The comorbidity between polycystic ovary syndrome (PCOS) and obesity has long been observed in clinical settings, but their shared genetic basis remains unclear.Nfemale=434,794; childhood BMI, N=39,620), waist-to-hip ratio , WHR adjusted for BMI , and PCOS , we performed a large-scale genome-wide cross-trait analysis to quantify overall and local genetic correlation, to identify shared loci, and to infer causal relationship.Leveraging summary statistics of large-scale GWAS(s) conducted in European-ancestry populations on body mass index , childhood BMI , and WHR , all withstanding Bonferroni correction. A suggestive significant genetic correlation was found between PCOS and WHRadjBMI . Partitioning the whole genome into 1703 nearly independent regions, we observed a significant local genetic correlation for adult BMI and PCOS at chromosome 18: 57630483–59020751. We identified 16 shared loci underlying PCOS and obesity-related traits via cross-trait meta-analysis including 9 loci shared between BMI and PCOS , 6 loci shared between WHR and PCOS, and 5 loci shared between WHRadjBMI and PCOS. Mendelian randomization (MR) supported the causal roles of both adult BMI  and childhood BMI  in PCOS, but not WHR  or WHRadjBMI . Genetic predisposition to PCOS did not seem to influence the risk of obesity-related traits.We found positive genetic correlations between PCOS and adult BMI (Our cross-trait analysis suggests a shared genetic basis underlying obesity and PCOS and provides novel insights into the biological mechanisms underlying these complex traits. Our work informs public health intervention by confirming the important role of weight management in PCOS prevention.The online version contains supplementary material available at 10.1186/s12916-022-02238-y. Polycystic ovary syndrome (PCOS) is the most common endocrine disorder affecting women of childbearing age, characterized by reproductive dysfunction including hyperandrogenism, menstrual and/or ovulatory irregularity together with subfertility, and metabolic dysfunction including hyperinsulinemia, insulin resistance, and type 2 diabetes , 2. MoreThe development of obesity and PCOS involves strong genetic components evidenced by recent discoveries from large-scale genome-wide associations studies (GWAS). These genetic data enable the utilization of a compiled analytical strategy—genome-wide cross-trait analysis—to determine shared and distinct genetic architecture which can provide better understandings and novel insights into disease mechanisms . Such anIn addition to the degree of adiposity, location and distribution of fat accumulation are informative predictors for obesity sequelae. For example, abdominal visceral fat, a known contributor to metabolic dysfunction including insulin resistance and abnormal adipokine and fatty acid release , is impoN=39,620) [adjBMI, adult)  in the development of PCOS  [Therefore, we aim to extend previous findings by providing a systematic evaluation of the relationship between obesity-related traits and PCOS, leveraging the hitherto largest GWAS summary statistics conducted for each trait. We examined the role of BMI (childhood (before age 10)   and adul=39,620) ), waist-=39,620)     were first used to obtain LD-based clumps [For HRadjBMI , 15. In d clumps , followechildhood BMI, the hitherto largest GWAS was conducted at the latest time point between 2 and 10 years old among 61,111 children of European ancestry [Ndiscovery = 39,620) imputed to the 1000 Genomes Project or the HRC were analyzed using a fixed-effect inverse variance-weighted meta-analysis. Top associated SNPs identified in the discovery stage at a P-threshold of 5×10−6 were taken forward for replication in 15 cohorts  and results of the two stages were combined using meta-analysis. To identify independent top-associated SNPs, Genome-wide Complex Trait Analysis based on summary statistics with LD estimation from the Generation R Study as a reference sample was applied. Top associated SNPs in the combined meta-analysis reaching a stringent P-threshold of 5×10−8 were identified.For ancestry . In the adjBMI-associated index SNPs, Additional file From these GWAS(s), we extracted the effect size and relevant information of instrumental variables (IVs) identified in women   quantifies the average sharing of genetic effect between two traits unaffected by environmental confounders. The estimate ranges from − 1 to 1, with − 1 indicating a perfect negative genetic correlation and 1 indicating a perfect positive genetic correlation. It can be quantified using GWAS summary data through an algorithm implemented in software linkage-disequilibrium score regression (LDSC) [Genome-wide genetic correlations (n (LDSC) , 18 alsoβj and γj are the effect sizes of SNP j on traits 1 and 2, rg is the genetic covariance, M is number of SNPs, N1 and N2 are the sample sizes for traits 1 and 2, Ns is the number of overlapping samples, r is the phenotypic correlation in overlapping samples, and lj is the linkage disequilibrium score. We used pre-computed LD scores obtained from ~ 1.2 million common SNPs in European ancestry represented in the HapMap3 reference panel, commonly recognized as of high imputation quality.where Genome-wide genetic correlations estimated by LDSC quantify the genome-wide contribution of genetic variation to the correlation between two traits. It is possible that even though two traits show negligible genome-wide genetic correlation, genetic variations localized at a specific genomic region contribute to the correlation between two traits. We, therefore, measured the pairwise local genetic correlations between each of the obesity-related traits and PCOS using ρ-HESS, an algorithm that partitions the genome-wide genetic sharing across 1703 nearly independent linkage disequilibrium (LD) regions of 1.5 Mb and precisely quantifies the genetic correlation between pairs of traits due to genetic variation restricted to these genomic regions.Hom and SHet. SHom is based on the fixed-effect meta-analysis method and is the most powerful when genetic effect sizes are homogenous, which is unlikely to be true especially when multiple traits are analyzed. SHet is an extension of SHom with improved power that allows for heterogeneous effects of a trait from different study designs, environmental factors, or populations, as well as heterogeneous effects for different phenotypes, which is more common in practice. We used pairwise SHet to combine summary statistics for each of the obesity-related traits with PCOS. We applied PLINK [Psingle trait< 1×10−3 (in each single trait) and PCPASSOC< 5×10−8 (in cross-traits). We used Ensembl Variant Effect Predictor (VEP) for detailed functional annotation for the variants identified by CPASSOC.Cross-phenotype association analysis (CPASSOC) integrates GWAS summary statistics from multiple correlated traits to detect evidence for variants associated with multiple traits across studies while controlling population structure and cryptic relatedness . CPASSOCed PLINK  clumpinghttps://github.com/hailianghuang/FM-summary) [Index SNP does not necessarily represent causal variants. We further identified a 99% credible set of causal variants through a simplified Bayesian fine-mapping method named FM-summary (summary) . Brieflysummary) , 22.To gain putative biological insights into the shared variants identified between obesity and PCOS, we performed GTEx tissue enrichment analysis including all genes in clumping regions for each trait identified by CPASSOC using software functional mapping and annotation (FUMA), the GENE2FUNC process with 54 tissue types from GTEx (version 8). FUMA obtained differentially expressed gene (DEG) sets for each tissue type by using the normalized expression (zero mean of log2(RPKM+1)) and conducting two-sided t-tests per gene per tissue. Genes were defined as DEG set in a specific tissue if Bonferroni corrected P-value<0.05 and had an absolute log-fold change ≥ 0.58 (background DEGs). Genes identified by CPASSOC were tested against those background DEG sets by hypergeometric tests to examine if they were overrepresented in DEG sets in specific tissue types, thus, identifying the most relevant tissue types.P-threshold (0.05/396) was used.To identify tissue and cell-type-specific enrichment of SNPs, we used LD score regression applied to specifically expressed genes (LDSC-SEG)  which teTo test for the causal relationship between each of the obesity-related traits and PCOS, we conducted a two-sample MR. We applied an inverse-variance weighted (IVW) approach  as our phttps://www.ebi.ac.uk/gwas/, accessed on 03/18/2021). We conducted a leave-one-out analysis where we removed one IV each time and performed IVW using the remaining IVs to identify outlying instruments. We also examined a scenario through MR-Clust [We performed important sensitivity analyses to validify MR model assumptions. We excluded palindromic IVs with strand ambiguity  and pleiotropic SNPs  according to GWAS catalog (MR-Clust  where seP< 0.05/4), we found a strong genetic correlation between BMI and PCOS  . Given the complex interplay between BMI and WHR [adjBMI, a residual component of WHR in which the effect of BMI was removed. Perhaps not surprisingly, when the effect of BMI was removed from WHR (WHRadjBMI), the prior positive genetic correlation between PCOS and WHR was attenuated to null .We first estimated the overall genetic correlation between obesity-related traits and PCOS using cross-trait LDSC. After correcting for multiple testing , a significant local genetic correlation was only observed for adult BMI and PCOS at chr18: 57630483–59020751, a genetic region harboring MC4R, a locus previously reported to be associated with adult BMI, childhood BMI and obesity in PCOS [Motivated by these findings, we further explored the local genetic correlation using ρ-HESS. As shown in Fig.  in PCOS , 30–33.adjBMI and PCOS  . Notably, none of these 16 SNPs identified by CPASSOC were previously reported to be associated with PCOS at genome-wide significance (0 out of 16 SNPs), while most of them were associated with obesity-related traits (14 out of 16 SNPs). For adult BMI and PCOS, the most significant shared SNP was rs10938397, (PCPASSOC=1.25×10−49) located at