Multi-locus genome-wide association mapping for major agronomic and yield-related traits in sorghum (Sorghum bicolor (L.) moench) landraces

Abstract

Background

Sorghum is a vital cereal crop for over 750 million people, ranking 5th globally. It has multiple purposes, including food, feed, and biofuels, and is essential in Ethiopia, which has a rich genetic diversity of various agroecological zones.

Objective

Explore marker-trait associations (MTAs) to identify quantitative trait nucleotides (QTNs) and new candidate genes associated with agronomic and yield contributing traits in Ethiopian sorghum landraces using multi-locus GWAS models to assist the genomic-assisted breeding strategies.

Method

This study investigates the genetic basis of agronomic traits in Ethiopian sorghum landraces through multi-locus Genome-Wide Association Studies (ML-GWAS). 216 landraces, improved varieties, and check cultivars were obtained from the Ethiopian Biodiversity Institute and the National Sorghum Improvement Program for this study. The experiment was conducted over two cropping seasons, employing an α-lattice design for phenotyping key traits such as days to flowering, days to maturity, plant height, seed number per plant, grain yield, and thousand seed weight. A mixed linear model (MLM) was used to analyze the phenotypic data and estimate the genetic parameters including variances and the broad sense heritability. GBS with the ApeKI restriction enzyme provided 50,165 high-quality SNP markers. The six ML-GWAS models identified significant QTNs with a LOD score threshold value of ≥ 4.0. The analysis revealed major QTNs associated with traits across multiple chromosomes, supported by a stringent filtering criterion that ensured reliability. Co-localization with known QTLs was explored using the Sorghum QTL Atlas database and candidate genes within significant QTN regions, providing the genetic architecture influencing agronomic performance were identified via the Phytozome platform using the biomaRt package.

Result

Pearson correlation analysis revealed significant associations among most traits, with p-values less than 0.0001, except for grain yield per plant which showed lower correlations with other traits. Genetic variability analysis indicated that days to flowering exhibited high heritability (0.7) and genetic advance (19.6%) as percent of mean, suggesting strong genetic control, while grain yield displayed extremely low h² (0.003). A total of 351,692 SNP markers were identified across 10 sorghum chromosomes from 216 Ethiopian sorghum landraces, and we have been refining this to 50,165 filtered SNPs. Manhattan plots indicated significant marker-trait associations (MTAs) across multiple chromosomes, particularly for days to flowering and plant height. Significant QTNs were associated with key traits including flowering time, plant height, and grain yield. ML-GWAS identified 176 QTNs with varying LOD scores and phenotypic effects. Multiple genes linked to these QTNs highlight the complexity of genetic interactions of studied traits with 36 unique and 12 major QTNs. Notable SNP markers were concentrated on chromosomes 1, 2, and 3, reinforcing the importance of these regions for breeding efforts. Candidate gene analysis revealed key genes regulating flowering time, stress response, and yield traits, which could serve as targets for genetic enhancement. In our study, key candidate genes have been successfully identified, these are regulating flowering time, maturity, and stress resilience. Genes such as Sobic.001G196700 and Sobic.002G183400 are identified as critical regulators of floral development. The stress-responsive gene Sobic.005G176100 (a mannose-6-phosphate isomerase), emphasizes the importance of resilience in sorghum cultivation under adverse conditions. Additionally, Sobic.003G324400 and Sobic.004G178300 are essential for regulating plant height and seed weight, making them valuable for yield enhancement breeding programs.

Conclusion

This study enhances our understanding of the genetic diversity of Ethiopian sorghum landraces, crucial for breeding programs. It identifies key QTNs and candidate genes associated with important agronomic traits, offering insights for marker-assisted and genomic-assisted breeding. The ML-GWAS models highlight the genetic complexity of flowering time and grain yield traits, emphasizing the need for targeted breeding efforts to maximize sorghum productivity.

Introduction

Sorghum (Sorghum bicolor (L.)Moench) is an annual C4 plant belonging to the family Poaceae under the Andropogoneae tribe [1]. It is the 5th most important cereal crop globally and a dietary staple for over 750 million people mainly living in semi-arid regions (Asia and Africa) [2]. It is a versatile cereal crop cultivated globally for diverse applications, including food, feed, and biofuel production. It is also a major crop in many regions worldwide, for instance; Asia, Africa, Australia, and the USA, and the 5 top sorghum-producing countries are; the United States (25%), India (21.5%), Mexico (11%), China (9%) and Nigeria (7%), and together these five countries account for 73% of total world production, and prized for its adaptability and nutritional value [3].

Sorghum is a vital staple food for millions, particularly in sub-Saharan Africa [4], in Ethiopia it serves as a staple food and livelihood source for millions [5]. It is a key energy source, of protein, vitamins, and minerals for many households [6]. Additionally, by-products of sorghum are used for animal feed, construction, fencing, and broom manufacturing [7].

Sorghum is a commercially significant crop utilized for producing lager beer, gluten-free food items, phytochemicals, sweet-stalked varieties, and biomass for biofuels, particularly in regions like Asia and Africa [8]. The average production reaches 23.35 million metric tons from an area of 23.14 million hectares, yielding an average productivity of 1.01 tons per hectare, and Ethiopia’s national average, sorghum productivity is 2.1 tons/ha which is very low compared to the global average of 3.2 tons/ha due to abiotic stress, biotic stress, soil fertility decline, and lack of high-yielding sorghum varieties [9].

Despite its economic importance, sorghum yield is affected by various biotic and abiotic challenges, including diseases, insect pests, weeds, nutrient deficiencies, aluminum toxicity, drought, salinity, waterlogging, and high temperatures [10]. Moreover, drought contributes to genetic erosion in sorghum, causing the loss of many landraces due to crop failures resulting from extreme drought conditions [11]. This has prompted numerous initiatives to explore the genetic and physiological mechanisms enabling crop drought resistance [10].

Ethiopia is recognized as a center of origin and diversity for sorghum, hosting a wealth of genetic variation for numerous traits [12]. Ethiopia boosts a rich genetic diversity of sorghum landraces adapted to various agroecological zones, ranging from lowlands to highlands [13]. A diverse set of popular Ethiopian sorghum landraces has been collected and preserved with a wealth of genetic resources and novel alleles for a range of agronomic, yield, and yield-related traits [14]. This diverse germplasm offers valuable opportunities for gaining insights into the genetic architecture of key traits, which can enhance breeding programs for more efficient genetic improvement of sorghum. Understanding the genetic diversity of landraces is crucial to identifying novel QTLs and genes [15].

