Yield Stability of Drought Tolerant Sorghum [Sorghum bicolor (L.) Moench] Genotypes in Southern and West Hararghe, Ethiopia

1. Introduction

Sorghum [Sorghum bicolor (L.) Monech ] is the fifth most important cereal crop in the world, after wheat, rice, maize, and barley[1]. It is a C4 plant that has high photosynthetic efficiency and originated in the Ethiopian region [2]. Multi-environment trials are used to select the best-performing genotype for different locations and environmental conditions. Plant breeders need to identify drought-tolerant genotypes with stable yield performance in various environments. Developing countries require stable cultivars with high yields.

In Ethiopia, several studies have been conducted to investigate the interaction between genotype and environment when it comes to crops like sorghum [3,4,5,6,7], maize [8,9], wheat [10], teff [11], and finger millet [12]. However, there is limited information available on the impact of genotype, environment, and GEI on sorghum yield using drought-tolerant genotypes in Ethiopia. To address this gap, a study was carried out to determine the extent of the effect of genotypes by environment interaction and to assess the performance and stability of drought-tolerant sorghum genotypes that show promise for adaptation to different conditions and cultivation under farmers’ conditions in Ethiopia.

2. Materials and Methods

2.1. Description of the Study Area

The experiment was conducted at six locations during the 2021 main cropping season. These locations represent the main lowland sorghum-growing areas of the country (Figure 1).

Figure 1. Study area map. Different colors designate land cover of study locations.

Figure 1. Study area map. Different colors designate land cover of study locations.

2.2. Trial Materials

Thirty-four genotypes were selected based on their drought performance from the moisture stress trial conducted at Weoito(Table A1 and Table A2), and two standard check varieties were included. A list of genotypes used for genotype-by-environment experiments is provided in (Table 2).

Table 2. List of genotypes used for genotypes by environment experiments.

Serial no.	Genotypes	Code	Source
1	27907	G1	EBI
2	69313	G2	EBI
3	69330	G3	EBI
4	70084	G4	EBI
5	70154	G5	EBI
6	70373	G6	EBI
7	71018	G7	EBI
8	74654	G8	EBI
9	74669	G9	EBI
10	74679	G10	EBI
11	74680	G11	EBI
12	74684	G12	EBI
13	74686	G13	EBI
14	74691	G14	EBI
15	74693	G15	EBI
16	74704	G16	EBI
17	74705	G17	EBI
18	200617	G18	EBI
19	201453	G21	EBI
20	204602	G22	EBI
21	204619	G23	EBI
22	204629	G24	EBI
23	204631	G25	EBI
24	204633	G26	EBI
25	204634	G27	EBI
26	206285	G28	EBI
27	206286	G29	EBI
28	213008	G30	EBI
29	213017	G31	EBI
30	213019	G32	EBI
31	213026	G33	EBI
32	214010	G34	EBI
33	214109	G35	EBI
34	216906	G36	EBI
35	Dekeba( Standard check )	G19	MARC
36	Melkam( Standard check)	G20	MARC

EBI =Ethiopian Biodiversity Institute (EBI), MARC=Melkassa Agricultural Research Center.

Table 2. List of genotypes used for genotypes by environment experiments.

Serial no.	Genotypes	Code	Source
1	27907	G1	EBI
2	69313	G2	EBI
3	69330	G3	EBI
4	70084	G4	EBI
5	70154	G5	EBI
6	70373	G6	EBI
7	71018	G7	EBI
8	74654	G8	EBI
9	74669	G9	EBI
10	74679	G10	EBI
11	74680	G11	EBI
12	74684	G12	EBI
13	74686	G13	EBI
14	74691	G14	EBI
15	74693	G15	EBI
16	74704	G16	EBI
17	74705	G17	EBI
18	200617	G18	EBI
19	201453	G21	EBI
20	204602	G22	EBI
21	204619	G23	EBI
22	204629	G24	EBI
23	204631	G25	EBI
24	204633	G26	EBI
25	204634	G27	EBI
26	206285	G28	EBI
27	206286	G29	EBI
28	213008	G30	EBI
29	213017	G31	EBI
30	213019	G32	EBI
31	213026	G33	EBI
32	214010	G34	EBI
33	214109	G35	EBI
34	216906	G36	EBI
35	Dekeba( Standard check )	G19	MARC
36	Melkam( Standard check)	G20	MARC

EBI =Ethiopian Biodiversity Institute (EBI), MARC=Melkassa Agricultural Research Center.