an intergenic region. The second most significant shared SNP  was located near GIPR, a gene associated with BMI and glucose tolerance [MIR642A, a gene involved in post-transcriptional regulation of gene expression. Notably, among the 5 adult BMI-PCOS shared SNPs, rs705696 was near ERBB3, a locus known to be associated with PCOS. For childhood BMI and PCOS, the most significant shared SNP  was near FTO, a locus known to affect BMI and the predisposition to childhood and adult obesity [PCPASSOC=1.97×10−51) was also near the FTO locus. Among the 6 variants associated with both WHR and PCOS, 4 were also found to be shared between WHRadjBMI and PCOS . For example, rs3767846 was near PROX1, a locus associated with fasting glucose-related traits [adjBMI and PCOS  was located near genes SLC38A11 and RNA5SP111. SLC38A11 encodes a protein that belongs to the solute carrier family and has a role in sodium and amino acid transportation [RNA5SP111 is a 5S ribosomal pseudogene [To identify individual SNPs affecting both obesity-related traits and PCOS, we next conducted a pairwise CPASSOC analysis. As shown in Table olerance , 35, andeudogene . DetaileadjBMI-PCOS shared genes, stomach showed the most significant enrichment although notwithstanding multiple correction. No significant tissue enrichment was identified for childhood BMI and PCOS. For LDSC-SEG enrichment analysis, as shown in Additional file P< 0.05/396) for PCOS.We attempted to understand the underlying biological mechanisms by identifying relevant tissues using FUMA. As shown in Additional file adjBMI and PCOS providing candidates for downstream experimental analysis.For each of the 16 shared loci identified as significant by the cross-trait meta-analysis, we identified a 99% credible set of causal variants. Lists of credible set SNPs in each shared locus for obesity-related traits and PCOS from fine mapping are shown in Additional file 2) in adult BMI  using 278 female-specific IVs. The effect did not alter using MR-Egger  or weighted median  approach. We did not observe any sign of horizontal pleiotropy (P for MR-Egger intercept=0.21). Sensitivity analysis removing palindromic SNPs or pleiotropic SNPs —a less than 10% number of IVs compared to adult BMI. Unfortunately, and perhaps not surprisingly, we were underpowered to perform sensitivity analyses for this trait due to the limited number of IVs. Directional consistent results were observed in MR-Egger analysis although the significance was attenuated to null  .On the contrary, we did not find any significant association between genetically predicted WHR and risk of PCOS . Our results imply a causal role of BMI but not WHR in the development of PCOS. We anticipate observing a null effect of WHRadjBMI-PCOS associations aggregated closely to 1.0. In the subsequent clustering analysis  was not driven by outlying variant. As shown in Additional file adjBMI beta = 0.02, 95% CI = − 0.01–0.04)  by Day et al. [rg=0.47, P=2.19×10−16) improved statistical power by using an enlarged sample size  as well as reduced heterogeneity by using sex-specific adult BMI GWAS summary statistics, both of which previous studies did not have a chance for. Findings on the [−9) so all were robustly associated with exposure of interest, guaranteeing the “relevance” assumption. We excluded SNPs associated with potential confounders on the exposure-outcome relationship to satisfy the “exclusion restriction” assumption.Findings from our study are largely in line with those from the conventional epidemiological studies yet provide novel insights in several aspects. In line with the positive overall genetic correlation identified for adult BMI and PCOS  and the biracial USA Babies substudy of the Bogalusa Heart Study (N=1247) have suggested an association between greater childhood BMI and PCOS among the white population  [N=39,620) is not sufficiently large for ρ-HESS recommendation . Future studies with larger sample sizes are warranted to replicate our findings.In addition to adult BMI, childhood BMI appears to influence the risk of PCOS later on , 43. FinadjBMI-PCOS causal association together with genetic correlation further confirmed the validity of our results. However, these results do not necessarily mean that abdominal visceral fat is not important in PCOS. While BMI is found to be highly correlated with excess fat mass (r=0.94) and abdominal visceral fat (r=0.71) [Using WHR as a proxy to abdominal fat, we did not find any significant causal association for this trait with PCOS. Raw WHR is likely to be confounded by BMI as indicated by our previous genetic correlation analysis . Dissect(r=0.71) , results(r=0.71) , however(r=0.71) –48. Inde(r=0.71) , which m(r=0.71) —therefor(r=0.71) .ERBB3, FTO, PROX1, GIPR, and MC4R in relation to potential pathogenesis. ERBB3 encodes epidermal growth factor receptors (EGFRs) and has been reported to be associated with PCOS by a meta-GWAS [ERBB3 expression and EGFR signaling mediates LH-induced steroidogenesis, which plays an important role in follicular development [FTO, despite a large number of studies that have confirmed its contribution to adult obesity, childhood obesity, and obesity-related traits [FTO and PCOS whereas others have not [FTO and PCOS may partially be mediated through obesity. Indeed, the most evident association between FTO and PCOS was observed in obese PCOS women, which was attenuated when adjusting for BMI [FTO on lipid oxidation in PCOS women might also contribute to the mechanism underlying the comorbidity of obesity and PCOS [PROX1 encodes one of the proteins of the homeobox transcription factor family, which plays an essential role in organ development during embryogenesis [PROX1 was associated with visceral fat accumulation [PROX1 has also been found to be differently methylated in adipose tissue in PCOS women and controls [PROX1 has also been linked to glycemic alteration (fasting glucose and type 2 diabetes) [GIPR influences glycemic traits including 2-h glucose level and insulin secretion [GIPR encodes a G-protein coupled receptor for gastric inhibitory polypeptide (GIP), which has been demonstrated to stimulate insulin release in the presence of elevated glucose. Evidence has suggested that modulation of GIPR affects progesterone synthesis and expression of many progestogenic factors and enzymes that may involve in the subfertility feature of PCOS [MC4R, a gene previously found to be associated with higher adult BMI and childhood BMI. Using BMI-matched samples or BMI-adjusted statistical models, studies have found MC4R to be associated with an elevated BMI in PCOS [MC4R encodes melanocortin 4 receptor that plays an important role in central melanocortin neuronal pathways [MC4R gene in the brain hypothalamus which may link to metabolic disorders [Genetic correlation provides genetic insights into the observational associations by estimating the degree of pleiotropy or causal overlaps shared by two traits while MR analysis infers causal relationships. We additionally performed a cross-trait meta-analysis to further dissect the complex genetic relationships between obesity and PCOS. Using cross-trait meta-analysis, we identified 16 SNPs shared between obesity-related traits and PCOS, indicating shared biological mechanisms underlying obesity and PCOS. Among these shared loci, we highlight the locus of eta-GWAS . Studieselopment . EGFRs aelopment . For gend traits , 54–56, have not , 57–59. and PCOS . PROX1 eogenesis . Resultsmulation , 63. PROcontrols . In addiiabetes) —another ecretion . GIPR en of PCOS . Notably in PCOS , 66. MC4pathways . Furtherisorders .Results from GTEx tissue enrichment analysis should be interpreted with caution due to the limited number of shared genes identified between obesity and PCOS. Similarly, the null findings from LDSC-SEG do not necessarily indicate a negligible shared biological mechanism given the limited sample size of PCOS GWAS and the positive findings identified by our other analyses.P=1.8×10−5) [We acknowledge several limitations. First, PCOS, as a complex disease, is classified into four phenotypes according to the presence or absence of ovulatory dysfunction, hyperandrogenism, and polycystic ovarian morphology . Our stu.8×10−5) , HoweverOur work investigated the shared genetic basis underlying obesity and PCOS. Future work should be to perform large, prospective longitudinal clinical studies to define whether PCOS women carrying a specific genotype are at increased risk for developing, e.g., cardiovascular disease, type 2 diabetes, non-alcoholic fatty liver disease, and link to mortality. Of outmost importance, our study confirmed the causative role of BMI in PCOS prevention, future studies on whether medical weight reduction or bariatric surgery alleviates PCOS-related comorbidities are needed. Moreover, the use of gene-modified mice, e.g., knock-in/knock-out of obesity/PCOS risk genes is of importance to define the role of identified specific genes and rare genetic variants and would provide novel insights into the biological mechanisms underlying these complex traits.In conclusion, leveraging the largest sex-specific GWAS summary statistics to date, the current study furthered our understanding of the observational association between obesity and PCOS by showing evidence of genetic correlation, revealing shared loci, and inferring causal relationships, all of which may provide insights into the biological pathways. Our work informs public health intervention by confirming the important role of weight management from childhood through adulthood in PCOS prevention.Additional file 1: Table S1. Adult BMI IVs. Table S2. WHR IVs. Table S3. WHRadjBMI IVs. Table S4. childhood BMI IVs. Table S50. PCOS IVs. Table S6. Data sources, sample sizes, number of IVs and F-statistics. Table S7. Summary of contributing cohorts/consortia/studies in each GWAS. Table S8. Annotation of genome-wide significant SNPs from CPASSOC. Table S9. 99% credible set SNPs.Additional file 2: Figure S1. Local genetic correlation between childhood BMI, WHR, WHRadjBMI and PCOS. Figure S2. GTEx tissue enrichment analysis. Figure S3. Cell-type specific enrichment analysis. Figure S4. Box plot of betas in leave-one-out analysis. Figure S5. MR-clust analysis.