Yield is a polygenic trait affected by multiple genes and factors, such as plant phenology, morphology, and physiological traits [16]. Unraveling the genetic basis of these traits is crucial for effective breeding thereby improving crop efficiency and resilience in a shifting climate [17]. Genomics-assisted breeding is an innovative approach that utilizes modern molecular tools and genomic information to improve the accuracy and efficiency of conventional plant breeding, In recent decades, substantial efforts have been devoted to genomic-assisted breeding in sorghum and other cereal crops [18]. Initially, genomic regions associated with agronomic traits in sorghum were identified using bi-parental linkage mapping methods [18]. This method often leads to low mapping resolution, restricted allelic diversity, and QTLs that are specific to certain populations [19], hindering the conversion of QTL discoveries into actionable strategies for plant breeding [20].

Genome-wide association study (GWAS) enables high-resolution QTL mapping by leveraging a diverse array of alleles across numerous accessions, making it a crucial tool for the genetic analysis of complex traits [21]. Sorghum is especially suitable for linkage mapping because of its moderate linkage disequilibrium and self-pollinating nature [21]. Recent investigations have applied GWAS in sorghum to examine the genetic regulation of several key traits, including flowering time [22], plant height, length of panicles, degree of panicle exertion, number of tillers, and seed count [22] as well as culm length and the number of panicles [23], inflorescence components [24], grain fill duration, panicle weight, and harvest index, and grain yield [25]. However, numerous studies encountered challenges, especially due to their dependence on germplasm that had undergone the sorghum conversion process.

Multi-locus GWAS models have emerged as powerful tool and that is useful for identifying Quantitative Trait Nucleotide (QTN) detection rather than QTLs and SNP markers effect estimation, including mrMLM [26], FASTmrMLM [27], FASTmrEMMA [28], ISIS EM-BLASSO [29], pLARmEB [30], and pKWmEB [31]. These approaches have successfully uncovered the genetic basis of important traits in various crops, including maize [32], rice [33], barley [34], and wheat [35]. The objectives of this study were to investigate marker trait associations (MTA) via ML-GWAS models to identify important QTNs, and candidate genes associated with agronomic, yield, and yield-related traits in Ethiopian sorghum landraces to promote genomic-assisted breeding (GAB) techniques and strategies [36].

Result

Pearson correlation analysis of agronomic & Yield-Related traits

The Pearson correlation probability of sorghum agronomic and yield association trait (Table S1) showed the p-values displayed are all less than 0.0001, except for grain yield per plant (GY) with days to flowering (DF): p = 0.1567, grain yield per plant (GY) with days to maturity: p = 0.5878, seed number per plant (SNPP) with thousand-seed weight (TSW): p = 0.0549, and the p-values less than 0.0001 indicate a highly significant correlation between the corresponding traits (Table S1).

Distribution of SNPs across Sorghum genome

A total of 351,692 SNP markers were identified across 10 chromosomes in 216 Ethiopian sorghum landraces and improved varieties. The dataset was filtered to exclude SNPs with MAF ≥ 0.05 (5%) yielding a robust final dataset of 50,165 SNPs. The genome-wide marker density plot (Fig. 1) showed that markers from the study panel were distributed across the sorghum genome. Further, examination of the genome-wide marker distribution revealed that the SNP markers were evenly dispersed. This comprehensive SNP dataset, with its even distribution and varying marker densities across the genome, provided a robust foundation for the subsequent genome-wide association analyses.

Fig. 1

Distribution of SNP marker heterozygosity, Minor Allele Frequency (MAF), and R-square (r²) across sorghum SNP markers, each parameter represented in separate panels

The three panels represent: (Fig. 1a) R-square (r²); (Fig. 1b) MAF; (Fig. 1c) SNP (Single Nucleotide Polymorphism) marker heterozygosity across sorghum genomes from bottom to top respectively. The x-axis indicates the marker number, while the y-axis displays the respective values for each parameter, highlighting variations across the markers.

The R² values represent the goodness of fit of the statistical model used to associate the genetic markers with the sorghum traits of interest, which include days to flowering, days to maturity, plant height, number of seeds per plant, grain yield, and thousand-seed weight. The higher the R² the stronger the association between the genetic markers and the phenotypic traits. Regions with high R² values indicate genomic areas that harbor significant QTLs or MTA for these sorghum agronomic traits. The MAF values in the middle panel provide information on genetic diversity.

The genomic data in Fig. 2 provides a good foundation for investigating the genetic architecture of important agronomic and yield-related traits, such as days to flowering, plant height, grain yield, and thousand-seed weight. The LD, marker density, and genetic distance information can inform the design and analysis of QTN mapping or GWAS experiments to identify marker-trait associations. In Fig. 2, The histograms display the frequency of genetic distances between markers, and they indicate a relatively even distribution of marker spacing, which is desirable for GWAS and QTN mapping.

Fig. 2

SNP integrity, analysis of genetic relationships in sorghum. The figure shows, (a) R values across markers; (b) a histogram showing the frequency distribution of R values; (c) a scatter plot of R values against distance (kb); (d) SNP distance and distribution across markers; (e) histogram of frequency suggests an adequate marker density for QTN mapping, covering the entire sorghum genome; (f) scatter plot illustrating R-square (r²) values against distance, with a trend line showing overall patterns

The color gradient (Fig. 3) helps quickly identify chromosomal regions with higher or lower SNP densities. Regions with higher SNP densities (represented by the red and orange shades) indicated areas of the genome that are likely to have greater genetic diversity and more potential marker-trait associations for the agronomic traits of interest, such as days to flowering, days to maturity, plant height, seed number per plant, grain yield, and thousand-seed weight. Conversely, the lighter-colored regions (blues and greens) suggest chromosomal segments with lower SNP densities, which may require additional marker development or optimization of genotyping strategies to ensure sufficient genome coverage for comprehensive QTN mapping and GWAS analyses.

Fig. 3

Distribution of single nucleotide polymorphisms (SNPs) markers across 10 sorghum chromosomes within a 1 Mb window size

Each bar represents a chromosome, with color intensity indicating the number of SNPs, ranging from 0 to over 50. The color scale on the right provides a key for interpreting SNP density. This visualization of the number of SNPs within a 1 Mb window size in the genome is relevant for understanding the genomic architecture and marker density for conducting QTN mapping and GWAS on agronomic and yield traits like days to flowering, days to maturity, plant height, seed number per plant, grain yield, and thousand-seed weight.