2.2.1. Experimental Design and Procedures

The experiment used randomized complete block design with three replications at all locations with plot size of 3.75mX5m. Seeds were drilled into 5-meter-long paired rows spaced 0.75 meters apart. Weeds were removed from the plots 2-3 weeks after sowing. The seed rate was 15 kg/ha, and plots received NPS fertilizer at planting (19 kg/ha N, 38 kg/ha P2O5, and 7 kg/ha S), with an additional 23 kg/ha of nitrogen in the form of urea applied at 45 days after planting. Data was collected from the four middle rows.

2.2.2. Data Collection

Data was collected on sorghum based on descriptors developed by the International Board for Plant Genetic Resources [13]. At maturity, yield components were recorded, including panicle length, panicle weight, panicle yield, and thousand kernel weight. Data was collected on a plot basis and plant basis, including measurements of straw weight, grain yield, total biomass, harvest index, and panicle weight.

2.2.3. Data Analyses

Various statistical software packages were used to analyze the data. SAS software 9.0 was used for combined analyses of variance and mean comparison with the LSD test [14]. Additionally, GEA-R Version 4.1 was used for several analyses, including AMMI analysis and GGE biplot stability analysis [15].

Analysis of Variance for Individual location and Combined Data over the Location

The data from different locations were analyzed using a mixed linear model through the analysis of variance based on Gomez and Gomez [16]. Bartlett’s test was used to check the homogeneity of error variances before combining the analysis [17]. The combined analysis of variance was conducted using SAS software 9.0[14] to determine the differences between genotypes across and among environments and their interaction. In the combined analysis, genotypes were considered as fixed while locations were considered a random variable. The following model was used for ANOVA of data of individual location:

Yij =µ + Gi +Bj + eij

where; Yij = observed value of genotype i in block j, µ = Grand mean of the experiment, Gi= the effect of genotype i, Bj = the effect of block j, eij =the error of genotype i in block j.

Combined analysis of variance over locations was carried out using the following statistical model:

Yijk=μ + Gi +Ej +GEij+ Bk(j)+ eijk

where; Yijk = observed value of genotype i in block k of environment (location) j, μ = Grand mean of the experiment, Gi = the effect of genotype i, GEj = the interaction effect of genotype i with environment j, Bk(j) =the effect of block k in location (environment) j, eijk =the error effect of genotype i in block k of environment j. Mean separation was done using Duncan multiple range test to discriminate the genotypes and identify superior ones based on yield.

Stability Analysis

Analysis of variance only detects genotype by environment interaction effects. To determine the stability of a genotype’s performance across different environments, breeders need additional information. Stability depends on the genetic structure of the cultivar’s population and the genotype of individual plants. So, the significance of genotype by environment interaction was further analyzed using stability parameters. Means of genotypes for grain yield across locations were analyzed using SAS [18]. AMMI model, biplot technique, and AMMI stability value analysis were computed per standard procedures.

AMMI Analysis

The Additive Main effect and Multiplicative Interaction (AMMI) model analysis was performed for grain yield and biomass. The AMMI model equation is given as:

$${\mathrm{y}}_{\mathrm{i}\mathrm{j}}=\mathsf{\mu }+{\mathrm{G}}_{\mathrm{i}}+{\mathrm{E}}_{\mathrm{j}}+(\sum {\mathrm{K}}_{\mathrm{n}}{\mathrm{V}}_{\mathrm{n}\mathrm{i}}{\mathrm{S}}_{\mathrm{n}\mathrm{j}})+{\mathrm{Q}}_{\mathrm{i}\mathrm{j}}+{\mathrm{e}}_{\mathrm{i}\mathrm{j}}$$

where, y_ij= is the observed yield of genotype i in environment j

μ = is the grand mean, ${\mathrm{G}}_{\mathrm{i}}$= the additive effect of the i^th genotype (genotype means minus the grand mean), ${\mathrm{E}}_{\mathrm{j}}$=is the additive effect of the j^th environment (environment mean deviation), ${\mathrm{K}}_{\mathrm{n}}$= is the eigenvalues of the PCA axis n, ${\mathrm{V}}_{\mathrm{n}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{d}}{\mathrm{S}}_{\mathrm{n}\mathrm{j}}$= are scores for the genotype i and environment j for the PCA axis n, ${\mathrm{Q}}_{\mathrm{i}\mathrm{j}}$ = is the residual for the first n multiplicative components, ${\mathrm{e}}_{\mathrm{i}\mathrm{j}}$ = is the error

AMMI Stability Value (ASV)