Use of genomic prediction (GP) in tetraploid is becoming more common. Therefore, we think it is the right time for a comparison of GP models for tetraploid potato. GP models were compared that contrasted shrinkage with variable selection, parametric vs. non-parametric models and different ways of accounting for non-additive genetic effects. As a complement to GP, association studies were carried out in an attempt to understand the differences in prediction accuracy. We compared our GP models on a data set consisting of 147 cultivars, representing worldwide diversity, with over 39 k GBS markers and measurements on four tuber traits collected in six trials at three locations during 2 years. GP accuracies ranged from 0.32 for tuber count to 0.77 for dry matter content. For all traits, differences between GP models that utilised shrinkage penalties and those that performed variable selection were negligible. This was surprising for dry matter, as only a few additive markers explained over 50% of phenotypic variation. Accuracy for tuber count increased from 0.35 to 0.41, when dominance was included in the model. This result is supported by Genome Wide Association Study (GWAS) that found additive and dominance effects accounted for 37% of phenotypic variation, while significant additive effects alone accounted for 14%. For tuber weight, the Reproducing Kernel Hilbert Space (RKHS) model gave a larger improvement in prediction accuracy than explicitly modelling epistatic effects. This is an indication that capturing the between locus epistatic effects of tuber weight can be done more effectively using the semi-parametric RKHS model. Our results show good opportunities for GP in 4x potato. Solanum tuberosum L.) is one of the most consumed food crops in the world, behind only rice and wheat  has been utilised previously in the study of GP of autopolyploid crops , year of commercial introduction, and availability of the cultivars. Some of these varieties were analysed in previous studies that used similar criteria for selection  was digested with ten units of EcoT22 (Clontech) and incubated at 37°C for 2 h and then heat killed. Samples were then ligated with 640 units of T4 ligase (NEB) and phased adaptors with TGCA overhangs at 22°C for 1 h and heat killed. The ligated samples were diluted in the ratio 1:10 with water, and then amplified for 18 cycles to add barcodes. Barcoded libraries were SPRI purified, quantified, and pooled in groups of 48 samples. Pooled samples were SPRI purified, quantified, and diluted to 2 nM for sequencing on the Illumina HiSeq 2500 using single-end 1 × 100 reads. Sequence reads were mapped against the potato reference genome sequence of DM v4.04, including the chloroplast and mitochondrial sequences using Burrows-Wheeler Aligner 0.7.12. After the removal of monomorphic markers, those with more than two alleles and markers from repetitive regions of the genome, 870 thousand bi-allelic markers were available for further filtering. Markers with minor allele frequency <0.01 and those with read depths <10 or >100 were removed. From the remaining markers, the posterior probability of allele dosage, conditional on both allele counts and sequencing error, was calculated see . SimilarGenotype assignment probabilities were used as a filter criterion. For each individual, markers were removed when the highest genotype assignment probability was below a threshold. Stricter thresholds created more missing information and decreased the number of markers, since markers without information for more than 25% of the individuals were removed. Allele dosage was then determined as the dosage with maximum genotype probability. Probability thresholds of 0.85, 0.75, and 0.5 resulted in marker matrices of 19, 26, and 39 thousand markers, respectively. Using an additive GBLUP model, a preliminary GP analysis was performed to decide which marker matrix should be used as there may be a trade-off between the quantity and quality of markers. In almost all cases, the 39 K marker matrix gave the most accurate predictions and will henceforth be used for all analyses . The larAlthough linkage disequilibrium (LD) was not calculated in this study, it was calculated for an overlapping panel of tetraploid potato , with 147 rows and 39,000 columns. Each element of X gives the discrete count of alternative alleles  assigned by genotype probabilities, at a given marker position for a given cultivar. When these counts are entered in a design or relationship matrix and a single parameter is estimated to quantify the dependence of the phenotype on the allele count, then this implies that marker effects are additive.For imputing the missing marker information, the mode was used. This was compared to mean imputation using the 39 K marker set mentioned above and a GBLUP model. The GP accuracies resulting from marker matrices imputed with the mode were slightly higher than those imputed from the mean.Field trials were performed in 2017 and 2018 at three locations: Spain, Poland, and the Netherlands. Seed tubers were planted in plots consisting of eight plants. A row-column resolvable design was implemented with two complete blocks, and varieties dispersed across the field using latinisation over rows and columns , plot tuber count (number of tubers), mean tuber length (millimetres), and dry matter content (percentage). Adjusted means were calculated by correcting for row and column trends, as well as block effects using the model:y is a vector of phenotypic observations. Equation (1) allows us to adjust for field trends  and extract the best linear unbiased estimate (BLUE) of each genotype (G). Complete blocks were used in each trial therefore a fixed term for the block effect is suitable in the statistical model. Rows and columns within blocks were incomplete and therefore treated as random effects having normal distributions as follows: where For investigating genotype by environment interaction (GxE), the BLUEs from the six trials  will be useful, however for this application of GP, we require one vector of observations for a given trait, as if they came from one single environment. To consolidate our six phenotypic values, we again calculated the adjusted means of each genotype, after correcting for the effect of different trials using Equation (2).y are the BLUEs calculated from Equation (1), and ϵ captures the variation from the interaction between genotype and trial as well as within trial error variation. Equation (2) is an across trial model, while Equation (1) was used for within trial analyses. This could have been combined in one statistical model, but for future GxE applications, and the ability to carefully assess each trial for outliers, it was conducted in two steps. A comparison of BLUEs calculated from the method described here vs. one single model was done and the results were the same. The BLUEs from Equation (2) will be used as the response variable for GP analyses going forward. This study is therefore a two-step analysis since phenotypic adjusted means and GP are done with separate models. ASREML  and 2 years (T):To have an understanding of how much phenotypic variation can be attributed to between-genotype variation, broad-sense heritability was calculated. Using the BLUEs from Equation (1) as the response variable, we apply the following model across our three locations . The BLUEs from Equation (1) give only one value for each genotype per trial (year and location combined), for this reason our error term (ϵ) in the heritability equation captures the variation from the three way interaction of genotype, location, and year. Averaging a genotypic effect across multiple trials without including marker information, is closer to an estimation of repeatability than heritability  based on the work of VanRaden . Za and Zd are design matrices to relate observations to additive genetic effects and dominance effects. The vector of dominance effects is indicated by d and follows a normal distribution: GD was built using the AGHmatrix R-package, as derived by Endelman et al.  is an extension of Equation (4), with the inclusion of a term to capture epistatic effects. GE, the Hadamard product of GA (GA#GA) was used , and to calculate Full Auto-tetraploid GBLUP:f, the vector of effects in Equation (6), has length 5R where R is the number of markers  is the same as described in Equation (3), but the random genetic values have a different distribution: GA, is replaced by the kernel matrix, Bayesian LASSO:y), overall mean (μ), and non genetic (or unmodelled) influences plus error (ϵ). Where it differs from our previous GP models is in the term Xb, which directly links the marker design matrix X, to the marker effects b. The marker effects are assumed to come from a distribution and in the case of Bayesian LASSO, a double exponential (Laplace) distribution, b ~ Lap, or alternatively:The first five genomic predictions described above estimate genotypic effects, the Bayesian models however estimate marker effects. Equation (7) includes terms for phenotype (j), up to a total of R markers.The λ parameter is inversely proportional to the variance of the distribution and is estimated from the data. The probability density function is multiplied across all markers , however Bayes A assumes that marker effects come from a scaled-t distribution with v degrees of freedom, BAYES Cπ: The Bayes Cπ model assumes that marker effects come from a mixture distribution where a proportion of markers (π) have zero effect and the remainder (1 − π) have non-zero effects from a normal distribution, such that:Because markers are separated into either having an effect or having no effect, this model is performing marker selection. The proportion of zero effect markers π, is estimated from the data.The three Bayesian models are better suited for traits controlled by few large effect loci, whereas the models mentioned before are better for predicting traits with many small effect loci  . These 105 individuals were sampled in order to minimise the genetic distance between the training and validation sets, using a sampling method based on the coefficient of determination . The error term ϵ captures non-genetic residuals plus error, and is assumed to follow a normal distribution as seen in prior models. The term β represents the marker effect and X is the marker matrix containing genetic information that may be coded differently depending on the assumed type of effect (see In Equation (8), fect see .From p-values for marker effects transformed to a log scale (−log10p). Not correcting for population structure will result in spurious associations, and this was investigated by a visual assessment for inflation of p-values.The impact of population structure on the GWAS analysis was evaluated by looking at the quantile-quantile plots of the Neff is estimated from the eigen values of the marker matrix. This resulted in 222 effective regions from the 39,000 markers. For each marker effect assumption , significant markers were extracted and used as explanatory variables, along with the first three principal components , in a linear regression model. The R2 statistic of this model is the fraction of the total sum of squares due to genotypic differences, that can be explained by markers  an assessment of population structure was conducted via Principal Components analysis , analysitatistic . A list FST and AMOVA calculations, the three small market classes were not included as they did not meet the requirement of minimum population size for these analyses . At this level of analysis, outliers were detected and removed and the extracted BLUEs were then pooled across all trials as described in the Materials and Methods section. The resulting distributions and correlations between phenotypic values can be seen in H2 values of 0.78, 0.79, 0.91, and 0.96, respectively. These heritability estimates are quite high and most likely because of the repeated trials at three locations and 2 years.Broad-sense heritability was calculated for tuber weight, tuber count, tuber length, and dry matter resulting in The results of GP analyses on the four traits, compared across eight statistical models