Soybean (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 (Seck et al., 2020). Soybean breeders continually breed soybean genotypes with improved desired traits of interest, such as yield (Yoosefzadeh-Najafabadi et al., 2021a). However, yield is a complex trait affected by intrinsic and extrinsic factors as well as their interactions (Anuarbek et al., 2020; Yoosefzadeh-Najafabadi et al., 2021a). Therefore, a sophisticated understanding of the biological aspects of plant genomes is required for sustainable improvements of yield potential in major crops (Somegowda et al., 2021), such as soybean. Soybean breeding programs are moving to implement new genomics, phenomics, and big data analysis for a deeper understanding of soybean yield formation. Having a phenotypic profile of a large plant population with high-density genetic markers are two of the most important factors for better understanding the phenotype and genotype of complex quantitative traits that are usually controlled by various genes with minor and major effects (Wang et al., 2020).

Proximal/remote sensing can be considered as one of the promising high throughput phenotyping tools that can measure the spectral properties of genotypes in a short time in a large breeding population. Most of the spectral measurements are focused on the visible (400–700 nm), red edge (680–780 nm), and near-infrared (700–1100 nm) spectral regions (Alonzo et al., 2014; Hennessy et al., 2020). The visible range can be dissected into blue/blue-green edge (400–499 nm), the green peak (550 nm), and the red (650–700 nm) regions (Rivard et al., 2008; Hennessy et al., 2020). Most of the reflection in the visible region is regulated by the absorption of different foliar pigments such as chlorophyll a and b, carotenoids, and anthocyanins (Castro-Esau et al., 2006; Pu, 2009; Peerbhay et al., 2013; Alonzo et al., 2014; Hennessy et al., 2020). The red-edge region resides between the red and the near-infrared (NIR) regions, which is correlated with internal leaf structure and chlorophyll absorptions (Clevers et al., 2002; Clark et al., 2005; Liu C. et al., 2021). The NIR plateau (780–1327 nm) is another important hyperspectral reflectance region that is dominated by the amount and interaction of water and air within the intercellular spaces (Hennessy et al., 2020; Paulus and Mahlein, 2020; Okubo, 2021).

Several studies reported the high potential of using spectral reflectance to estimate and classify the yield (Yoosefzadeh-Najafabadi et al., 2021a), leaf area index (Chen et al., 2020), plant stress (Feng et al., 2020), and carbon and nitrogen contents (Omidi et al., 2020). In a study done by Zhang et al. (2019), significant association of red and NIR regions with yield are reported. They also demonstrated R5 as the best growth stage for predicting yield and the efficiency of using regression models in predicting soybean yield from the selected hyperspectral reflectance bands. This potential would allow breeders to accurately predict complex traits such as yield, which are typically controlled by several secondary correlated traits, in a short time at early growth stages (Yoosefzadeh-Najafabadi et al., 2021a). While hyperspectral sensors can measure hundreds of wavebands, most of them are redundant due to their high correlation with the adjacent ones (Omidi et al., 2020). Therefore, there is a dire need to find the redundancy of wavebands not only based on the correlation with adjacent bands but also with the estimation of the interaction with other bands in different regions. Genome-wide association studies (GWAS) can be considered as one of the common genetic approaches used for discovering quantitative trait loci (QTL) that are highly associated with a trait of interest (Eltaher et al., 2021). By using GWAS, a QTL associated with a trait of interest can be detected using linkage disequilibrium (LD), which is the non-random association of alleles at specific loci (Somegowda et al., 2021). The detected QTL can be implemented in marker-assisted selection (MAS) for screening large breeding populations in a time- and cost-effective manner (Dababat et al., 2021; Eltaher et al., 2021). Over the past two decades, several statistical methods were used in GWAS to improve statistical power and computational speed (Brachi et al., 2011; Xu et al., 2018). The mixed linear model (MLM) and the fixed and random model circulating probability unification (FarmCPU) approach are known as two of the most common GWAS methods that are currently used in a wide range of genetic studies (Brachi et al., 2011; Lee et al., 2020; Singh et al., 2020). Also, Bonferroni correction and false discovery rate (FDR) are commonly used to set up a threshold for selecting associated QTL with major effects (Brachi et al., 2011; Xu et al., 2018; Lee et al., 2020; Singh et al., 2020).