The AMMI stability value as described by Purchase [19] was calculated as follows:

$$\mathrm{ASV}=\sqrt{\left[{\left[{\displaystyle \frac{\mathrm{I}\mathrm{P}\mathrm{C}\mathrm{A}\mathrm{A}1\mathrm{S}\mathrm{u}\mathrm{m}\mathrm{o}\mathrm{f}\mathrm{s}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{s}}{\mathrm{I}\mathrm{P}\mathrm{C}\mathrm{A}\mathrm{A}2\mathrm{S}\mathrm{u}\mathrm{m}\mathrm{o}\mathrm{f}\mathrm{s}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{s}}}\left(\mathrm{I}\mathrm{P}\mathrm{C}\mathrm{A}\mathrm{A}1\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{s}\right)\right]}^2+{\left[\mathrm{I}\mathrm{P}\mathrm{C}\mathrm{A}\mathrm{A}2\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{s}\right]}^2\right]}$$

Where;

ASV= AMMI stability value, IPCAA1 = interaction principal component analysis 1, IPCAA2 = interaction principal component analysis 2, SSIPCAA1 = sum of square of the interaction principal component one, SSIPCAA2 = sum of square of the interaction principal component two.

3. Results and Discussion

3.1. Combined Analysis of Variance

In the study, significant differences were found in the environment, genotype, and genotype by environment interactions for all traits studied (Table 1). Our findings are in agreement with an earlier study on bread wheat [20]. The AMMI analysis revealed that a large portion of the variation was attributed to environmental effects (69.29%) followed by genotype by environment interactions (24.49%) and genotype effects (6.22%). This suggests that the performance of sorghum genotypes varied across different locations, highlighting the need for further evaluation of genotypes with wider adaptability and testing them in diverse environments. The diversity in environments indicated by the large sum of squares emphasizes the importance of testing sorghum genotypes at multiple locations to account for variations in climatic and soil conditions. These findings are consistent with earlier studies [21,22,23] on sorghum and support the idea that testing genotypes across various environments is crucial for understanding their performance and adaptation.

3.2. Mean Performance of Genotypes

Grain Yield

The analysis of variance results for each environment showed significant differences (P≤0.01) in grain yield among sorghum genotypes tested at multiple locations (Table 1). This aligns with previous studies on sorghum that also reported significant variations in grain yield among different varieties [24]. The tested genotypes exhibited varying performances for grain yield across the different environments, with the mean grain yield ranging from 1148.1 kg/ha for genotype G34 at Arfayide to 9137 kg/ha for genotype G36 at Jinka, with an overall environmental mean yield of 4250.12 kg/ha (Table 2). The average environmental grain yield varied from 1721.61 kg/ha at Arfayide to 6182.31 kg/ha at Jinka, while the average genotype grain yield across environments ranged from 3314.50 kg/ha for genotype G3 to 5119.93 kg/ha for G1(Table 2). These findings indicate that it is crucial to evaluate sorghum genotypes in various environments to comprehend their adaptability and performance variations. Additionally, the study demonstrated that the GEI sum square magnitudes were around 3.9 times greater than those of the genotypes sum squares for grain yield. This suggests significant differences in genotypic responses across different environments, resulting in observed variations in genotypic responses across environments. These findings align with the research by Amare et al. [24], which also highlighted a threefold difference in the magnitude of the GEI sum of squares compared to wheat genotypes, indicating substantial variations in genotypic responses across environments. The larger sum of squares of GEI relative to genotypes underscores the significant differences in genotypic responses across environments, emphasizing the considerable variance in genotypic responses across different conditions. Consequently, GEI poses challenges to the selection process by complicating the assessment of genotypes’ yield performance and weakening the correlation between genotypic and phenotypic values [25]. The GEI observed in this study follows a cross-over pattern, leading to shifts in genotype rankings for specific environments, making it challenging to interpret grain yield based solely on genotype and environment means. These findings are consistent with the findings of Tekle et al. [26] regarding mung bean.

The highest mean grain yields across the environment were recorded for the genotypes (G1 and G14), with a mean yield of (5119.93 and 4834.57 kg ha-1), respectively. Whereas, the lowest mean grain yield was recorded from the genotype (G3) with an average mean yield of 3314.50 kg ha-1 (Table 2), indicating that the tested genotypes had inconsistent performance across the tested environments. In this study, most of the tested genotypes gave relatively good grain yield performance, and it could be suggested that there is an opportunity to get high-yielding sorghum genotypes for future variety development. The large variation due to the environments in our study also confirmed the high diversity of weather conditions during growing seasons and the locations had different soil types, temperature, and rainfall as well as altitude, directly affecting the performances of the genotypes. Thus, the selection and development of sorghum varieties in the future should follow environment-specific approaches. This result is in agreement with the work of Yitayeh et al. [22] and Abiy[27] on the early maturing sorghum genotype, who reported that the performance of sorghum genotypes was different from location to location, similar to that of Tegegn et al. [28] in finger millet. Ranking based on the genotype-focused scaling assumed that stability and mean yield were equally important [29].

