missingness above 1% were removed due to poor quality  and a further 321 participants due to potential ID mismatches. This resulted in a dataset of 17,842 participants containing 465,740 SNPs (112 removed during liftover and 234 were out of Hardy Weinberg Equilibrium after combination). Haplotypes were estimated using ShapeIT (v2.r644), utilizing relatedness during phasing. A phased version of the 1000 genomes reference panel  from the Impute2 reference data repository  was obtained. Imputation of the target data was performed using Impute V2.2.2 against the reference panel , using all 2186 reference haplotypes (including non-Europeans). This gave 8237 eligible children and 8196 eligible mothers with available genotype data after exclusion of related participants using cryptic relatedness measures described previously.51 using all SNPs that were identified to associate with years of education. The scores were calculated as a weighted sum of educational attainment associated SNPs weighted by their effect size. SNPs were clumped and the SNP with the smallest P-value in each 250 kb window was retained. All other SNPs in linkage disequilibrium with an r2 > 0.1 were removed.A PGS was generated from the largest GWAS of educational attainment. ALSPAC participants were excluded from the meta-analysis used to generate the PGS to reduce bias due to overfitting alongside 23andMe participants due to data sharing agreements. The PGS was created using the software package PRSice52, we conducted multiple imputation by chained equations (MICE)53 under the assumption that data were missing at random (MAR) conditional upon the data included in the imputation model54. To help overcome this assumption, additional covariates were included as predictors in the imputed dataset to incorporate additional information and improve imputation accuracy56. MICE is a method based on data augmentation, iteratively estimating parameters for the distribution of each variable, and using this to predict the missing values. All variables except for genotype were imputed and variables that did not follow a normal distribution were transformed. Imputation was conducted in Stata 16 using the mim command58. A total of 100 imputed datasets were generated, and the results were pooled for each regression analyses. We only imputed phenotypic data using this approach  that can be explained by common genetic variation in all measured SNPs35, akin to a correlation coefficient60. GCTA first estimates the genetic similarity between every pair of unrelated individuals using measured variation across the genome, and compares this similarity with the phenotypic similarity of each pair. If more genetically similar pairs are more phenotypically similar than genetically dissimilar pairs, then the heritability estimate for a phenotype will be higher.We estimated the SNP heritability of the teacher expectation accuracy using genome-wide complex trait analysis (GCTA) with genomic-relatedness-based restricted maximum-likelihood estimation (GREML)For all genotypic analyses we make two further sample restrictions. First, we restrict the sample to unrelated participants in ALSPAC (less related than 2nd cousins) as indicated by their genotypic similarity. Second, we restrict our sample to participants of European ancestry only due to poor polygenic score performance in diverse ancestral groups. Further to these selections, we control for the first 20 principal components of population structure in all genotypic analyses to reduce population stratification bias.Supplementary Information.


Sweet corn and waxy corn has a better taste and higher accumulated nutritional value than regular maize, and is widely planted and popularly consumed throughout the world. Plant height (PH), ear height (EH), and tassel branch number (TBN) are key plant architecture traits, which play an important role in improving grain yield in maize. In this study, a genome-wide association study (GWAS) and genomic prediction analysis were conducted on plant architecture traits of PH, EH, and TBN in a fresh edible maize population consisting of 190 sweet corn inbred lines and 287 waxy corn inbred lines. Phenotypic data from two locations showed high heritability for all three traits, with significant differences observed between sweet corn and waxy corn for both PH and EH. The differences between the three subgroups of sweet corn were not obvious for all three traits. Population structure and PCA analysis results divided the whole population into three subgroups, i.e., sweet corn, waxy corn, and the subgroup mixed with sweet and waxy corn. Analysis of GWAS was conducted with 278,592 SNPs obtained from resequencing data; 184, 45, and 68 significantly associated SNPs were detected for PH, EH, and TBN, respectively. The phenotypic variance explained (PVE) values of these significant SNPs ranged from 3.50% to 7.0%. The results of this study lay the foundation for further understanding the genetic basis of plant architecture traits in sweet corn and waxy corn. Genomic selection (GS) is a new approach for improving quantitative traits in large plant breeding populations that uses whole-genome molecular markers. The marker number and marker quality are essential for the application of GS in maize breeding. GWAS can choose the most related markers with the traits, so it can be used to improve the predictive accuracy of GS. Zea mays L.) is the most important food, feed, and economic energy crop in the world. Its production safety plays an extremely important role in ensuring national grain production, promoting the development of animal husbandry, and improving people’s quality of life [Maize  are powerful tools for gene mapping in plants and animals and have been widely used for genetic analysis of complex quantitative traits in many important crop. In recent years, many scholars have used genome-wide association study (GWAS) to study the loci that control various traits such as PH, EH , yield , diseaseGenomic prediction is a method of using markers to predict the genetic value of complex traits in offspring for selection and breeding . When geIn this study, the association mapping panel comprised sweet corn and waxy corn inbred lines; a total of 477 accessions was used to perform GWAS analysis to dissect the genetic basis of the plant architecture traits of PH, EH, and TBN. The main objectives of the present study are (1) To analyze the genetic diversity of Chinese sweet maize and waxy maize elite inbred lines; (2) Using GWAS to locate and analyze the genetic basis of plant architecture traits, locate the significant SNPs controlling the three traits, identify candidate genes according to GWAS results, and annotate the function of candidate genes; (3) Estimate the prediction accuracy of genome-wide selection. Genetically analyze the maize PH, EH, and TBN by a genome-wide association study, find the quantitative trait loci regulating agronomic traits of maize, and determine a series of candidate genes related to plant growth. The candidate genes and mutation sites that control PH, EH, and TBN were mined, and the genetic evolution rules of key loci were analyzed. It provides theoretical guidance for further developing new germplasm resources and improving varieties more effectively.p ≤ 0.001)  .Between sweet corn and waxy corn, significant difference was observed for PH, as well as for EH. Waxy corn had higher means of PH and EH than that sweet corn A. In theThe results of the correlation analysis between different environments for the same trait and the correlation analysis results between PH and EH were shown in r2 = 0.2  and population structure were taken into account to avoid spurious associations. Q–Q plots showed that the population structure has been well controlled. A mixed linear model (MLM) can reduce the false positive significant markers, but also lead to some false negative significant markers not being identified.p = 1 × 10−4) associated with the PH were identified, which were spread across 10 chromosomes  associated with EH were identified, which were located on chromosomes 1, 2, 3, 4, 5, 6, 7, 9, and 10, respectively  associated with the TBN were detected, and they were located on chromosomes 1, 2, 3, 4, 5, 6, 7, 9, and 10, respectively  was one of the most important transcription factors in eukaryotes [Zm00001d022427, Zm00001d010380, Zm00001d047539, Zm00001d034639, Zm00001d034642, Zm00001d007121, Zm00001d038926, Zm00001d027312, Zm00001d040302, and Zm00001d01801 in this experiment encode RING zinc finger domain superfamily proteins and zinc finger CCHC domain proteins, which may regulate the growth and development of plants. Gene Zm00001d022437, Zm00001d044162, Zm00001d023332, Zm00001d023336, and Zm00001d038451 encode a WRKY gene family protein. WRKY were widely involved in regulating rice growth and development by regulating growth regulator-mediated signaling pathways. The plant basic leucine zipper (bZIP) transcription factor protein is encoded by the gene Zm00001d022442, Zm00001d03169 [Zm00001d038682 encodes a GPI-anchored protein [Previous studies have cloned some genes that related to TBN, such as mutations in ramosa1 , ramosa2 ramosa3  with incike rows . The ramodes ra1 . The cytodes ra1 . The genkaryotes ,40. It pkaryotes . The canGenomic selection, especially early selection, was more accurate. Genotyping uses high-density molecular markers to estimate all QTL effects and explain genetic variation for most traits. However, MAS uses fewer markers for trait selection and genomic selection was more accurate than MAS. A previous study shows that GWAS-derived markers improved the prediction accuracy