Analyzing genotype-environment interactions and identifying stable and high-yielding sorghum (Sorghum bicolor [L.] Moench) genotypes using different stability models

Abstract

This research sought to develop high-yielding and stable sorghum genotypes by comprehensively evaluating Genotype Environment Interaction (GEI). Fifteen sorghum genotypes were assessed across three locations over three years in a randomized complete block design with three replications. Significant genetic variation was observed among genotypes for all evaluated traits, indicating substantial potential for genetic improvement. Environmental factors profoundly influenced genotype performance, and GEI significantly impacted key traits such as Days to Heading, Days to Maturity, and Thousand Seed Weight, particularly Days to Heading, suggesting the presence of distinct mega-environments. The average grain yield across all locations was 4.14 t ha-1. ETSC 300,552 (G1) recorded the highest yield. The observed substantial yield variations across environments and strong GEI confirmed the critical need for multi-environment testing in cultivar development. AMMI analysis revealed highly significant main effects for genotype, environment, and their interaction on sorghum grain yield, underscoring considerable genetic differences and varied performance across environments. The first two interaction principal component axes accounted for 49.6% of the total GEI variation. The Environment contributed a dominant 27% of the total sum of squares, compared to only 10% from genotype, highlighting the influence of environmental factors on sorghum grain yield. The “which-won-where” polygon view from GGE biplot analysis effectively elucidated genotype-environment relationships, explaining 59.39% of the total variation and identifying three distinct mega-environments. Within the first mega-environment (E3, E8, E7), G1, G5, G7, and G14 performed best, with G1 identified as the winning genotype. Analysis of grain yield alongside 16 stability parameters identified G1 and G7 as the most stable genotypes. Specifically, G1 combined high grain yield with superior stability (low variance and deviation), while the parameter proved to be an excellent indicator of both performance and consistency. Finally, based on its consistently superior performance, high stability, and positive farmer evaluation, G1 was officially approved by the Ethiopian variety releasing committee for national release.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12870-026-08310-6.

Introduction

Sorghum (Sorghum bicolor (L.) Monech) is a warm-season tropical cereal crop belonging to the Poaceae family with a chromosome number of 2n = 20 [1]. It ranks as the fifth most important cereal crop globally [2] and thrives under challenging environmental. Sorghum is a staple for more than 500 million people across over 30 countries, particularly in sub-Saharan Africa [3]. In Ethiopia, sorghum is the fourth most produced cereal contributing 11% of the total cereal production, following maize, teff, and wheat [4]. Ethiopia ranks sixth among the world’s top sorghum producers with a production of 3.4 million tons. In sub-Saharan Africa, South Africa (2.8 t ha^{− 1}) and Ethiopia (2.0 t ha-1) have the highest average yields per hectare in terms of the crop’s multi-year average productivity [5].

The crop is one among others, exhibiting notable tolerance to high temperatures and drought. However, the increasing frequency and intensity of these conditions, driven by climate change, are beginning to exceed the crop’s resilience thresholds, thereby constraining its productivity. This phenomenon is particularly noticeable in the most arid lowlands of Ethiopia, where sorghum is a staple crop for both human consumption and livestock feed. Reflecting this challenge, the national average sorghum yield in Ethiopia declined from 2.8 t ha⁻¹ in 2019 to 2.6 t ha⁻¹ in 2022 [4]. Similarly, a large reduction in sorghum yield was reported in Sudan and India, a drop of 55% and 70% from 1961 to 2020, respectively. In Ethiopia, this decrease in yield poses a threat to food security and is caused by the combination of extreme and erratic rainfall coupled with the lack of sorghum varieties’ resilience to climate risk [6]. In this precarious environment, the stability of staple crops like sorghum is not just a matter of an agricultural issue but a source for national stability and human welfare. Because the contribution of sorghum to Ethiopian food security, particularly in the arid and semi-arid lowlands, can’t be overstated; instead, it is the primary staple for millions of households [7, 8].

Despite its national importance, sorghum productivity in Ethiopia remains low due to a lack of stable, high-yielding varieties that have been rigorously validated through both multi-environment trials (MET) and participatory variety selection (PVS). The existing improved varieties, while traditionally tolerant, are proving insufficient against the unprecedented rate and intensity of current climate change, characterized by prolonged drought during critical growth stages, such as flowering, and erratic rainfall patterns [7]. Therefore, a failure in the sorghum harvest translates directly into both a food and a fodder crisis. Given this context, the urgent need to develop and disseminate climate-resilient sorghum varieties becomes an imperative and strategic priority for sorghum breeders. In the meantime, to eliminate bottlenecks in the variety evaluation process and adoption, variety evaluation in the hands of farmers has significant importance. In any variety development, the presence of participatory approaches overcomes the limitations of conventional breeding by allowing farmers to select varieties directly in their fields. This decentralized approach positively leverages genotype-environment interactions, ensuring new varieties are specifically adapted to meet local needs and conditions [9]. Building on the above background, this study has the following objectives: (1) to identify stable and high-performing sorghum genotypes for new variety registration using AMMI, GGE biplot, and parametric and non-parametric statistical indices; and (2) to identify farmer-preferred genotypes through a participatory approach.