The application of GWAS was reported in different plant species such as soybean (Brown et al., 2021), maize (Xu et al., 2018), wheat (Tsai et al., 2020), rice (Zhong et al., 2021), and sorghum (Somegowda et al., 2021). While there is no report on the genetic dissection of soybean yield-related hyperspectral reflectance bands, genetic dissection of vegetation index was previously reported in wheat (Wang, 2019; Galán et al., 2020; Wang et al., 2021). Several detected candidate genes related to NDVI, SPAD, and LR in durum wheat (Wang et al., 2021) overlapped with dry biomass, grain yield, and chlorophyll contents. Although GWAS can be considered as a powerful tool to detect the associated genomic regions with major effects, there are several barriers in applying conventional statistical methods in GWAS for identifying genomic regions associated with complex traits (Szymczak et al., 2009). One of the major challenges in GWAS is the high possibility of a false-positive rate that is due to the stochastic noise arise when the population structure is not well defined (Platt et al., 2010) or a high false-negative rate because of the unappropriated way of selecting the threshold (Kaler and Purcell, 2019). Another challenge associated with using the conventional statistical procedures is the “large markers (p), small samples (n)” problem that habitually happens in GWAS when these methods are applied to datasets where the number of markers (i.e., single nucleotide polymorphisms (SNPs)) is significantly larger (p≫n) than the number of genotypes (Kaler et al., 2020; Mohammadi et al., 2020; Xavier and Rainey, 2020). It is well documented that current conventional GWAS methods are only powerful to detect common SNPs with large effects on the target traits that can reach the minimum level of significance (Lee et al., 2020). Therefore, current conventional GWAS approaches may not be well-suited for discovering minor effect SNPs associated with the target traits, especially in plants with a significantly narrow genetic background (Zhou et al., 2019). For example, several crops, such as soybean, suffer from narrow genetic diversity mainly due to the genetic bottlenecks associated with their domestications and the lack of introducing new sources of genetic diversity (Mikel et al., 2010). While recent advances in sequencing technologies facilitate the accessibility of high-density genetic markers in a short time at a reduced cost, using sophisticated big data analysis methods combined with accurate and rapid large scale phenotyping methods, especially for complex traits, represent major bottlenecks (Hennessy et al., 2020; Yoosefzadeh-Najafabadi et al., 2021a). Recently, Machine Learning (ML) algorithms were shown to be promising computational strategies when applied to plant sciences because of their potential to analyze complex multivariable and nonlinear biological processes, which are commonly observed in complex traits in plants (Jafari and Shahsavar, 2020; Hesami et al., 2021; Yoosefzadeh-Najafabadi et al., 2021a). In general, ML algorithms can be programmed based on existing patterns present in the dataset. Recent studies showed the effectiveness of using ML algorithms to predict complex traits using secondary traits that are highly correlated with the trait of interest (Pantazi et al., 2016; Liakos et al., 2018; Palanivel and Surianarayanan, 2019; Yoosefzadeh-Najafabadi et al., 2021a). Based on the type of problems they solve, ML algorithms can be characterized in four categories as follows: (i) identification, (ii) classification, (iii) quantification, and (iv) prediction. These four categories could be used to identify important variables from multi-dimensional datasets (Liakos et al., 2018; Hesami et al., 2020; Sharifi, 2021). Variable selection methods are commonly used to improve the prediction performance and avoid overfitting rates for classification and prediction problems in high-dimensional datasets (George, 2000). The variable selection methods are, in general, classified into three distinct groups: wrappers, filters, and embedded methods (George, 2000; Heinze and Dunkler, 2017). In filter methods, subsets of variables are selected based on selection criteria that are independent from those used for the final classifier (Chowdhury and Turin, 2020). However, both wrapper and embedded methods implement variable selection based on individual learners (Albashish et al., 2021). For example, recursive feature elimination (RFE) is a representative wrapper-type variable selection algorithm widely used to extract important features from phenomics and genomics data (Gupta and Gupta, 2020; Albashish et al., 2021; Yoosefzadeh-Najafabadi et al., 2021a). RFE discards in an iterative fashion the weak and unstable variables until a target number of variables is reached and thus retains independent variables from the dataset resulting in significant improvements in performance and reduced overfitting of ML algorithms (Sanz et al., 2018).