As shown in Fig. 3, the color scheme used to represent the number of SNPs within the 1 Mb window size across the sorghum chromosomes. The color gradient is as follows; White (0 SNPs), Light blue (1–6 SNPs), Dark blue (6–11 SNPs), Light green (11–16 SNPs), Dark green (16–21 SNPs), Light yellow (21–26 SNPs), Dark yellow (26–31 SNPs), Light orange (31–36 SNPs), Dark orange (36–41 SNPs), Light red (41–46 SNPs), and Dark red (≥ 50 SNPs). This color coding allows for a visual representation of the SNP density variation across the different chromosomal regions. The darker the color, the higher the number of SNPs. A gradient of SNP counts within the 1 Mb windows, ranging from 0 SNPs (white) to greater than/equal to 50 SNPs (dark red) indicates that the sorghum genome has varying levels of SNP density across different chromosomal regions (Fig. 3). Some chromosomes, such as Chr1 and 10, appear to have higher overall SNP densities compared to other chromosomes like Chr3 and 6. This suggests that the genomic architecture and recombination rates may differ across the chromosomes. The uneven distribution of SNP density across the genome has important implications for QTN mapping and GWAS analysis.

Each plot (Fig. 4) displays the negative logarithm of the p-values (-log10) on the y-axis against the chromosome numbers on the x-axis. The X-axis (Chromosomes) is represented by 1 to 10 chromosome numbers, indicating the locations of SNPs across the genome. Y-Axis (-log10(p)) showed stronger associations between SNPs and traits of interest. The threshold for significance can be determined by applying corrections for multiple testing, such as the Bonferroni correction and false discovery rate (FDR) [37]. The Manhattan plot showing p-values, MTA, and GWAS for agronomic, yield, and yield-related traits is indicated in Fig. 4.

Fig. 4

Represents the Manhattan plot showing p-values, MTA, and GWAS for agronomic, and yield-related traits. Note: The plot represents the traits of; (a) days to flowering; (b) days to maturity; (c) plant height; (d) number of seeds per plant; (e) grain yield; (f) thousand seed weight from top to bottom, respectively. Each marker median of the − log10(p), mrMLM, FASTmrMLM, and FASTmrEMMA approaches was used to draw the Manhattan plot. The dots are indicated by colors QTNs. Pink dots with dotted vertical lines indicate all QTNs commonly identified by three approaches

Pink SNPs also represent SNPs that are significant after applying the Bonferroni correction. The Blue SNPs show significant associations but may not pass the Bonferroni threshold line, indicating associations that could be considered significant under the FDR. The Bonferroni correction adjusts the p-value threshold by dividing the desired alpha level (0.05) by the SNPs. The FDR method controls the expected proportion of false discoveries among the rejected null hypotheses. A common threshold for significance using FDR is q < 0.05 [37].

The upper plot indicates several SNPs with significant associations, particularly in chromosomes 1, 5, and 8. The lower plot shows notable associations, especially on chromosomes 3 and 9. Like flowering time, several pink SNPs were evident, indicating they have significantly influenced maturation time.

QTNs identified by ML-GWAS

A multi-locus Q-Q plot (Fig. S1) is an effective tool for evaluating associations in GWAS providing insights into the genetic architecture of traits such as days to flowering, days to maturity, plant height, seed number per panicle, grain yield, and thousand seed weight. Significant associations are indicated by points in the lower tail of the plot, showing that traits like plant height and grain yield are influenced by various genetic factors. Using the mrMLM model, 176 QTNs were identified with varying LOD scores and R-squared values, reflecting their effect on trait variability. Multiple genes linked to these QTNs highlight the complexity of genetic interactions in sorghum, with unique QTNs (36), major QTNs (12), and polygenic QTNs indicating intricate genetic relationships. The QTNs identified differ among traits, with the mrMLM model displaying a range of QTN effects from − 119.11 to 206.78 (Table 1), reflecting intricate genetic interactions. LOD scores, which assess the strength of these associations, are highest in the FASTmrMLM model, ranging from 4.04 to 36.13, indicating robust associations and potential QTLs worthy of further exploration. R-squared values, which measure the variance explained (PVE) by QTNs, range from 2.52 to 23.93% in the mrMLM model, showcasing varying impacts on trait variability. 176 QTNs were identified across all 6 models (Table 1), with mrMLM uncovering the most (42 QTNs) and FASTmrEMMA the least (13 QTNs), offering a thorough assessment of genetic variation linked to these traits. Specific traits, such as days to flowering, reveal multiple QTNs across chromosomes 1 to 10, each with different LOD (4.16 to 8.22) scores and R-squared values (Table 2). For example, QTN S1_73955151 on chromosome 1 shows a LOD score between 4.09 and 4.59 and an R-squared value of 13.22–19.38%, indicating its significant role in the trait. Conversely, the plant height trait has a notable QTN (S1_67415907) with a high LOD score of 10.14 and an R-squared value of 7.63%, suggesting a strong association. In contrast, lower LOD scores associated with certain QTNs for grain yield highlight weaker associations that may require further investigation.

Table 1 Summary of QTNs identified for the major agronomic, yield, and yield-related traits investigated in the present study using the six MrMLM models

Table 2 The list of significant QTNs identified through ML-GWAS models for various agronomic and yield-related traits

The QTN analysis results reveal a substantial genetic complexity across various traits, with a total of 176 QTNs identified using multiple models. The mrMLM model identified the most QTNs (42) with strong LOD scores (4.03 to 17.01) and moderate explanatory power (r² of 2.52 to 23.93). The FASTmrMLM model showed even higher LOD scores (up to 36.13) and a wide range of QTN effects (-299.26 to -129.76), accounting for significant trait variance (r² of 1.78 to 33.58). Other models like FASTmrEMMA, pLARmEB, pKWmEB, and ISIS EM-BLASSO.

Each QTN was uniquely identified (S1_73955151) and linked to a specific chromosome and base pair position. Higher LOD scores indicate stronger associations. For instance, the QTN for plant height (S1_67415907) has a notably high LOD score of 10.14, suggesting a strong genetic influence on this trait. R² values indicate the proportion of variance in the trait explained by the QTN. For example, the QTN associated with SNPP (S1_1359747) has an R² value ranging from 15.84 to 17.02%, which explains a significant portion of the trait variability. The number of Genes ± LD in a 1 Mb window size indicates the number of genes associated with each QTN, accounting for linkage disequilibrium (LD). QTN for days to flowering (S2_6784036) was associated with five genes (Table 2), reflecting the complexity of the genetic interactions involved. The varying number of associated genes per QTN highlights the complex interactions in the genetic architecture of these traits. For instance, certain QTNs were linked to multiple genes, suggesting that several genetic factors may influence a single trait.

The QTN mapping displays the locations of QTNs on each chromosome. Chromosome 1 contains multiple QTNs associated with days to flowering (DF), plant height (PH), and thousand seed weight (TSW). Notable QTNs include S1_1359747 seed number per plant (SNPP), which correlates significantly with the plant height (PH) trait. Chromosome 2 hosts several critical QTNs, including S2_116291 and S2_54254801, indicating their potential impact on drought resistance and growth. Chromosome 3 displays QTNs for grain yield (GY) and plant height (PH), with S3_63127731 showing strong associations. Chromosomes 4–10 harbor QTNs linked to various traits, with some QTNs appearing in multiple traits, suggesting pleiotropic effects (Table S2). Trait Associations and Statistical Significance LOD scores and R-squared values for each QTN indicate their significance in trait expression, for instance, QTNs with LOD scores exceeding 4.0 are considered significant, while R-squared values above 10% suggest substantial contributions to trait variances (Table S2).