of GS . ConsistGenomic prediction and GS have been successfully applied to a variety of crops to accelerate genetic gain and improve complex traits in breeding programs ,48. The su1), shriken-2 (sh2) and Sugar Extender (se).This study utilized an association mapping panel composed of 477 fresh edible maize inbred lines, in which 190 sweet corn inbred lines and 287 waxy corn inbred lines were collected or developed by Shanghai Academy of Agricultural Sciences, China. This panel represents a core collection of sweet corn and waxy corn germplasm in China, and includes most of the parents of the recently released waxy corn and sweet corn varieties. The 190 sweet corn inbred lines could be divided into three subgroups, i.e., enhanced sweet corn, super sweet corn and ordinary sweet corn, according to the sweetness regulatory genes of Sugar-1  of the Crop Research Institute of Shanghai Academy of Agricultural Sciences in Shanghai, and at the winter season breeding station  in Lingshui County, Hainan Province in 2019 and 2020. The phenotypic data of PH and EH were collected in the summer of 2019 and 2020 from the trials planted in Shanghai, and the phenotypic data of TBN were collected from the trials planted in Hainan in the summer of 2020, and in Shanghai in the winter of 2020. A single row plot was planted with 2.5 m in length and 0.6 m between plots, with 0.25m between plants, and at a planting density of 52,500 plants haAt the maturity stage, after the plant height of the maize inbred line in the natural population was stable, five plants from each row were randomly selected and measured with a tower ruler. The mean value of each trait was used for association analysis. The length from the root to the top of the tassel was the PH of the maize inbred line. EH is measured as the length from the root of the maize to the knot of the uppermost ear of the maize.The phenotypic data were analyzed using Microsoft Excel 2007 software to generate descriptive statistics, including the mean, minimum, maximum, standard deviation (SD), coefficient of variation (CV), skewness and kurtosis. The coefficient of variation was calculated as CV (coefficient of variation) = SD (standard deviation)/mean. The frequency distribution of phenotypic data was also checked using Microsoft Excel 2007 software. The kurtosis and skewness were used to estimate the frequency distribution normality. Corrplot in R was used to generate plots using Pearson correlation analysis.Best Linear Unbiased Estimator (BLUE) and generalized heritability were estimated in META-R .ijk is the plant architecture trait, μ is the overall mean effect, Repi is the effect of the ith replicate, Blockj (Repi) is the effect of the jth incomplete block within the ith replicate, Genk is the effect of the kth genotype, and ijkε is the effect of the error associated with three factors.The formula for calculating the BLUE value is:g2 and σε2 are the genotype and error variance components, respectively, σge2 is the variance of the G × E cross-variance component, nEnv is the number of environments, and nRep is the number of repetitions. To calculate BLUE and generalized heritability, all effects were declared as random.The formula for calculating the generalized heritability is:For genotyping, fresh young leaves of all accessions were collected, and genomic DNA was extracted using a DNA extraction kit. All samples were sent for genotype detection at Novogene Company using the single nucleotide polymorphism (SNP) Illumina platform. The panel of 477 inbred lines was genotyped on the Illumina platform, and the reference genome was B73 RefGen_v4 for SNP calling. The raw reads were filtered via a standard quality control (QC) process, and the clean reads were obtained for SNP calling. A total of 108,457,756 SNPs were obtained. SNP calling using VCFtools software, the SNPs with missing rate (<20%) and minor allele frequency (MAF > 0.05) were retained, resulting in a final set of 278,592 high-quality SNPs.Population structure analysis: a model-based clustering algorithm in ADMIXTURE Software Version 1.3  was applhttps://github.com/BGI-shenzhen/PopLDdecay (accessed on 13 April 2022)) [The PopLDdecay 3.40 software (l 2022))  and perlp-value) of 4.0 as the threshold to determine the SNPs significantly associated with the target traits of PH, EH, and TBN, respectively. The Manhattan plot and quantile–quantile (Q–Q) plot were produced using the “CMplot” package in R. The proportion of the explained phenotypic variation by each marker was estimated by the phenotype variance explained. Linkage disequilibrium heat maps were constructed using “LDBlockShow” [The GWAS analysis was conducted in TASSEL 5.0 software  by incorockShow” .http://www.maizegdb.org (accessed on 19 May 2022)). The physical locations of the genes and SNPs were based on the maize B73 RefGen_V4 genome. The annotation functions and related information of the candidate genes are obtained from the Maize Genetics and Genomics Database and the National Center for Biotechnology Information (http://www.ncbi.nlm.nih.gov/ (accessed on 1 June 2022)).All the putative candidate genes within 50 kb of the detected loci were identified. The expression data and gene annotation information were collected from the maizeGDB database  model in R . To esti


The assessment of cassava clones across multiple environments is often carried out at the uniform yield trial, a late evaluation stage, before variety release. This is to assess the differential response of the varieties across the testing environments, a phenomenon referred to as genotype-by-environment interaction (GEI). This phenomenon is considered a critical challenge confronted by plant breeders in developing crop varieties. This study used the data from variety trials established as randomized complete block design (RCBD) in three replicates across 11 locations in different agro-ecological zones in Nigeria over four cropping seasons . We evaluated a total of 96 varieties, including five checks, across 48 trials. We exploited the intricate pattern of GEI by fitting variance–covariance structure models on fresh root yield. The goodness-of-fit statistics revealed that the factor analytic model of order 3 (FA3) is the most parsimonious model based on Akaike Information Criterion (AIC). The three-factor loadings from the FA3 model explained, on average across the 27 environments, 53.5% [FA (1)], 14.0% [FA (2)], and 11.5% [FA (3)] of the genetic effect, and altogether accounted for 79.0% of total genetic variability. The association of factor loadings with weather covariates using partial least squares regression (PLSR) revealed that minimum temperature, precipitation and relative humidity are weather conditions influencing the genotypic response across the testing environments in the southern region and maximum temperature, wind speed, and temperature range for those in the northern region of Nigeria. We conclude that the FA3 model identified the common latent factors to dissect and account for complex interaction in multi-environment field trials, and the PLSR is an effective approach for describing GEI variability in the context of multi-environment trials where external environmental covariables are included in modeling. Manihot esculenta Crantz) is one of the most essential food-security crops in developing countries, particularly in tropical and subtropical regions , cassava bacteria blight (CBB), early vigor, and other agronomic traits of interest in earlier evaluation stages. The clones in the UYT were high yielding materials that have passed several stages of field evaluation and selection to eliminate disease susceptible clones. The clones were evaluated in UYT trials in 11 locations across different agro-ecological zones in Nigeria  over fouEach trial was established as a Randomized Complete Block Design (RCBD) with two or three replicates. The experimental plot consisted of six rows of length 5.6 m with an inter-row spacing of 1 m and intra-row spacing of 0.8 m and only the interior 20 plants (4 m × 4 m) were harvested. Across the full dataset, there were 28 environments (location by year combinations) and a total of 4,575 plots, varying in number across the testing environments from 72 (Onne20) to 318  of more than 0.3 were retained for subsequent analyses. Data quality control was carried out on the SNP dataset using the qc.filtering function in the ASRgenomics library (Following a modified cetyltrimethyl ammonium bromide (CTAB) method, we extracted high-quality genomic DNA from freeze-dried cassava leaf samples . The Nan library  prior toAmatrix function of the AGHmatrix library (G) and its inverse (−1G) were estimated from SNP marker data using the G.matrix and G.inverse functions of the ASRgenomics library (The pedigree-based additive numerator relationship matrix (A-matrix) was constructed following the recursive method presented in  library . The mar library , respectThe H-matrix relates all individuals through the A-matrix but integrates the additional information provided by the G-matrix. The main notion is to replace entries of the A-matrix by the corresponding entries of G-matrix and then adjust the remaining relationships accordingly. 