In addition to the proper ML algorithm choice, adopting an accurate data integration strategy is required for a better understanding of the structure of complex multidimensional traits at different omics levels (Tarazona et al., 2021). These days, more and more data are generated using different omics such as genomics and phenomics, and several data integration strategies such as early, intermediate, late, mixed, and hierarchical strategies are available (Jamil et al., 2020; Picard et al., 2021). A hierarchical data integration strategy is built upon prior knowledge about the relationship between and among different tested omics layers (Picard et al., 2021). For instance, a hierarchical data integration strategy can be used for a better understanding of soybean yield formation by having prior knowledge about the physiological concept of each hyperspectral reflectance in explaining the overall yield variation. The effectiveness of using RFE was reported previously by Yoosefzadeh-Najafabadi et al. (2021a) to extract the important wavelengths for predicting soybean seed yield. In addition, a few studies used ML algorithms in GWAS for detecting QTL associated with complex traits (Zhou et al., 2019; Xavier and Rainey, 2020; Najafabadi et al., 2021). In a GWAS study, Xavier and Rainey (2020) investigated the potential use of Random Forest (RF) for detecting QTL associated with soybean yield components, such as the number of pods and nodes. In addition, the use of RF for detecting QTL with minor effects was reported in a study by Asif et al. (2020). However, using other promising ML algorithms such as support vector regression (SVR) and implementing a hierarchical data integration strategy for better understanding soybean yield using hyperspectral and genome-wide association studies is long overdue. Therefore, this study aimed to: (1) investigate the use of RFE for selecting hyperspectral reflectance wavelengths influencing soybean yield, (2) evaluate the potential use of SVR- mediated GWAS for genetic dissection of important hyperspectral reflectance bands affecting soybean yield, and (3) discover candidate genes linked to identified hyperspectral reflectance bands associated with yield. To the best of our knowledge, this study is the first report where GWAS was used to discover hyperspectral reflectance bands associated with soybean yield. This study also demonstrates the benefits of using ML algorithms and variable selection methods in phenome-phenome and phenome-genome association studies for discovering yield-related physiological traits and genomic regions associated with these traits in soybean. The results of this study can be useful for selecting high yielding soybean genotypes at early growth stages and, therefore, increasing the rate of genetic gain for yield in cultivar development programs.

Accurate predictions of the final performance of germplasm at early growth stages is paramount for breeders to make early selection decisions in germplasm advancement and cultivar development programs (Maimaitijiang et al., 2020). The end-season selection based on yield per se may result in overlooking other factors such as selecting for other yield-unrelated traits and environmental factors (Yoosefzadeh Najafabadi, 2021). Yet, trait measurement in large breeding nurseries and working with large phenotypic and genotypic data is still a bottleneck in the genome-to-phenome analysis process (Parmley et al., 2019). In recent years, the combination of high throughput phenotyping and genotyping tools has greatly accelerated the plant breeding progress (Yang et al., 2020). However, merging different omics datasets for better characterization of the complex traits extensively depends on an appropriate selection of a data integration strategy (Picard et al., 2021). Extracting the biological information from the secondary related traits that are in high correlation with the trait of interest, detecting the associated SNPs, and identifying candidate genes for each detected peak SNPs provided a valuable complement for understanding the biological mechanism of a trait of interest. The hierarchical strategy is based on including prior knowledge of relationships between different omics layers (Wang et al., 2013; Picard et al., 2021). In this study, we used this strategy in a soybean hyperspectral reflectance-yield association study to acquire a better understanding of the genetic architecture of soybean yield using GWAS.

As one of the important high-throughput phenotyping tools, hyperspectral reflectance has provided plant breeders with an efficient plant evaluation strategy in a large population at early growth stages for important agronomic traits (Yoosefzadeh-Najafabadi et al., 2021a). The use of spectral reflectance for predicting crop yield has been extensively investigated. For example, Qiao et al. (2021) reported the efficiency of using long-time series multi-spectral images for yield mapping of different crop species using an automated spatial-spectral feature extractor. The application of hyperspectral reflectance in predicting the wheat grain yield was studied by Fei et al. (2021), who reported the effectiveness of red and NIR regions in predicting the grain yield in different irrigation regimes. The use of hyperspectral reflectance in predicting yield was not limited to agronomy crops and used for vegetables (Awika et al., 2021), trees (Ali and Imran, 2021), and industrial plants (Holmes et al., 2020). Therefore, breeders can use spectral data to establish phenome-to-genome relationships by performing HypWAS and applying it via phenomics selection. Genomic selection methods suffer from the lack of consideration for environmental effects (Zhong et al., 2009; Tong and Nikoloski, 2021). However, by using HypWAS, both environmental and genetic effects can be considered in the final decision. The proposed idea of HypWAS is novel, and, to our best knowledge, there is no example in the literature.