Discussion

Analysis of genetic variability, heritability, and genetic advance

Days to flowering have high broad sense heritability (h²⁾ (0.7) and genetic advance (GA) as a percentage of the mean (19.6%) indicating that this trait has a strong genetic component and can be effectively improved through selection. The large genotypic variance (142.6) compared to the environmental variance (75.2) suggested that genetic factors play a significant role in determining days to 50% flowering.

Days to maturity have moderate h² (0.5) and GA as a percentage of the mean (8.4%). This suggests that genetic improvement is possible but may be more challenging than for days to flowering. The genotypic and environmental variances are more balanced for this trait, indicating that genetic and environmental factors contribute to the expression of days to physiological maturity.

The number of seeds per plant had low h² (0.0) and GAM (3.6%), indicating that environmental factors highly influence it and may be challenging to improve through selection alone. The EV (501.1) was much larger than the GV (26.2), supporting the low heritability estimate. The GCV (7.9%) was relatively low, suggesting limited genetic variability for this trait.

Grain yield has extremely low h² (0.003) and GAM (0.2%), indicating that environmental factors predominantly influence it and may be difficult to improve through selection. The EV (494552.3) is much larger than the GV (149090.8), confirming the high environmental influence on this trait. The GCV (2.1%) is very low, suggesting limited GV for grain yield in the population.

Traits that are coupled and exhibit high h² and GA, like days to flowering and plant height, offer good prospects for effective selection [38]. Conversely, traits with low h² and GA, such as the number of seeds per plant and grain yield, can be more difficult to enhance through selection alone and may necessitate more intricate breeding strategies (Table S3).

The high GCV (11.7%) indicated a good amount of genetic variability for this trait in the population, which is desirable for selection. The high broad-sense h² in this study was consistent with previous findings Subudhi, Rosenow, & Nguyen [39] reported for days to flowering in sorghum ranging from 0.61 to 0.92, depending on the population and environment. Ayana & Bekele [40] also found high h² estimates (0.70–0.80) for days to flowering in sorghum, indicating the strong genetic control of this trait.

The moderate h² (0.4) in plant height in this study aligns with the findings by Ayana and Bekele [41], who reported h² estimates ranging from 0.38 to 0.59 for plant height traits in sorghum. Also, Subudhi et al. [42] reported moderate to high h² (0.48–0.77) for plant height in sorghum, depending on the population and environment. The h² for plant height is moderate (0.4), and the GAM is relatively high (22.5%). The large GV (3689.8) compared to the EV (5227.7) suggests that genetic factors are pre-dominant in determining plant height. The GCV (16.9%) is reasonably high, indicating the presence of substantial genetic variability for plant height.

The moderate h² (0.5) for days to physiological maturity observed in this study was consistent with the previous findings by Ayana and Bekele [41] which reported the estimated h² value ranging from 0.45 to 0.56. Subudhi et al. [42] also reported moderate to high h² (0.57–0.87) for days to maturity (Table S3).

The very low h² (0.0) for the number of seeds per plant observed in this study was consistent with the findings of Ayana and Bekele [41] who reported low h² estimates (0.08–0.19) for this trait in sorghum. Subudhi et al. [42] also found low h² (0.19–0.45) for the number of seeds per plant in sorghum, indicating the strong influence of environmental factors (Table S3).

The extremely low h² (0.003) for grain yield in this study was in line with the findings of Ayana and Bekele [41], who reported very low h² estimates (0.01–0.12) for grain yield in sorghum. Subudhi et al. [42] also found low h² (0.15–0.47) for grain yield, suggesting that environmental factors highly influence this trait and may be challenging to improve through selection alone.

Analysis of genetic diversity and MTA association using SNP markers

The analysis of SNP heterozygosity, MAF, and R² values provides valuable insights into the genetic landscape of sorghum (Fig. 1). The observed variation in heterozygosity across chromosomes indicates differing levels of genetic diversity within the population. This diversity is vital for adaptive traits that enhance resilience to environmental stresses. The MAF findings suggest that specific alleles may be more prevalent, crucial for identifying genetic resources that can be utilized in breeding programs. For instance, higher MAF regions may harbor alleles associated with beneficial traits, providing a genetic basis for improving sorghum varieties [43]. The R² analysis highlights regions with strong associations with traits, guiding future marker-assisted selection efforts [44]. Previous studies have found that genetic diversity is essential for the adaptability of sorghum to varying environmental conditions, Baye et al. [45] reported that this supports our findings of higher MAF correlating with beneficial traits [46]. This reinforces the idea that genetic diversity is key to successful breeding. Zhao et al. [47] demonstrated the utility of R² values in identifying QTLs for important traits in sorghum. Our results similarly highlight regions with high R² values, suggesting that these markers are valuable for targeted breeding efforts.

Distribution of SNPs across Sorghum chromosomes

Regions with high SNP density, found on chromosomes 1, 5, and 7, indicated areas where selective pressure may have influenced genetic variation (Fig. 1). The clustering of SNPs can also facilitate the identification of genomic regions associated with traits of interest, as the high-density markers allow for finer mapping of QTLs [48]. In our studies, the presence of SNP hotspots could indicate historical selection events that have shaped the current genetic landscape of sorghum. Previous studies by Liu et al. [49] have reported similar patterns of SNP distribution across sorghum chromosomes. These findings confirm that certain genomic regions are more genetically diverse, which can enhance the breeding potential for specific traits. Hotspots of SNP variation reported by Baye et al. [45] identified specific genomic regions associated with important agronomic traits, aligning with the observations of SNP hotspots in our study. These hotspots are essential for breeding programs as they may harbor alleles that confer desirable traits. Zhao et al. [47] emphasized the importance of high SNP density in facilitating marker-assisted selection (MAS) for complex traits. Each pink-colored MTA represents a significant association between a specific SNP and the trait of interest (Fig. 4). The number of these pink MTAs indicates how many genetic markers show a strong statistical link to the trait being studied. The higher number of pink MTAs suggests that the trait is influenced by multiple genetic factors. This may indicate a complex genetic architecture, where several genes contribute to the trait’s expression. The lower number of pink MTAs could imply that the trait is controlled by fewer genetic factors, potentially indicating a simpler genetic basis (Fig. 4). Our findings perfectly aligned with this report by illustrating how regions with many SNPs can serve as valuable targets for breeding strategies.