The best candidate genotypes were expected to have a high mean seed yield with stable performance across all test locations. However, such genotypes are very rare to find in practice. Therefore, high-yielding and relatively stable genotypes can be considered as a reference for genotype evaluation [30].

Table 1. Analysis of variance of morphological traits between genotypes (G), environment (E) and GEI interaction for 36 sorghum genotypes across six locations.

Trait		DF		MD		GFP			PHT
Source of variation	df	MS	Percent	MS	Percent	MS	Percent		MS	Percent
Environment(E)	5	3026.16**	28.64	17357.93**	56.66	8170.96**	44.99		120104.56**	28.38
Genotype (G)	35	150.20**	9.95	150.84**	3.45	77.04**	3.01		13494.25**	22.32
GxE interactions Rep(E) Error	175 12 420	71.95** 226.2** 40.77	23.84 5.14	61.46** 3167.80**	7.02 24.82	72.61** 1337.36**	13.97 17.64		2023.64** 9735.66**	16.74 5.52
			32.42	29.39	8.06	44.27	20.45		44.27	27.05
Trait		PL		PY		PW			SW
Source of variation	df	MS	Percent	MS	Percent	MS	Percent		MS	Percent
Environment(E)	5	3631.75**	34.65	418611.32**	58.85	366168.77**	40.70		419507928**	47.34
Genotype (G)	35	137.87**	9.21	2025.96*	3.18	7848.58**	6.11		15762275**	12.45
GxE interactions Rep(E) Error	175 12 420	85.18** 82.24** 32.21	28.44 1.88 25.82	3042.56** 9413.07** 1779.34	14.97 3.18 21.01	5260.07** 19546.56** 2946.62	20.46 5.21 27.51		2353159**	9.29
									70190040**	19.01
									1255266	11.90
Trait		BM		TKW		GY			HI
Source of variation	df	MS	Percent	MS	Percent	MS		Percent	MS	Percent
Environment(E)	5	597883554**	43.59	1799.68**	43.90	298875131**		48.30	419507928**	39.58
Genotype (G)	35	16989501**	8.67	74.47**	12.72	3897432**		4.14	15762275**	7.68
GxE interactions Rep(E) Error	175 12 420	4667812** 103932563** 2881993	11.91 18.18 17.65	16.20** 75.54** 12.27	13.83 4.42 0.06	3031950** 12269443** 1877757		16.98 4.77 25.81	2353159**	21.12
									70190040**	3.24
									1255266	28.38

*, **, =Significant at 5% and 1% level of probability respectively, DF=days to flowering, DM=days to maturity, GFP=grain filling period PHT=plant height (cm), PL=panicle length (cm), PY=panicle yield (g), PW=panicle weight (g), SW=Straw weight (kg), BM= biomass (kg), TKW= thousand- kernel weight (g) and GY=grain yield (kg).

Table 1. Analysis of variance of morphological traits between genotypes (G), environment (E) and GEI interaction for 36 sorghum genotypes across six locations.

Trait		DF		MD		GFP			PHT
Source of variation	df	MS	Percent	MS	Percent	MS	Percent		MS	Percent
Environment(E)	5	3026.16**	28.64	17357.93**	56.66	8170.96**	44.99		120104.56**	28.38
Genotype (G)	35	150.20**	9.95	150.84**	3.45	77.04**	3.01		13494.25**	22.32
GxE interactions Rep(E) Error	175 12 420	71.95** 226.2** 40.77	23.84 5.14	61.46** 3167.80**	7.02 24.82	72.61** 1337.36**	13.97 17.64		2023.64** 9735.66**	16.74 5.52
			32.42	29.39	8.06	44.27	20.45		44.27	27.05
Trait		PL		PY		PW			SW
Source of variation	df	MS	Percent	MS	Percent	MS	Percent		MS	Percent
Environment(E)	5	3631.75**	34.65	418611.32**	58.85	366168.77**	40.70		419507928**	47.34
Genotype (G)	35	137.87**	9.21	2025.96*	3.18	7848.58**	6.11		15762275**	12.45
GxE interactions Rep(E) Error	175 12 420	85.18** 82.24** 32.21	28.44 1.88 25.82	3042.56** 9413.07** 1779.34	14.97 3.18 21.01	5260.07** 19546.56** 2946.62	20.46 5.21 27.51		2353159**	9.29
									70190040**	19.01
									1255266	11.90
Trait		BM		TKW		GY			HI
Source of variation	df	MS	Percent	MS	Percent	MS		Percent	MS	Percent
Environment(E)	5	597883554**	43.59	1799.68**	43.90	298875131**		48.30	419507928**	39.58
Genotype (G)	35	16989501**	8.67	74.47**	12.72	3897432**		4.14	15762275**	7.68
GxE interactions Rep(E) Error	175 12 420	4667812** 103932563** 2881993	11.91 18.18 17.65	16.20** 75.54** 12.27	13.83 4.42 0.06	3031950** 12269443** 1877757		16.98 4.77 25.81	2353159**	21.12
									70190040**	3.24
									1255266	28.38