Materials and methods

Plant genetic materials

Fourteen sorghum genotypes were selected for this field research from an initial pool of 100 in an observation nursery. The genotypes were sourced from the Melkasa Agricultural Research Center (MARC). For comparison, a recently released and popular variety named ‘Beletew’ from the Debre Birhan Agricultural Research Center (DBARC) was included as a standard check (Table 1).

Table 1.

Description of the fifteen sorghum genotypes used in the experiment, including their pedigree and source

Genotypes	Pedigree	Sources
ETSC 300,552 (G1)	(Teshale x E36-1) BC3F3	MARC
ETSC 300,510 (G2)	(76T1 × 23XB-35) BC3F3	MARC
ETSC 300,547 (G3)	(TeshalexB-35) BC3F3	MARC
ETSC-14019-1-2 (G4)	Teshale/SRN39	MARC
ETSC-14225-2-2 (G5)	Gambella1107/S35	MARC
ETSC-14368-1-1 (G6)	ICSR93034/ICSTG2372	MARC
ETSC-14223-9-1 (G7)	Melkam/S35	MARC
ETSC-14321-5-1 (G8)	05MW6028/ICSTG2372	MARC
ETSC-14325-4-1(G9)	Macia/S35	MARC
ETSC-14404-5-1 (G10)	Teshale/ Gambella1107	MARC
ETSC-14483-5-2 (G11)	13MI5076/Meko	MARC
ETSC-14487-7-1 (G12)	13MI5024/ Gambella1107	MARC
ETSC-14173-2-2 (G13)	ICSR56/N-13	MARC
ETSC-14325-6-2 (G14)	Macia/S35	MARC
Beletew (standard check) (G15)		DBARC

Environments and agronomic practices

The field trials were conducted at three sites in the Amhara region (Shewa Robit, Jema, and Kobo) over three cropping seasons from 2020 to 2022. In 2022, Shewa Robit was represented by two distinct sites. The trials were arranged in a randomized complete block design (RCBD) with three replications at each location. Each experimental plot measured 5 m x 3.75 m. Spacing was set at 0.5, 1, 0.75, and 0.15 m between plots, blocks, rows, and between plants, respectively. Standard agronomic practices, including land preparation, hand weeding, and thinning, were performed as required. Following recommendations, seeds were sown at a rate of 13 kg ha^− 1, and fertilizers were applied at rates of 40 kg ha^− 1 for Urea and 121 kg ha^− 1 for NPS (Table 2).

Table 2.

Description of the 3 testing sites for the sorghum regional variety trial in the Amhara region (2020–2022)

Location	Altitude (m)	Latitude	Longitude	Min T. (°C)	Max T. (°C)	Min Rf. (mm/year)	Max RF. (mm/year)
Shewarobit	1,280	10.0175° N	39.8741° E	15	30	600	1,000
Jema	1,780	9.7167° N	39.5° E	12	28	500	900
Kobo	1,460	12.1525° N	39.6280° E	18	35	500	700

Data collection

For this study, quantitative and phenological traits were evaluated. The quantitative traits were plant height (PH), head length (HL), head weight (HW), thousand seed weight (TSW), and grain yield (GY). Additionally, we recorded phenological markers, specifically the number of days to reach 50% heading and 75% maturity. Data were collected on both a plot-wide and individual-plant basis. Plot-level data were sourced from the three central rows (an area of 5 m × 2.25 m), while plant-level data represent the average measurements from five randomly chosen plants within that area.

Statistical analysis

The collected data were subjected to ANOVA to estimate the occurrence of variations among sorghum genotypes, environments, and genotype by environment interactions using R software. Before doing the combined analysis of variance, the Bartlett’s and Shapiro-Wilk tests were used to determine the homogeneity of error variance and the normality of the data, respectively. To assess yield potential and stability across Ethiopia’s diverse agro ecological landscape, genotypes were subjected to multi-environment testing across various locations and seasons. Given the limitations of ANOVA in explaining Genotype by Environment Interaction (GEI), the Additive Main Effects and Multiplicative Interaction (AMMI) model was employed, integrating ANOVA with Principal Component Analysis (PCA) to dissect GEI patterns [9].

Additionally, various statistical indices were utilized to further quantify the stability of the evaluated genotypes [10]. The AMMI for analyzing yield data in sorghum genotypes is represented by the following equation [11].

where represents the yield of genotypes (G) in the environment (E); is the general mean; is the genotype average deviation; is the eigenvalue of the n^th principal component (PCA) axis, and are the genotype and environment PCA scores for the n^th PCA axis, and is the residual.

Means of the genotype were used for GGE biplot analysis. The linear statistical model for GGE biplot analysis is presented as follows:

where the yield value of genotype g in environment e for the r^th replication; is the overall mean; represents the main effects of environment e; is the residual of genotype g in environment e; represents the overall error; is the singular value of the n^th principal component; is the genotype g’s score for the nth eigenvector; is the environment’s score for the n^th eigenvector.