can be seen in There is no clear ranking of model performance across all traits, however Model ranking can better be assessed on a per trait basis, as the best performing model depends on the trait analysed. An additional result from the Bayes Cπ model is the fraction of markers selected because of their potential QTL effects. For dry matter 0.27 markers were selected while the for tuber weight, half (0.5) of the markers were selected. The proportion of selected markers for tuber length and count was 0.35 and 0.34, respectively. This gives an idea of trait architecture which is investigated further in the next section.p-values when these fixed effects were excluded (results not shown), and no difference when they were introduced to the GWAS model. This can be attributed to the lack of population structure as reported previously, thus a model simply with a genomic relationship matrix was enough to avoid spurious associations between markers and traits. The threshold for identifying significant markers was −log10p = 3.65, after the 0.05 threshold was adapted for multiple testing  was applied. Two further models were tested, one that included fixed effects for market class assignments and another that included fixed effects for the first three principal component axes. A look at the QQ-plot showed no significant inflation of log10(p)] and the most abundant markers appearing above the threshold. For tuber count we see significant markers in more abundance when a dominant coding of the marker matrix is considered. There are multiple flanking “hits” on chromosomes 1 and 3 when we assume simplex dominance for the reference allele. Chromosomes 4 (the two significant markers overlap on the plot) and 8 also show neighbouring markers with significant associations to tuber count when dominance is assumed to occur in the presence of a single alternative allele.Across the five tested GWAS models for dry matter content, the most significant association with markers is observed when an additive effect is assumed . When coManhattan plots of tuber weight did not show much evidence of significant QTLs in this analysis . There aR2), which can be interpreted as the amount of phenotypic variance that can be explained by the significant markers and/or population structure.Manhattan plots can be ambiguous, therefore further analysis was done by performing a linear regression to uncover which marker effect type is more important for trait expression. Reported in Of the four traits, the variance of dry matter is best explained from marker information, and also has the biggest influence from principal components alone. This does not agree with previous population structure analysis , but thoThe primary focus of this study was to explore and compare statistical models for genomic prediction in tetraploid potato. As a secondary focus, a genome wide association analysis was conducted to identify trait architecture and thus explain the reasons for differences in prediction accuracies from trait to trait. The same marker profile was used for both GP and GWAS. It is worth noting that Bayes-R and Genome-wide Complex Trait Analysis (GCTA) can simultaneously perform GP and GWAS, therefore deserving of further study. However, for this study, we focused on a tetraploid species and therefore wanted to ensure that both the GP and GWAS analyses were tailored for tetraploids.Translating these findings to a traditional breeding program expose the limitations of this study. Only 147 cultivars were analysed in this study, spread over several market classes. In a traditional breeding program thousands of new hybrids can be evaluated within one particular market class. Despite these limitations, the work done here still shows that there is merit using genomic selection, especially after the first round of phenotypic selection where a majority of the material has been discarded. After this stage genomic selection can then significantly speed up the breeding cycle.Broad-sense Heritability estimates were quite high. As mentioned previously, our heritability estimates can more accurately be defined as repeatability estimates . The trait architecture revealed in the GWAS section, showed that significant dominant markers explained the most phenotypic variation, therefore targetting these non-additive effects resulted in the highest prediction accuracy. Trying to capture these non-additive effects with the full tetraploid model did not increase prediction accuracy.Yield was one of the traits analysed by Amadeu et al. , howeverThe explicit modelling of epistasis for specific gravity in Endelman et al.  gave a sThe full tetraploid model  when traits are controlled by a few high impact loci  when moving from mixed to marker effect modelling, however GWAS findings were unable to explain this result. The significant additive markers for yield explained very little phenotypic variation (12.92%), therefore it was unexpected that a marker effect model would have even slightly outperformed a GBLUP model. Habyarimana et al.  also fouFor GP in auto-tetraploids, there are very little differences between different types of shrinkage methods, and models that do both shrinkage and variable selection.GWAS can assist in deciding what model strategies should be considered, especially when considering capturing non-additive effects. When GWAS reveals significant dominant effect markers (simplex), this should be modelled specifically in GP models.Tuber weight shows evidence of epistasis, therefore semi- and non-parametric models should be used to predict this trait. Further investigation can include extending the dominance relationship matrix to include duplex dominance and modelling higher levels of epistasis.There is no one-size-fits-all model, especially when capturing non-additive effects. Understanding the nature of these effects, example dominance in tuber count vs. epistasis in tuber weight, is important information when choosing the most suitable model.The original contributions presented in the study are included in the article/SW performed the analyses and drafted the manuscript. CZ developed the scripts for calculating genotype probabilities. CM, HM, and RV contributed to the discussion on analytical models and data preparation. AB performed bioinformatic analyses on the sequence data. FE guided analyses and was the general overseer for the project. All authors significantly contributed to the present study and read and approved the final manuscript.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.


Implementation of genomic tools is desirable to increase the efficiency of apple breeding. Recently, the multi-environment apple reference population (apple REFPOP) proved useful for rediscovering loci, estimating genomic predictive ability, and studying genotype by environment interactions (G × E). So far, only two phenological traits were investigated using the apple REFPOP, although the population may be valuable when dissecting genetic architecture and reporting predictive abilities for additional key traits in apple breeding. Here we show contrasting genetic architecture and genomic predictive abilities for 30 quantitative traits across up to six European locations using the apple REFPOP. A total of 59 stable and 277 location-specific associations were found using GWAS, 69.2% of which are novel when compared with 41 reviewed publications. Average genomic predictive abilities of 0.18–0.88 were estimated using main-effect univariate, main-effect multivariate, multi-environment univariate, and multi-environment multivariate models. The G × E accounted for up to 24% of the phenotypic variability. This most comprehensive genomic study in apple in terms of trait-environment combinations provided knowledge of trait biology and prediction models that can be readily applied for marker-assisted or genomic selection, thus facilitating increased breeding efficiency. Malus × domestica Borkh.) is the third most produced fruit crop worldwide [Apple  . The appThe accession and progeny groups of the apple REFPOP were evaluated for 30 quantitative traits at up to six locations. The measurements for ten traits were collected at one location, while the remaining 20 traits were available from at least two locations  that are also known to carry the apple scab resistance gene Rvi6, which is located about 1.8 Mb from the SNP associated with trunk increment  and marker by environment interaction G-BLUP (G-BLUP.E.G × E) – and the multi-environment multivariate factor-analytic model (MTM.FA), the prediction performance of G-BLUP.E, G-BLUP.E.G × E and MTM.FA was generally lower under the first cross-validation scenario (CV1) than under the second cross-validation scenario CV2, . For alld traits . The MTMThe across-environment clonal mean heritability was generally very high in the evaluated traits, the value being close to one for harvest date and red over color and not lower than 0.80 for all the other traits with the exception of full flowering (0.74), end of flowering (0.79) and water core grade 0.79, . The genThe effects of genotype and significantly associated markers together explained a substantial part of the phenotypic variance of traits, the largest sums of these genotypic effects were observed for harvest date (82.8%) and red over color 74.6%, . AltogetThree clusters of traits were determined from the hierarchical clustering of the table of traits by proportion of phenotypic variance explained by different sources . A stronBoth study aims were successfully achieved. Dissection of the genetic architecture of 30 key traits in apple breeding and identification of associated loci stable across locations and location-specific loci using GWAS provided 336 stable and location-specific marker-trait associations discovered across all traits under study. Of these loci, 69.2% were novel when compared with previously published associations. Additionally, signs of selection were found for associations of large effect. The multi-environment and multi-trait experimental design of the apple REFPOP allowed to estimate patterns of G × E for the studied traits and assess their predictive ability. Our results showed that G × E accounted for up to 24% of the phenotypic variability and genomic predictive abilities of up to 0.88 were observed. Based on the outputs of this research, recommendations for future implementation of the prediction tools in apple breeding were derived.Our GWAS enlightened the architecture of analyzed traits as well as the identification of numerous marker-trait associations stable across, and specific to, the locations of the apple REFPOP. The particular design of the experiment, including the diversity of the plant material used , multiple locations, and multiple years of evaluation, are likely to have resulted in about two thirds of the discovered associations being novel when compared with the loci published in studies spanning more than two decades. Our study design also allowed us to replicate the identification of many previously known loci associated with the studied traits.NAC18.1), 10 , 15 (Md-ACS1) and 16 [The association of one locus with two or more seemingly independent traits (i.e. caused by pleiotropy) and linkage disequilibrium between loci associated with different traits are frequent for complex traits . The GWA) and 16 , 49–52.et al. [NAC18.1. The authors hypothesized that the lack of associations on other chromosomes was likely due to low SNP density around the causal loci (the study used a GBS-derived 8 K SNP dataset for 689 genotypes). The larger number of associations reported here might be a result of the high SNP density (303 K SNPs) deployed in GWAS, however, not all previously reported loci were re-discovered.In this work, closely located (distance <100 kb) associations with both harvest date and fruit firmness were found on chromosome 3. Migicovsky et al.  reportedMd-PG1 gene, is responsible for the loss of fruit firmness after storage [Md-PG1 in our GWAS.The SNPs associated with harvest date and fruit firmness on chromosome 10 were further apart (~6 Mb). For harvest date, one of the associations on chromosome 10 was stable across locations and several associations