*, **, =Significant at 5% and 1% level of probability respectively, DF=days to flowering, DM=days to maturity, GFP=grain filling period PHT=plant height (cm), PL=panicle length (cm), PY=panicle yield (g), PW=panicle weight (g), SW=Straw weight (kg), BM= biomass (kg), TKW= thousand- kernel weight (g) and GY=grain yield (kg).

Table 2. Mean grain yield (kg ha^-1) of 36 sorghum genotypes across six different test locations.

Genotype	Jinka	Kako	Alduba	Arfayide	Gato	Mieso	Mean
G1	7694abcd	5852abc	8440ab	1816.0abcde	3669.6a	3248abcd	5119.93
G2	7749abcd	3639c	5096bcdefg	1957.2abcde	1455.8bc	3311abcd	3868.00
G3	5176abcd	3555c	4992dcefg	1331.6bcde	1269.4c	3563abcd	3314.50
G4	4957bcd	6080abc	4851defg	1034.9e	4092.1ab	4859abc	4312.33
G5	4134d	5354abc	4277efg	1333.3bcde	3581.1a	4596abc	3879.23
G6	5406abcd	5347abc	2677g	1837.3abcde	3490.6a	2737bcd	3582.48
G7	7798abcd	6844a	5511bcdefg	1503.7bcde	3864.1ab	2878bcd	4733.13
G8	5596abcd	5665abc	4533defg	1639.2bcde	3694.4ab	5063abc	4365.10
G9	6058abcd	5230abc	7816abcd	1612.5bcde	3658.1a	3211abcd	4597.60
G10	3879d	4167bc	5872abcdefg	1960.0abcde	2447.2abc	3893abcd	3703.03
G11	8869ab	5301abc	6528abcdef	1573.3bcde	3173.0a	3074abcd	4753.05
G12	4353cd	4876abc	8336abc	2010.6abcd	3675.1a	4941abc	4698.62
G13	6425abcd	6093abc	5126bcdefg	1277.0cde	3887.6ab	2737bcd	4257.60
G14	8333abc	5267abc	6654abcdef	1917.5abcde	3539.9a	3296abcd	4834.57
G15	4467cd	5923abc	4109efg	1475.6bcde	3916.1ab	5678a	4261.45
G16	7674abcd	4350bc	4543defg	1787.7abcde	3113.2a	4485abcd	4325.48
G17	8209abc	4350bc	5333bcdefg	1360.5bcde	3665.4a	4015abcd	4488.82
G18	7658abcd	5722abc	6383abcdef	1158.5ed	3415.7a	4470abcd	4801.20
G19	4556cd	4706abc	5291bcdefg	2234.1ab	2585.8abc	3141abcd	3752.32
G20	4636cd	4706abc	4365efg	1410.4bcde	3416.4a	4563abc	3849.47
G21	5484abcd	4765abc	4230efg	2020.7abcd	3199.3a	3300abcd	3833.17
G22	6019abcd	7274a	6519abcdef	1583.5bcde	3488.7a	3530abcd	4735.70
G23	7649abcd	5101abc	4285efg	2013.8abcd	3161.9a	3093abcd	4217.28
G24	4952bcd	4303bc	7467abcde	1867.7abcde	2579.5abc	5270ab	4406.53
G25	6015abcd	4134bc	5956abcdef	2136.3abc	2985.3ab	1778d	3834.10
G26	5548abcd	3534c	5600bcdefg	1226.7cde	2610.7abc	3584abcd	3683.90
G27	5168abcd	4862abc	6198abcdef	1459.3bcde	4045.2ab	4078abcd	4301.75
G28	5342abcd	5559abc	5353bcdefg	2151.1abc	3149.0a	4007abcd	4260.18
G29	4067d	4683abc	5084bcdefg	1828.5abcde	3008.4ab	2567bcd	3539.65
G30	7212abcd	3957c	4312efg	2638.8a	2722.7ab	2723bcd	3927.58
G31	7339abcd	5362abc	6257abcdef	1860.7abcde	3676.4a	4211abcd	4784.35
G32	6064abcd	5849abc	5481bcdefg	2088.1abcd	3451.3a	4080abcd	4502.23
G33	5627abcd	4548abc	9022a	1837.0abcde	3316.1a	4381abcd	4788.52
G34	7669abcd	5647abc	5931abcdefg	1148.1de	3758.4ab	4252abcd	4734.25
G35	5644abcd	4934abc	5719abcdefg	1983.8abcd	3626.5a	2489cd	4066.05
G36	9137a	3554c	3531fg	1902.9abcde	3353.8a	4022abcd	4250.12
Mean	6182.31	5030.36	5602.17	1721.61	3270.66	3753.44