To ensure a robust and comprehensive evaluation of genotype performance, a diverse set of 16 stability parameters was employed, encompassing both parametric and non-parametric approaches. Non-parametric indices ( and ) were selected for their ability to provide rank-based stability estimates that remain robust against outliers and non-normal yield distributions common in multi-environment trials. These were complemented by parametric measures including Wricke’s equivalence (), Shukla’s stability variance (), and Eberhart & Russell’s deviation from regression () to quantify the specific contribution of each genotype to the G×E interaction. Finally, integrated indices such as Kang’s rank-sum () and Eskridge’s safety-first parameters () were utilized to simultaneously account for high mean performance and minimized environmental risk, providing a holistic basis for variety recommendation (Table 3).

Table 3.

List of parametric and non-parametric stability statistics estimated in this study

Statistics	Symbol	Pattern of selection	Type of method	References
Mean variance component	θi	Low value	Parametric	[10]
GE variance component	θ(i)	High value	Parametric	[12]
Wrickes ecovalence	Wi2	Low value	Parametric	[13]
Regression coefficient	bi		Parametric	[14]
Deviation from regression	S2di	Low value	Parametric	[15]
Shukla’s Stability variance	σ 2 i	Low value	parametric	[16]
Coefficient of variance	CVi	Low value		[17]
Nassar and Huhn’s and Huhn’s statistics	(S1,2,3,6)	Low value	Non-parametric	[18, 19]
Thennarasu’s stability statistics	(NPi 1–4)	Low value	Non-parametric	Thennarasu (1995)
Kangs Rank Sum	KR	Low value	Non-parametric	[20]

To evaluate farmer preferences, a participatory evaluation was conducted at the crop’s physiological maturity using a direct matrix ranking methodology. Seven “model farmers” were purposefully selected based on their extensive experience and recognized expertise in local sorghum cultivation; this small, expert-led group served as a pilot to integrate farmer feedback during the evaluation phase, addressing the limitation in the traditional Ethiopian system where farmers are typically only involved after official variety release. The ranking process involved two distinct steps: first, farmers identified seven key selection criteria and assigned a relative weight to each based on importance (3 = very important, 2 = important, 1 = less important). Second, they rated the performance of each genotype against these criteria using a 5-point Likert scale (1 = very poor to 5 = excellent). The final matrix scores were calculated by multiplying the trait weights by the genotype ratings, providing a quantitative measure of farmer preference to complement the multi-environment trial data.

Results and discussion

Combined analysis of variance and mean performance

This study reveals highly significant genetic variability among the tested genotypes for all measured traits (Table 4). ANOVA (indicated by the *** symbols for Genotypes) confirms that the observed differences in performance are due to their genetic makeup, which is an opportunity for a breeding program seeking to select superior varieties. Previous research has consistently shown that traits such as DH, PH, TGW, and GY are subjected to sizable genotypic influences on sorghum genotypes [21, 22]. Furthermore, the powerful influence of the environment (E^***) demonstrates the major impact of growing conditions (e.g., soil fertility, temperature) across all measured traits. This indicates that the test locations and/or years were distinctly different, exerting a dominant influence on crop performance. GEI also had a notable influence on DH, DM, and TSW. These findings are consistent with the result by Birhanu et al. [23], who also reported a significant effect of the GEI on the performance of similar sorghum traits. GEI exerted a stronger effect on Days to Heading (DH) than the main genotypic effect, suggesting that the testing locations represent distinct mega-environments. However, ANOVA alone is insufficient to provide detailed information about the GEI interaction; rather, additional methods, such as stability analysis, are required. Furthermore, the presence of such a substantial GEI interaction suggests that genotype stability statistics of such traits should be further investigated [21, 23].

Table 4.

Mean performance of 15 sorghum genotypes for yield and related traits over six environments and Estimation of significant levels for different source of variation

Genotypes	DH	DM	PH	HL	HW	GY	TGW
ETSC 300,552	78	108	231	21	63.34	5.32	25
ETSC 300,510	78	110	204	24	55.33	4.37	29
ETSC 300,547	71	106	231	21	61.17	4.25	28
ETSC-14019-1-2	79	110	232	23	46.90	3.13	30
ETSC-14225-2-2	72	109	217	22	57.88	4.34	27
ETSC-14368-1-1	79	112	212	24	57.57	3.98	30
ETSC-14223-9-1	75	107	209	23	68.36	4.70	30
ETSC-14321-5-1	76	110	251	23	53.75	3.83	28
ETSC-14325-4-1	75	110	230	21	62.99	4.29	26
ETSC-14404-5-1	77	111	212	21	51.74	3.62	27
ETSC-14483-5-2	81	110	241	19	54.64	3.49	28
ETSC-14487-7-1	73	108	215	21	66.74	4.64	26
ETSC-14173-2-2	77	108	203	18	65.64	4.34	27
ETSC-14325-6-2	72	108	232	21	65.08	4.52	27
Beletew	78	107	155	27	61.65	4.13	24
Mean	77	109	225	22	58.81	4.14	27
Genotypes (G)	***	*	***	***	***	***	***
Environments (E)	***	***	***	***	****	**	***
GEI	***	***	*	*	**	**	***
CV	5	3	10	9	21	19	14
LSD	**	***	***	***	***	***	***

Abbreviations: DH days to heading, DM days to maturity, PH plant height (cm), HL Head length (cm), HW head weight (g), TGW 1000−grain weight (g), GY grain yield (t), LSD least significant difference, GEI genotype by environment interaction, and CV, coefficient of variation

