The Sustainability Index and Other Stability Analyses for Evaluating Superior Fe-Tolerant Rice (Oryza sativa L.)

Abstract

Rice (Oryza sativa L.) is an important agricultural commodity in Indonesia. The combination of stability analysis on yields was considered accurate in selecting superior genotypes. The objectives of this study were as follows: identify the effects of genotypes, the environment, and their interactions (GEIs) on the yields of Fe-tolerant rice; select superior genotypes (stable and high yields) under diverse environment conditions in Indonesia; and determine the mega-environments (MEs) and representative environments for Fe-tolerant rice development. Fifteen genotypes of Fe-tolerant rice were used for this study. Field experiments were conducted at six experimental fields in Indonesia using a randomized block design with two replications. A combined analysis of variance (ANOVA) was used to determine the effect of genotypes, the environment, and their interactions on Fe-tolerant rice yields. Parametric, non-parametric, AMMI (additive main effects and multiplicative interaction), GGE biplot, and SI (sustainability index) measurements were used to determine the superior genotypes. GGE biplot was also used to determine MEs and representative environments. The measurement results showed that genotypes, the environment, and their interactions significantly affected rice yields with contributions of 13.30%, 35.78%, and 50.92%, respectively. One superior Fe-tolerant rice genotype (stable and high yield) was selected based on all measurements, namely G4 (B14316E-KA-4). In this experiment, two MEs were generated. Lampung was identified as a representative environment for the development of superior genotypes. The results of this study can be used as a consideration in the release and development of new superior varieties of Fe-tolerant rice in Indonesia.

1. Introduction

Rice (Oryza sativa L.) is one of the most important staple foods for billions of people in the world [1]. Rice is the main food source for more than 50% of the world’s population and a very important commodity for the Indonesian community [2]. In 2021–2022, rice production, reached 525 million tons, with a consumption of 53.4 kg/year per capita [3]. Furthermore, rice production in Indonesia reached 31.36 million tons in 2021 [4]. One of the problems in rice production is iron (Fe) toxicity [5]. Rice production is also influenced by various environmental factors [6,7]. Hence, it is important to develop Fe-tolerant rice, and rice that can adapt to environmental changes, in high yields.

As a staple food, rice is the greatest human energy source. Rice content is generally composed of protein, which mostly consists of glutamate and aspartic acid, carbohydrates, fiber, fat, thiamine (vitamin B1), riboflavin (vitamin B2), and niacin (vitamin B3) [8,9]. Thus, rice can be used as a nutritional source for humans.

Recently, rice with high yield potential has been widely developed. High yields are obtained via plant breeding programs. In the process of selecting superior genotypes (high and stable yields), it is obtained via multi-environmental testing. The multi-environment test is a test carried out to evaluate the performance and stability of a variety of plants in various agroecological environments [7,10]. Multi-environmental testing is important to carry out in the selection of Fe-tolerant rice with high yield and stability because it can determine genotypes by environmental interactions (GEIs). The existence of GEIs is influenced by biotic and abiotic factors. Biotic factors consist of pests and diseases [11,12], while abiotic factors are from the environment [7]. The existence of GEIs indicates that various genotypes can have different responses to environmental changes. By carrying out multi-environment tests, stable genotypes in various environments that are also adaptive to specific environments can be determined [13]. However, GEIs make the selection process difficult and inefficient under various environmental conditions [7,13,14]. Several studies have reported that GEIs complicate the selection process in sweet potatoes [7,15], durum wheat [16], soybeans [17,18,19], maize [20], Stevia [21], and turmeric [22]. Therefore, a study is needed to evaluate Fe-resistant rice genotypes under a wide range of environmental conditions to obtain superior genotypes (high and stable yields).

Iron toxicity in rice is a common problem in areas where the soil contains excessive iron. This condition adversely affects plant growth and productivity, leading to significant yield losses [23]. In order to develop rice genotypes that are resistant to iron toxicity and perform well under diverse environmental conditions, genotypes should be evaluated on various types of land. There are numerous important land types for genotypic evaluation: (1) High iron content soils. Genotypes that exhibit good growth and high yields on high iron content soils can be considered superior candidates for further development. (2) Low iron content soils. Genotypes that show good growth and high yields on low iron content soils can provide solutions for areas experiencing iron deficiency. (3) Different soil pH. Genotypes that can withstand and produce good, as well as low pH (acidic), soils can be considered genotypes that are tolerant to soil pH fluctuations and have the potential to be grown on various types of land [24,25].

Several researchers conducted multi-environmental evaluations using various stability measures. Combining stability measurements is considered to be more accurate in selecting genotypes that are stable and have a high yield [7,26]. Some of the stability analyses used are parametric estimation models, namely linear regression [27], Wricke’s equivalence [28], Shukla’s stability variance [29], coefficient of variation (CVi) [30], GE variance component (θ_(i)) [31], component of mean-variance (θi) [32], and Hanson genotypic stability (Di) [33]; non-parametric estimation models, namely the Thennarasu model (NP⁽ⁱ⁾) [34], non-parametric stability (S⁽ⁱ⁾) [35], and Kang ranks (KR) [36]; as well as graphical models, i.e., AMMI [37] and GGE biplot [38]. Several researchers have also used the sustainability index (SI) to identify or select superior genotypes [39,40,41,42]. The use of the sustainability index was considered to increase selection accuracy. In addition, the concept of sustainable agriculture was also an important factor in the advancement of agricultural crops [43]. In plant breeding programs, multi-environment testing is a crucial step to increase productivity and maintain food security [44]. The use of these various methods was expected to be able to identify and evaluate genotypes in a wide range of environments.

Currently, many researchers have used the combined stability analysis model to select superior genotypes, such as in grass peas [45], barley [26], peanuts [46], maize [47], sweet potato [7], and black soybean [18]. Because the combined stability method was considered more effective and accurate in selecting stable and high-yielding genotypes compared to a single stability estimation [40]. The advantages of this model are that it is (i) suitable for data with statistical assumptions such as interaction effects and a normal distribution of errors; (ii) simple because estimation is based on genotypic performance and does not require assumptions for homogeneity of variance; and (iii) suitable for visually determining the response of a genotype to the environmental testing [26,48]. The objectives of this study were to identify the effects of genotypes, environment, and their interactions (GEIs) on the yields of Fe-tolerant rice; select superior genotypes (stable and high yields) under diverse environmental conditions in Indonesia; and determine the mega-environments (MEs) and representative environments for Fe-tolerant rice development.

2. Materials and Methods

2.1. Plant Material

The genetic materials used include 15 new Fe-tolerant rice genotypes (

Table 1. Genotypes used during experiment.