G= genotype, G1-G36 (Genotypes one up to thirty six), a=highest, b=medium, c=poor, d=poorest, e-g=bad mean grain yield, genotype having same letters are same in mean yield.

Table 2. Mean grain yield (kg ha^-1) of 36 sorghum genotypes across six different test locations.

Genotype	Jinka	Kako	Alduba	Arfayide	Gato	Mieso	Mean
G1	7694abcd	5852abc	8440ab	1816.0abcde	3669.6a	3248abcd	5119.93
G2	7749abcd	3639c	5096bcdefg	1957.2abcde	1455.8bc	3311abcd	3868.00
G3	5176abcd	3555c	4992dcefg	1331.6bcde	1269.4c	3563abcd	3314.50
G4	4957bcd	6080abc	4851defg	1034.9e	4092.1ab	4859abc	4312.33
G5	4134d	5354abc	4277efg	1333.3bcde	3581.1a	4596abc	3879.23
G6	5406abcd	5347abc	2677g	1837.3abcde	3490.6a	2737bcd	3582.48
G7	7798abcd	6844a	5511bcdefg	1503.7bcde	3864.1ab	2878bcd	4733.13
G8	5596abcd	5665abc	4533defg	1639.2bcde	3694.4ab	5063abc	4365.10
G9	6058abcd	5230abc	7816abcd	1612.5bcde	3658.1a	3211abcd	4597.60
G10	3879d	4167bc	5872abcdefg	1960.0abcde	2447.2abc	3893abcd	3703.03
G11	8869ab	5301abc	6528abcdef	1573.3bcde	3173.0a	3074abcd	4753.05
G12	4353cd	4876abc	8336abc	2010.6abcd	3675.1a	4941abc	4698.62
G13	6425abcd	6093abc	5126bcdefg	1277.0cde	3887.6ab	2737bcd	4257.60
G14	8333abc	5267abc	6654abcdef	1917.5abcde	3539.9a	3296abcd	4834.57
G15	4467cd	5923abc	4109efg	1475.6bcde	3916.1ab	5678a	4261.45
G16	7674abcd	4350bc	4543defg	1787.7abcde	3113.2a	4485abcd	4325.48
G17	8209abc	4350bc	5333bcdefg	1360.5bcde	3665.4a	4015abcd	4488.82
G18	7658abcd	5722abc	6383abcdef	1158.5ed	3415.7a	4470abcd	4801.20
G19	4556cd	4706abc	5291bcdefg	2234.1ab	2585.8abc	3141abcd	3752.32
G20	4636cd	4706abc	4365efg	1410.4bcde	3416.4a	4563abc	3849.47
G21	5484abcd	4765abc	4230efg	2020.7abcd	3199.3a	3300abcd	3833.17
G22	6019abcd	7274a	6519abcdef	1583.5bcde	3488.7a	3530abcd	4735.70
G23	7649abcd	5101abc	4285efg	2013.8abcd	3161.9a	3093abcd	4217.28
G24	4952bcd	4303bc	7467abcde	1867.7abcde	2579.5abc	5270ab	4406.53
G25	6015abcd	4134bc	5956abcdef	2136.3abc	2985.3ab	1778d	3834.10
G26	5548abcd	3534c	5600bcdefg	1226.7cde	2610.7abc	3584abcd	3683.90
G27	5168abcd	4862abc	6198abcdef	1459.3bcde	4045.2ab	4078abcd	4301.75
G28	5342abcd	5559abc	5353bcdefg	2151.1abc	3149.0a	4007abcd	4260.18
G29	4067d	4683abc	5084bcdefg	1828.5abcde	3008.4ab	2567bcd	3539.65
G30	7212abcd	3957c	4312efg	2638.8a	2722.7ab	2723bcd	3927.58
G31	7339abcd	5362abc	6257abcdef	1860.7abcde	3676.4a	4211abcd	4784.35
G32	6064abcd	5849abc	5481bcdefg	2088.1abcd	3451.3a	4080abcd	4502.23
G33	5627abcd	4548abc	9022a	1837.0abcde	3316.1a	4381abcd	4788.52
G34	7669abcd	5647abc	5931abcdefg	1148.1de	3758.4ab	4252abcd	4734.25
G35	5644abcd	4934abc	5719abcdefg	1983.8abcd	3626.5a	2489cd	4066.05
G36	9137a	3554c	3531fg	1902.9abcde	3353.8a	4022abcd	4250.12
Mean	6182.31	5030.36	5602.17	1721.61	3270.66	3753.44