Asterisks indicate statistical significance levels based on: *p< .05, **p < .01, and *** p< .001

As shown in Table 4, the overall mean grain yield (GY) for the trial was 4.14 t ha^− 1, ranging from 3.13 t ha^− 1 (ETSC-14019-1-2) to 5.32 t ha^− 1(ETSC 300552). In terms of phenology, ETSC 300547 was the earliest to mature (71 DH), making it a promising candidate for cultivation in short-season environments. A notable contrast in plant architecture was observed, with the standard check variety ‘Beletew ' exhibiting a very short plant height (155 cm) compared to the overall mean (225 cm), a desirable trait for lodging resistance. This wide range of performance demonstrates that breeders have excellent options for developing cultivars tailored to specific objectives, whether the priority is maximizing yield, ensuring earliness, or improving plant structure. The boxplot (Fig. 1) illustrates the distribution of grain yield across environments. Grain yield varied substantially across the eight environments, with E4 being the most favorable (highest GY) and E3 the most restrictive (lowest GY). The differing ranges of yield within each environment, especially the wide spreads in E3 and E5, indicate a strong Genotype × Environment interaction. This highlights the importance of multi-environment testing to select genotypes that are either broadly adapted or specialized for specific high-potential locations.

Fig. 1.

Boxplot showing a visual summary of grain yield by environment. Where; E1 - Jema 2020, E2 - Jema 2021, E3- Jema 2022, E7- Kobo 2020, E8- Kobo 2022, E4 -Shewa Robit 2020, E5- Shewa Robit 2022, E6 - Shewa Robit 2022

AMMI analysis of grain yield for sorghum genotype selection

AMMI analysis for grain yield depicted highly significant variation (p ≤ 0.001) for main effects of genotype, environment, and their interaction as displayed in Table 5. The highly significant mean square for genotypes indicates that there are significant genetic differences among sorghum genotypes. Some genotypes inherently perform better or worse than others, regardless of environment. Genotypic variation is essential for sorghum improvement; without it, selecting high-yielding lines would be impossible. This variation is fundamental for plant breeding and selection, because if there were no significant difference among genotypes there would be no basis for improving grain yield of sorghum by selecting superior genotypes. The highly significant mean square for environment and GEI indicates that sorghum grain yield performed differently across different environment, a genotype perform well in one environment might perform poorly in another, and vice-versa. The significant interaction effects highlight the importance considering both factors together. Consistent with the current study [21–24], also observed highly significant effects for genotypes, environments, and GEI, thereby reinforcing the complex interplay of these factors in sorghum performance.

Table 5.

Analysis of variance of 15 sorghum genotype for grain yield over six environment using AMMI analysis

Sources	Degree of freedom	Mean squares	Proportion of variance explained (%)
Environments	7	23.53***	27.1
Genotypes	14	4.5***	10.3
Interactions	98	1.23***	19.8
IPCA 1	20	1.57***	26.2
IPCA 2	18	1.56***	23.4
IPCA 3	16	1.39***	18.5
IPCA 4	14	1.33**	15.5
IPCA 5	12	1.08*	10.8
Residuals	224	0.55
Total	457	1.3

Asterisks indicate statistical significance levels based on: *p< .05, **p < .01, and *** p< .001

The significant interaction between environment and genotype was decomposed into interaction principal component axes, IPCA 1–5. Of which, the first two principal component axes explained 49.6% of the total variation caused by GEI. This result suggests that genotypes and environments have a strong interaction, and previous research has also demonstrated that the first two IPCA components is the most accurate in predicting total variation caused by GEI [11]. The result from the AMMI analysis showed that 27% of the total sum of squares was attributable to the environment component, and whereas only 10% was due to genotype, indicating a large significant effect of environmental variables on changes in sorghum grain yields. Former research [25, 26] also found that environmental factors, not genotype, were the main drivers of sorghum yield. The strong impact of environmental factors highlights the need for (MET) data to pinpoint genotypes that consistently perform well. Because, in such scenario a single genotype can develop different observable traits depending on environmental pressure such as soil fertility, climate, pests, disease, which all limit yield [27].

GGE biplot analysis for grain yield

The relationship between genotypes and environments was depicted in a “which-won-where” polygon view for grain yield (Fig. 2A). The GGE biplot analysis captured 59.39% of the total variation, explaining the complex GEI among the tested sorghum genotypes. The GGE biplot analysis, which captured 59.39% of the total variation, clarified the complex GEI among the tested sorghum genotypes across diverse environments. In this study, three distinct mega-environments were identified. The first includes E3, E8, and E7, where G1, G5, G7, and G14 performed best, with G1 as the top genotype; E2 and E6 forming the second cluster; E4 and E5 comprising a third, isolated environment. The first two principal components (PC1 at 42.45% and PC2 at 16.94%) underscore the substantial influence of environmental factors on genotype expression, as evidenced by the formation of these distinct environmental groupings. Genotypes like G1 exhibited broad adaptability, while others, such as G4 and G10, appeared less adapted to the tested condition or potentially suited to environments outside the scope of the study. The clear demarcation of mega-environments and varying performance of genotypes within them advocates pronounced phenotypic plasticity in response to environmental variation. This finding is highly consistent with previous studies by [24, 25], who found that environmental factors exert a primary influence on sorghum yield performance, often overshadowing the direct contribution of genotype alone. The presence of these mega-environments requires targeted breeding strategies to develop genotype-specific adaptations. Specific locations within larger environmental categories often exhibit similar optimal genetic varieties [28]. Testing new genotypes at a few representative sites per mega-environment can yield comparable results, reducing trial costs.