QTN effect analysis for agronomic and Yield-related traits

The variability in QTN effects and the strength of associations across agronomic and yield-related traits highlighted the need for utilizing multiple analytical approaches to capture the full spectrum of genetic influences [50]. The mrMLM and FASTmrMLM models effectively identify significant QTNs, with high LOD scores and substantial R² values. In contrast, FASTmrEMMA identified fewer QTNs, suggesting that different models can yield varying insights into genetic architecture (Table 2).

Table 2 presents significant Quantitative Trait Nucleotides (QTNs) identified through Multi-Locus-Genome-Wide Association Study (ML-GWAS) models for various agronomic and yield-related traits in sorghum, including days to flowering (DF), days to maturity (DM), plant height (PH), seed number per panicle (SNPP), grain yield (GY), and thousand seed weight (TSW). Each QTN is characterized by its chromosomal location, allele information, position in base pairs (bp), LOD (Logarithm of Odds) score, r² (coefficient of determination or phenotypic variance explained), the methods used for identification, and the number of genes within the linkage disequilibrium (LD) region. The methods employed include mrMLM, FASTmrMLM, FASTmrEMMA, pLARmEB, pKWmEB, and ISIS EM-BLASSO, which collectively enhance the power to detect associations, especially for complex traits influenced by multiple genetic and environmental factors (Table S2, Table 2).

Identification and characterization of QTNs associated with various genes

For days to flowering (DF), several QTNs were identified, including S1_73955151 on chromosome SBI-01, which is near the Ma1 gene (Sb01g010260/QTNGL1.2, (Total number of green leaves at maturity), a well-known regulator gene of flowering time in sorghum [51, 52]. This QTN showed a high r² value (13.22–19.38), indicating a strong association with flowering time. Similarly, S2_6784036 on SBI-02 is near the Dw2 locus, associated with plant height and flowering time [52, 53], and S6_49875883 on SBI-06, with a high LOD score (6.60–6.66), is likely linked to the Sb06g023260 gene, previously associated with flowering time [54]. For days to maturity (DM), S1_76529338 on SBI-01, also near the Ma1 gene, showed a high r² value (5.14–19.59), suggesting a strong association with maturity. S5_623466 on SBI-05, near the Sb05g004000 gene, also showed a moderate r² value (3.92–8.36), indicating a reliable association with maturity [54].

In the case of plant height (PH), S1_67415907 on SBI-01, with a very high LOD score (10.14), is likely associated with the Dw1 gene, a major determinant of plant height in sorghum [53], the high r² value (7.63) further supports this strong association. S2_1166841 on SBI-02, near the Dw2 locus, also showed a moderate r² value (1.53–10.63), consistent with previous findings [53]. For seed number per panicle (SNPP), S1_1359747 on SBI-01, with a high LOD score (7.17–10.38), is likely associated with the Sb01g001000 gene, previously linked to seed number [54], and S9_50050063 on SBI-09, with a wide range of LOD scores (4.13–8.76) and r² values (3.03-18.00), suggests a complex genetic architecture for seed number per panicle, supported by multiple methods.

For grain yield (GY), S6_32754749 on SBI-06, with a very high LOD score (4.45–17.01), is likely associated with the Sb06g023260 gene, previously linked to grain yield [54]. Similarly, S10_60795709 on SBI-10, with a very high LOD score (5.27–36.13), is likely associated with the Sb10g025000 gene, also linked to grain yield [55]. Finally, for thousand seed weight (TSW), S1_25033782 on SBI-01, with a high r² value (12.57–16.85), is likely associated with the Sb01g010260 gene, previously linked to seed weight [55]. S5_14397024 on SBI-05, with a high LOD score (6.98), is likely associated with the Sb05g004000 gene, also linked to seed weight [54]. QTNs identified in this study are consistent with previous research findings, and the use of ML-GWAS models provides a robust approach to uncovering the genetic basis of complex agronomic and yield-related traits in sorghum. The high LOD scores and r² values, along with the use of multiple methods, can validate the reliability of these associations. These findings contribute to a deeper understanding of the genetic architecture of sorghum and provide valuable insights for future breeding programs aimed at improving yield and agronomic traits.

The Cross-Validation of alleles with previously identified Sorghum genes

To compare our findings with previous research and validate the alleles identified, we have examined each trait and the associated QTNs, referencing relevant studies that have identified similar genetic loci or alleles in sorghum or related crops. Below is a detailed comparison and validation of the alleles in our result (Table 2), supported by references to previously investigated research.

Days to Flowering (S1_73955151 (SBI-01, T/C): This QTN is located on chromosome SBI-01, near the Ma1 gene (Sb01g010260), which is a well-known regulator of flowering time in sorghum. The Ma1 gene has been extensively studied and is associated with delayed flowering under long-day conditions [51]. The T/C allele variation in this region is consistent with previous findings that link this locus to flowering time [56, 57]. S2_6784036 (SBI-02, T/G): This QTN is near the Dw2 locus, which is associated with plant height and flowering time in sorghum. The T/G allele variation aligns with previous studies that identified this region as a major QTL for flowering time [51, 58]. S6_49875883 (SBI-06, G/C): This QTN is likely associated with the Sb06g023260 gene, which has been linked to flowering time in sorghum. The G/C allele variation is consistent with previous findings that identified this region as a significant QTL for flowering time [59].

Days to maturity (S1_76529338 (SBI-01, A/G): This QTN is near the Ma1 gene, which regulates maturity in sorghum. The A/G allele variation is consistent with previous studies that identified this locus as a major determinant of maturity [59,60,61], S5_623466 (SBI-05, A/C): This QTN is near the Sb05g004000 gene, which has been associated with maturity in sorghum. The A/C allele variation aligns with previous findings that identified this region as a significant QTL for maturity [59].

Plant height (S1_67415907 (SBI-01, G/T): This QTN is likely associated with the Dw1 gene, a major determinant of plant height in sorghum. The G/T allele variation is consistent with previous studies that identified this locus as a significant QTL for plant height [58, 59]. S2_1166841 (SBI-02, C/A): This QTN is near the Dw2 locus, which is associated with plant height in sorghum. The C/A allele variation aligns with previous findings that identified this region as a major QTL for plant height [59].

Seed number per plant/panicle (S1_1359747 (SBI-01, T/C): This QTN is likely associated with the Sb01g001000 gene, which has been linked to seed number in sorghum. The T/C allele variation is consistent with previous findings that identified this region as a significant QTL for seed number [59]. S9_50050063 (SBI-09, C/G): This QTN is likely associated with the Sb09g025000 gene, which has been linked to seed number per plant. The C/G allele variation aligns with previous findings that identified this region as a significant QTL for seed number [59].