The rationale behind the HypWAS is to increase the efficiency of indirect selection for breeders and to offer them a strategy to reduce noise and possible errors from the hyperspectral reflectance data that is used in genetic studies. HypWAS makes it possible to select reflectance bands with high importance scores for complex traits such as yield. Therefore, plant breeders and geneticists can investigate more aspects of the selected reflectance bands to find the genomic regions, gene candidates, and physiological processes behind each reflectance band. Previously, we implemented one of the most common variable selection methods, RFE, to select important reflectance bands in association with soybean yield production (Yoosefzadeh-Najafabadi et al., 2021a). However, there was no further information about the genetic background of the selected reflectance bands. In this study, we selected the five most important reflectance bands and we used HypWAS to investigate various aspects of the physiological and genetic background of each reflectance band.

Among the five selected reflectance bands, three of them were located in the visible range of the spectrum. Most of the reflection in the visible region is significantly dominated by the foliar pigments’ absorption (Hennessy et al., 2020). Chlorophyll a and b have a stronger reflection in comparison with other foliar pigments in the visible region (Fernandes et al., 2013). Chlorophylls play a major role in photosynthesis due to all the photosynthesis structures, such as the antenna systems of photosystem I and photosystem II (Pettai et al., 2005; Hennessy et al., 2020). Light energy absorbed by antenna systems of photosystem I and II, is then rapidly transferred to the respective reaction centers (Pettai et al., 2005). Several studies reported the strong correlation of the 680–700 nm bands with photosystem I and II (Ke, 2001; Pettai et al., 2005; Hoa et al., 2017; Hennessy et al., 2020). In this study, the 680 nm band was selected as one of the high-importance reflectance bands that explains the total soybean seed yield. This can reveal the importance of photosynthesis components in determining the overall soybean yield (Yoosefzadeh-Najafabadi et al., 2021c). The 660 nm band can be used to screen a large population of plants in a short time for selecting genotypes with a high potential for photosynthesis activity. Similarly, another important reflectance band in this study (390 nm) is located in the blue region of the spectrum, which is highly correlated with the chlorophyll content (Richter et al., 2016; Hennessy et al., 2020). The 390 nm band had the highest importance value in predicting the final soybean yield among all the selected reflectance bands, confirming the importance of photosynthesis in the final soybean yield formation. The third detected reflectance band in this study (550 nm), represents the green peak in the visible spectrum (Stommel et al., 2009; Liu et al., 2018). This reflectance band was reported to be correlated with Chlorophyll and Anthocyanin contents in plants (Hennessy et al., 2020). Anthocyanins are known as a diverse class of flavonoid components that play a significant role in protecting plants against abiotic and biotic stresses (Gitelson et al., 2001; Hennessy et al., 2020). Since most of the soybean fields in North America are grown in rainfed areas, water deficit stress would be inevitable during the soybean growing season in these areas.

Many studies reported the strong correlation between red-edge and near-infrared regions and water content as well as spongy mesophyll conditions in plants. Based on the HypWAS analysis, the 730 and 820 nm bands were selected as the important reflectance bands in predicting the overall soybean yield. The 730 nm band is located in the red-edge region and correlated with the leaf water content, chlorophyll concentration, and leaf layering (Horler et al., 1983). The 820 nm band is located in the near-infrared region and reflects the spongy mesophyll condition in leaves (Gao et al., 2014; Salvatori et al., 2015). The major role of spongy mesophyll in plants is to interchange the required CO₂ for photosynthesis (Veromann-Jürgenson et al., 2020). All spongy mesophylls are covered by a thin layer of water, hence environmental stresses can significantly affect mesophylls resulting in a reduced photosynthesis activity level in plants (Veromann-Jürgenson et al., 2020; Liu M. et al., 2021). Therefore, changes in the water and gas level in mesophylls is the first sign of detecting stresses in plants, so the difference between the reflectance of the 730 nm as well as the 820 nm band in normal and stress conditions can be considered as a measurement for abiotic and biotic stresses (Momayyezi et al., 2020). Overall, adjusting breeding selection criteria based on the selected reflectance bands might lead to select a genotype with significant levels of tolerance against stresses and high photosynthesis activity. This can be done by measuring those reflectance bands by remote sensing tools in a short time in a less labor-intensive manner. Also, understanding the genetic background of each selected reflectance band would be helpful to design appropriate genetic markers for the fast screening of genotypes.