were location specific. However, the association on chromosome 10 with fruit firmness was found for the Italian location only. It has been shown that chromosome 10 contains more than one QTL controlling fruit firmness –51, but  storage . In applMd-ACS1 related to ethylene production was previously mapped on chromosome 15 [Two associations with harvest date measured in Italy but no association with fruit firmness were found on chromosome 15. Although a marker for osome 15 , and QTLosome 15 , these mosome 15 , 50. LikOur GWAS showed associations with harvest date and fruit firmness on chromosome 16, which were located 38 kb apart. In the past, loci associated with harvest date and fruit firmness have been reported in the same region on chromosome 16 , 49. TheNAC18.1 locus on chromosome 3 with overall russet frequency would support the known enhanced expression of NAC transcription factors in russet skin [In practice, ripeness of fruit (harvest date) is decided based on ground color and starch content. The GWAS results showed that the association on chromosome 3 was not only found for harvest date and nearby markers associated with fruit firmness, but also corresponded to associations with ground color and soluble solids content. This might be explained by the fact that these traits are used to define ripeness and thus harvest date. Further, the association of the set skin .Co-localizations between associations found for different measures of bitter pit on chromosome 16, russet on chromosomes 12 and 17, fruit size on chromosomes 1, 8 and 11, and skin color on chromosome 9 are likely the result of relatedness among trait measurements. The measures that are easiest to score can be used in future to phenotype these traits.Ma locus frequently detected in various germplasm [Ma and Ma3, which is another regularly detected acidity locus, was shown to be higher in parents of a European breeding program  than in parents used in the US breeding programs [Rvi6 gene responsible for resistance against apple scab [Rvi6 [Rvi6. The allele on chromosome 1 associated with increased trunk increment may have been co-selected with the Rvi6 locus responsible for resistance against apple scab.The design of apple REFPOP allowed for the discovery of major marker-trait associations and for the analysis of changes in allele frequency between 30 ancestral accessions and 265 progeny included in the apple REFPOP. Although the progeny group did not undergo phenotypic selection before the establishment of the apple REFPOP, the parents of the progeny were a matter of choice within the European breeding programs. This allowed us to assess the impact of the past phenotypic selection on the studied germplasm. Comparing ancestors with the progeny, higher frequencies of the alleles associated with later harvest date and increased flowering intensity, titratable acidity, fruit firmness and trunk increment were found for the progeny. Of these traits, harvest date and fruit firmness are correlated, probably due to pleiotropy or linkage disequilibrium of causal loci, as it was shown in this and previous studies . Consequermplasm , 11. Theprograms . The desprograms . The incple scab . These tple scab ) but alsab [Rvi6 ), were aSigns of intense selection for red skin were recently detected in the USDA germplasm collection when compared with progenitor species of the cultivated apple . Our resMain-effect univariate genomic prediction models were applied to the global clonal values. The observed small differences between genomic predictive abilities of various models  were in The predictive ability for red over color reached ~0.4 in several former prediction studies , 29, 34 Opposite to harvest date and red over color, the predictive ability of yellow color and russet cover was low, although the genotypic effects explained 45% and 47% of the phenotypic variance, respectively. The across-environment clonal-mean heritability of russet cover was high (0.97), while the heritability for yellow color was slightly lower 0.81, . Yellow All main-effect univariate genomic prediction models as well as other genomic prediction models compared in this study depended on predictions of clonal values obtained during the phenotypic data analysis. Further extension of the models should consider if adding a term to account for the permanent non-genetic effect of the tree over years into the mixed-effects models (Equation 1) improves accuracy of the clonal values predictions and so increases the genomic predictive ability.The multi-environment univariate genomic prediction models either assumed that effects of markers were the same across environments  or additionally estimated marker effects separately for each environment and thus considered the G × E  . The aveet al. [The G-BLUP.E.G × E model assumes positive correlations between environments and is therefore mostly suitable for the joint analysis of correlated environments , 63. As et al.  and in oet al. , 64.Multivariate  models were shown to improve predictive ability for traits that are costly to phenotype when a correlated trait less expensive to phenotype was available . In our In place of the correlated traits, environments of a single trait can be implemented in a multivariate model . CompareThe cross-validation scenarios CV1 and CV2 were applied with multi-environment genomic prediction models to test two genomic prediction approaches typically faced in breeding. The CV1 imitated evaluation of breeding material that was yet untested in field trials. The CV2 was implemented to simulate incomplete field trials where breeding material was evaluated in some but not all target environments. More specifically, the CV2 investigated a situation where the breeding material has been evaluated at one location  and the material’s potential over other European sites was predicted without its assessment in a multi-environment trial, which may increase selection efficiency at latter stages of evaluation. As CV2 provided more phenotypic information to the models than CV1, a higher genomic predictive ability was found under CV2 when compared with CV1, which was anticipated , 42. ThePhenotypic variance decomposition into genetic, environmental, G × E and residual effects was compared with the results of GWAS and genomic prediction as well as heritability estimates. The comprehensive comparison indicated three classes of traits with contrasting genetic architecture and prediction performance. Characteristics of these trait classes and proposals for their efficient prediction strategies are described in the following paragraphs.The first class included harvest date and red over color that showed a few loci of large effect and some additional loci of low effect, the highest predictive abilities, and the highest across-environment clonal-mean heritability among all traits. Both traits showed a very high proportion of the genotypic effect explaining ~75% of the phenotypic variance. For harvest date and red over color, the marker with the largest effect explained 52% and 59% of the phenotypic variance and all marker effects in genomic prediction captured together 88% and 85% of the phenotypic variance (i.e. genomic heritability of 0.88 and 0.85), respectively. Selection for these traits exhibiting a strong genetic effect of one locus could be done using marker-assisted selection, although only a part of the variance would be explained by a single marker. Better results can be achieved using genomic prediction, as this was able to explain a substantially larger amount of the phenotypic variance. Other traits such as fruit firmness, titratable acidity, end of flowering or traits related to fruit size and water core were grouped in the same cluster as harvest date and red over color . These tThe second class of traits was represented by floral emergence and trunk diameter displaying a high proportion of the environmental effect (~70%) and a similar ratio of variance explained by genotypic effects compared to variance explained by G × E effects (~2.5). The genomic predictive ability did not considerably deviate from the average accuracy over all traits. Several marker associations with these traits were identified using location-specific GWAS. However, in the across-location GWAS, only one association explaining a very small part of phenotypic variance  or no association (trunk diameter) were discovered. Consequently, such traits predominantly driven by the effect of environment can be successfully selected based on genomic prediction, but the lack of associations stable across environments limits the applicability of marker-assisted selection to this class of traits.In the third class, the productivity traits  showed the largest proportion of variance explained by G × E (~20%), with similar amounts of variance explained by genotypic effects for weight of fruits and number of fruits, but half as much variance explained by genotypic effects for flowering intensity . As a coThe decision to apply either marker-assisted or genomic selection can be based on genetic architecture of traits of interest and resources available in a breeding program. For breeding of yet genetically unexplored traits, variance decomposition of historical phenotypic data prior to genomic analyses may help describe trait architecture, assign traits to one of the three classes described in the previous paragraphs, and finally determine the most appropriate method of genomics-assisted breeding. From all traits explored in this study, the marker-trait associations with large and stable effects across environments found for harvest date, flowering intensity, green color, red over color, titratable acidity, fruit firmness and trunk increment could be implemented into DNA tests for marker-assisted selection. These tests would allow for a reduction of labor costs in a breeding program when removing inferior seedlings without phenotyping . AlthougThis study laid the groundwork for marker-assisted and genomic selection across European environments for 30 quantitative apple traits. The apple REFPOP experimental design facilitated identification of a multitude of novel and known marker-trait associations. Our multi-environment trial provided accurate genomics-estimated breeding values for apple genotypes under various environmental conditions. Limited G × E detected in this work suggested consistent performance of genotypes across different European environments for most studied traits. Utilizing our dataset, genomic selection of traits related to yield may lead to higher productivity and increased genetic gain in the future . The genet al. [Plant material in this study was comprised of the apple REFPOP, which was designed and established by the collaborators of the FruitBreedomics project  as descret al. . The appet al. [The plant material was accompanied by a high-density genome-wide SNP marker dataset, which was produced as reported by Jung et al. . Brieflyet al.  and (ii)et al. , were cuet al.  using thet al. . Non-polet al. .et al. [Thirty phenotypic traits related to phenology, productivity, fruit size, outer fruit, inner fruit, and vigor were evaluated at up to six locations of the apple REFPOP during up to three seasons (2018–2020). Trunk diameter was measured in 2017 in some locations, enabling for a trunk increment calculation for 2018. The traits were recorded as described in the et al. .Spatial heterogeneity was modeled separately for each trait and environment (combined factor of location and year) using the spatial analysis of field trials with splines (SpATS) to correct for the replicate effects and differences due to soil characteristics . PhenotyFurther analyses were performed to estimate trait heritability and remove the effects of location and year from the collected phenotypes. The general statistical model for the following phenotypic data analyses fitted via restricted maximum likelihood (R package lme4 ) was:, an additional mixed-effects model following the Equation 1 was fitted to the adjusted phenotypic values of each tree  of trait by proportion of phenotype variances explained by different sources  was constructed and hierarchical clustering following Ward  was