Fig. 2.

GGE biplot analysis for genotype by environment interaction: The which-won-where view of the GGE biplot to show which genotypes best performed in which test environment A. Ranking of genotypes based on yield and stability B. Best environment view of the GGE biplot C. and the environment vector view of the GGE biplot show similarity among test environments D. E1 - Jema 2020, E2 - Jema 2021, E3- Jema 2022, E7- Kobo 2020, E8- Kobo 2022, E4 -Shoa Robit 2020, E5- Shoa Robit 2022, E6 - Shoa Robit 2022

Ranking of genotypes relative to ideal genotypes and environment vector view

Figure 2B presents a GGE biplot, which ranks genotypes according to both their performance and stability, following the methodology proposed by [29] In this biplot, the central origin signifies the average performance of all genotypes, while the concentric circles serve as visual indicators of a genotype’s deviation from this average, thereby reflecting stability. Utilizing the average environment coordinate (AEC) view of the ranking biplot, genotypes G1, G7, and G14 appeared as the top performers, demonstrating superior grain yield and overall desirability compared to the other genotypes. Specifically, G1 exhibited the highest projection along the primary axis, indicating its exceptionally high mean yield. While G7 also showed a strong performance, being positioned significantly to the right, it was notably closer to the horizontal PC1 axis than G1, suggesting a greater degree of stability. Conversely, despite G4 displaying good stability, its consistently low performance renders it undesirable, as an ideal genotype must couple stability with robust grain production. GGE biplot analysis is an effective method for identifying ideal genotypes that exhibit both stability and high grain yield. This approach has been successfully employed in previous GEI studies to identify stable and high-yielding sorghum genotypes [21–23]. GGE biplot highlights E2 as the most representative environment, with genotypes G1 and G3 appearing as the most stable and high-yielding, located closest to the ideal environment concentric circles (Fig. 2C).

According to Yan et al. [28], the environment vector is represented by the line connecting the test environment to the biplot origin, in the current study it is presented in Fig. 2D. The angle between the environment vectors revealed two types of correlation between the test environment: a strong negative correlation at the obtuse angle and a positive correlation at the acute angle. Accordingly, environments with small angles between their vectors, such as E4 (Shoa Robit 2020) and E5 (Shoa Robit 2022), are highly correlated and provide similar information about the genotypes. This indicates that these environments consistently rank genotypes in the same pattern. Conversely, environments with large angles, such as E1 (Jema 2020) relative to the Shoa Robit group, show weaker correlations, suggesting they discriminate genotypes differently. Understanding these correlations helps to allocate resources effectively, design targeted breeding programs, and make informed decisions on genotype testing.

Stability analysis using different stability parameters

Grain yield (Y) values and 16 stability values of sorghum genotypes for eight environments are presented in Table 6 and supplement 1. Accordingly, genotypes G1 and G7 had the lowest values for total ranking and grain yield ranking for most of the stability parameters, and these genotypes were identified as the most stable ones. Genotypes with a value of deviation from the regression (s²d_i) close to zero are accepted as stable. The genotypes with a low Wricke’s Ecovalence (Wi2) value [13] and a low σ²_i value are also accepted as stable. Therefore, in our study using parametric stability parameters of s2, Wi2, and σ2, genotype G1 with high grain yield was identified as a stable genotype. As noted by [17], genotypes with a low CVi (environmental variation coefficient) and high mean yield are mostly desired. Similarly, with these stability parameters, the CVi value for G1 was very low (13.6) compared to other genotypes and was considered stable and the most desired genotype. Genotypes having regression coefficients less than one (b_i <1) and grain yield greater than the average mean are considered well-adapted genotypes in all environments [14] This parametric stability statistic (bi) is the most commonly used method [30]. Thus, genotypes G1, G12, and G13 had regression coefficients less than one, 0.8 for G1 and 0.9 for the other two. However, the average yield of G12 and G13 was lower, though they had a bi value less than one, and these genotypes are expected to adapt well to well environmental conditions, but G1 can adapt in all environments because it had a lower b_i value coupled with higher grain yield.

Table 6.