Genome-wide association studies is currently considered as an imperative approach for discovering genomic regions associated with complex traits in diverse areas from human genetics to plant and animal breeding (Alqudah et al., 2020; Khanzadeh et al., 2020; Li et al., 2020; Tibbs Cortes et al., 2021). Insufficient statistical power is the most fundamental challenge when it comes to using conventional GWAS for characterizing quantitative traits (Nicholls et al., 2020), especially in plants with narrow genetic bases. In ML-mediated GWAS analyses, the significance levels or thresholds for identifying SNP-trait associations are estimated using variable importance methods, which are different from statistical methods that are used for estimating p-value in conventional GWAS (Szymczak et al., 2009). The main advantage of using variable importance, rather than p-values, for individual SNP-trait association tests, consists in the ability of these approaches to consider the interaction effects between SNPs (Szymczak et al., 2009; Asif et al., 2020). In other words, ML algorithms are more practical in terms of allowing for high-order interactions that are not pre-specified in the model using non-linear kernels (Sun et al., 2021). Conventional statistical methods need to have pre-identified parameters for the analysis of special traits of interest (Sun et al., 2021). Conventional statistical methods are significantly useful in the presence of inherent uncertainty, small signal-to-noise ratio, insufficient training dataset, a small number of variables, predefining the parameters involved in the variance of the trait of interest. Therefore, conventional GWAS are appropriate approaches for detecting SNPs with large main effects on complex traits. However, they are underpowered to simultaneously consider a wide range of interconnected biological processes and mechanisms that shape the phenotype of complex traits (Lee et al., 2020). By using ML algorithms in GWAS, the interaction and joint effect of multiple SNPs can be estimated using variable importance methods, and the best set of SNPs will be selected to give the best performance (Pahikkala et al., 2012). Recent studies showed that the SNPs with high importance scores are not necessarily the SNPs with significant p-values resulted from single SNP analyses (Arshadi et al., 2009; Grömping, 2009; Szymczak et al., 2009; Ziliak, 2017; Di Leo and Sardanelli, 2020). Therefore, using variable importance values estimated by ML algorithms for identifying SNP-trait associations may improve the power of ML-mediated GWAS for discovering variant-trait associations with higher resolution (Szymczak et al., 2009). The variable importance methods based on linear and logistic regressions, Support vector machines, and random forest algorithms are well established in the literature (Grömping, 2009; Wu and Liu, 2009; Chun and Keleş, 2010; Williamson et al., 2020; Yoosefzadeh-Najafabadi et al., 2021b). In this study, we found that SVR-mediated GWAS had the same performance in detecting numbers of QTL when compared to conventional GWAS methods. However, the detected QTL by SVR-mediated GWAS was more related to the physiological background of each tested hyperspectral reflectance bands. For instance, in the 820 nm band, the SVR-mediated GWAS detected 5 QTL related to water use efficiency, which is clearly in agreement with the physiological background of this trait. The same scenario happened in the 660 nm band, where most of the detected QTL by SVR-mediated GWAS were related to flowing and soybean cyst resistance. In all the tested hyperspectral reflectance bands, several QTL related to the soybean seed protein, oil, pod number, seed yield, and seed thickness were detected in all GWAS methods. Meanwhile, seed protein, oil, pod number, seed yield, and seed thickness can be considered as the yield component traits, which directly and indirectly regulate the final soybean seed yield. Therefore, the detected QTL confirmed the efficiency of HypWAS and GWAS in indirect selection for complex traits such as yield.