Code	Genotype	Note
G1	B14301E-KA-17-a	Kao Daok Mali-105-9/B13143-8-MR-3-KA-14//inpara 5
G2	B14308E-KA-38	Setail/Inpara 2//Code
G3	B14315E-KA-1	B11844-MR-29-7-1/Inpara 3//Cisantana
G4	B14316E-KA-4	B11844-MR-29-7-1/Inpara 5//Code
G5	B14339E-KA-14	IR42/Ciherang
G6	B14354E-KA-4	Banyuasin/Ketan kutuk
G7	B14357E-KA-4-b	Siak raya/B13132-7-MR-1-KA-6
G8	B13925E-KA-1-a	Swarna Sub-1/Mekongga
G9	B13926E-KA-29-a	Swarna Sub-1/Ciherang
G10	B13957E-KA-50	Batanghari/Conde
G11	B13983E-KA-44	Inpari 9/Swarna Sub-1
G12	B13988E-KA-40	Cimelati/Inpara 3//Inpari 9/FR13A
G13	IR70213-10-CPA-2-UBN-B-1-1-3	Mekongga/Inpara 3//Mekongga/Inpara 3
G14	B13522E-KA-5-B	IR64 Kebo/BR11 Sub-1
G15	B13545E-KA-1-B	Ciherang/Swarna Sub-1//Ciherang///Inpara 3

). The rice genotypes tested were the result of selection with varying degrees of Fe tolerance [49]. These genotypes resulted from a plant breeding program at the National Research and Innovation Agency, Indonesia. The rice genotypes tested had different genetic backgrounds and high genetic diversity.

2.2. Field Experiment and Data Collection

Field experiments were conducted in six environments in Indonesia, i.e., Banjar Baru (South Kalimantan), Bogor (West Java), Sorong (West Papua), Lampung (South Sumatera), Blandean (South Kalimantan), and Riau (South Sumatera). These locations were chosen because they are rice production centers in Indonesia. The experiment used a randomized completed block design that was repeated two times. Each genotype was planted at a spacing of 40 × 40 cm. The data were taken at harvest, following the standard descriptor for rice. The yield of each genotype in each experimental plot was converted in t·ha⁻¹. Information about the experimental environment was presented in

Table 2. Information about the location used during the field experiment.

Location	Altitude (m asl)	Geographic Coordinates	Type of Agro-Climate	Mean Yield (t·ha−1)
Lampung	67	5°005′320.5″ S, 105°487′133.5″ E	B.III.2: Annual rainfall 1500–2500 mm; dry months per year < 3 months; wet months per year 5–9 months.	4.60
West Papua	14	1°03′39.2″ S, 31°16′30.9″ E	B.III.3: Annual rainfall 1500–2500 mm; dry months per year < 3 months; wet months per year 3–4 months.	2.82
Banjar baru	31	3°45′006.5″ S, 114°75′352.8″ Ë	B.II.2: Annual rainfall 1500–2500 mm; dry months per year 3–7 months; wet months per year 5–9 months.	3.93
Bogor	207	6°61′403.5″ S, 106°79′259.3″ E	A.III.2: Annual rainfall > 2500 mm; dry months per year < 3 months; wet months per year 5–9 months.	4.32
Belandean	53	4°101′141.1″ S, 57°191′131.1″ E	B.II.2: Annual rainfall 1500–2500 mm; dry months per year 3–7 months; wet months per year 5–9 months.	4.86
Riau	27	0°86′914.0″ S, 102°03′723.1″ E	A.III.3: Annual rainfall > 2500 mm; dry months per year < 3 months; wet months per year 3–4.	5.95

m asl = Meters above sea level; mm = millimeter.

.

2.3. Data Analysis

The combined ANOVA statistical model to estimate GEIs follows the Equation (1):

Y_opqr = μ + G_o + E_p + GE_op + R_q(p) + B_r(q) + ε_opqr

(1)

where Y_opqr is the value of rice genotype o in plot r and the value in environment p of each replication q; μ is the grand mean of grain yield; G_o is the effect of rice genotype o; E_p is the effect of the environment p; GE_op is the effect of GEIs on rice genotype o and environment p; R_q(p) is the effect of replicate q on environment p; B_r(q) is the effect of replication q on plot r; and ε_opqr is the error effects from rice genotype o in plot r and repeat q of environment p, respectively. To calculate the combined ANOVA, we used Genstat 12th. If the data show that GEIs have a significant effect, then the yield stability analysis was carried out using parametric and non-parametric measurements, AMMI, GGE biplot, and the sustainability index (SI). Various measurements aim to improve the accuracy of the superior genotype selections.

Parametric and non-parametric stability measurements are used to identify stable genotypes. Linear regressions were measured following Eberhart and Russell, (1966) [27]. According to Eberhart and Russell (1966) [27], a genotype is declared stable if it has a regression deviation = 1 and a variance deviation value (S²di) = 0. To estimate the mean-variance component (θi), following Plaisted and Peterson, (1959) [32], we used the following formula:

$${\theta }_i=\frac{p}{2(p-1)(q-1)}{\sum }_{j-1}^q{(x_{ij}-{\overline{X}}_{i.}+{\overline{X}}_{.j})}^2+\frac{SSGE}{2(p-2)(q-1)}$$

(2)

The GE variance component (θ_(i)) was calculated according to [31] as

$${\theta }_{\left(i\right)}=\frac{-p}{(p-1)(p-2)(q-1)}{\sum }_{j-1}^q{(x_{ij}-{\overline{X}}_{i.}-{\overline{X}}_{.j}+{\overline{X}}_{..})}^2+\frac{SSGE}{(p-2)(q-1)}$$

(3)

Wricke’s ecovalence (Wi²) was calculated according to [50] as

$${\mathrm{W}}_i^2=\sum {{(X}_{ij}-{\overline{X}}_{i.}-{\overline{X}}_{.j}+{\overline{X}}_{..})}^2$$

(4)

Shukla’s stability variance $\left({\sigma }^{2}i\right)$ was calculated according to [29] as

$${\sigma }_i^2=\left|\frac{p}{(p-2)(q-1)}\right|{\mathrm{W}}_i^2-\frac{\sum W_i^2}{(p-1)(p-2)(q-1)}$$

(5)

and the coefficient of variance (CVi) was calculated according to [30] as

$${CV}_i=\frac{{SD}_g}{\overline{X}}\times 100$$

(6)

Hanson’s genotype stability measure (Di) was calculated [33] with the following formula:

$$Di={\left[{\sum }_j{Z}_{ij}^2\right]}^2$$

(7)

For all measurements used, the variables were defined as follows: xij: grand yield from the rice genotype i across all environments; ${\overline{X}}_{i.}$: mean of yield from rice genotype i; ${\overline{X}}_{.j}$: mean of yield in environment j; ${\overline{X}}_{..}$: overall average yield; p and q: the numbers of rice genotypes and environments; SDg: the standard deviation of all GEIs.