11 contains cells of the A-matrix with relationships within the first group, A12 and A21 contain cells of the A-matrix with relationships between the individuals of the two groups, and A22 contains cell of the A-matrix with relationships within the second group. In this definition of the H-matrix, the inner group pedigree relationship of second group was replaced by the G-matrix indicating that H22 = G. The term where individuals are partitioned into those without (group 1) versus with (group 2) marker data. Therefore, Atructure .Since many analyses use the inverse of H that allows for simpler computations, Eq. (1) is often written in terms of its inverse  as−1 is the inverse of genomic relationship matrix and where Gormation , leadingThe G matrix was derived following :M is an allele-sharing matrix with m columns  and n rows , and P is a matrix containing, in each column, the frequency of second allele (pj) expressed as 2pj. Mij was 0 if the genotype of individual i for SNP j was homozygous aa, 1 if heterozygous Aa, or 2 if the genotype was homozygous AA. We note that because all columns of matrix M from which G is constructed are centered, G should not be invertible (contrary to its use in Equation 3). In practice, a number of options are available for matrices that are close to being positive definite (where definite  and we d2), surface soil wetness (%), root zone soil wetness (%), and profile soil moisture (%) for the whole crop growth cycle, i.e., from planting to harvesting of each field trial.Weather data was exploited to identify the potential environmental covariates that influence differential response of the clonal lines across the testing environments. According to each trial’s location and growth dates, weather data were collected from the database of the National Aeronautics and Space Administration Prediction of Worldwide Energy Resource (NASA POWER) project.ggplot2 package  vector of observed phenotypic values, in which n is the number of observations in the trial; r is the (r × 1) vector of fixed effect of replicates with its associated incidence matrix 1X of dimension n × r; p denotes the proportion of plant stands harvested as a covariate ; p and y; g is the (g × 1) vector of random effect of genotype with its associated design matrix Z1 of dimension n × g, and where 2) on an entry-mean basis, and experimental accuracy (Ac) proposed by r is the number of replicates, and PEV is the average of prediction error variance. A trial was removed from a combined analysis based on any of these conditions: The thresholds of CV above 40.5%, H2 below 0.14 or Ac below 0.40.The quality of each trial was assessed by calculating the coefficient of variation (CV), broad-sense heritability  vector of fixed effect of the environment where s is the number of environments; set(e) is the fixed effect of the trial set nested within the environment; r(set e) is the fixed replicate effect nested with set and environment; g is random effect of genotype nested within environments: g = j with its associated hybrid relationship matrix (H); where I is the identity matrix. The non-additive component captures other effects such as dominance, epistasis, and residual additive effects which are not captured by H-matrix. We used an identity matrix to capture that residual after fitting the non-additive effect. This necessitated the scaling of the hybrid matrix associated with additive genetic effect by multiplying main additive genetic and interaction variance matrices by the average of diagonal element of H-matrix which was estimated to be approximately 0.97, closely corresponding to the diagonal element of an identity matrix.We partitioned the total genetic effects (g) into additive (a) and non-additive (i) components  which arWe fitted a diagonal variance (DIAG) model as a baseline. This variance–covariance model postulates independence of genetic effects among environments. Being an environment or trial-specific model, if a trial is found to have no genetic variance (variance estimated to be zero), such trial will be excluded from the analysis. The estimates from this model are often used as a starting values when fitting a more complex model like the factor analytic (FA) model. The covariance structure is of the form (assuming four environments):H is the hybrid relationship matrix combining pedigree and genomic relationship matrices to account for the relatedness among the cassava clones and same for other models described below.where the main diagonal elements are the unique genetic variances within environments. For example, The compound symmetry (CS) is the most restrictive variance–covariance model. It postulates homogeneity across environments of genetic variance The compound symmetry heterogeneous (CSH) is an extension of the CS model which postulates a uniform correlation between any pair of environments but heterogeneity across environments of genetic variance and covariance. Its covariance structure is of the formwhere the main diagonal elements were as in Eq. (7), and off-diagonal elements are unique genetic covariances between pairs of environments. For example, s) increases, it requires a high number of parameters (The unstructured (US) model is the least restrictive variance–covariance model, and describes the covariance based on the assumption of heterogeneity of variance within environments and unique covariance between any two environments. As the number of environments  model is the random effect analogue of AMMI model  for desck in the jth environment ; ith genotype (genotypic sensitivity) for latent factor k related to the jth environment in ith genotype in the jth environment as a linear function of latent factors k = 1, 2, …, t plus an error term where The specification of FA model in a covariance form iswheres × t matrix of loadings, with the kth column containing the environment loadings for the kth latent factor , and Ψ is an s × s diagonal matrix with a specific variance for each environment. As above, s is the number of environments.where Λ is a jk), with each genotype having a distinct slope  but a common intercept provided main effect of genotypes are not distinguished from GEI  below to denote rotated loadings and scores.The number of latent factors is called the order of the model and we use FAk to represent an FA model of order k. We fitted FA1 to FA4 models. The model with the minimum value of AIC was chosen as the most parsimonious model. For FAk models where erefore,  recommenith genotype is computed asWe used the factor analytic selection tools proposed by  to assesjth environment in the first latent factor, and ith genotype in the first latent factor. The OP measure was based on the first factor loadings because they were all positive and thus represented non-crossover GE interaction (where eraction . The OP k > 1) which have a mixture of both positive and negative loadings. This practice is justified by the fact that changes in genotype performance due primarily to changes in scale, which are accounted for in the first factor should be eliminated from stability analysis  Computing the Euclidean distance between a pair of environments from the s × 3 factor loadings matrix; (ii) Hierarchical clustering on the derived distance matrix using Ward’s minimum variance linkage method (ward.D2) where dissimilarities were squared before clustering; (iii) plotting and visualizing the cluster dendrogram resulting from (ii); and (iv) subjectively determining the number of clusters by imposing a threshold of minimum similarity to be in the same cluster.We used the rotated factor loadings resulting from the FA3 model for clustering and delineating the subset of environments and locations into mega-environment using the To cluster locations (as opposed to environments = location-by-year combination), we computed for each factor separately, the average loadings of the environment that each location was a part of. We then used the approach above to cluster the locations.We further used an approach proposed by X and Y data matrices in one single estimation procedure . The factor loadings were data matrix Y of size 27 × 3 (27 rows for testing environments and 3 columns corresponding to the latent factor loadings). Since the PLSR method is variant to the scale of measurement, the columns of X and Y data matrices were centered (zero mean) and scaled (unit variance).The environmental covariables associated with GEI were identified by correlating each environmental covariable to each of the three latent factor loadings extracted from the FA3 model. Then, we fitted a partial least square regression to describe GEI in terms of differential genotypic responses to environmental covariables. The PLSR is a form of multivariate regression that maximizes covariance between rocedure . The envplsr function of pls library  and projections of Y (Y scores); P and Q denote m × l and p × l orthogonal loading matrices respectively; E and F are residual matrices assumed to be independent and identically distributed random normal variables.where We recognize that in this analysis we are using the environmental loadings from FA3 model as if they were observed data as opposed to derived parameters. A better approach would have been to develop a kind of factor analytic model to work directly on the continuous environmental covariables as opposed to using environment labels as a categorical variables. We do not know of a method to do such an analysis, let alone software to fit it. We look forward to the development of such a method.2) ranged from 0.06 (19UYT36setAMK) to 0.85 (18UYT36setBIK) across trials. We observed experimental accuracy (Ac) values varying from 0.24 (19UYT36SETAMK) to 0.91 (18UYT36setBIK). The coefficients of variation (CV%) ranged from 14% (17UYT36setAIK) to 42% (18UYT36setAKN). The four trials  displayed in red  to 82.3 (Ikenne20) under the assumption that genetic correlation between pairs of environments was zero . The comWe reported the total number of parameters, the model log-likelihood (Loglik), Akaike information criterion (AIC), Bayesian information criterion (BIC) and percentage of genetic variance captured by factor analytic models . The firPairwise genetic correlations among environments, as estimated by the FA3 model, were predominantly positive , varyingThe first factor loadings after rotation to the principal component solution were all positive, indicating non-crossover GEI, varying from 0.3 to 8.6 with a median of 3.2 and a mean of 3.6 . The remThe characteristics of first and higher factor loadings can be used to determine the overall performance (OP) and stability of the genotypes. A scatter plot of the OP against the root mean square deviation (RMSD) visualizes genotype performance and its stability . GenotypGenotype stability may be best viewed using latent regression plots which revealed genotypic responses to each factor loading . We cons3 = 8 iClasses with 5, 6, 10, and 6 environments each (Dendrogram clusters of 27 environments  and 11 lnts each . Each ofnts each .r) with the first factor loading of the FA3 model. However, these environmental covariables were in contrast to RH1, RH2, RH3, RH4, RZSW1, RZSW2, RZSW3, RZSW4, SM1, SM2, SM3, SM4, SSW1, SSW2, SSW3, SSW4, and TMIN2 showing high negative X-loadings in the first PLSR component and positively correlated to first factor loading. Conversely, the second PLSR component identified WS1, WS2, WS3, and WS4 as environmental covariables that had moderately high negative X-loadings.The first PLSR component had relatively high positive X-loadings for environmental covariables TRAN1, TRAN2, TRAN3, TRAN4, TMAX1, TMAX2, TMAX3, TMAX4, SRAD1, SRAD2, SRAD3, and SRAD4  and showBased on Pearson’s correlation coefficients, we observed that RH2, RH3, SM1, SM2, and SM3 were weather conditions that had high positive association to factor 1 but in contrast to TRAN1, TRAN2, TRAN3, TRAN4, TMAX1, TMAX3, TMAX4, SRAD1, and SRAD4 which revealed high negative correlation ; SSW1, RPLSR was used to maximize covariance between the factor loadings and the environmental covariables at four developmental phases of cassava root crop. It identified the most significant environmental conditions influencing differential genotypic yield response in the testing environments. The first latent component resulting from fitting PLSR model explained 63% of variance in factor loadings. The addition of second component resulted in capturing 70% of total variation, and after the third component which accounted for 78% of variation, no significant improvement in the variance explained in the factor loadings. It was revealed that the first component separated the environments into two clustered groups and conversely its second component did not have a clear interpretation . The envX and Y loadings revealed the association between environmental covariables at different developmental phases and factor loadings. The second component separated the third factor loading (FL3) from the remaining two factor loadings , and solar radiation affecting GEI in the northern region of Nigeria.https://github.com/mab658/variance_covariance_model_GxE.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 at: MB, IR, J-LJ, CE, and PK: design and study conceptualization. IR, MB, SK, CA, and EP: study methodology and implementation. MB, SK, MW, J-LJ, and IR: formal data curation, analysis, and manuscript drafting. MB, SK, CA, MW, J-LJ, PK, and IR: manuscript reviewing and editing. IR, J-LJ, and PK: supervision, coordination and funding acquisition. All authors contributed to the article and approved the submitted version.https://www.gatesfoundation.org) and the United Kingdom’s Foreign, Commonwealth & Development Office  through the “Next Generation Cassava Breeding project”  managed by Cornell University.The research reported in this manuscript was generously funded by the Bill & Melinda Gates Foundation (The authors declare 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.


Milk yield and fine composition in sheep depend on the volatile and long-chain fatty acids, microbial proteins, vitamins produced through feedstuff digestion by the rumen microbiota. In cattle, the host genome has been shown to have a low to moderate genetic control on rumen microbiota abundance but a high control on dairy traits with heritabilities higher than 0.30. There is little information on the genetic correlations and quantitative trait loci (QTL) that simultaneously affect rumen microbiota abundance and dairy traits in ruminants, especially in sheep. Thus, our aim was to quantify the effect of the host genetics on rumen bacterial abundance and the genetic correlations between rumen bacterial abundance and several dairy traits, and to identify QTL that are associated with both rumen bacterial abundance and milk traits.Prevotellaceae, Lachnospiraceae and Ruminococcaceae bacterial families show strong genetic correlations with milk fatty acids and proteins . Genome-wide association studies revealed a QTL for alpha-lactalbumin concentration in milk on Ovis aries chromosome (OAR) 11, and six QTL for rumen bacterial abundances i.e., for two OTU belonging to the genera Prevotella (OAR3 and 5), Rikeneleaceae_RC9_gut_group (OAR5), Ruminococcus (OAR5), an unknown genus of order Clostridia UCG-014 (OAR10), and CAG-352 (OAR11). None of these detected regions are simultaneously associated with rumen bacterial abundance and dairy traits, but the bacterial families Prevotellaceae, Lachnospiraceae and F082 show colocalized signals on OAR3, 5, 15 and 26.Our results in Lacaune sheep show that the heritability of rumen bacterial abundance ranges from 0 to 0.29 and that the heritability of 306 operational taxonomic units (OTU) is significantly different from 0. Of these 306 OTU, 96 that belong mainly to the Prevotellaceae, Lachnospiraceae and F082, show specific associations with OAR3, 5, 15 and 26.In Lacaune dairy sheep, rumen microbiota abundance is partially controlled by the host genetics and is poorly genetically linked with milk protein and fatty acid compositions, and three main bacterial families, The online version contains supplementary material available at 10.1186/s12711-022-00769-9. Ruminants can digest plant fiber thanks to the symbiotic microbiota in their rumen. This complex microbial community is composed mainly of bacteria but also includes archaea, fungi and protozoa. Bacteria degrade and ferment fibrous feedstuffs to produce volatile fatty acids (FA), microbial proteins and vitamins and to transform dietary lipids, all of which are used by the animal for maintenance, growth and lactation . The rumIn dairy sheep, fine milk composition traits are extremely important for the production of high-quality cheese. The FA present in milk influence its texture and nutritional value, and the proteins influence its coagulation capacity, which in turn affect its heat stability and the cheese yield . Dairy t to 0.60 , 8, and  to 0.60 , 9–11. TWe hypothesised that, in Lacaune ewes, rumen microbiota abundance is affected by the host genetics and is genetically linked to dairy traits through shared metabolic pathways. Thus, based on the use of the dataset that was previously described by Martinez Boggio et al. , the objsuppressor of cytokine signalling 2 (SOCS2) gene in the experimental Lacaune population to investigate possible associations with other traits. This allele corresponds to a mutation that was identified in 2015 [SOCS2 mutation.Data were obtained from the INRAE Experimental Unit of La Fage  between 2015 and 2019. Multiparous Lacaune dairy ewes (mean weight of 77 ± 9 kg) were raised indoors and fed a mixed ration of on average 90% meadow hay and silage plus 10% barley (on a gross matter basis) supplemented with approximately 150 g of a commercial protein concentrate (38% of crude protein on a dry matter basis) distributed in the milking parlor. Adjustment of the percentage of concentrates and forages was done each year according to the feeding value of the forages to cover the needs of the ewes, thus they received the same amount of nutrients during the 5 years. On average during this period, the ewes ingested 3.27 kg of dry matter that contained 16% of crude protein and 30% of crude fiber. The genetic structure of the INRAE La Fage flock consists of two independent groups of ewes, which were both divergently selected, as described by Martinez Boggio et al. [Rumen sampling was performed within 3 days of milk recording. Ruminal contents were sampled from each ewe using a vacuum pump and a medical gastric tube. Then, DNA was extracted and purified from a ruminal sample of 80 μL using the QIAamp DNA Stool Mini Kit  according to the manufacturer’s instructions, with a previous bead-beating step in a FastPrep instrument . The 16S rRNA V3–V4 regions were amplified by a first round of PCR with 30 cycles using the following primers: forward F343  and revOfficial daily records of milk yield (MY), milk somatic cell count as quantified with a Fossomatic cell counter , and milk fat and protein contents  were obtained on the 795 adult ewes between 28 and 133 days in milk (DIM). Two milk samples collected per animal during morning and afternoon milking were sent for analysis at the Interprofessional Milk Analysis Laboratory . Milk FC and PC were analyzed with mid-infrared (MIR) techniques on a Milko-Scan™ FT6000 instrument . Thus, we analyzed MY, FC and PC, with FC and PC taken as averages weighted by morning and afternoon milk yield records.s1-CN), alpha-S2-casein (αs2-CN), beta-casein (β-CN) and kappa-casein (κ-CN), and two whey proteins: alpha-lactalbumin  and beta-lactoglobulin (β-lactoglobulin), and of the FA, i.e., saturated FA (SFA), such as butyric acid (C4:0), caproic acid (C6:0), caprylic acid (C8:0), capric acid (C10:0), lauric acid (C12:0), and palmitic acid (C16:0), and unsaturated FA (UFA), such as oleic acid (cis-9 C18:1), rumenic acid (cis-9 trans-11 C18:2) and alpha-linolenic acid (C18:3n-3). Milk proteins and FA are expressed in g per 100 mL as averages weighted by morning and afternoon milk yield records. The MIR prediction accuracy, as estimated by the value of the coefficient of determination (R2), were retrieved from Ferrand et al. [2 for caseins are higher than 0.82, and for β-lactoglobulin and α-lactalbumin are equal to 0.77 and 0.26, respectively. The R2 for the SFA and cis-9 C18:1 are higher than 0.93, and for cis-9 trans-11 C18:2 and C18:3n-3 are equal to 0.91 and 0.74, respectively. Two additional traits, i.e., average lactation somatic cell score (LSCS) and CV milk were included in the analysis to account for the genetic structure of the population that is formed of two divergent lines for SCS and PERS.From these official milk records, the MIR spectra for 563 ewes were retrieved to predict the fine profile of the daily milk proteins, i.e., the four caseins: alpha-S1-casein  autosomes and mapped to the Ovis aries genome assembly Oar_v3.1 [SOCS2 gene was included in the map of OAR3 .DNA extraction from blood samples and genotyping were performed for the 795 ewes. Of these 795 ewes, 743 were genotyped using a medium-density single nucleotide polymorphism (SNP) chip , 314 at the Laboratoire d’Analyses Génétiques pour les Espèces Animales  and 429 at Aveyron-Labo . The remaining 52 ewes were genotyped with a low-density SNP chip  at Neogen , followed by imputation to a medium-density SNP chip within the framework of the Lacaune dairy sheep genomic selection programme . GenotypOar_v3.1 . The SNPMicrobiota abundance data are compositional data . The abuEnvironmental factors were tested by analyzing the variance of each trait. Statistical significance was defined at P < 0.05. Environmental factors that were significant for the abundance of more than 10% of the OTU were included in the model  and performed the random shuffling 10,000 times. For each permutation and OTU, we estimated the heritability of OTU abundance using a three-trait model, as presented in Eq.  of dairy traits and OTU abundances were performed using the single-step genomic best linear unbiased prediction (ssGBLUP) approach . The folmentclass2pt{minimionships  and \docpi(1-pi)  from gene (0.05) –36. The e (0.05) .After solving the ssGBLUP model in Eq. , we estiOSTGSF90 .10 on the y-axis.We corrected for multiple testing by using the false discovery rate (FDR) in the p.adjust package in R (v4.0.2) . A genomWe estimated the allele substitution effect for significant SNPs that were detected on the same chromosome and at the same position. The following single-trait model was used:mentclass2pt{minimLinkage disequilibrium (LD) along the genome was calculated as the squared correlation of allele counts for two SNPs on each chromosome. The proportion of phenotypic variance explained was calculated for each SNP by defining a window variance of 20 adjacent SNPs and for each QTL region defined in this study. The LD and variance explained were calculated using POSTGSF90 .Ovis aries genome assembly Oar_v3.1 [Genes that were identified for the significant SNPs were retrieved from the Ensembl database using the BioMart web interface based on the Oar_v3.1 . Then thOar_v3.1  was usedOar_v3.1 .After bioinformatic analysis, 63% of the 9,552,103 initial DNA sequences obtained from the rumen samples of the 795 ewes were retained. The abundance table included 2059 affiliated OTU, represented by 751 to 168,785 sequences, with a median of 1761 DNA sequences per OTU. The finest taxonomic level was the genus level due to an unknown species frequency of 95%.Bacteroidota (51%), Firmicutes (44%), and Proteobacteria (3%). At the next taxonomic level, the most abundant families were Prevotellaceae (38%) mainly represented by the Prevotella genus, Lachnospiraceae (18%) represented by 40 genera, Ruminococcaceae (9%) mainly represented by the Ruminococcus genus, Oscillospiraceae (5%) represented mainly by the NK4A214_group, and three families each represented by one genus: Christensenellaceae represented by Christensenellaceae_R-7_group (5%), and Rikenellaceae represented by Rikenellaceae_RC9_gut_group (4%). The average percentage of zeros (OTU not detected in the rumen sample) in the OTU abundance table was 37.5%.Overall, the 2059 OTU from the 795 rumen samples were attributed to 11 phyla, 56 families and 112 genera. Expressed as a percentage of the total sequences for all samples, the most representative phyla were The descriptive statistics for the dairy traits analyzed in our study are in Table Bacteroidota (61%), Firmicutes (34%) and Spirochaetota (2%), and the 10 most represented genera are in Table The heritability of rumen bacterial abundance ranged from 0 to 0.29 ± 0.07 with a mean of 0.04 ± 0.03  among the OTU with a significant heritability based on Fisher’s exact test (P > 0.05).The We estimated the genetic correlation between each of the 306 OTU and each of the 18 dairy traits included in this study. We obtained 5508 genetic correlations of which 301  were significant . This corresponds to 96 OTU abundances that had a significant genetic correlation with one or several dairy traits: 81 OTU were correlated with FC and milk FA .Daily fat content and milk FA showed significant genetic correlations with OTU from 26 genera belonging to 17 families. The bacterial families that shared the largest number of significant genetic correlations were Prevotellaceae, Lachnospiraceae and Oscilllospiraceae families  correlated with 62 OTU, half of which belonged to the Prevotellaceae and Rikenellaceae families. Two OTU from the Prevotellaceae family correlated with all the UFA but showed opposite correlation signs.Milk SFA C4:0 to C16:0) correlated with 41 OTU, of which 26 OTU were positively correlated with at least one SFA. Five OTU were linked with all SFA, with variable genetic correlations, and a closely clustered group consisting of C8:0, C10:0 and C12:0 shared positive correlations with 12 OTU from the 6:0 correPrevotellaceae and Lachnospiraceae  and beta-lactoglobulin, which correlated mostly negatively with OTU.The daily protein content and milk proteins showed significant genetic correlations with OTU from 23 genera belonging to 17 families. The bacterial families that shared the largest number of significant genetic correlations were Leifsonia OTU1479 belonging to the Microbacteriaceae family showed negative correlations with all CN, and four OTU from the Lachnospiraceae and Prevotellaceae families were also correlated with two CN (αs2-CN and κ-CN). The whey proteins  correlated with 47 OTU, of which eight were in common. Four OTU from the Prevotellaceae, Lachnospiraceae and Muribaculaceae families showed the same correlation sign with α-lactalbumin and β-lactoglobulin.All caseins were correlated with 30 OTU, of which five were negatively correlated with three or more CN. Prevotella, Christensenellaceae_R-7_group and Ruminococcus. In the core microbiome, 44 OTU showed a significant heritability  of 5.77. On OAR6, we detected one significant SNP and one suggestive SNP in the region between 100.1 and 101.3 Mbp with an LD score of 0.56.The largest number of significant SNPs was detected for alpha-lactalbumin on seven chromosomes, with a QTL on OAR11 Fig. . This QT10 of 8.18) obtained in this study for all dairy traits.For alpha-S2-casein, we detected a significant SNP (rs423428584) on OAR6, with the highest P value  of 5.52  of 5.25.For the SFA C6:0 and C8:0, we detected the same significant SNP rs405420878) on OAR17  that were distributed across 22 chromosomes for 56 OTU  of which 19 were Prevotella OTU, followed by Lachnospiraceae (20%) and Ruminococcaceae (9%).The group of 56 OTU with significant SNPs belonged to three phyla, 11 families, and 23 genera. Expressed as a percentage of OTU, the For the 94 significant SNPs detected in the host genome and associated with rumen bacterial abundance, several genomic regions showed QTL and significant SNPs for OTU abundance and dairy traits Table .Prevotella OTU196 that includes two significant SNPs in high LD (LD score of 0.67). The SNP rs419358934 presented a colocalized signal with Prevotellaceae_UCG-001 OTU906, and the allele substitution effect for that SNP varied in the same direction for both Prevotellaceae OTU. In addition, for each OTU, we detected two other significant SNPs that were located outside of the QTL for which two candidate genes were identified (Table cytotoxic granule-associated RNA binding protein (TIA1) gene that is involved in the negative regulation of cytokines (GO:0001818), negative regulation of translation (GO:0017148) and regulation of mRNA splicing (GO:0048024), and (2) the interleukin 18 receptor (IL18R1) gene that has a role in natural killer cell activation (GO:0030101), positive regulation of interferon-gamma production (GO:0032729) and cell signalling and inflammatory processes (KEGG: oas04060).On OAR3, we detected a QTL for Prevotella OTU1843, Rikenellaceae_RC9_gut_group OTU546 and Ruminococcus OTU1191. The QTL for OTU1843 includes two significant SNPs, of which one (rs402307868) showed a colocalized signal with the Possible_genus_sk018 OTU1631. The allele substitution effects for the SNP with colocalized signals showed contrasting signs for the Prevotella and Possible_genus_sk018 OTU. The QTL for Rikenellaceae_RC9_gut_group OTU546 includes two significant SNPs in high LD (LD score of 0.74). The QTL for Ruminococcus OTU1191 includes two significant SNPs separated by 0.04 Mbp, but