applFour univariate and one multivariate main-effect genomic prediction models were used to evaluate predictive ability for 30 phenotypic traits. These models differed in the way of estimating the marker effects. For all models, the The first univariate model examined was regression with random forest (RF) , which iFor the remaining three univariate and one multivariate main-effect genomic prediction models, the general random effects model was defined as:The second univariate model BayesCπ is a parametric model, which estimates prior probability o effect . Followi. The vectors The third examined univariate model, the semi-parametric Bayesian reproducing kernel Hilbert spaces regression (RKHS), is able to capture additive as well as non-additive effects and was implemented here using a multi-kernel approach . The mulThe fourth univariate model genomic-BLUP (G-BLUP) was fitted using a semi-parametric RKHS algorithm. To facilitate efficient incorporation of a large number of markers, the additive genomic relationship matrix traditionally used for genomic prediction was replaced in G-BLUP by a genomic relationship matrix . The genhttp://quantgen.github.io/MTM/vignette.html). The MTM.UN followed the Equation 4 with the response vector The fifth model applied was a multivariate model with an unstructured covariance matrix of the random effect (here abbreviated as MTM.UN). The model was fitted for chosen pairs of traits using the Bayesian multivariate Gaussian model environment MTM  and the predicted values for the same genotypes .80 and the MTM.UN model in the R package MTM (http://quantgen.github.io/MTM/vignette.html).BayesCπ, RKHS, G-BLUP and MTM.UN were applied with 12 000 iterations of the Gibbs sampler, a thinning of 5, and a burn-in of 2000 discarded samples. The RF model was implemented in the R package ranger , the modet al. [To explore the effects of genotypes, environments and their interaction in genomic prediction, the predictive ability for 30 traits was estimated using an across-environment and a marker by environment interaction univariate genomic prediction algorithms that assumed constant or changing random marker effects across environments, respectively. The random effects model for the examined univariate multi-environment models that were reported by Lopez-Cruz et al.  was:(Equhttp://quantgen.github.io/MTM/vignette.html). The traits measured at only one location during two seasons  were not modeled using MTM.FA because the analysis required at least three environments. Following the Equation 5, the vector of random effects assumed To test multivariate multi-environment genomic prediction for the traits under study, a multivariate multi-environment factor-analytic model (here abbreviated as MTM.FA) was fitted to the genomic and phenotypic data using the Bayesian multivariate Gaussian model environment MTM , the phenotypes of 20% of the genotypes were masked across all environments. For the second cross-validation scenario (CV2), the phenotypes of 20% of the genotypes were masked across all environments except for three Swiss environments, i.e. phenotypes of all genotypes from the environments “CHE.2018”, “CHE.2019” and “CHE.2020” were used for model training. Ten traits were measured in only one location and therefore excluded from CV2 . Predictive ability was estimated as a Pearson correlation coefficient between the phenotypes of the masked genotypes  and the predicted values for these genotypes in each environment . The correlations were estimated for each predicted environment separately. The models following the Equation 5 did not account for the permanent non-genetic effect of the tree over years.http://quantgen.github.io/MTM/vignette.html).All three multi-environment genomic prediction models were applied with 12 000 iterations of the Gibbs sampler, a thinning of 5 and a burn-in of 2000 discarded samples. The models G-BLUP.E and G-BLUP.E.G × E were implemented in the R package BGLR , the modThe BayesCπ model was applied for each trait as described before but trained with a full set of the global clonal values as response. The genomic heritability ectively , 82. TheThe authors thank the field technicians and staff, especially Sylvain Hanteville, at INRAe IRHS and Experimental Unit (UE Horti), Angers, France, and technical staff at other apple REFPOP sites for the maintenance of the orchards and phenotypic data collection. We thank Dr. Graham Dow for English language editing. Phenotypic data collection was partially supported by the Horizon 2020 Framework Program of the European Union under grant agreement No 817970 (project INVITE: “Innovations in plant variety testing in Europe to foster the introduction of new varieties better adapted to varying biotic and abiotic conditions and to more sustainable crop management practices”). This work was partially supported by the project RIS3CAT (COTPA-FRUIT3CAT) financed by the European Regional Development Fund through the FEDER frame of Catalonia 2014-2020 and by the CERCA Program from Generalitat de Catalunya. We acknowledge financial support from the Spanish Ministry of Economy and Competitiveness through the “Severo Ochoa Programme for Centres of Excellence in R&D” 2016-2019 (SEV-20150533) and 2020-2023 (CEX2019-000902-S). C.D. was supported by “DON CARLOS ANTONIO LOPEZ” Abroad Postgraduate Scholarship Program, BECAL-Paraguay. We dedicate this paper to Prof. Edward Zurawicz of the National Institute of Horticultural Research in Skierniewice, Poland who co-promoted this study, but sadly recently passed away.M.J.A., W.G., F.L., H.M. and A.P. conceived the research plans; B.S., H.M. and A.P. supervised the project; M.J., B.K., M. Roth, M.J.A., A.A., M.A., M.L., N.S., M. Rymenants, F.D., C.D., C.F.F. and A.K. contributed to data collection; M.J. carried out the data analysis and wrote the article in consultation with B.K., M. Roth, H.M. and A.P.; M.J.A., A.A., W.G., N.S., M. Rymenants, F.L. and B.S. provided critical feedback to the article.https://data.inrae.fr/) at https://doi.org/10.15454/IOPGYF. All SNP genotypic data generated using the 20 K array used in this study have been deposited in the INRAe dataset archive at https://doi.org/10.15454/1ERHGX. The raw phenotypic data are available in the INRAe dataset archive at https://doi.org/10.15454/VARJYJ.All SNP genotypic data generated with the 480 K array used in this study have been deposited in the INRAe dataset archive (The authors declare no competing interests.Horticulture Research Journal online.Web_Material_uhac028Click here for additional data file.


In dairy cattle populations in which crossbreeding has been used, animals show some level of diversity in their origins. In rotational crossbreeding, for instance, crossbred dams are mated with purebred sires from different pure breeds, and the genetic composition of crossbred animals is an admixture of the breeds included in the rotation. How to use the data of such individuals in genomic evaluations is still an open question. In this study, we aimed at providing methodologies for the use of data from crossbred individuals with an admixed genetic background together with data from multiple pure breeds, for the purpose of genomic evaluations for both purebred and crossbred animals. A three-breed rotational crossbreeding system was mimicked using simulations based on animals genotyped with the 50 K single nucleotide polymorphism (SNP) chip.For purebred populations, within-breed genomic predictions generally led to higher accuracies than those from multi-breed predictions using combined data of pure breeds. Adding admixed population’s (MIX) data to the combined pure breed data considering MIX as a different breed led to higher accuracies. When prediction models were able to account for breed origin of alleles, accuracies were generally higher than those from combining all available data, depending on the correlation of quantitative trait loci (QTL) effects between the breeds. Accuracies varied when using SNP effects from any of the pure breeds to predict the breeding values of MIX. Using those breed-specific SNP effects that were estimated separately in each pure breed, while accounting for breed origin of alleles for the selection candidates of MIX, generally improved the accuracies. Models that are able to accommodate MIX data with the breed origin of alleles approach generally led to higher accuracies than models without breed origin of alleles, depending on the correlation of QTL effects between the breeds.Combining all available data, pure breeds’ and admixed population’s data, in a multi-breed reference population is beneficial for the estimation of breeding values for pure breeds with a small reference population. For MIX, such an approach can lead to higher accuracies than considering breed origin of alleles for the selection candidates, and using breed-specific SNP effects estimated separately in each pure breed. Including MIX data in the reference population of multiple breeds by considering the breed origin of alleles, accuracies can be further improved. Our findings are relevant for breeding programs in which crossbreeding is systematically applied, and also for populations that involve different subpopulations and between which exchange of genetic material is routine practice.The online version contains supplementary material available at 10.1186/s12711-021-00637-y. Genomic evaluation facilitates the accurate selection of genetically superior individuals as early as their DNA samples are obtained . GeneticFor an accurate genomic prediction, a large population of individuals with both phenotypes and genotypes is needed, which may not be possible for all traits and/or all breeds –6. In suWhen multiple breeds are combined to form a reference population, predictions rely on the SNP-QTL LD across breeds. However, LD may be different , 12, or Crossbreeding emerges as an efficient strategy for dairy cattle breeding to achieve better productivity and robustness at the animal as well as the system level. The improved performance is due to the use of specific combining abilities and heterosis . In dairAn appealing approach to make use of data of admixed individuals in genomic prediction is to incorporate breed proportions in genomic prediction models. Makgahlela et al.  extendedIn this article, we propose a methodology that is suitable for genomic prediction using a reference population of multiple purebred and admixed individuals. Through simulations, we investigated the impact of the correlation of QTL effects between the breeds, and the heritability of the trait on the accuracy of genomic prediction using different approaches: (i) treating the combined data as a single homogeneous population, (ii) considering breed-specific SNP effects with or without accounting for correlations between the breeds, and (iii) considering priors that lead to the use of region-specific correlations among the breeds.Genotype data at 51,477 loci were available for animals from each of the three dairy cattle breeds: Danish Holstein (HOL), Swedish Red (RED) and Danish Jersey (JER), from which a subset of 1050 (HOL and RED) or 220 (JER) individuals formed the base populations for this study. The SNPs that were fixed for the same allele in all three breeds were removed. For computational reasons, only the SNPs  on first five chromosomes were considered. A plot summarising the principle component analysis of genomic relationships among all animals was depicted to assess the genetic relationships between the pure breeds  or 220 (JER) individuals (generation 0–G0), of which 50 (HOL and RED) or 20 (JER) were assigned as males and the rest as females. The purebred populations were generated by mating sires and dams from the same breed  is the lambda parameter . RecombiThe total number of QTL was set at 250, which were selected randomly among the SNPs that satisfied Even if additive and dominance effects of QTL are the same in different breeds, the difference in QTL allele frequencies may cause substitution effects of QTL  to diffei , respectively. The k, in breed j. The QTL effects were scaled such that the mean of the breed-specific genetic variances  is 100 at G0. A random residual