Stability non-parametric (S⁽ⁱ⁾) components were applied according to [35,51] with the following formulas:

$$S_i^{\left(1\right)}=2{\sum }_j^{n-1}\frac{{\sum }_{j\prime =j+1}^n\left|r_{ij}-r_{ij}^{\prime }\right|}{\left[N(n-1)\right]}$$

(8)

$$S_i^{\left(2\right)}=\frac{{\sum }_{j=1}^n{(r_{ij}-{\overline{r}}_{i.})}^2}{(N-1)}$$

(9)

$$S_i^{\left(3\right)}=\frac{{\sum }_{j=1}^n{(r_{ij}-{\overline{r}}_{i.})}^2}{{\overline{r}}_i}$$

(10)

$$S_i^{\left(6\right)}=\frac{{\sum }_{j=1}^n\left|r_{ij}-{\overline{r}}_{i.}\right|}{{\overline{r}}_{i.}}$$

(11)

where r_ij: rank of stability from rice genotype i in the environment j; ${\overline{r}}_{i.}$: mean rank across all environments for each rice genotype; and N: number of environments. Parametric stability (NP⁽ⁱ⁾) were measured following Thennarasu (1995) [34] with the following formulas:

$${NP}^{\left(1\right)}=\frac{{\sum }_{j=1}^n\left|r_{ij}^{*}-M_{di}^{*}\right|}{N}$$

(12)

$${NP}^{\left(2\right)}=\frac{\left[{\sum }_{j=1}^n\left|r_{ij}^{*}-M_{di}^{*}\right|/M_{di}\right]}{N}$$

(13)

$${NP}^{\left(3\right)}=\frac{\sqrt{\frac{\sum {(r_{ij}^{*}-r_{i.}^{*})}^2}{N}}}{{\overline{r}}_{i.}}$$

(14)

$${NP}^{\left(6\right)}=\frac{2x\left[{\sum }_{j=1}^{n-1}{\sum }_{j^{\prime }=j+1}^n\left|r_{ij}^{*}-r_{i.}^{*}\right|/{\overline{r}}_{i.}\right]}{N(\mathrm{N}-1)}$$

(15)

where $r_{ij}^{*}$: stability rank in environment j from rice genotype i based on adjusted data; $M_{di}^{*}$: median rank for adjusted data (yield); M_di: original data from the same parameters; N: number of environments. Kang rank’s (KR) non-parametric stability model following Kang (1988) was used [36]. In this method, yield performance and stability variance are used to identify high yielding and stable genotypes given a weighting of 1. We identified stable genotypes based on non-parametric and parametric stability measurements using STABILITYSOFT (online software) [52]. The results of parametric and non-parametric measurements were grouped using cluster analysis (dendrogram) based on the stability rank of each measurement. Cluster analysis was estimated using SPSS v19 software [53].

AMMI is used to estimate the stability of Fe-tolerant rice yields, following [37]:

$$Y_{ef}=\mu +Ge+E_f+{\sum }_{k=1}^n\left({\lambda }_g{\mathsf{\alpha }}_{\mathrm{eg}}{\mathsf{\gamma }}_{\mathrm{f}\mathrm{g}}\right)+{\mathsf{\rho }}_{\mathrm{e}\mathrm{f}}$$

(16)

where Y_ef is the yield performance of the genotype eth in the year fth; $\mu$ is the average of all yield performances from genotypes used; G_e is the genotype eth mean deviation; E_f is the year fth mean deviation; λ_k is the square root of the eigenvalue of the PCA axis g; α_eg and γ_fg were the PC score for PCA axis g of the genotype ith and the year fth, respectively; $\mathsf{\rho }$_ef is the residual. According to AMMI measurement, genotypes were considered stable if they were within the radius of the circle and close to the axis (0.0). In contrast, the adaptive genotypes are far from the axis and close to the environment line vector. AMMI was analyzed used PBStat online [54].

AMMI stability value (ASV) was used to estimate the stability of Fe-tolerant rice yields, applying the following formula [55]:

$$\mathrm{ASV}=\sqrt{\frac{ssIPCA1}{ssIPCA2}{\left(IPCA1\right)}^2+{\left(IPCA2\right)}^2}$$

(17)

where ss IPCA 1 and ss IPCA 2 were the weight given to the IPCA 1 and IPCA 2 scores by divided the ss IPCA 1 and ss IPCA 2. IPCA 1 score and IPCA 2 score were the first and second from the IPCA scores for each genotype from the AMMI analysis. Genotypes that were stable across the years were indicated by a small ASV value and vice versa.

The genotype stability index (GSI) for Fe-tolerant rice genotypes was calculated based on the ASV Rank (RASV) from the genotypes tested in three environments (years) and the yield performance ranks (RGM) of genotypes tested in three years with Equation (18). Genotypes that were stable across the years were indicated by a small GSI value and vice versa.

GSI = RASV + RAY

(18)

The model for GGE biplot following [56] uses the formula below:

$$Y_{ij}-\overline{Y_j}={\lambda }_1{\zeta }_{i1}{\eta }_{j1}+{\lambda }_2{\zeta }_{i2}{\eta }_{j2}+{\epsilon }_{ij}$$

(19)

where, Yij is the average yield of somaclone i in season j; $\overline{Y_j}$ is the average yield over all somaclone in season j; ${\lambda }_1$ and ${\lambda }_2$ are the singular values for PC1 and PC2, respectively; ${\zeta }_{i1}$ and ${\zeta }_{i2}$ are the PC1 and PC2 scores, respectively, for somaclone i; ${\eta }_{j1}$ and ${\eta }_{j2}$ are the PC1 and PC2 scores, respectively, for season j; ${\epsilon }_{ij}$ is the residual of the model associated with the somaclone i in season j.

The sustainability index (SI) was estimated by the following formula used by [57]:

$$SI=\left[\frac{\left(Y-\mathsf{\sigma }\mathrm{n}\right)}{YM}\right]\times 100$$

(20)

where Y is the mean yield performance of a rice genotype, σn is the standard deviation, and YM is the best yield performance of a rice genotype in any environment. The SI values were classified arbitrarily into five groups, i.e., very low (up to 20%), low (21% to 40%), moderate (41% to 60%), high (61% to 80%), and very high (above 80%) [58]. SI was calculated using ms. Excel 2013. The best rice genotypes were obtained based on the slices of all measurements. The selected rice genotypes were considered to have stable and high yields in all growing environments.