the LD score was very low in that region (< 0.10). The SNP rs418870684 was associated with the novel gene ENSOARG00000025325.On OAR5, we detected three QTL for Acetitomaculum OTU612, however, the LD score was low (< 0.20), and no shared SNPs were detected for these two traits.On OAR6, we detected six significant SNPs for five OTU but no QTL. In the region where a significant SNP was detected for alpha-S2-casein (81.2 Mbp), we identified two significant SNPs for Clostridia UCG-014. The two significant SNPs were located in a region in high LD (LD score of 0.78), and the same gene, E3 ubiquitin-protein ligase (W5PCZ6_SHEEP), was detected. The W5PCZ6_SHEEP gene is involved in the ubiquitin-dependent protein catabolic process (GO:0006511), multicellular organism development (GO:0007275) and regulation of protein stability (GO:0031647).On OAR10, we detected a QTL with two significant SNPs at 16.2 Mbp for OTU1386 belonging to the order CAG-352 OTU304 belonging to the Ruminococcaceae family. However, this QTL for OTU304 was located far from the QTL detected for alpha-lactalbumin on OAR11 (32.6 to 34.2 Mbp). The candidate gene helicase with zinc finger (HELZ), that was located in this QTL, was not associated with any GO biological process or KEGG pathway.On OAR11, we detected a QTL with two significant SNPs in complete LD for Prevotella OTU , which is involved in the negative regulation of cell adhesion (GO:0007162), negative regulation of lipid catabolic process (GO:0050995), and metabolic pathways (KEGG: oas01100).On OAR15, we detected the same significant SNP, rs409362751, for three Prevotella OTU1336, Prevotellaceae_UCG-001 OTU906 and OTU167 that belongs to the F082 family. The allele substitution effects for the two Prevotellaceae OTU varied in the same direction, but in opposite directions for F082 OTU167.On OAR26, we detected the same significant SNP, rs412469804, for Prevotellaceae, F082, and Lachnospiraceae families  having a low to moderate heritability (0.10 to 0.29), which is similar to the results reported for rumen bacteria in other ruminants 059 OTU h, 43. HowBacteroidota and Firmicutes, as reported by Li et al. [Prevotella, which was overrepresented among the OTU with a significant heritability and showed an average estimate of 0.15 ± 0.04, is considered as a highly heritable genus in the literature [Proteobacteria, Actinobacteria and Firmicutes being the main represented phyla, but these differences could be due to the “shotgun” sequencing technique that reveals all the microbial genomes within a sample.The group of 306 heritable OTU belonged to the most abundant phyla, such as i et al. , Wallacei et al.  and Zhanterature . The maiterature , with PrIn general, the differences in gut bacteria observed between studies can be due to several factors: (1) the sequencing technology used, which does not give enough information to obtain affiliations at lower taxonomic levels , meaning that most studies report results at the genus level , 6, 42 aHowever, a core microbiome cannot be declared based on these heritable OTU only, as was done by Wallace et al. , becauseTo the best of our knowledge, our study is the first to estimate the genetic parameters of rumen bacteria from approximately 800 dairy ewes from the same farm under the same housing conditions.For daily milk traits, we obtained moderate to high heritabilities, with values of 0.28 ± 0.06 for MY, 0.57 ± 0.06 for PC and 0.59 ± 0.06 for FC. Compared to two previous studies [2 of 0.26 [For the milk composition traits, milk FA presented moderate to high heritabilities, as reported by Boichard et al.  in Lacau of 0.26 . Thus, tPrevotellaceae, Lachnospiraceae and Ruminococcaceae were moderately to highly genetically correlated  with one or more milk FA and proteins. The overall quantification of these correlations is of interest to understand the relationship between rumen microbiota and phenotypes, in spite of the limitations of our study due to the low precision of 16S rRNA gene sequencing at the species level and the large number of estimated genetic correlations (more than 5500) based on a small dataset of 800 ewes, which, even if those with large standard errors are discarded, may lead to some spurious correlations.Rumen bacteria are undeniably of crucial importance to their host, providing FA and microbial amino acids that contribute to milk fat and protein production . HoweverThe impact of the heritable OTU on the dairy traits was weak, as evidenced by the small number of significant genetic correlations obtained in our study (on average 301), i.e., only 5% of the total estimates. This figure was even smaller when we evaluated the number of OTU that were significantly associated with dairy traits in the core microbiome since only 13 of 96 OTU were genetically linked. However, interestingly, some of these OTU might have host-relevant functions since they are part of the core microbiome. Although the number of genetic correlations between rumen bacteria and milk traits was small, their values were moderate to high, which suggests that it could be useful to include microbiota composition in the genetic models, when the objective is to determine how the genetic effect impacts the phenotype not directly but with an indirect effect through microbiota abundance. In this regard, some authors have proposed methodologies to account for this indirect genetic effect mediated by the microbiota –48.Our results show that most of the heritable OTU do not impact dairy traits. For this reason, the genetic associations that are observed mainly with milk FA and proteins can be difficult to use as selection criterion to improve fine milk composition traits, but this does not limit their inclusion in genetic models as an additional source of information to estimate the indirect genetic effect on those phenotypes of interest.CSN1S2 was reported in the literature on caseins [LALBA, which encodes alpha-lactalbumin in sheep, was identified on OAR3 [ACACA and FASN) on this chromosome.After having demonstrated that a group of heritable OTU was genetically linked to milk composition traits, we performed GWAS to identify host genomic regions that simultaneously affect rumen bacterial abundance and dairy traits. In the GWAS of dairy traits, we detected 22 significant SNPs that were distributed across nine chromosomes. Among these regions, two on OAR6 showed associations with alpha-lactalbumin and alpha-S2-casein. The SNP rs423428574 detected for alpha-S2-casein was located in the region of OAR6 where the major gene  caseins , 11, 49. on OAR3  reportedPrevotellaceae OTU that colocalized with the same SNP, i.e., colocalizations for Prevotellaceae and Lachnospiraceae OTU on OAR5, and colocalizations for Prevotellaceae and F082 OTU on OAR26. This suggests that some regions of the host genome are associated with rumen bacterial abundance, but given the limitations raised by Pérez-Enciso et al. [TIA1, IL18R1, W5PCZ6_SHEEP and PDE3B, which are involved in host immune system processes, regulation and catabolic processes, as reported by Abbas et al. [In the GWAS of rumen bacterial abundances, we detected signals that were distributed across the host genome, as reported by Li et al. , Abbas eo et al.  about ths et al. . Howevers et al. , 53.Our findings, based on a large and unique microbiome database, demonstrate that a small proportion of the total bacterial abundance in the rumen of Lacaune ewes is partially controlled by the host genome, for both the total and core microbiome, and that a few of the bacteria are associated with specific genomic regions on OAR3, 5, 15 and 26. Only very few of the genetic correlations between milk fine composition and rumen bacteria were significant, and it was not possible to identify genomic regions and metabolic pathways shared between rumen bacterial abundance and dairy traits. The use of 16S rRNA gene sequencing in this study did not allow for species-level affiliation, and additional work is needed to identify which microbial functions are involved and to associate the functions with milk traits. Then, it will be possible to consider the incorporation of microbiota abundance and microbial functions into genetic evaluation models to account for indirect genetic effects through the microbiota.Additional file 1: Table S1. Operational taxonomic unit (OTU) sequences with corresponding taxonomy affiliation. Consensus sequences of the OTU with corresponding affiliation from Kingdom to species.Additional file 2: Table S2. Heritability , milk fatty acids and operational taxonomic units (OTU). Genetic correlations between OTU abundances, fat content and milk fatty acids, such as butyric acid (C4:0), caproic acid (C6:0), caprylic acid (C8:0), capric acid (C10:0), lauric acid (C12:0), and palmitic acid (C16:0), oleic acid (cis-9 C18:1), rumenic acid (cis-9 trans-11 C18:2) and alpha-linolenic acid (C18:3n-3).Additional file 4: Table S4. Genetic correlations between protein content (PC), milk proteins and operational taxonomic units (OTU). Genetic correlations between OTU abundances, protein content and milk proteins, such as alpha-S1-casein, alpha-S2-casein, beta-casein, kappa-casein, alpha-lactalbumin and beta-lactoglobulin.Additional file 5: Table S5. Significant SNPs from GWAS of operational taxonomic units (OTU). Significant SNPs from GWAS of operational taxonomic units with candidate genes detected for each SNP.Additional file 6: Table S6. Functional annotation for gene IDs recovered from detected SNPs for microbiome GWAS. Description of the functional annotations for genes recovered from Ensembl platform and metabolic processes and KEGG pathways from DAVID platform.