Ranks of 15 sorghum genotypes on mean yield and stability methods

Genotypes	Y	S⁽¹⁾	S⁽²⁾	S⁽³⁾	S⁽⁶⁾	NP⁽¹⁾	NP⁽²⁾	NP⁽³⁾	NP⁽⁴⁾	Wi²	σ²i	s²di	CVi	𝘒R	θ₍i₎	θi	SR	AR	SD
G1	1	2	2	1	1	5	7	2	1	5	5	5	1	2	5	11	56	4	3
G2	11	15	15	14	14	15	11	12	14	15	15	15	15	14	15	1	211	13	4
G3	14	3	3	6	9	12	12	14	9	8	8	8	10	12	8	8	144	9	3
G4	3	9	8	5	4	2	14	1	4	12	2	2	2	11	2	14	65	4	4
G5	9	7	6	10	10	6	9	11	10	6	6	6	11	9	6	10	132	8	2
G6	4	4	14	3	3	4	5	13	3	4	4	14	3	3	4	12	67	4	2
G7	2	5	7	4	2	10	6	4	2	10	10	10	5	5	10	6	98	6	3
G8	6	10	9	9	7	6	1	7	6	7	7	7	4	6	7	9	108	7	2
G9	8	6	5	8	6	3	1	5	7	3	3	3	7	4	3	13	85	5	3
G10	15	12	13	15	15	13	15	15	15	14	14	14	14	15	14	2	215	13	3
G11	5	8	9	7	5	9	3	6	5	9	9	9	6	7	9	7	113	7	2
G12	12	13	12	12	13	11	13	13	13	12	12	12	12	13	12	4	189	12	2
G13	10	11	11	11	11	6	10	9	11	11	11	11	9	11	11	5	159	10	2
G14	13	5	1	2	8	3	14	8	7	7	1	4	8	7	6	15	89	6	5
Beletew	7	14	14	13	12	13	8	10	12	13	13	13	13	10	13	3	181	11	3

Y: Yield mean ranks, S(1), S(2):, S(3) and S(6) : Nassar and Huehn’s non-parametric statistics and Huehns statistic, NP (1–4) :Ranks of adjusted seed yield means of genotypes, Wi2: Wricke’s ecovalence stability index, σi2 : Shukla’s stability variance, S2di : Deviation from regression, b_i : regression coefficient, CVi: Environmental coefficient of variance, SR-Rank Sum stability statistic, θ(i) : GE variance component, θi: Mean variance component (Plaisted and Peterson [10]),

Genotypes, G2, and the standard check had a specific adaptation, as confirmed by (bi > 1), but will have a hard time adapting to the current environmental changes. A similar result was reported by [30], genotypes with specific environmental adaptations exhibit poor performance when environmental conditions change. Therefore, G1 (ETSC 300552) exhibited the highest productivity and stability among the 15 sorghum genotypes evaluated across the test environments.

The analysis of mean grain yield (Y) ranks showed significant differentiation among the entries. Genotype G1 was unequivocally the highest yielder, securing the top rank (1). It was followed by a group of other high-performing genotypes, including G7 (rank 2), G4 (rank 3), and G6 (rank 4). In contrast, genotypes G10 (rank 15), G3 (rank 14), and G12 (rank 12) were the lowest yielders. The standard check variety, Beletew, was placed in the middle with a yield rank of 7, indicating that several new genotypes offer a distinct advantage in productivity.

Stability, a critical trait for wide adaptation, was assessed using the ranks of various parametric and non-parametric statistics. A genotype was considered stable if it consistently achieved low ranks across these different measures. Based on this criterion, genotype G4 distinguished itself with outstanding stability, achieving top-tier ranks for key parameters like Wricke’s ecovalence (W_i², rank 2) and deviation from regression (s²d_i, rank 2). Similarly, G9 demonstrated exceptional stability, ranking 3rd for both W_i² and s²d_i. Genotype G6 also performed well, though its stability was less consistent, ranking 4th for W_i² but 14th for s²d_i. This highlights the importance of using multiple statistics, as a genotype can be stable by one measure but not another. To synthesize the combined performance of yield and stability, we utilized aggregate rank metrics such as the Sum of Ranks (SR) and Average Rank (AR), where a lower value indicates superior overall performance. According to these integrated metrics, G1 emerged as the best all-around genotype with the lowest Sum of Ranks (SR = 56) and a low Average Rank (AR = 4), driven by its top-ranking yield and respectable stability. Close behind were G4 (SR = 65, AR = 4) and G6 (SR = 67, AR = 4), which balanced high-ranking yields with excellent stability profiles. In stark contrast, the unstable genotypes G2 (SR = 211) and G10 (SR = 215) had the highest aggregate ranks, confirming their poor overall suitability. In conclusion, this rank-based evaluation successfully identified a set of elite genotypes that surpass the current check variety, Beletew. G1 is highly recommended for its unmatched grain yield.

Relationships between agronomic performance (Y) and various stability statistics

An analysis of the interrelationships among the 16 studied parameters was conducted using Pearson correlation, with the results visualized in a correlation matrix (Fig. 3). The matrix reveals several statistically significant relationships that provide critical insights for genotype selection and evaluation. In this study, the parameter (Huehn’s non-parametric stability statistic) emerges as a highly effective selection criterion for identifying superior genotypes due to its ability to simultaneously account for yield performance and environmental stability. As illustrated in the correlation analysis, maintains a robust positive correlation with grain yield (; ), significantly outperforming traditional indices like the regression coefficient () and coefficient of variation () in its association with productivity. Furthermore, the perfect negative correlation () between and both (Wricke’s ecovalence) and (Shukla’s stability variance) demonstrates that this non-parametric measure captures the same critical information regarding environmental consistency as parametric models, but without the stringent requirements for data normality. Because is based on rank-order, it is inherently less sensitive to outliers in multi-environment trials, making it a reliable “dual-purpose” filter. Consequently, using as a primary selection tool enables breeders to pinpoint “ideal” genotypes those that consistently rank at the top across diverse environments while maintaining low variance, thereby ensuring high yield potential with minimal environmental risk.