3. Results

3.1. Combined Analysis of Variance (ANOVA) on Fe-Tolerant Rice Yields in Six Environments

The results of the combined ANOVA of Fe-tolerant rice in six environments are presented in

Table 3. Combined ANOVA of new promising Fe-tolerant rice genotypes in six environments.

Source	df	SS	MS	F		Contribution
Total	179	649.05	3.63
Treatments	89	450.07	5.06	3.49	**
Genotypes (G)	14	59.85	4.28	2.95	**	13.30%
Environments (E)	5	161.02	32.20	2.50	*	35.78%
Block	6	77.33	12.89	8.90	**
Interactions (GEIs)	70	229.18	3.27	2.26	**	50.92%
IPCA	18	130.77	7.27	5.02	**
IPCA	16	53.98	3.37	2.33	*
Residuals	36	44.4	1.235	0.85
Error	84	121.7	1.448
Mean (t·ha−1)	4.41
CV (%)	27.28

df = Degree of freedom; SS = sum of square; MS = mean of square; CV = coefficient of variation; * p < 0.05; ** p < 0.01.

. The genotypes, environments, and their interactions showed a significant effect on yield variation with contributions of 13.30%, 35.78%, and 50.92%, respectively. The large influence of the environment and the interactions indicated a very large effect of the environment on the variation in yields. Yields were in the range of 0.27–14.52 t·ha⁻¹, where the average yields were highest in Riau and lowest in West Papua. The resulting CV value is also high, namely 27.28% (Table 3), which indicates that external factors, including the environment, highly influence the resulting data. Therefore, further analysis was needed to express GEIs in selecting superior genotypes.

3.2. Parametric and Non-Parametric Stability Measurements on Rice Yields

The average yields and parametric stability measurements of the rice genotypes are shown in

Table 4. The stability analysis of 15 Fe-tolerant rice genotypes in Indonesia using parametric and non-parametric measurements.

Genotype	Y	S(1)	S(2)	S(3)	S(6)	NP(1)	NP(2)	NP(3)	NP(4)	KR	Wi2	σ2i	s2di	bi	CVi	θ(i)	θi	Di	ASV	GSI
G1	3.99	5.93	25.77	20.89	3.78	2.67	0.81	0.61	0.96	21	6.23	1.31	0.89	0.99	37.96	1.66	1.55	3.41	0.89	19
G2	3.62	4.00	10.67	9.41	2.59	2.67	0.56	0.57	0.71	17	1.75	0.28	0.13	0.61	21.18	1.73	1.07	3.13	0.08	16
G3	3.82	4.93	16.27	14.35	3.18	3.50	0.73	0.68	0.87	18	3.17	0.61	0.45	0.97	33.63	1.71	1.22	2.51	0.45	18
G4	4.93	2.93	5.87	2.59	1.06	2.17	0.36	0.27	0.26	5	2.68	0.49	0.34	0.77	21.54	1.72	1.17	2.92	0.20	5
G5	4.64	4.87	16.70	8.79	2.11	3.50	0.29	0.43	0.51	13	5.05	1.04	0.71	1.10	32.78	1.68	1.42	2.79	0.92	14
G6	4.41	6.93	32.00	20.00	3.25	4.50	0.58	0.63	0.87	19	6.85	1.45	0.54	0.24	20.41	1.65	1.61	3.22	1.14	18
G7	6.05	4.87	16.30	7.76	1.81	4.00	0.76	0.49	0.46	16	41.70	9.50	5.94	0.87	49.98	1.08	5.35	3.02	3.18	16
G8	4.66	5.93	26.17	13.31	2.37	3.00	0.33	0.43	0.60	17	7.99	1.72	1.14	0.93	34.02	1.63	1.74	6.85	1.49	17
G9	4.40	4.80	15.07	9.83	2.35	3.83	0.38	0.59	0.63	17	6.13	1.29	0.87	0.88	32.50	1.66	1.54	3.65	1.10	18
G10	4.31	6.07	27.10	20.85	4.15	4.67	0.90	0.74	0.93	20	6.35	1.34	0.90	0.95	34.66	1.66	1.56	3.38	1.23	21
G11	3.82	2.93	6.00	5.00	1.67	2.17	0.44	0.43	0.49	14	0.74	0.04	0.11	0.99	28.59	1.75	0.96	3.42	0.18	15
G12	4.86	7.40	38.97	21.25	3.60	5.83	0.55	0.65	0.81	17	12.08	2.66	1.20	1.83	47.24	1.56	2.18	2.47	1.61	17
G13	3.96	5.53	21.10	16.23	3.38	3.67	0.73	0.68	0.85	19	4.99	1.03	0.42	1.62	46.60	1.68	1.42	3.71	0.80	18
G14	4.44	3.40	8.57	5.24	1.59	2.17	0.24	0.37	0.42	11	3.95	0.78	0.56	0.95	29.85	1.70	1.30	2.88	0.88	13
G15	4.28	4.00	11.47	7.48	2.17	3.67	0.30	0.55	0.52	16	4.90	1.01	0.63	1.30	38.34	1.68	1.41	3.05	0.74	15

Y = Yield. For genotype codes, see Table 1.

. The average yields of the rice genotypes were in the range of 3.62–6.05 t/ha. Eight genotypes were identified that had higher yields than the overall average value (>4.18 t·ha⁻¹), with G7 being the highest. Seven other genotypes were identified as having below-average yields, with G2 being the lowest. Genotype stability based on regression measurements by Eberhart and Russell (1996) [27] was determined by the regression coefficient, (bi) = 1, and the deviation of variance (S²d_i) being low (close to zero). Genotypes G11, G1, and G3 had bi values close to 1, but all three had lower yields than the average overall yield. Therefore, these three are less adapted to a range of environments. The genotypes G5, G12, G13, and G15 (bi > 1) had a low level of stability, indicating that they were adapted specifically to certain environments and produced high yields in certain environments. Genotype G2 has a value of bi < 1, and the average yield is lower than the overall average yield. This indicates that the genotype has a low and unstable yield in all test environments. Based on S²di measurements, genotype G11 had the lowest score, followed by genotypes G2 and G4; therefore, these three genotypes were considered the most stable according to this measurement. However, only G4 had an average yield higher than the overall average, so G4 was considered the most ideal genotype according to this measurement. Based on the stability variant parametric model of Francis and Kannenberg (CVi), the genotypes G6, G2, and G4 were classified as highly stable genotypes. Plaisted and Peterson’s mean variance component (θ_i) defined G7, G12, and G8 as the most stable genotypes. Three other parametric stability models (Wricke ecovalence (Wi²), Shukla stability variant (σ²_i), and GE Plaisted component variant (θ_(i)) showed that G11, G2, and G4 were the most stable genotypes. The Di measurement showed that G12 is the most stable, followed by G2 and G5. ASV measurements chose G2 as the most stable, followed by G11 and G4. While the GSI measurement chose G4 as the most stable, followed by G14 and G5.