Each individual had two alleles  at each locus, inherited from its dam and sire. The breed origin of each allele for all loci was traced back to pure breeds at G0, and was known without error. The breeding value of each individual j = H,R,J and k QTL. The genetic correlations between HOL–RED, HOL–JER and RED–JER were 0.88, 0.75 and 0.78, respectively, for a correlation between QTL of 1.00, over 10 replicates and at G0. These genetic correlations were 0.45, 0.38 and 0.38 for a correlation between QTL of 0.50, and 0.22, 0.19 and 0.19 for a correlation between QTL of 0.25, respectively. The differences between QTL effect correlations and genetic correlations were due to the difference in QTL allele frequencies between the breeds. The correlations between QTL allele frequencies of HOL–RED, HOL–JER and RED–JER were 0.33, 0.22 and 0.41, respectively. The correlations between SNP allele frequencies were 0.47, 0.32 and 0.46. The QTL effect correlations of 0.50 and 0.25 are consistent with the reported genomic correlations (genetic correlations estimated based on available SNP sets) between some cattle breeds for milk [True (simulated) genetic correlations between the breeds were computed from the genetic variances, nt}j≠j′)  at k QTLfor milk , 25 and for milk , respectGenerations 6,7 and 8 (G6–G8) were used to form reference populations, while generation 9 (G9) was used to form validation populations. Hence, 660 JER individuals, and 3150 individuals from each of the HOL, RED and MIX were available for forming reference populations to estimate SNP effects.The SNP effects were estimated using different reference populations: (i) a single pure breed , (ii) combined data of multiple pure breeds (HOL + RED + JER), and (iii) combined data of multiple pure breeds and admixed (MIX) individuals. The MIX dataset was either used as a different “breed”, assuming homogeneous SNP effects across all breeds (HOL + RED + JER + MIX), or truly treated as an admixed population considering the breed origin of alleles (BOA) approach and uncorrelated (uncor) or correlated (cor) SNP effects between the breeds (HOL + RED + JER + MIX uncor/cor) , 56, 57.The prediction of breeding values for each pure breed was performed using: 1) the estimated SNP effects from their own breed (within-breed prediction), (2) the estimated SNP effects from each of the other breeds (across-breed prediction), (3) the estimated SNP effects from a combined reference population (multi-breed prediction) and (4) the estimated SNP effects from a combined reference population considering the BOA approach. The breeding values were predicted by multiplying SNP effects with allele dosages, with (4) or without (1–3) considering breed origin of alleles. These same strategies (1–4) were used to predict the breeding values of admixed individuals, with the addition of fixed breed contributions in multi-breed prediction [see model , multiple breeds data without considering breed origin of alleles as “combined”, and multiple breed’s and MIX data considering breed origin of alleles as “BOA”.n depends on the reference population size, and l is the number of SNPs. Model  to accoS subsets each with df) and a scale parameter (S): A Bayesian approach was considered in the parameter estimation, which requires assigning prior distributions to the unknowns of the model. Analyses were carried out separately for each trait. To investigate the impact of assuming a heterogeneous (co)variance of SNP effects between different genome regions, three region sizes were considered based on a fixed number of SNPs; 1 SNP, 100 SNPs and the whole genome (WG). Region sizes of 1 SNP and WG can be regarded as BayesA and SNP-best linear unbiased prediction (SNP–BLUP) ) when us , 30. TheS subsets each with j : In the analyses using model , all genentclass1pt{minimaIn both models  and 2),,2), resij, and lth SNP in breed j. Only one j = H,R,J and The hyper-parameters of the prior distributions for the variance components were derived from the simulated genetic (co)variances and residual variances at G0 as follows. For the analysis using model  assuming,l1-pj,l . Here, \entclass1pt{minimaThe Markov-chain Monte Carlo (McMC) algorithm was used to obtain samples of each parameter from its full-conditional posterior distribution. The chain length for the analyses consisted of 50,000 cycles, of which the first 10,000 were discarded as burn-in. Every 10th sample of the post burn-in cycles was kept for posterior analysis, yielding 4000 posterior samples. The mean value of the posterior samples was used as the estimate of each parameter. All the analyses were performed using self-written scripts in Julia .Prediction accuracy was assessed as the correlation between true and predicted breeding values of validation individuals  at G9. The accuracies of prediction using different data sets and models to estimate SNP effects were compared for each trait, QTL correlation and region size, separately. The accuracies of prediction for different region sizes were compared for each data set and model, trait and QTL correlation, separately. All comparisons were performed using a two-sided paired t-test, for which accuracies were paired across each replicate for the same validation population. A Bonferroni correction was used to control the type 1 error rate of 0.05.Accuracies for all scenarios and all region sizes are given in Additional file Accuracies were lowest when using SNP effects from any of the pure breeds to predict the breeding values of admixed individuals. For the high heritability trait, predictions using SNP effects of HOL, RED and JER yielded accuracies of 0.411, 0.275 and 0.114, respectively, when the region size was 1 SNP Fig. .Fig. 3AcThe efficiency of the methods considering breed origin of alleles in model training became more apparent as the correlation of the simulated QTL effects between the breeds decreased , yielded much lower accuracies than within-breed predictions. This was true even when the simulated QTL effects had a correlation of 1.00. It should be noted that, although the simulated QTL effects were identical in the scenario with a correlation of 1.00, some QTL were not segregating in each breed Table . The resFor within-breed predictions, both family relationships and LD between SNPs and QTL contribute to accuracy –39. For Although the simulated traits in this study were relatively polygenic, the variance structure at the SNP level may be different from that at the QTL level along the genome , 43, favFor a high heritability trait and purebred analysis, accuracies obtained for different region sizes were generally ranked as 100 SNPs > 1 SNP > WG. It was shown earlier by simulations , 35 and If the studied population is small, it might be challenging to establish a large reference population, and in turn the accuracy of genomic prediction might also be limited . For breecreased .In a study based on real genotypes of imputed sequence variants , an appealing strategy is to apply multi-trait methods where the same trait in different breeds is considered as different but two correlated traits, e.g. , 25. In If a large amount of commercial farm data for admixed populations becomes available, it can help to improve selection accuracy by expanding the data size for each pure breed population . Such daIncluding the data of an admixed population (MIX) along with the data of pure breeds in the reference population led to higher accuracies than the combined reference population of pure breeds. The JER benefited relatively more from adding MIX data. Because we mimicked a rotational cross breeding system, at each generation, admixed population dams were sired by a purebred individual. Consequently, when an admixed female was mated with a purebred male, the offspring had an entire paternal chromosome from a pure breed, and a maternal chromosome including large chunks of the (i) admixture of all breeds and (ii) the pure breed of the maternal grand-sire. This means that, at each generation following G1, pure breeds were not equally represented in the genome of admixed individuals. Consider a single admixed individual at generation 6. That individual has an expected breed composition for a maternal chromosome of roughly 28% JER, 16% HOL, and 56% RED, and for a paternal chromosome of %100 HOL. Those proportions change to 14% JER, 58% HOL, and 28% RED for a maternal chromosome, and 100% JER for a paternal chromosome at generation 7, and to 57% JER, 29% HOL, and 14% RED for a maternal chromosome, and 100% RED for a paternal chromosome at generation 8. Because a full rotation cycle of three generations (G6–G8) was considered when forming the reference populations, each pure breed was represented in the MIX data almost equally. Thereby, the reference population size increased almost equally for all breeds by adding MIX data to the combined data of three breeds, HOL + RED + JER + MIX. As one would expect, JER benefited more from this increase in data size, since it is the breed with the smallest pure breed reference population. It should be noted that the validation individuals of RED had the grand-sires which were also the sires of MIX at G8, and G8 was included in the reference population. Hence, although the data size increased almost equally for each breed, the added value of this may not be equal for all the breeds.More elaborative ways to include individuals with admixed genetic background in the genomic evaluations, were proposed. Makgahlela et al.  fitted aModels accounting for breed origin of each SNP allele, rather than genome-wide breed proportions estimated from pedigree or markers, have been proposed, and were shown to improve genomic predictions for simple 2 or 3-way crosses. Those studies applied either univariate whole genome regression models at the SNP level ignoring that the SNP effects might be correlated between the pure breeds , 55, or Our results did not show any clear evidence of the benefit of accounting for correlations among the breeds when MIX data were used with the BOA approach, even for the breed (JER) with a small reference population, for which one would expect more gain in accuracy compared with breeds with a large reference population (HOL and RED). A possible explanation of the unobserved benefit for JER could be due to this breed being genetically distinct from HOL and RED , and theThe differences in LD pattern and phase persistency across different breeds  may resuvan den Berg et al.  showed tentclass1pt{minimaEstimation of the breed composition of individuals with admixed genomic background is of relevance for genomic prediction, because if it is not accounted for, it may lead to spurious estimates of SNP effects . In realGenetic background, as well as environment, alters the effects of QTL , 19. Thuh2), and the effective number of chromosomal segments segregating in the population , and also for populations involving different subpopulations between which exchange of genetic material has become routine practice .The aim of this simulation study was to provide a model allowing the inclusion of data from individuals with an admixed genetic background in genomic evaluations, while accounting for the differences in marker effects for each purebred population in the gene pool. Combining pure breeds’ and admixed population’s data in a multi-breed reference population was beneficial for the estimation of breeding values for pure breeds with a small reference population. For the admixed population, combining all available data  and realizing a combined genomic evaluation led to higher accuracies than considering BOA for selection candidates only and using breed-specific SNP effects estimated separately in each pure breed. Including data from admixed individuals in the reference population of multiple breeds by considering BOA, accuracies were further improved. Our findings are relevant for breeding programs in which crossbreeding is systematically applied  for a trait with high heritability h2 = 0.40. Table S4. Accuracies for admixed individuals (MIX) for a trait with low heritability h2 = 0.05. Table S5. Accuracy for the low heritability h2 = 0.05 trait, using only 250 QTL and region size of 1 SNP.