Fig. 3.

Correlation plot visualizing the relationships between grain yield performance (Y) and various stability statistics

A perfect positive correlation (r = 1.00) was observed between Wricke’s ecovalence (W_i²) and Shukla’s stability variance (σ²_i). This result confirms their statistical equivalence in this dataset, indicating a redundancy in using both metrics simultaneously. These two parameters were also almost perfectly correlated with the superiority measure S⁽³⁾ (r = 0.99) and strongly correlated with non-parametric statistics such as NP⁽⁴⁾ (r = 0.92) and NP⁽²⁾ (r = 0.92). The formation of this large, positively correlated group (also including s²d_i, NP⁽³⁾, and S⁽²⁾) suggests that these parametric and non-parametric statistics are effectively measuring the same underlying biological concept: a genotype’s contribution to genotype-by-environment interaction, which is a quantitative measure of its instability across diverse environments.

The most significant implication of this instability cluster becomes evident when examining its relationship with the target variable, Y (grain yield). Y exhibited strong and consistent negative correlations with all members of the instability cluster. The strongest associations were with NP⁽²⁾ (r = -0.90), NP⁽⁴⁾ (r = -0.88), σ²_i (r = -0.86), and W_i² (r = -0.85). This clear antagonism robustly demonstrates that genotypes exhibiting higher variance and instability across environments tend to have lower overall performance.

These findings are consistent with and supported by a substantial body of previous research in plant breeding and agronomy. The observed strong negative correlation between the performance variable Y and the metrics of instability is a well-documented phenomenon. Numerous studies across various crops, including maize, and wheat, have reported this inverse relationship, which highlights the fundamental challenge in simultaneously breeding for high yield potential and broad environmental stability [31, 32]. Furthermore, the high degree of multicollinearity among the stability parameters themselves, particularly the perfect correlation between Wricke’s ecovalence (W_i²) and Shukla’s stability variance (σ²_i), aligns with theoretical expectations and empirical reports himself demonstrated the linear relationship between these two statistics, and subsequent comparative studies have frequently grouped stability parameters into conceptual clusters based on their statistical properties, similar to the instability cluster identified in our analysis. The equivalence of our results with established literature lends strong support to our conclusions and underscores their relevance for practical application.

Farmers’ participatory variety selection at the earlier breeding stage

Participatory varietal selection at an earlier breeding stage helps to know farmers’ selection criteria and increases adoption rates of varieties [33]. In this study the matrix ranking results reveal that ETSC 300,552 was the most preferred genotype, securing the first rank with a total score of 83. This top performance was driven by maximum scores (5) in critical categories including grain yield, biomass yield, and grain filling. ETSC-14223-9-1 and ETSC-14225-2-2 followed as the second and third most preferred genotypes, respectively, demonstrating strong multi-trait performance across both vegetative and reproductive characteristics. Notably, the local check ranked lower (7th), primarily due to its poor score in earliness, which hindered its overall competitiveness. These results indicate that farmers prioritized genotypes that combined high grain and biomass productivity with efficient grain filling and early maturity, making ETSC 300,552 (G1) the most suitable candidate based on participatory evaluation (Table 7).

Table 7.

Evaluation of sorghum genotypes by farmers’ participation using direct matrix ranking

Genotypes	Head length	Biomass yield	Grain filling	Tillering ability	Color	Grain Yield	Earliness
	3	3	3	2	3	3	3	T.score	Rank
ETSC-14368-1-1	4(12)	4(12)	3(9)	3(6)	3(9)	3(9)	4(9)	66	6
ETSC-14487-7-1	2(6)	3(9)	3(9)	4(8)	3(9)	3(9)	4(9)	59	9
ETSC-14404-5-1	3(9)	3(9)	3(9)	3(9)	3(9)	4(12)	4(9))	57	10
ETSC 300,510	2(6)	3(9)	3(9)	4(8)	3(9)	3(9)	4(9))	66	6
ETSC-14173-2-2	4(12)	4(12)	3(9)	3(6)	3(9)	2(6)	4(9)	63	7
Local check	4(12)	5(15)	3(9)	3(6)	3(9)	3(9)	1(3)	63	7
ETSC-14325-4-1	2(6)	4(12)	3(9)	3(6)	3(9)	3(9)	4(9)	60	8
ETSC-14483-5-2	4(12)	4(12)	3(9)	3(6)	3(9)	3(9)	4(9)	66	6
Beletew	4(12)	3(9)	4(12)	4(8)	3(9)	4(12)	4(9)	71	4
ETSC 300,552	4(12)	5(15)	5(15)	4(8)	3(9)	5(15)	4(9)	83	1
ETSC-14325-6-2	2(6)	4(12)	3(9)	3(6)	3(9)	3(9)	4(9)	60	8
ETSC-14225-2-2	4(12)	4(12)	4(12)	3(6)	4(12)	4(12)	4(9)	75	3
ETSC-14223-9-1	3(9)	5(15)	4(12)	4(8)	4(15)	3(9)	4(9)	77	2
ETSC 300,547	2(6)	4(12)	3(9)	3(6)	2(6)	3(9)	4(9)	57	10
ETSC-14321-5-1	2(6)	4(12)	3(9)	3(6)	3(9)	3(9)	4(9)	60	8
ETSC-14019-1-2	4(12)	4(12)	3(9)	3(6)	3(9)	3(9)	4(12)	69	5