The estimation of stability using non-parametric measurements was also presented in Table 4. Almost all non-parametric stability measurements chose G4 as the most stable genotype, except for NP⁽²⁾, which chose G14 as the most stable. On the other hand, S⁽¹⁾, S⁽²⁾, S⁽³⁾, and NP⁽¹⁾ measurements identified G12 as the most unstable genotype. S⁽⁶⁾, NP⁽²⁾, and NP⁽³⁾ measurements identified G10 as the most unstable genotype, while NP⁽⁴⁾ and KR measurements identified G1 as the most unstable genotype.

Table 5. Rank of stability for 15 Fe-tolerant rice genotypes in Indonesia based on parametric and non-parametric measurements.

Genotype	Y	S(1)	S(2)	S(3)	S(6)	NP(1)	NP(2)	NP(3)	NP(4)	KR	Wi2	σ2i	s2di	bi	CVi	θ(i)	θi	Di	ASV	GSI	SR	AR	SD
G1	11	11	11	14	14	4	14	10	15	15	10	10	11	2	11	10	6	11	8	14	212	10.60	3.41
G2	15	4	4	7	9	4	9	8	9	7	2	2	2	12	2	2	14	8	1	6	127	6.35	4.08
G3	14	9	7	10	10	7	11	13	13	11	4	4	5	3	8	4	12	2	4	10	161	8.05	3.67
G4	2	1	1	1	1	1	5	1	1	1	3	3	3	10	3	3	13	5	3	1	62	3.10	3.11
G5	5	7	9	6	5	7	2	5	5	3	8	8	9	7	7	8	8	3	9	3	124	6.20	2.16
G6	7	14	14	12	11	13	10	11	12	12	12	12	6	14	1	12	4	9	11	11	208	10.40	3.35
G7	1	7	8	5	4	12	13	6	3	5	15	15	15	9	15	15	1	6	15	7	177	8.85	4.94
G8	4	11	12	9	8	6	4	3	7	7	13	13	13	6	9	13	3	15	13	8	177	8.85	3.73
G9	8	6	6	8	7	11	6	9	8	7	9	9	10	8	6	9	7	13	10	12	169	8.45	1.96
G10	9	13	13	13	15	14	15	15	14	14	11	11	12	5	10	11	5	10	12	15	237	11.85	2.90
G11	13	1	2	2	3	1	7	4	4	4	1	1	1	1	4	1	15	12	2	4	83	4.15	4.19
G12	3	15	15	15	13	15	8	12	10	7	14	14	14	15	14	14	2	1	14	9	224	11.20	4.55
G13	12	10	10	11	12	9	11	14	11	12	7	7	4	13	13	7	9	14	6	13	205	10.25	2.77
G14	6	3	3	3	2	1	1	2	2	2	5	5	7	4	5	5	11	4	7	2	80	4.00	2.41
G15	10	4	5	4	6	9	3	7	6	5	6	6	8	11	12	6	10	7	5	5	135	6.75	2.43

Y = Yield; SR = sum of rank; AR = average rank; SD = standard deviation. For genotype codes, see Table 1.

provides information on the sum of ranks (SR), the average rank (AR), and the standard deviation of the stability ranks (SD) for each genotype based on all parametric and non-parametric measurements. Based on Table 5, the G4 genotype has the smallest average rank (AR); hence, it is the most stable genotype. Meanwhile, G10 has the largest AR value; it is the most unstable, or the least adaptable, genotype in certain environments.

To classify superior rice genotypes, cluster analysis (dendrogram) was used based on the stability rank of each measurement. The dendrogram in this analysis divided the rice genotypes into two main groups (Figure 1). The first group is the stable genotype group and is divided into two sub-clusters: (1) the sub-cluster that has a high average yield (above the overall average yield) and a low average stability rank, consisting of genotypes G4, G5, G14, and G15; (2) a sub-cluster that has a yield lower than the overall average but has a low average stability rank (stable low grain yield), consisting of genotypes G2 and G11. The second group is the unstable group and is also divided into two sub-clusters: (1) the sub-cluster that has yields above the overall average and high average stability rank (unstable high grain yield), which consists of genotypes G7, G8, G9, and G12; (2) sub-clusters with yields below the overall average and relatively high average rankings (unstable low grain yield), consisting of genotypes G1, G3, G6, G10, and G13.

3.3. The Relationship between Parametric and Non-Parametric Stability Measurements with Rice Yields

The relationship between yield and stability measurements, as well as between each stability measurement was indicated by the value marked in bold (

Table 6. Spearman correlation rank of parametric and non-parametric stability measurements.

	Y	S(1)	S(2)	S(3)	S(6)	NP(1)	NP(2)	NP(3)	NP(4)	KR	Wi2	σ2i	s2di	bi	CVi	θ(i)	θi	Di	ASV
S(1)	−0.13
S(2)	−0.20	0.99
S(3)	0.14	0.93	0.89
S(6)	0.34	0.85	0.79	0.96
NP(1)	−0.23	0.72	0.74	0.63	0.58
NP(2)	0.29	0.52	0.44	0.61	0.68	0.41
NP(3)	0.43	0.69	0.63	0.82	0.88	0.69	0.73
NP(4)	0.50	0.75	0.67	0.90	0.95	0.45	0.70	0.88
KR	0.43	0.76	0.69	0.88	0.94	0.48	0.77	0.85	0.96
Wi2	−0.60	0.77	0.82	0.59	0.43	0.73	0.30	0.29	0.27	0.38
σ2i	−0.60	0.77	0.82	0.59	0.43	0.73	0.30	0.29	0.27	0.38	1.00
s2di	−0.59	0.58	0.63	0.44	0.30	0.59	0.16	0.15	0.15	0.21	0.90	0.90
bi	−0.26	0.27	0.29	0.20	0.17	0.52	−0.03	0.23	0.01	0.04	0.28	0.28	0.04
Cvi	−0.21	0.41	0.44	0.37	0.35	0.49	0.32	0.36	0.19	0.25	0.56	0.56	0.67	0.09
θ(i)	−0.60	0.77	0.82	0.59	0.43	0.73	0.30	0.29	0.27	0.38	1.00	1.00	0.90	0.28	0.56
θi	0.60	−0.77	−0.82	−0.59	−0.43	−0.73	−0.30	−0.29	−0.27	−0.38	−1.00	−1.00	−0.90	−0.28	−0.56	−1.00
Di	0.28	0.07	0.10	0.12	0.20	−0.07	0.19	0.07	0.21	0.40	0.07	0.07	−0.06	−0.14	−0.04	0.07	−0.07
ASV	−0.66	0.69	0.75	0.49	0.31	0.70	0.19	0.20	0.15	0.25	0.97	0.97	0.91	0.19	0.51	0.97	−0.97	0.02
GSI	0.30	0.74	0.69	0.85	0.88	0.59	0.76	0.85	0.89	0.95	0.48	0.48	0.35	0.03	0.36	0.48	−0.48	0.45	0.39

The value in bold print indicate a significant correlation.