A genome-wide association study (GWAS) is currently one of the most recommended approaches for discovering marker-trait associations (MTAs) for complex traits in plant species. Insufficient statistical power is a limiting factor, especially in narrow genetic basis species, that conventional GWAS methods are suffering from. Using sophisticated mathematical methods such as machine learning (ML) algorithms may address this issue and advance the implication of this valuable genetic method in applied plant-breeding programs. In this study, we evaluated the potential use of two ML algorithms, support-vector machine (SVR) and random forest (RF), in a GWAS and compared them with two conventional methods of mixed linear models (MLM) and fixed and random model circulating probability unification (FarmCPU), for identifying MTAs for soybean-yield components. In this study, important soybean-yield component traits, including the number of reproductive nodes (RNP), non-reproductive nodes (NRNP), total nodes (NP), and total pods (PP) per plant along with yield and maturity, were assessed using a panel of 227 soybean genotypes evaluated at two locations over two years (four environments). Using the SVR-mediated GWAS method, we were able to discover MTAs colocalized with previously reported quantitative trait loci (QTL) with potential causal effects on the target traits, supported by the functional annotation of candidate gene analyses. This study demonstrated the potential benefit of using sophisticated mathematical approaches, such as SVR, in a GWAS to complement conventional GWAS methods for identifying MTAs that can improve the efficiency of genomic-based soybean-breeding programs. Glycine max [L.] Merr.) is known as one of the most important legume crops worldwide with substantial economic value [Soybean  algorithms, as powerful and reliable mathematical methods, have been considered as an alternative to conventional statistical methods in GWAS analyses ,16. ReceIn this study, we aimed to (1) gain a better understanding of the genetic relationships between soybean yield and its component traits, and (2) investigate the potential use of RF and SVM algorithms in a GWAS for discovering MTAs for soybean-yield components in comparison with the most commonly used conventional GWAS methods. The results of this study may shed light on the potential use of ML algorithms in soybean GWAS studies and may offer new genomic tools for screening high-yielding genotypes with improved genetic gain in large breeding populations. −1, 15.21 ± 0.77 nodes, 3.33 ± 0.28 nodes, 11.89 ± 0.98 nodes, and 45.02 ± 8.54 pods, respectively (r) among all the measured traits were estimated using the Pearson coefficients of correlation (r = 0.97) and the NRNP (r = −0.63). RNP had the highest correlation with yield (r = 0.86) among all the tested yield components  and Glyma.19g224200 (GO:0010201), which, respectively, encode the chlorophyll catabolic process and phytochrome A (PHYA)-related genes, were identified as the strong candidate genes for maturity. Glyma.02g006500 (GO:0015996) was exactly detected in the peak SNP position of Chr2_695362, whereas Glyma.19g224200 (GO:0010201) was 119 Kbp from the detected peak SNP at Chr19_47513536. The yield-related QTL with the peak SNP positioned on Chr7_1032587 had the highest allelic effect compared to other detected peak SNPs (Glyma.07G014100 (GO:0010817), which encodes the regulation of hormone levels, was identified as the strongest candidate gene in yield. Two peak SNPs, Chr7_1032587 and Chr7_1092403, had the highest allelic effects for the NP trait among all the detected peak SNPs (Glyma.07G205500 (GO:0009693) and Glyma.08G065300 (GO:0042546) genes, which encode UBP1-associated protein 2C and cell-wall biogenesis, respectively, were detected as plausible genes influencing both NP and NRNP. Both detected candidate genes were collocated at the corresponding peak SNPs at Chr7_1032587 and Chr8_5005929 (Glyma.15G214600 (GO:0009920) and Glyma.15G214700 (GO:0009910) genes, which encode cell plate formation involved in plant-type cell-wall biogenesis and acetyl-CoA biosynthetic process, respectively, were nominated as strong candidate genes governing NRNP. Glyma.15G214600 (GO:0009920) and Glyma.15G214700 (GO:0009910) were 127 and 90 Kbp far from the peak SNP at Chr15_3495836, respectively. For the PP trait, the highest allelic effects were found in peak SNPs at Chr7_15331676, Chr11_5245870, and Chr18_55469601 (Glyma.07G128100 (GO:0009909) gene, which encodes the regulation of flower development, was the strongest candidate gene that can potentially affect PP. Glyma.07G128100 (GO:0009909) is located in the peak SNP position, Chr7_15331676.To identify the potential candidate genes of each of the detected MTAs, we used the LD decay distance of the panel and selected 150-kbp upstream and downstream of each SNP’s peak as the target regions . The fuleak SNPs B. Withineak SNPs C. In thi_5005929 D. Regard_5005929 E. The Gl55469601 F. The GlOne of the objectives of this study was to attain a better understanding of the roles of soybean-yield component traits in the production of total seed yield and how these traits can be used to facilitate the development of high-yielding soybeans with improved genetic gains. The genetic dissection of soybean-yield components and establishing genetic and genomics toolkits can be used for designing crosses and screening large breeding populations for selecting genotypes with improved yield components ,68. The p-values for individual SNP-trait GWAS tests. The performance of four GWAS methods was compared in this study, and the results showed that all the methods had acceptable performance in detecting MTAs for the tested traits in this particular population. Among all the tested GWAS methods, SVR-mediated GWASs had a higher aptitude to detect SNP markers with high allelic effects associated with the tested traits in this study. The SVR-mediated GWAS method considers the presence of a nonlinear relationship between input and output variables. This ability is used to build an algorithm with greater prediction accuracies . While cIn this study, several previously reported QTL were colocalized with identified MTAs using all tested GWAS methods. For maturity, for example, five soybean maturity QTL detected by SVR-mediated GWASs were colocalized with previously reported QTL associated with maturity ,43. At tGlyma.02g006500 (GO:0015996) is a protein ABC transporter 1 that is annotated as a chlorophyll catabolic process and located exactly in the peak SNP position at Chr02_695362. ATP-binding cassette (ABC) transporter genes play conspicuous roles in different plant-growth and developmental stages by transporting different phytochemicals across endoplasmic reticulum (ER) membranes [Glyma.19g224200 (GO:0010201) in E3 locus, which was previously discovered by Buzzell [Regarding the results of candidate gene identification within identified QTL, several candidate genes were detected using different GWAS methods. For example, among all the detected candidate genes associated with maturity, gene embranes . Becauseembranes ,82. Moreembranes . Additio Buzzell  and mole Buzzell , was det Buzzell . In addi Buzzell ,88. ThisGlyma.07G205500 (GO:0009693- UBP1-associated protein 2C) that annotated as the ethylene biosynthetic process was located exactly at the peak SNP position at Chr7_37469678. An interaction screen with the heterogeneous nuclear ribonucleoprotein (hnRNP) results in the production of oligouridylatebinding protein 1 (UBP1)-associated protein [Glyma.08G065300 (GO:0042546- MADS-box transcription factor), which is associated with cell-wall biogenesis, was located in the SNP position of Chr8_5005929. The genes of the MADS-box family can be considered as the main regulators for cell differentiation and organ determination [Among the candidate genes related to NRNP, gene  protein . It has  protein , leaf se protein , floral  protein , and chr protein ,95. In amination . Indeed,mination ,99,100.Gene expression dataset developed by Severin, et al.  showed tIn general, our results showed that ML-mediated GWAS methods are able to complement the conventional GWAS methods for better identification of the MTAs for traits of interest in soybean. However, the effectiveness of using ML methods in a GWAS should be tested in different soybean populations grown across different environments. In this study, a limited soybean population, which partially covers all the potential genetic variations in the soybean germplasm, was used. Therefore, for further evaluation of the effectiveness of an ML-mediated GWAS, it would be valuable to test the same approaches in a wide range of soybean genotypes using whole-genome sequencing data. In addition, although we used the cross-validation technique and considered several cofactors in our analyses to eliminate the potential false-positive errors, the optimal ML calibrations would be highly recommended to improve capturing the true signals and minimizing the level of errors in ML-based analyses. 