In conjunction with big data analysis methods, plant omics technologies have provided scientists with cost-effective and promising tools for discovering genetic architectures of complex agronomic traits using large breeding populations. In recent years, there has been significant progress in plant phenomics and genomics approaches for generating reliable large datasets. However, selecting an appropriate data integration and analysis method to improve the efficiency of phenome-phenome and phenome-genome association studies is still a bottleneck. This study proposes a hyperspectral wide association study (HypWAS) approach as a phenome-phenome association analysis through a hierarchical data integration strategy to estimate the prediction power of hyperspectral reflectance bands in predicting soybean seed yield. Using HypWAS, five important hyperspectral reflectance bands in visible, red-edge, and near-infrared regions were identified significantly associated with seed yield. The phenome-genome association analysis of each tested hyperspectral reflectance band was performed using two conventional genome-wide association studies (GWAS) methods and a machine learning mediated GWAS based on the support vector regression (SVR) method. Using SVR-mediated GWAS, more relevant QTL with the physiological background of the tested hyperspectral reflectance bands were detected, supported by the functional annotation of candidate gene analyses. The results of this study have indicated the advantages of using hierarchical data integration strategy and advanced mathematical methods coupled with phenome-phenome and phenome-genome association analyses for a better understanding of the biology and genetic backgrounds of hyperspectral reflectance bands affecting soybean yield formation. The identified yield-related hyperspectral reflectance bands using HypWAS can be used as indirect selection criteria for selecting superior genotypes with improved yield genetic gains in large breeding populations. Glycine max [L.] Merr.) can be considered one of the super crops that is substantially used for food and feed, green manure, biodiesel, and fiber , red edge (680–780 nm), and near-infrared (700–1100 nm) spectral regions . The visSeveral studies reported the high potential of using spectral reflectance to estimate and classify the yield , leaf arp≫n) than the number of genotypes , as one of the most common error control methods, was used to estimate the accuracy of the phenotypic evaluations and control the spatial variability in the field  and Palmyra , Ontario, Canada, over two consecutive years, 2018 and 2019. The experimental design was conducted based on the randomized complete block design (RCBD) in four environments (two locations × two years) with two replications in each environment. Each phenotypic plot for each genotype was consisted of five rows, each 4.2 m long with a row spacing and seedling rate of 43 cm and 57 per mhe field .–1) was estimated for each plot after harvesting of three middle rows and adjusting for day to maturity and the seed moisture to 13%.Soybean seed yield , where seeds are 1/8 inches long in pods at one of the four uppermost nodes , in compThe pre-processing step is one of the most important steps in hyperspectral reflectance analysis, which reduces the possible electronic fluctuations and sensor noises in datasets. By checking the quality of hyperspectral reflectance data for the tested panel and the result of sensor-specific artifacts, hyperspectral reflectance data of 1,005–1,100 and 350–395 nm, were removed from the original data. The number of reflectance bands was decreased from 250 bands to 62 by increasing the bandwidth from 3 to 10 nm. In order to improve the signal-to-noise ratio, a Savitzky–Golay filter was applied for each reflectance band and data scaling, centering, and principal component analysis (PCA) was conducted in order to detect potential outliers in the dataset. All the pre-processing steps were performed using R software (version 3.6.1).In order to estimate the genetic values of each soybean genotype, the BLUP was used as one of the most well-known mixed models . For thi2g), i is the vector of random GxE interaction effects, in which i ∼ N, and e is the vector of residuals, in which e ∼ N. X, Z, and W represent the incidence matrices of b, g, and i effects, respectively.where Y is the vector of trait of interest , b is the vector of block effects, encompasses all the replications and locations, added to the overall mean (assumed fixed), g in the vector of genotype effects (assumed random), in which g ∼ N of each tested trait was calculated based on the following equation:2g is the genotypic variance; σ2int is the variance of GxE; σ2e is error variance; n is the number of locations; r is the number of replications.where σcaret package  for detecting hyperspectral reflectance bands associated with the trait of interest. In order to detect the important hyperspectral reflectance bands associated with the trait of interest, RFE, as one of the most common variable selection methods , was use package  in R sof® 2.0 fluorometer . The extracted DNA were sent to Genomic Analysis Platform at Université Laval  for genotyping-by sequencing (GBS) based on the enzymatic digestion with ApeKI . DNA was isolated using NucleoSpin Plant II kit  as per the manufacturer’s instructions, and the quality of DNA was checked with Qubitth ApeKI . GBS forth ApeKI , using GA total of 17,958 high-quality SNPs were used to conduct the population structure analysis using fastSTRUCTURE  with K vMVP ; u is the vector of additive genetic effects for genotypes (assumed random); e is the vector of residuals (assumed random). X and Z represent the incidence matrices of b and u effects, respectively.This GWAS method was first introduced by i stands for the observation on the ith sample, Si1, Si2,…, Sit stand for the genotypes of the t pseudo-QTNs, B1, B2, B3, …, Bt is the corresponding effect for the pseudo-QTNs, Mij is the genotype of the jth SNPs and ith sample, Kj is known as the corresponding effect of the jth SNPs, and ei is the residual.Where Yp-values as follows (Eq. 5):The REM model is used in the FarmCPU method to optimize the selection of the genetic markers based on the i stands for the observation on the ith sample, ei is the residual, and Ui is the total genetic effect of the ith sample.Where YAlso, false discovery rate (FDR) was used for MLM and FarmCPU to set the significant threshold .Support vector regression represents a support vector machine (SVMs) approach used to solve regression problems . SVR is Y = Wβ(c) + b + e+ and Y = Wβ(c) + b-e, respectively.Where Y is the output, W stands for the weights for each high dimensional input (β) that is constructed non-linearly on the input space of (c). The upper and lower borderlines are presented as The five-fold cross-validation strategy  was usedGlycine max William 82 reference gene models 2.0 using the SoyBase database1. The flanking regions of associated peak SNPs with the trait of interest were obtained based on the LD decay distance  of −0.80, and the lowest negative correlation was found between the 730 nm band and seed yield with r = −0.16 , Glyma.02G008700 (GO:0006970), Glyma. 03G033100 (GO:0019748), Glyma.03G033100 (GO:0031347), Glyma.09G168700 (GO:0009624 and GO:0042742), and Glyma.16G073100 (GO:0050660 and GO:0016491). These genes have been annotated for oxidative and osmotic stresses, secondary metabolic process, regulation of defense response, response to nematode, defense response to bacterium, flavin adenine dinucleotide binding, and oxidoreductase activity, respectively. For the 550 nm band, two peak SNPs (Chr3_22283256 and Chr5_40467080) had the highest allelic effects compared to other detected peak SNPs (Glyma.03G081700 (GO:0010224) and Glyma.05G226000  were selected candidates for the 550 nm band, which encode response to UV-B and to UV, and flavonoid biosynthetic process, respectively. Based on Glyma.19G108200  was the selected candidate gene for the 660 nm band, which encodes positive regulation of flower development, photosynthesis, flowering, light reaction, and regulation of flower development. The allelic effect analysis of the 730 nm band indicated a high allelic effect for two peak SNPs at Chr2_42645195 and Chr18_6728432 (Glyma.02G237700 (GO:0009853) and Glyma.02G237400 (GO:0031347)] associated with the 730 nm band, which encode photorespiration and regulation of defense response. On the 820 nm band, the highest allelic effect was found in two peak SNPs (Chr4_20000416 and Chr6_11029779) that were detected by the SVR-mediated GWAS method  and the patterns of isoflavonoid accumulation, which shows the biosynthesis of isoflavonoid might be activated by violet spectra through the up-regulation of these genes  that can play a pivotal role in a plant’s defense systems . It has se genes . The spase genes , RNA metse genes , singletse genes , abscisise genes . Chloropse genes , (ii) thse genes , (iii) tse genes , and (ivse genes . The comse genes . CLD1 case genes .It has been well documented that three main families of carbonic anhydrase (CA) genes, including α-CAs, β-CAs, and γ-CAs, play essential roles in the conductance of inorganic carbon through carbon fixation rates and the mesophyll . They maIndirect selection of complex traits would be of paramount importance in analytical breeding strategies. Nowadays, the use of advanced high throughput phenotyping and genotyping combined with big data analysis methods can ease the assessment of large plant breeding populations in a very effective short time. For the first time in this study, we are proposing the HypWAS method for identifying hyperspectral reflectance bands associated with complex traits such as yield. Based on this method, we were able to discover, five hyperspectral reflectance bands significantly associated with the soybean seed yield. The visible region of the spectra was found to be the most informative region related to the seed yield. The GWAS analyses of the selected hyperspectral reflectance bands using MLM, FarmCPU, and a newly developed SVR-mediated GWAS method revealed several QTL revealing the bands that seem to be related to the soybean seed yield, water use efficiency, and soybean cyst nematodes resistance based on previous studies. In general, all of the tested GWAS methods had acceptable performance. However, we were able to detect more relevant QTL using the SVR-mediated GWAS. Regarding the Gene Ontology of the selected traits, most of the detected genes were reported to be related to the water status, photosynthesis, and light intensity. The obtained genetic results confirmed the physiological background of the selected hyperspectral reflectance bands. The result of this study can be used to accelerate the indirect breeding selection strategy for selecting high-yielding genotypes based on specific hyperspectral reflectance bands at early plant growth stages. In addition, the genetic results can be employed to use the detected QTL in each hyperspectral reflectance band for MAS selection in large breeding populations.https://github.com/Mo hsen1080/Available-Datasets/blob/92f27c80fa3e460900589b4218 8a943570dee86d/FastGBS.SNPs.232.imputed.Het50.maf0.05.hm p.txt, GitHub.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 below: ME conceptualized, designed and directed the experiments. MY-N conducted the experiments, modeled, summarized the results, and writing the manuscript. ST participated in candidate gene analyses. ST, DT, IR, and ME revised the manuscript and validated the results. All authors have read and approved the final manuscript.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.