). The coefficient of Spearman’s correlation rank revealed that the average yield has a positive and significant correlation with NP⁽⁴⁾ and θ_i and that it is significantly and negatively correlated with W_i², σ²_i, s²d_i, θ_(i), and ASV (Table 6). In addition, Table 6 also presents information regarding the relationship between each stability measurement. Measures that have a positive and significant correlation indicate that they have equal power in selecting stable genotypes. However, if they have a significant and negative correlation coefficient, then they have the opposite power when choosing a stable genotype.

The relationship between the various stability measurements was determined using principal component analysis (PCA), which also combined them into distinct groups. The first three PCs with an eigenvalue > 1 produce a cumulative value of 85.783% of the total variation between parametric and non-parametric measurements (

Table 7. Eigenvalue, percent, and cumulative value of stability measurements.

PC	1	2	3
Eigenvalue	11.040	4.742	1.375
Percent (%)	55.201	23.709	6.873
Cumulative (%)	55.201	78.910	85.783

PC = Principal component.

). The first two components are used to visualize the PCA biplot because they have the highest variability values (PC1 = 55.20% and PC2 = 23.71%), as shown in Figure 2. Parametric and non-parametric measurements are grouped into five main groups, namely the first group consists of Di, NP⁽²⁾, NP⁽³⁾, NP⁽⁴⁾, S⁽³⁾, S⁽⁶⁾, KR, and GSI; the second group consists of S⁽¹⁾, S⁽²⁾, NP⁽¹⁾, CVi, and bi; the third group consists of s²d_i, θ_(i), Wi², σ²_i, and ASV measurements; the fourth group consists of yield (Y); and the fifth group consists of θ_i.

3.4. Fe-Tolerant Rice Yield Stability Based on AMMI Analysis

A visualization of rice yield stability using AMMI analysis was presented in Figure 3. PC1 and PC2 show a total contribution of 80.7% to the variation in yield. This number is high enough to represent the yield variance across all genotypes examined. This means that the level of accuracy of the resulting data is good enough to assess the genotypes tested in six environments. Based on Figure 3, Lampung has the longest environment vector. This shows that Lampung is a representative environment in selecting superior genotypes and has a large influence on GEIs. Meanwhile, Banjarbaru and West Papua have the shortest environmental vectors, indicating that they have a small effect on GEIs and do not represent the actual yield. In the AMMI biplot, five rice genotypes were identified that were close to the axis (0.0) and within the radius of the circle. They were G2, G3, G4, G11, and G15. This shows that the five of them have stable yields in the six test environments. Other genotypes identified as adaptive to specific environments, namely G7 and G10 in Lampung; G5, G12, and G13 in Blandean; G14 in Riau; G8 and G9 in West Papua; and G1 and G6 in Bogor.

3.5. Mega-Environments, Representative Location, and Yield Stability Based on GGE Biplot

The results of GGE biplot analysis on 15 genotypes of Fe-tolerant rice showed that PC1 and PC2 contributed 54.2% and 19.1% of the total yield variation, respectively (Figure 4, Figure 5 and Figure 6). According to the ‘representative versus discriminative’ display of the GGE biplot (Figure 4), the test environments can be classified into three types, namely the type I environment has a short vector and provides little information about the genotype being tested, so it should not be used as a test environment. The type II environment has a long and small angle vector with an average abscissa, making it ideal for selecting superior genotypes. Type III environments have long and large angle vectors with abscissa mean environments, so they cannot be used to select ideal genotypes but are useful for selecting unstable genotypes (adapt-specific) [59,60].

The results of research on rice populations are presented in Figure 4, indicating that the West Papua, Riau, and Blandean environments were Type I environments and should not be used as test environments. Lampung is an ideal environment (Type II) to select superior genotypes because of its high discriminatory and representativeness and has a small angle with the abscissa. The Banjarbaru and Bogor environments were Type III environments and could not be used to select superior genotypes but could be used to determine adaptive or region-specific genotypes.

The ‘mean vs. stability” biplot is presented in Figure 5. The Y-axis shows the average yield of each genotype, and the X-axis shows the yield stability for each genotype tested. In this study, the genotypes to the left of the Y-axis had higher yields than the average overall yield. In contrast, the genotypes to the right of the Y-axis had lower yields than the average overall yield. If the genotype is close to the X-axis, then the genotype is stable and vice versa [56]. The measurement results showed that five genotypes had yields above the overall average yield: G4, G6, G7, G10, and G12. In contrast, the other ten genotypes had yields below the overall average yield. G4 tends to be stable and has high yields because it is close to the X-axis and is to the left of the Y-axis. G7 has the highest average yield (6.05 t·ha⁻¹), which was indicated by its farthest position from the Y-axis. G13 is the genotype that has the worst yields in all environments.

The ‘which wins where’ pattern shows that the six environments have five sectors with different peak genotypes (Figure 6). There are two sectors that consist of more than one environment to form a mega-environment. The first mega-environment is in Sector I, consisting of Lampung and Banjar Baru environments, with G7 as the peak genotype. The second mega-environment is in the second sector, which consists of the Bogor and West Papua environments, with G6 as the peak genotype. In the third sector, G8 is the peak genotype, but there is no environment in this sector. In sector four, there is the Riau environment with G13 as the peak genotype. Sector Five has a Blandean environment with G12 as the peak genotype. In this study, G1, G3, G4, G5, and G14 tend to be close to the central axis, which indicates that they have a small (stable) GEI effect.

3.6. Yield Stability Based on Sustainability Index (SI)

An evaluation of the Fe-tolerant rice yield stability based on the sustainability index (SI) was presented in

Table 8. The result of the sustainability index (SI) analysis on 15 Fe-tolerant rice genotypes in Indonesia.