Grain yield (S6_32754749 (SBI-06, C/G): This QTN is likely associated with the Sb06g023260 gene, which has been linked to grain yield in sorghum. The C/G allele variation is consistent with previous findings that identified this region as a significant QTL for grain yield [59] S10_60795709 (SBI-10, C/T): This QTN is likely associated with the Sb10g025000 gene, which has been linked to grain yield in sorghum. The C/T allele variation aligns with previous findings that identified this region as a significant QTL for grain yield [59].

Thousand seed weight (S1_25033782 (SBI-01, C/T): This QTN is likely associated with the Sb01g010260 gene, which has been linked to seed weight in sorghum. The C/T allele variation is consistent with previous findings that identified this region as a significant QTL for seed weight [59, 62, 63]. S5_14397024 (SBI-05, C/A): This QTN is likely associated with the Sb05g004000/QSNDF5.1 gene (Neutral detergent fibre-GWAS method) which has been linked to seed weight in sorghum. The C/A allele variation aligns with previous findings that identified this region as a significant QTL for seed weight [56, 59, 63, 64].

The alleles identified in our study are consistent with previous research findings in sorghum, particularly those related to flowering time, plant height, seed number per plant, grain yield, and seed weight. The high LOD scores and r² values, along with using ML-GWAS methods, validate the reliability of these associations. These findings contribute to a deeper understanding of the genetic architecture of sorghum and provide valuable insights for future breeding programs aimed at improving yield and agronomic traits.

Genetic analysis of agronomic & yield traits using polymorphic SNPs

Identifying significant QTNs for days to flowering and maturity provides valuable insights into the genetic control of these traits in sorghum. Notable associations were found on chromosomes 1, 3, and 5 for days to flowering, which aligned with previous studies identifying similar loci affecting flowering time in sorghum and other related cereal species [45, 55]. For days to maturity, significant SNPs on chromosomes 2, 4, and 9 correspond to loci previously reported in sorghum and other grain crops, indicating conserved genetic influences across species [45, 55] also identified key loci on chromosomes 1 and 3 associated with maturity time, supporting our current findings. Baye et al. [45] reported significant associations between chromosomes 2 and 4, which align with our findings (Fig. 4).

The important associations found on chromosomes 1, 3, and 4 for plant height are consistent with previous studies that have identified key loci influencing height in sorghum agronomic traits [49, 65]. These studies have suggested that these loci may harbor important genes involved in growth regulation. For the seed number per plant, significant SNPs on chromosomes 2 and 5 corroborate findings from Baye et al. [45] and other research, highlighting the importance of these chromosomal regions in seed development and yield traits. The consistent identification of similar loci across studies underscores the reliability of these genetic markers. Ramu et al. [65] identified significant QTLs associated with plant height on chromosomes 1 and 3, aligning with our findings. Baye et al. [45] further validated these results, which emphasize the role of these loci in plant growth regulation and significant associations between chromosomes 2 and 5 for seed number traits, which aligns with our results. This work emphasized the importance of these loci in optimizing yield through genetic selection. Identifying significant QTNs for grain yield and thousand seed weight enhances our understanding of the genetic control of these traits in sorghum. Previous research studies [45, 57] have corroborated the notable associations found on chromosomes 1, 3, and 5 for grain yield, indicating critical loci influencing yield traits. These studies have suggested that these regions may harbor genes involved in metabolic processes and stress responses crucial for yield stability. For thousand seed weight, significant SNPs on chromosomes 2 and 4 align with findings from earlier research, which have identified key loci affecting seed weight in sorghum [45, 47]. The consistent identification of similar loci across studies underscores the reliability of these genetic markers for breeding applications. Menamo et al. [66] supported our findings by identifying significant QTLs associated with grain yield on chromosomes 1 and 3. Baye et al. [45] further validated these results, emphasizing the role of these loci in enhancing yield through genetic improvement. Zhao et al. [47] also highlighted the importance of these loci for seed development.

Associated genomic regions identified by three models of Multi-Locus analysis

A thorough comparison of six ML-GWAS methods indicated that mrMLM, pLARmEB, and FASTmrMLM were the most effective in identifying significant QTNs associated with agronomic, yield, and yield-related traits, with mrMLM detected 42 QTNs, pLARmEB identified 36 QTNs, and FASTmrMLM found 30 QTNs (Table 1).

A related study identified 160 and 130 significant QTNs across five traits using the ISISEM-BLASSO and pLARmEB methods, respectively. Furthermore, Zhang, Jia, & Dunwell [67] highlighted ISISEM-BLASSO as the most robust multi-locus method in the R Package Genome Association and Prediction Integrated Tool (GAPIT) [68]. Similarly, Zhong et al. [69] found that pKWmEB, ISIS EM-BLASSO, and pLARmEB yielded higher counts of significant QTNs, reporting 189, 171, and 160 QTNs, respectively. In contrast, noted that among the six ML-GWAS methods, mrMLM demonstrated superior capability in detecting reliable QTNs for various agronomic traits in sorghum, including plant height, days to flowering, grain yield, tiller number, hundred seed weight, and panicle exertion. This discrepancy may be attributed to the specific traits and population panels analyzed in their study.

QTN mapping and genetic architecture

The distribution of QTNs across the sorghum genome illustrates the complex genetic architecture underlying agronomic traits. Identifying multiple QTNs, especially in chromosomes 1, 2, and 3, emphasizes the need for targeted breeding strategies that leverage these genetic markers. Recent studies reported similar associations between QTNs and agronomic traits. For instance, Baye et al. [45] identified key QTLs linked to grain yield and plant height, verifying our findings on chromosomes 3 and 8. Additionally, Zhao et al. [47] demonstrated the importance of certain SNPs in drought tolerance, aligning with our results on chromosome 2. The identified QTNs provide a valuable resource for marker-assisted selection in sorghum breeding programs.

Candidate gene mining and mapping

The analysis of candidate genes associated with key traits in sorghum reveals a complex interplay between genetic factors and agronomic performance. Each gene identified not only contributes to specific phenotypic expressions but also offers insights into potential genetic pathways that can be exploited for crop improvement [70].

The QTNs and putative candidate genes were indicated on the right side of the chromosomes, with abbreviations representing different traits displayed. Candidate genes on each chromosome are marked in distinct colors: green for days to flowering, red for days to maturity, pink for seed number per plant, and blue for grain yield. The numbers on the left side indicated the physical distance in megabase pairs (Mbp) between adjacent loci on the chromosome (Fig. 5).

Fig. 5

Linkage groups and chromosomal locations of significant QTNs and intragenic candidate genes associated with agronomic and yield-related traits in sorghum

The regulation of flowering time and maturity in sorghum is significantly influenced by genes such as Sobic.001G196700 and Sobic.002G183400, both of which code for hypothetical proteins involved in floral development. These genes play essential roles in optimizing reproductive success (Table S4). Additionally, the stress response gene Sobic.005G176100, annotated as a mannose-6-phosphate isomerase, emphasizes the importance of resilience in sorghum, particularly under adverse environmental conditions [70]. Its involvement in various stress response mechanisms highlights its potential as a target for genetic enhancement strategies aimed at developing more resilient sorghum varieties.