To understand the alignment of selection criteria between technical experts and end-users, the overall acceptance scores from both breeders and farmers were visualized using a density plot (Fig. 4). This plot illustrates the distribution and frequency of scores given by each evaluator group, providing insights into their preferences and level of consensus. The evaluation by farmers, represented by the teal distribution, shows a distinct and relatively narrow peak, with the mode (the most frequent score) centered at approximately 3.2. This sharp peak indicates a high degree of consensus among farmers; their opinions on the overall acceptance of the genotypes were closely clustered around this value. The distribution is positively skewed, with a tail extending towards the higher scores, suggesting that while the most common rating was moderate, a subset of genotypes was rated more favorably by some farmers. In contrast, the evaluation by breeders, shown in the red distribution, reveals a markedly different pattern. The breeders’ distribution is significantly broader and flatter, indicating a much lower level of consensus and a wider diversity of opinions compared to the farmers. The central tendency of the breeders’ scores is also visibly higher, with the primary peak located around a score of 3.6–3.7. This suggests that, on average, breeders rated the genotypes more favorably than farmers. The shape of the breeders’ distribution appears to be bimodal or multimodal, with less defined peaks, reflecting a more varied assessment across the group.

Fig. 4.

Distribution of overall appreciation scores by breeders and sorghum producing

Modern literature increasingly emphasizes that farmers and breeders frequently prioritize different trait combinations. While breeders traditionally focus on maximizing yield under optimal or controlled conditions, farmers operate within a complex socio-ecological system where risk aversion, household food security, and market dynamics shape their preference. Farmers often employ a multi-criteria assessment that values stability, storability, and processing quality as much as, or even more than, absolute yield. This discrepancy powerfully underscores the critical importance of participatory variety selection (PVS) as a strategy to bridge this gap. Engaging farmers directly in the selection process has been repeatedly shown to increase the rate and scale of variety adoption by ensuring that newly developed varieties meet the complex needs and preferences of end-users [34]. While breeders identify genotypes with high genetic merit, farmer input is essential to ensure that the selected varieties are not only high-yielding but also locally adapted and desirable, thereby maximizing the likelihood of successful adoption and impact.

Conclusion

This research evaluated 14 sorghum genotypes and a standard check variety (‘Beletew’) to understand GEI and identify stable, high-yielding genotypes. Significant genetic variation was observed for all traits, highlighting breeding potential. Environmental factors and GEI strongly influenced Days to Heading, Days to Maturity, and Thousand Seed Weight, suggesting distinct mega-environments. The average grain yield was 4.14 t ha-1, with ETSC 300552 (G1) showing the highest yield and ETSC-14019-1-2 the lowest. ETSC 300547 was identified as an early-maturing genotype suitable for short-season areas, and ‘Beletew’ exhibited beneficial lodging resistance due to its shorter stature. Substantial yield variations across environments underscored the necessity of multi-environment testing. AMMI analysis confirmed significant main effects for genotype, environment, and their interaction on grain yield. The strong environmental influence (27%) necessitates multi-environment trials. GGE biplot analysis identified G1 and G7 as the most stable, high-yielding genotypes, with G1 emerging as the ideal candidate for broad adaptation. Although G1, G12, and G13 all had regression coefficients less than one, indicating good adaptation, G1 uniquely combined this with a superior grain yield, suggesting broad adaptability. G1 emerged as the best all-around genotype, with the lowest Sum of Ranks (SR = 56) and a low Average Rank (AR = 4), driven by its top-ranking yield and respectable stability. Grain yield showed strong negative correlations with instability parameters, while the parameter θ₀ displayed a perfect negative correlation with instability metrics and a strong positive correlation with grain yield, positioning it as an excellent indicator of both high performance and high stability. Farmers’ participatory variety selection also supported these findings, with ETSC 300552 (G1) ranked first based on criteria such as head length, biomass yield, grain filling, tillering ability, color, grain yield, and earliness. Having demonstrated superior performance and stability throughout evaluations, G1 was officially approved by the Ethiopian variety releasing committee for national release. This significant decision paves the way for its widespread adoption by farmers across the country.

Authors’ contributions

AT and AB, conceptualization, designing the experiment, data analysis, writing original draft and editing. SC, TM, AL, AA, DT, EA, TS, NT and KT: Investigation, data curation, analysis and editing. All authors read and approved the final manuscript.

Funding

This research work was conducted with finical support from a government/public fund dedicated for Ethiopian agricultural research.

Data availability

The datasets generated during this study are not publicly available due to privacy and confidentiality. However, they may be available from the corresponding author upon reasonable request and with a formal data-sharing agreement of the Research Institute.

Declarations

Ethics approval and consent to participate

This study underwent ethical review and received official approval from the research directorate of the Amhara Agricultural Institute (ARARI). The institute’s research review committee thoroughly assessed the study protocol, acknowledging its potential benefits, and granted permission for its execution in accordance with institutional guidelines.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.