Genotypes	Y	Σn	YM	SI (%)
G1	3.99	1.38	6.15	42.40	Moderate
G2	3.62	0.70	4.59	63.58	High
G3	3.82	1.17	5.39	49.13	Moderate
G4	4.92	0.97	5.99	66.11	High
G5	4.64	1.39	6.71	48.37	Moderate
G6	4.41	0.82	5.92	60.65	High
G7	6.04	2.76	11.83	27.78	Low
G8	4.66	1.45	6.98	46.05	Moderate
G9	4.40	1.31	6.31	49.04	Moderate
G10	4.30	1.36	6.18	47.59	Moderate
G11	3.82	1.00	5.79	48.85	Moderate
G12	4.86	2.10	7.38	37.46	Low
G13	3.96	1.69	6.85	33.19	Low
G14	4.44	1.21	6.51	49.57	Moderate
G15	4.28	1.50	6.51	42.73	Moderate

Y = Yield; Σn = standard deviation; YM = yield maximum.

. In this study, the SI criteria obtained were divided into three groups, namely low, medium, and high (Table 8). SI estimates for rice yields range from 27.78% (low) to 66.11% (high). SI in the high category was indicated by G2, G4, and G6, but only G4 and G6 had yields above the overall average yield (4.18 t·ha⁻¹), so these two genotypes are included in the selected category. There are nine rice genotypes that have a medium SI (40–60%) (Table 8). They were G1, G3, G5, G8, G9, G10, G11, G14, and G15; however, only three genotypes had yields above the overall average yield (>4.18 t·ha⁻¹), namely G5, G8, and G14 (Table 8). They belong to the ideal group because they have high yields and are stable in six different environments. The SI with a low category (20–40%) is shown by G7, G12, and G13 (Table 8). Low SI values indicate unstable yields for the three genotypes, whereas G7 and G12 have average yields above the overall average yield, which indicates that both are adapted to a representative environment.

To select superior (stable and high yielding) rice genotypes, slices were taken from all measurements used. Information on selected genotypes is presented in

Table 9. Selected superior rice genotypes based on stability measurements.

Measurements	Selected Mutants	Percent (%)
AMMI	G2, G3, G4, G11, G15	33.33
GGE biplot	G4, G6, G7, G10, G12	33.33
Combined stability (parametric and non-parametric)	G4, G5, G14, G15	26.67
Sustainability index (SI)	G4, G5, G6, G8, G14	33.33
Slice	G4	6.67

. AMMI, GGE biplot, and the SI each succeeded in selecting stable genotypes by 33.33%, while combined stability (parametric and non-parametric) succeeded in selecting 26.67%. However, only one genotype was selected based on all measurements (6.67%), namely G4. Thus, G4 is highly recommended to be used as a new superior rice variety that is stable and has a high yield.

4. Discussion

Genotype, environmental, and GEI factors showed a significant effect on Fe-tolerant rice yields. GEIs (50.92%) contributed more, followed by environment (35.78%) and genotype (13.30%). This indicates that the variation in rice yields tested in six different environments was dominantly influenced by external effects, in this case, the environment. The emergence of GEIs in multi-location testing makes plant breeding programs difficult, especially in selecting ideal genotypes [7]. Several studies have reported that GEIs significantly affect rice yields [6,61,62]. In other studies, GEIs also have a significant effect on crop yields, such as maize [13,40,41], sweet potatoes [7], butterfly pea [42], and soybean [18,19]. The large contribution of GEIs also indicates a high environmental effect, where the six test environments have different conditions. Environmental differences can be seen in the type of agro-climate and altitude (Table 2). In addition, the resulting CV also shows a value of 27.28%. This value was included in the high criteria (>20%). The high CV value was caused by various factors, one of which is the environment [14]. Therefore, highly significant GEIs for rice yields justify using parametric, non-parametric, AMMI, GGE biplot, and sustainability index (SI) stability measures to represent GEIs against tested genotypes and estimate the yield stability of rice genotypes that are evaluated.

In plant breeding programs, the presence of GEIs complicates the plant selection process. This situation indicates that the selection of rice genotypes based on yields must be carried out in certain environments, resulting in inefficient breeding programs [13]. In addition, the appearance of GEIs indicates that the tested rice genotypes have different potential when planted in different locations [7], so the development program must be adjusted based on a representative environment. The influence of GEIs also causes sub-optimal genotypic potential under different environmental conditions [47]. However, the presence of GEIs can also provide an opportunity to select rice genotypes that have high yields in certain environments (adapt-specific). These conditions indicate that the selection of appropriate rice genotypes must be carried out in each environment. This is very interesting because Indonesia has very varied land requirements, so the use of specific (adaptive) genotypes will greatly assist the development of certain areas in terms of rice production. Therefore, plant breeding activities must be directed according to the appropriate environmental conditions so that the plant varieties developed are able to adapt well to various environments.

In the process of selecting high yielding varieties that are stable in a wide range of environments, various methods have been proposed. The use of a single stability measure is still considered difficult for determining stable and high yielding genotypes [7,13,26], so another selection model was needed to obtain the ideal genotype. Several studies have reported the selection of stable genotypes and high yields by applying a combination of stability models, including grass peas [45], barley [26], soybeans [18,19], turmeric [22], and maize hybrid [13,40]. In this study, parametric and non-parametric stability models, AMMI, GGE biplot, and the sustainability index (SI) were applied to identify stable and high-yielding Fe-tolerant rice genotypes in six different environments. The average rank (AR) values of all stability models (parametric and non-parametric) were used to select high-yielding and stable rice genotypes (with low AR values). This was also expressed by Vaezi et al. (2019) [26]. Genotypes G4 and G14 had the lowest AR values, indicating a high level of stability and production (above the average overall yield), as shown in Table 5.

A grouping of Fe-tolerant rice genotypes using a dendrogram based on stability rating was used to confirm these results. The dendrogram was developed based on ranking the average yield of all parametric and non-parametric measurements. The resulting dendrogram divides the Fe-tolerant rice genotypes into two main clusters (Figure 1): stable and unstable. Each main cluster was divided into two sub-clusters. The stable high-grain-yield sub-cluster consists of genotypes G4, G5, G14, and G15. This group is an ideal group because the genotypes are able to adapt to a wide range of environments and have high yields. This is followed by the stable low-grain-yield sub-cluster, which consists of genotypes G2 and G11. The next sub-cluster is the unstable high grain yield, which contains the genotypes G7, G8, G9, and G12. This group is a group that can be recommended as a genotype with a specific adaptation because the genotypes in this group will have high production in a representative environment [7]. Finally, the unstable low grain yield group consists of genotypes G1, G3, G6, G10, and G13. This group is the worst and is not recommended for development on a large scale. This was also conveyed by Ruswandi et al. (2022) [47], where genotypes that were in the stable high-grain-yield group were more desirable, and, conversely, genotypes that were in the unstable low-grain-yield group were not expected and were not used for the development of superior varieties.