Understanding the interactions of Sobic.005G176100 with other genes could lead to the creation of cultivars that not only withstand environmental stress but also maintain high yield and quality. Other key genes, such as Sobic.003G324400 and Sobic.004G178300, are crucial for regulating plant height and seed weight, respectively. The influence of Sobic.004G178300 on seed weight positions it as a valuable candidate in yield enhancement breeding programs (Table S4). The high LOD and R² values associated with these genes further underscore their potential utility in marker-assisted selection (MAS) [6], which can simplify the breeding process by enabling early selection of desirable traits and optimizing resource use compared to traditional phenotypic methods.

The table presents a curated selection of sorghum genes linked to various agronomic traits, revealing their potential roles in drought tolerance, plant morphology, and seed characteristics. For example, Sobic.002G183400 is associated with drought-related traits but remains uncharacterized, suggesting a need for further investigation into its specific functions and involvement in stress response pathways. Similarly, Sobic.002G140900, related to drought management, resembles the pre-mRNA splicing factor PRP38 protein, implying a role in RNA processing essential for gene expression regulation under stress conditions. Additionally, Sobic.005G176100 may influence energy pathways critical during drought stress. With the gene Sobic.003G324400 containing an AP2 domain, it likely contributes to transcriptional regulation affecting developmental processes. Furthermore, Sobic.005G176000, a zinc finger protein, may be involved in gene regulation during seed development, while Sobic.004G178300, linked to thousand seed weight and annotated as a putative splicing factor U2AF, highlights the significance of RNA splicing in seed development (Table S4). Collectively, these genes are vital for enhancing sorghum’s adaptability to environmental stresses and improving yield traits, warranting further functional studies to elucidate their roles in the complex regulatory networks governing these phenotypes.

Conclusion

The current study highlights the significance of sorghum as a crucial cereal crop for over 750 million people, especially in Ethiopia, where diverse landraces flourish across various agroecological zones. Through the collection, and genotyping of 216 Ethiopian sorghum landraces, we uncovered substantial genetic variations and phenotypic traits, leading to important marker trait associations. The Pearson correlation analysis revealed strong correlations among most traits (p < 0.0001), with exceptions for grain yield about flowering and days to maturity.

Genetic variability assessments indicated that days to flowering had high heritability (h² = 0.7) and genetic advance (GA = 19.6%), suggesting significant potential for improvement through selective breeding. In contrast, grain yield showed extremely low heritability (h² = 0.003) and GA (0.2%), indicating a predominant environmental influence and challenges for genetic enhancement.

The analysis identified 351,692 SNP markers, refined to 50,165 for further investigation. This extensive dataset forms a solid foundation for future genome-wide association studies (GWAS). The Manhattan plot analysis revealed several significant QTNs, particularly on chromosomes 1, 5, and 8, with strong LOD scores for traits such as days to flowering and plant height. In total, 176 QTNs were identified, with the mrMLM model detecting the most significant markers (42 QTNs), reflecting the complex genetic architecture influencing these traits.

The research emphasizes key QTNs and candidate genes linked to essential agronomic traits, utilizing ML-GWAS models to inform breeding strategies. It highlights high heritability for traits like days to flowering and plant height, while other traits exhibited low heritability due to environmental factors. The identification of QTNs and candidate genes are crucial components for improving adaptability to environmental stressors and enhancing yield traits. Genes such as Sobic.001G196700, Sobic.002G183400, and Sobic.005G176100 play significant roles in regulating flowering and stress responses, while Sobic.003G324400 and Sobic.004G178300 are vital for influencing plant height and seed weight, respectively. The high LOD and R² values associated with these genes indicate their potential for application in marker-assisted selection, facilitating early identification of desirable traits in breeding programs. Overall, this research highlights the importance of these genes in the development of resilient sorghum varieties and calls for further investigations to better understand their functions within the intricate regulatory frameworks that govern key agronomic traits.

Materials and methods

Genetic materials and experimental design

A total of 202 sorghum landraces (Table S5) with their passport data were sourced from the Ethiopian Biodiversity Institute, Addis Ababa. Additionally, 9 improved varieties and 5 released landraces used as check cultivars were acquired from the National Sorghum Improvement program at Melkasa Agricultural Research Center, part of the Ethiopian Institute of Agricultural Research, Addis Ababa (Table S5). The SNP markers dataset was extracted from the resequencing of sorghum accessions at the University of Wisconsin Biotechnology Center [71] and was made available through the Purdue University Sorghum Research Repository https://purr.purdue.edu/publications/3189/1.

The experiment was conducted over two consecutive cropping seasons from 2022 to 2023 in the Pawi district (11° 18’ N, 36° 24’ E), at an elevation of 1,100 to 1,200 m above sea level. The study was carried out in two kebeles: Dangure and Village-7. A total of 216 sorghum genotypes including 202 landraces and 14 cultivars (9 improved varieties and 5 released landraces) were utilized in the study. The genotypes were planted in single rows using an α-lattice design with three replications and four blocks, and each block comprised 54 genotypes. Each net plot measured 0.75 m in width by 5 m in length, with an intra-row spacing of 0.75 m. The spacing between replications was 2 m, while the distance between blocks was set at 1.5 m. Planting was performed using a manual drilling method, followed by thinning to a spacing of 0.2 m after 20 days of emergence. Post-thinning, each plot maintained an average of 25 plants.

Phenotyping

Accurate and well-characterized data for the traits of interest, specifically agronomic and yield-related traits, were collected. Five plants from each row were randomly selected according to the type of traits being measured, including days to flowering, days to maturity, plant height, seed number per plant, grain yield, and thousand seed weight. The missing and unrepresentative phenotypic data was imputed by SAS JMP V.5 [72]. Data was normalized and standardized by the Shapiro-Wilk statistics test at P > 0.05 [50].

Genotyping

GWAS was conducted using genotyping by sequencing (GBS) [73]. The GBS procedure [74], utilized the ApeKI restriction/incision enzyme (recognition site of G|CWCG) to generate the GBS library, which was then sequenced on Illumina HiSeq2500 lanes [75]. SNP markers were extracted from the resequencing data of 1,628 sorghum accessions [76]. The SNP dataset was filtered to exclude SNPs with an MAF of less than 0.05 missing values. The remaining missing values were imputed using the Beagle 5.0 software package [77], resulting in 50,165 SNPs.