Furthermore, several candidate genes were detected by SVR-mediated GWAS related to the oxidative and osmotic stresses, regulation of defense response, response to nematode, defense response to bacterium, and oxidoreductase activity. It is well documented that the violet spectrum and UV radiation are key factors in secondary metabolite production (e.g., terpenes, alkaloids, phenolic compounds, glucosinolates, and carotenoids) that can play a pivotal role in a plant’s defense systems (Schreiner et al., 2012; Matsuura et al., 2013). It has also been shown that these spectra lead to the activation of several signaling pathways such as defense signaling, reactive oxygen species (ROS), and photomorphogenic signaling (Schreiner et al., 2012; Matsuura et al., 2013). These signaling can stimulate and induce the specific gene expression patterns involved in different secondary metabolism pathways, such as the isoflavonoid biosynthesis pathway (Kim et al., 2014). MYB family is one of the most important transcriptional factors that may interact with light-responsive elements and thereby activate selected genes involved in isoflavonoid biosynthesis (Du et al., 2010). Moreover, a positive correlation was reported between the expression profiles of the selected genes (Glyma.02G008700 and Glyma.09G168700) 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 (Du et al., 2010). The spatiotemporal regulation of chlorophyll metabolism is necessary for various cellular processes such as chloroplast development, photosynthesis, plastid-derived retrograde signaling (Chan et al., 2016), RNA metabolism (Zhang et al., 2014), singlet oxygen-mediated signaling (Shen et al., 2006), abscisic acid signaling, and programmed cell death (Woodson et al., 2015; Dogra et al., 2019). Chlorophyll metabolism can be categorized into four functional classes including (i) Chlorophyll a synthesis through the branched tetrapyrrole biosynthesis pathway (Tanaka and Tanaka, 2007; Mochizuki et al., 2010), (ii) the ‘Chlorophyll cycle,’ which catalyzes the interconversion of Chlorophyll a and Chlorophyll b (Tanaka and Tanaka, 2011), (iii) the degradation of Chlorophyll a to yield colorless through the pheophorbide a oxygenase (PAO)/phyllobilin pathway (Christ and Hörtensteiner, 2014), and (iv) Chlorophyll recycling pathway through dephytylase 1 (CLD1) (Lin et al., 2016). The combination of divinyl reductase (DVR) and light-dependent protochlorophyllide oxidoreductase (POR) produces chlorophyllide (Chlide) a. Subsequently, Chlorophyll synthase (CHLG) catalyzes Chlorophyll a biosynthesis through the combination of Chlide a and phytyl pyrophosphate (phytyl-PP) (Wang and Grimm, 2021). CLD1 can reversibly convert Chlorophyll a into Chlide a during Chlorophyll recycling. Also, it is well documented that high-light inducible proteins (Hlips) play an important role in binding Chlorophyll a and β-carotene and consequently the photosynthesis capacity (Chidgey et al., 2014; Staleva et al., 2015; Shukla et al., 2018).

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 (de Araujo et al., 2014; Cano et al., 2019). They may also be involved in sensing light, CO2, and water availability (Momayyezi et al., 2020). Therefore, CAs can affect photosynthetic efficiency through their impacts on stomatal response to light, CO2-facilitating components (aquaporins), ABA signaling, and other signaling pathways (de Araujo et al., 2014; Cano et al., 2019; Momayyezi et al., 2020). ABA is a key phytohormone associated with stomatal closure. ABA receptors (e.g., PYL, PYR, RCAR proteins) play an important role in executing ABA’s function in water relations (Cutler et al., 2010; Kim et al., 2010). ABA regulates the stress-activated kinase signaling network that controls stomatal closure (Mega et al., 2019). In reacting to water deficit, the level of ABA increases, which regulates the ligand-receptor complex formation that represses the clade A protein phosphatase 2Cs (PP2Cs) activity, which is considered negative regulators for ABA signaling (Fujii et al., 2009; Ma et al., 2009; Park et al., 2009). Because of the central role of ABA receptors in transpiration regulation, they can be considered as promising targets for breeding programs in order to manipulate ABA sensitivity and water productivity (Mega et al., 2019).

Indirect 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.

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: https://github.com/Mo hsen1080/Available-Datasets/blob/92f27c80fa3e460900589b4218 8a943570dee86d/FastGBS.SNPs.232.imputed.Het50.maf0.05.hm p.txt, GitHub.

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.