G= genotype, G1-G36 (Genotypes one up to thirty six), a=highest, b=medium, c=poor, d=poorest, e-g=bad mean grain yield, genotype having same letters are same in mean yield.

3.3. Stability Analyses

Additive Main Effects and Multiplicative Interaction Analysis

The Additive Main Effects and Multiplicative Interaction (AMMI) analysis of variance for grain yield (kg/ha) and biomass (kg/ha) of 36 sorghum genotypes tested across six environments is presented in Table 4. The analysis revealed that genotypes had a significant impact on grain yield, while the environment (p≤0.001) also had a significant effect on grain yield. This finding aligns with a study by Jifar et al. [31] on tef genotypes, where they observed significant effects (P≤0.01) attributed to the environment, genotype, and their interaction (G×E) on seed yield and yield components.

In this research, environmental factors explained the majority of the variance in grain yield (69.29%), with genotype-environment interaction (24.49%) and genotype (6.22%) following. The impact of the environment was the most significant, while that of genotype was the least. The result aligns with earlier studies on sorghum [32,33]. Thus, the primary source of variation in grain yield was attributed to environments, suggesting their diversity and potential subdivision into mega-environments. Significant discrepancies among environments predominantly accounted for the variability in grain yield. Similar outcomes have been noted in other studies on sorghum [22,34], where environments displayed a higher sum of squares compared to genotypes.

The interaction between genotype and environment had a significant impact on grain and biomass. Two principal components were found to be the most precise predictors for both grain and biomass. These components explained 73.86% of grain yield variability and 88.57% of the total GEI sum of squares in biomass. These findings have been observed by several researchers across various locations and years [35,36]. Similar findings have been documented for sorghum genotypes assessed across various locations and years [3,37,32]. Moreover, the mean square of IPCA1 was higher than that of IPCA2, IPCA3, and IPCA4 for grain and biomass, indicating variations in genotype performance due to GEI. This aligns with previous studies on sorghum [3,33,38].

Table 4. Analysis of variance for the AMMI model for grain and biomass yield.

Source of variations	Grain yield				biomass
	df	S.S.	Percent	Accumulated	MS	Percent	Accumulated
Genotype(G)	35	44594242*	6.22	6.22	1.99E+08	13.61	13.61
Environments(E)	5	496649374**	69.29	75.51	9.93E+08	67.78	81.39
Interactions(GxE)	175	175547472**	24.49	100.00	2.72E+08	18.61	100.00
PC1	39	75845622**	43.21	43.21	1.94E+08	71.07	71.07
PC2	37	53814007**	30.65	73.86	47685656	17.50	88.57
PC3	35	24616969**	14.02	87.88	25943186	9.52	98.10
PC4	33	15600190**	8.89	96.77	4233067	1.55	99.65
Residuals	31	5670685	3.23		953107	0.35
Total	215	7.17E+08			1.46E+09

*, **, significant at 5% & 1% probability level; ns, non-significant.

Table 4. Analysis of variance for the AMMI model for grain and biomass yield.

Source of variations	Grain yield				biomass
	df	S.S.	Percent	Accumulated	MS	Percent	Accumulated
Genotype(G)	35	44594242*	6.22	6.22	1.99E+08	13.61	13.61
Environments(E)	5	496649374**	69.29	75.51	9.93E+08	67.78	81.39
Interactions(GxE)	175	175547472**	24.49	100.00	2.72E+08	18.61	100.00
PC1	39	75845622**	43.21	43.21	1.94E+08	71.07	71.07
PC2	37	53814007**	30.65	73.86	47685656	17.50	88.57
PC3	35	24616969**	14.02	87.88	25943186	9.52	98.10
PC4	33	15600190**	8.89	96.77	4233067	1.55	99.65
Residuals	31	5670685	3.23		953107	0.35
Total	215	7.17E+08			1.46E+09

*, **, significant at 5% & 1% probability level; ns, non-significant.