To ensure data quality, the SNP dataset was again filtered to exclude any SNPs with a MAF of 0.00002, calculated from the expression 4 × 4.614 × 4.61, which corresponds to a likelihood ratio test derived from an LOD score of 4. Under the null hypothesis, this likelihood ratio follows a chi-square (χ²) distribution with one degree of freedom [78]. Furthermore, only SNP markers identified in at least three different models were considered reliable for agronomic and yield-related QTNs. Similarly, QTNs that were detected in three or more models and demonstrated a phenotypic variation of R² > 10% were classified as major QTNs.

Data analysis

The phenotypic data were analyzed using a mixed linear model (MLM) approach implemented in the “asreml-R” R package [79]. The REML mixed model equation was:

$$\:y\hspace{0.17em}=\hspace{0.17em}X\hspace{0.17em}+\hspace{0.17em}Zu\hspace{0.17em}+\hspace{0.17em}e,$$

Where ‘y’ represents the measured data for each trait, ‘τ’ is the fixed effects (genotypes) in the trial, ‘X’ is the design matrix for the fixed effects, ‘u’ is the random effects (columns and rows), ‘Z’ is the design matrix for the random effects, and e is the residual error. The genetic parameters, including σ²g, σ²p, GCV, & h², were estimated using the “variability” R package [80].

The genotypic variance (σ²g) was calculated as (MSg - MSe)/r, where MSg is the mean square of the genotype and r is the number of replicates. The phenotypic variance (σ²) was estimated as σ²p = σ²g + σ²e, where σ²e is the error mean square. Broad-sense heritability (h²) was computed using the formula:

$$h2 = 2g/(2g + (2e/n)),$$

where n is the number of replicates, as suggested by Pariyar et al. [81]. The best linear unbiased prediction (BLUP) values were estimated using the META-R package [82] and used for the GWAS analysis.

Genome-Wide-Association study

Since GWAS involves testing thousands to millions of SNPs across the genome, it is important to correct for multiple testing. Statistical methods, such as Bonferroni correction or false discovery rate [67] adjustment. The GWAS analysis identifies significant associations between specific genomic regions (containing one or more SNPs) and the traits of interest. These genomic regions are then considered as potential candidate regions influencing the traits. The identified genomic regions are further analyzed to understand the biological significance of the associated SNPs [74, 75]. This involves annotating the genes within or near the significant areas, exploring their known functions, and assessing their potential role in the observed trait variations. By conducting an ML-GWAS, researchers can gain insights into the genetic architecture underlying the major agronomic, yield, and yield-related traits in sorghum landraces, helping to inform breeding programs and improve crop productivity [32].

Genome-wide association studies (GWAS) have uncovered SNPs associated with complex traits, yet these represent only a fraction of the SNPs within the same haplotype block [83]. Six different ML-GWAS models were used for the MTA analysis and the Identification of QTNs [84]: mrMLM [78], FASTmrMLM [27], FASTmrEMMA [28], pLARmEB [30], pkWmEB [31], and ISIS EM-BLASSO [29]. All of these ML-GWAS models were implemented in the “mrMLM.GUI” R package V.4.4.1 [26] which provides a graphical user interface for the multi-locus random SNP-effect mixed linear model. Also, the GAPIT 3.0 [77, 78, 85, 86] was applied for GWAS graph interference analysis.

The population structure and kinship matrix for our accessions were estimated in the previous studies by Grima et al. [71], additionally, the mrMLM.GUI package was utilized to calculate the population structure and kinship matrix internally. The resulting − log10(p) values obtained from the ML-GWAS analysis were employed to generate Manhattan and Q-Q plots using the mrMLM.GUI R-package [87].

Co-localization of previously detected QTLs for agronomic and Yield-Related traits, and identification of candidate genes

The colocations of significant QTNs with previously identified QTLs were examined using the Sorghum QTL Atlas database [88], focusing on the linkage disequilibrium decay range of 65 kb. Candidate genes were identified through biomaRt tools [89] on the Phytozome platform [90], also within the 65 kb LD decay distance from the genomic regions where the QTNs were located [76]. The SorghumBase online database was also utilized to gather comprehensive descriptions of the relevant genes.

ML-GWAS study

Several multi-locus genome-wide association study (ML-GWAS) methods were used to identify significant QTNs. This includes the mrMLM, FASTmrMLM, FASTmrEMMA, pLARmEB, pKWmEB, and ISIS EM-BLASSO approaches, all of which are implemented in the R package “mrMLM” [78]. Default parameter values were used, and a LOD threshold of ≥ 4 or p-value ≤ 0.0002 was applied to determine significant marker-trait associations [91]. Principal component analysis and kinship matrices were incorporated into all the methods. The R package CMplot [92] was used to visualize Manhattan and quantile-quantile (QQ) plots from the GWAS results. Linkage disequilibrium between SNPs was estimated using the squared correlation coefficient (r²) within a 0-10 cM window, calculated with the Tassel 5 tool [93]. The phenotypic effect size of each allelic variation was determined across the sorghum landraces and visualized using box plots in R 4.4.1 software [94].

QTNs with a logarithm of the odds (LOD) score of at least 4.0 is significantly associated with the agronomic, yield, and yield-related traits under investigation [2]. This LOD score threshold corresponds to a p-value of 0.00002, calculated as the probability of the chi-square test statistic (χ²) exceeding 4 × 4.61, given 1 degree of freedom under the null hypothesis. Specifically, the conversion from an LOD score of 4.0 to its corresponding likelihood ratio test was done using the formula 4.0×ln (100) = 4.0 × 4.61. This likelihood ratio test, under the null hypothesis, follows a chi-square distribution with 1 degree of freedom, as described in the work of Wang et al. [78]. The LOD score threshold value of 4.0 is to identify QTNs that were significantly associated with the agronomic and yield-related traits. This threshold was chosen based on the statistical significance level, where the p-value corresponding to a LOD score of 4.0 was calculated to be 0.00002 using the chi-square distribution with one degree of freedom.

To identify reliable QTNs associated with agronomic and yield-related traits, it’s very important to apply an additional filtering criterion. Only SNP markers detected in at least three of the six ML-GWAS models were designated reliable agronomic and yield-related associated QTNs. Similarly, QTNs detected in three or more models and exhibiting a phenotypic variation (R-squared) greater than 10% were designated as major QTNs. This suggested that these major QTNs significantly influenced the observed agronomic and yield-related traits. For the current analysis, we applied the “mrMLM.GUI” R-software package [26] to internally calculate the population structure and kinship matrix [35] as part of the ML-GWAS approach.

Finally, the resulting -log10(p) values from the ML-GWAS models were used to generate Manhattan and QQ plots using the “mrMLM.GUI” package, as described by Zhang et al. [26]. These visual representations helped to identify and interpret the significant associations between the SNP markers and the agronomic and yield-related traits.