2 seeding rate. The soil type and trials were maintained using standard tillage and cultural practices in both tested locations. No fertilizers were added during the soybean growth and development stages. The herbicides were applied twice before planting and in the middle of the growth period.A panel of 250 soybean genotypes was grown at the University of Guelph, Ridgetown Campus, in two locations, Palmyra  and Ridgetown , in ON, Canada, over the course of two years, 2018 and 2019. The randomized complete block designs (RCBD) with two replications were used for all four environments (two locations × two years). In general, there were 500 and 1000 research plots per environment and year, respectively. Each plot consisted of five 4.2 m long rows with 57 seeds per m−1 at 13% moisture) for each plot was estimated by harvesting three middle rows and adjusted based on the maturity date. Soybean seed yield components, including the total number of reproductive nodes per plant (RNP), the total number of non-reproductive nodes per plant (NRNP), the total nodes per plant (NP), and the total number of pods per plant (PP), were measured using 10 randomly selected plants from each plot. The maturity was recorded as the number of days from planting to physiological maturity (R7) [The soybean seed yield (t haity (R7)  for each®, Saint Louis, MO, USA), DNA was extracted for soybean genotypes, and the quantity of DNAs was checked via Qubit® 2.0 fluorometer . For genotyping-by-sequencing (GBS), DNA samples were sent to Genomic Analysis Platform at Université Laval . The GWAS panel was genotyped via a GBS protocol based on the enzymatic digestion with ApeKI [Young trifoliate leaf tissue for each soybean genotype from the first replication of the trial at Ridgetown in 2018 was collected in a 2 mL screw-cap tube. The leaf samples were freeze-dried for 72 h, using the Savant ModulyoD Thermoquest . By using the DNA Extraction Kit  was used as one of the common error control methods [Y stands for the trait of interest (soybean seed yield and yield component traits); b is the vector of block effects that incorporates all the locations and replications, which are added to the overall mean (fixed); g is the vector of random genotype effect, in which g ~ N; i is the vector of GxE interaction effects (random), in which i ~ N; and εij stands for the residual effect. A, B, and C stand for the incidence matrices of b, g, and i effects, respectively.The best linear unbiased prediction (BLUP) as one of the common linear mixed models  was used methods ,123,124.H2cal function in the inti open-source R package (https://inkaverse.com accessed on 1 May 2022) using the following equation: The heritability (Equation (2)) was calculated for soybean seed yield and yield components using the A total of 17,958 high-quality SNPs from 227 soybean genotypes were used to conduct the population structure analysis using fastSTRUCTURE . Five ruGAPIT and rmvp packages [Caret package [Since different GWAS methods may capture different genomic regions , MLM andpackages ,128, and package  in R sofY is the phenotypic value, X is the incident matrix effect, a stands for the vector for the incident matrix, MZ represents the genotype indicator for the Mth SNPs, yM is equal to the effect of the SNPM with an assumed normal distribution and mean zero of variance, and ie represents the residual.This GWAS method is based on the likelihood ratio between the full model, consisting of the marker of interest, and the reduced model, which is known as the model without the marker of interest . MLM is iY is the observation on the ith sample, ie stands for the residual, and iU represents the total genetic effect of the ith sample.This GWAS takes the advantages of using MLM as the random model and stepwise regression as the fixed model iteratively . FarmCPUiY is the observation on the ith sample; Ni1, Ni2, …, itN represents the genotypes of the t pseudo-QTNs; F1, F2, F3, …, tF is equal to the corresponding effect for the pseudo-QTNs; ijM represents the genotype of the jth SNPs and ith sample; jK stands for the corresponding effect of the jth SNPs; and ie represents the residual. Additionally, the fixed-effect model (FEM) is used in FarmCPU to test the N number of SNPs simultaneously (Equation (5)):iY stands for the predicted value of the genotype iX, T is the total number of constructed trees, and B is the total number of samples. In this experiment, a 1000-set of decision trees was constructed in the forest, and the GWAS analysis was conducted by measuring the importance of each feature [Random forest (RF) is known as one of the powerful non-parametric regression approaches that is derived from aggregating the bootstrapping in various decision trees . Several feature , which wb is equal to the degree of the kernel, a is equal to the constant number, and T stands for transpose element.Support-vector regression (SVR) is known as one of the common supervised learning methods in prediction problems . This alThe association statistics in this algorithm can be achieved by estimating the feature importance that was previously proposed by Weston, et al. . In thisThe implementation of ML algorithms in GWASs was reviewed well by Enoma, et al. . In brieAs one of the common indices for tree-based algorithms, the impurity index was chosen as the metric of the feature importance for the RF algorithm. Regarding the SVR algorithm, the variable importance method for SVR  was implG. max cv. William 82 reference-genome gene models 2.0 in SoyBase (https://www.soybase.org accessed on 1 May 2022). After listing potential candidate genes in defined windows around each significant SNP, at the peak of each QTL, the gene ontology annotation, the GO term enrichment (https://www.soybase.org accessed on 1 May 2022), and the report from previous studies were used as the criteria to select and report the most relevant candidate genes associated with the identified QTL. The Electronic Fluorescent Pictograph (eFP) browser for soybean (www.bar.utoronto.ca accessed on 1 May 2022) was also used to generate additional information such as tissue- and developmental-stage-dependent expression  for the, et al. .A better understanding of the genetic architecture of the yield component traits in soybean may enable breeders to establish more efficient selection strategies for developing high-yielding cultivars with improved genetic gains through marker-assisted selections within large breeding populations. Major yield component traits such as maturity, NP, NRNP, RNP, and PP play important roles in determining the overall yield production in soybean. Using correlation and distribution analyses, this study showed the importance of those traits in determining the total soybean seed yield. Furthermore, this study demonstrated the potential benefit of exploiting SVR-mediated GWASs for discovering MTAs associated with yield component traits in soybean. SVR-mediated can be recommended to complement conventional GWAS methods with greater power for detecting MTAs for complex traits such as yield and its components in soybean and possibly other crop species. In order to verify the causal relationship between identified MTAs and the target phenotypic traits, we identified candidate genes within each QTL using gene annotation procedures and information, and the results were promising. Nevertheless, further studies are required to characterize the identified candidate genes in this study and confirm the efficiency of SVR-mediated GWASs for discovering genomic regions with causal relationships with complex traits in plant species.