The Additive main effects and multiplicative interaction one (AMMI 1) biplot

AMMI 1 biplot shows genotype and environment interaction effects on yield [25]. The X-axis represents yield, while the Y-axis shows IPCA1 scores. It helps interpret interaction effects and evaluate adaptability (Figure 1 and Figure 2). The study identified stable genotypes G21, G25, G13, G32, G35, G28, and G8, with G21 and G25 underperforming and G32, G8, G28, and G13 exhibiting high grain yield (Figure 1). For biomass, genotypes G20, G22, G5, G13, G30, G28, G35, G6, and G12 were stable but G22, G20, and G28 didn’t perform well. Genotypes G11, G2, and G1 were generally adaptable to all environments, while G6, G15, and G29 exhibited specific adaptability. Yitayeh et al. [22] utilized this model to assess the yield stability of early maturing sorghum. Genotypes on the right of the perpendicular line midpoint had higher yields than those on the left. G13, G34, G14, G31, G18, G16, G7, G17, G11, and G1 had higher grain yields, while G26, G19, G20, G29, G5, and G3 had lower yields. G1, G11, G25, and G16 had higher biomass, while G19, G29, G12, G28, and G5 had lower yields (Figure 2).

In summary, Alduba, Jinka, and Kako were favorable testing locations while Arifyde, Gato, and Meioso were unfavorable. Genotypes G22 and G33 showed higher grain yields in Kako and Alduba. For biomass, Jinka and Kako were favorable while Arifyde, Gato, and Meioso were unfavorable. Locations far from the origin, such as Arifyde, Kako, and Jinka, played a crucial role in the genotype-environment interaction, affecting the stability of biomass performance. Genotypes G1 and 11 showed higher biomass at Jinka, indicating their adaptability to this location. Crossa et al. [25] also noted that Genotype and location combinations with IPCA1 scores of the same sign resulted in positive specific interaction effects, while combinations with opposite signs led to negative specific interactions.

Figure 1. AMMI1 biplot of IPCA1 against grain yield for 36 sorghum genotypes tested across six locations (Jin:Jinka, KA:Kako,Ald:Alduba,ARF:Arifyde,Gat:Gato,MS:Meioso).

Figure 1. AMMI1 biplot of IPCA1 against grain yield for 36 sorghum genotypes tested across six locations (Jin:Jinka, KA:Kako,Ald:Alduba,ARF:Arifyde,Gat:Gato,MS:Meioso).

Figure 2. AMMI1 biplot of IPCA 1 against biomass for 36 sorghum genotypes tested across six locations.

Figure 2. AMMI1 biplot of IPCA 1 against biomass for 36 sorghum genotypes tested across six locations.

3.4. AMMI Stability Value (ASV)

The Interaction Principal Component One (IPCA1) and Interaction Principal Component Two (IPCA2) scores in the AMMI model serve as stability indicators. The AMMI Stability Value (ASV) provides a balanced measure of stability [19]. Genotypes with lower ASV values are deemed stable, while those with higher ASV values are considered unstable. As per Appendix Table A1, G35 exhibited the highest stability with an ASV of 4.54, followed by G3 (6.60), G32 (7.51), G26 (8.29), G31 (9.17), G22 (9.57), and G18 (11.87) as the most unstable genotypes for grain yield. The stable genotypes (G31, G22, G32, and G18) showed mean grain yield above the grand mean, aligning with findings from Alemu et al. [39] and Yitayeh et al. [22] who utilized this stability parameter to assess sorghum genotypes’ stability. Concerning biomass, genotype G26 (3.90) demonstrated the highest stability, followed by G4 (7.31), G13 (9.40), and G19 (10.90), while G36 (218.71), G2 (146.83), G14 (146.72), and G10 (133.48) were identified as the most unstable genotypes.

4. Conclusions

The combined analysis of variance showed significant variation among the sorghum genotypes, environments, and their interaction (G x E). In the AMMI analysis, genotypes (G) and environments (E) contributed to 24.49% and 69.29% of the treatment sum of squares, respectively, whereas the G x E interaction accounted for 14.8%. The environment played a more significant role in the total sum of squares than genotypes. The two IPCAs validated the grain yield variation explained by genotype-environment interaction, explaining 73.86% of the interaction sum of squares. The AMMI1 and AMMI2 biplots identified the most stable genotypes for grain and biomass. For various stability measures, genotypes G18, G22, G31, and G32 were identified as the most stable genotypes for grain and biomass.

The study identified sorghum genotypes G18 and G31 as stable and high-yielding candidates for variety development programs in Ethiopia. These genotypes exhibit consistent performance across different environments and show promise for further enhancement in sorghum production.