The results of Spearman’s rank correlation analysis revealed that the stability measures NP⁽⁴⁾ and θ_i were clearly related to the average yield (Y), indicating that these two were included in the category of dynamic stability measures. Stability measures that are positively correlated with yields can be used to recommend genotypes in a specific environment (adapt) [63]. Both of these measurements are useful for selecting Fe-tolerant rice genotypes with high average yields in an environment with good growing conditions (representative). In contrast, stability measures were significantly and negatively correlated with crop yields, indicating them to be a static stability term that can be used to select genotypes in unfavorable environments [26]. W_i² with σ²_i, s²d_i, θ_(i), and ASV measurements have a negative and significant correlation with yield (Table 6), so they are included in the concept of static stability. Stability measurements that have positive and significant correlations indicate that they have a strong strength in selecting stable genotypes [7]. However, if they have significant and negative correlation coefficients, then they have the opposite power in choosing a stable genotype. For example, in this study, S⁽¹⁾ has almost the same power as S⁽²⁾, S⁽³⁾, S⁽⁶⁾, NP⁽¹⁾, NP⁽²⁾, NP⁽³⁾, NP⁽⁴⁾, KR, Wi², σ²_i, s²d_i, θ_(i), ASV, and GSI. In addition, there is also a measure of stability that has the same power in selecting stable genotypes (correlation coefficient = 1.00), namely Wi² with σ²_i and θ_(i). In a graphical visualization based on the PCA biplot, the three are also in the same group (Figure 2), so one can use one of them to select a stable genotype [13,19]. The PCA’s visualization of stability measurements divides them into five groups. The first group consists of Di, NP⁽²⁾, NP⁽³⁾, NP⁽⁴⁾, S⁽³⁾, S⁽⁶⁾, KR, and GSI; the second group consists of S⁽¹⁾, S⁽²⁾, NP⁽¹⁾, CVi, and bi; the third group consists of s²d_i, θ_(i), Wi², σ²_i, and ASV measurements; the fourth group consists of yield (Y); and the fifth group consists of θ_i. The first three groups and the fifth group represent the concept of static stability. According to Vaezi et al. 2019 [26], the concept of stability is divided into two, i.e., the concept of static and dynamic stability. The concept of static stability can be used to select genotypes under unfavorable environmental conditions. Conversely, the concept of dynamic stability can be used to recommend genotypes in favorable environments [40]. Thus, both parametric and non-parametric measurements provide recommendations for selecting rice in unfavorable environments.

To select stable and high yielding genotypes, graphical visualization is essential. In this study, two graphical measurements were used, namely AMMI and GGE biplots. The AMMI biplot presented in Figure 3 shows that PC1 contributed 57.1% to diversity and 23.6% to PC2. The large contribution of PC1 to yield diversity implies that the interaction of rice genotypes with the six growing environments in Indonesia was predicted by the first PC from genotype and environment. Several researchers also revealed the same thing, where the PC1 value plays an important role in the diversity of yields in the AMMI biplot [21,42,64]. In the AMMI biplot, genotypes that are close to the biplot axis are stable and have low GEIs [37]. In this study, five Fe-tolerant rice genotypes were identified that were close to the axis (0.0) and within the radius of the circle. They were G2, G3, G4, G11, and G15. This shows that the five of them have stable yields in the six test environments. Other genotypes identified as adaptive to specific environments, namely G7 and G10 in Lampung; G5, G12, and G13 in Blandean; G14 in Riau; G8 and G9 in West Papua; and G1 and G6 in Bogor. Thus, the identified genotypes can be developed according to their position in relation to their environment. Based on Figure 3, Lampung has the longest environmental vector. This shows that Lampung is a representative environment in selecting superior genotypes and has a large influence on GEIs. This is in line with the results of the GGE biplot analysis, where Lampung is included in environmental type II, which means it is very representative for testing [13]. Meanwhile, Banjar Baru and West Papua have the shortest environmental vectors in the AMMI and GGE biplots and were included as a Type I environment, which indicates that both have a small effect on GEIs and do not represent the actual yields.

In the GGE biplot, the ‘representative versus discriminative’ display (Figure 4) shows that the West Papua, Riau, and Blandean environments are Type I environments, so they should not be used as test environments. Among the six test environments, Lampung is a Type II environment that has selective influence and high representativeness; hence, Lampung is an ideal location to select superior genotypes (Figure 4) [7]. The Banjar Baru and Bogor environments are Type III environments and should not be used to select superior genotypes but can be used to select adaptive or region-specific genotypes [60]. The ‘mean vs. stability’ biplot display shows that five genotypes have yields above the overall average, including G4, G6, G7, G10, and G12 (Figure 5), while the other ten genotypes had yields below the overall average yield. G4 tends to be stable and has high yields because it is close to the X-axis and to the left of the Y-axis [60]. G7 has the highest average yield (6.05 t·ha⁻¹), which is indicated by its farthest position from the Y-axis. On the other hand, G13 is the genotype that has the worst yield in all environments, so this genotype is not recommended for large-scale development.

The ‘which won where’ display shows that the six environments have five sectors with different peak genotypes (Figure 6). Several researchers revealed that this biplot could indicate the existence of a mega-environment [7,40,48]. There are two sectors that consist of more than one environment so as to form a mega-environment. The first mega-environment is in sector I, which consists of Lampung and Banjar Baru, with G7 as the peak genotype. The second mega-environment is in the second sector, consisting of Bogor and West Papua, with G6 as the peak genotype. These results indicate that there were various environmental groupings during the trials. The first PC explained 54.2% of the total variation due to environmental effects (E) and GEIs during the experiment (Figure 4, Figure 5 and Figure 6). The grouping of environments and mega-environments in various regions in Indonesia with different peak genotypes indicates a genotype-specific adaptation to the mega-environment and the positive utilization of GEIs [7,10,19]. Our findings reveal that several Fe-tolerant rice genotypes have adapted to different environments in Indonesia. This will facilitate the selection process for wider development. In the third sector, G8 is the peak genotype but there is no environment. In sector four, there is the Riau environment with G13 as the peak genotype. Sector five has a Blandean environment with G12 as the peak genotype. Genotypes that are at the top of each sector indicate that these genotypes have high yields in the environment in that sector [20,21]. Genotypes that are in a sector containing more than one environment or mega-environment show the ideal genotype [19,40,65]. Conversely, genotypes at the top of the sector but that do not have an environment show low yields [7]. Therefore, the genotypes in this sector are not recommended for further development.

The evaluation of the yield stability of Fe-tolerant rice based on the sustainability index (SI) divided the genotypes into three groups, namely low, medium, and high (Table 8). SI estimates for rice yields range from 27.78% (low) to 66.11% (high). Genotypes with high and very high SI categories are expected [39,41,42]. Our results show that the genotypes with the highest SI category were shown by G2, G4, and G6, but only G4 and G6 had yields above the overall average yield (4.18 t·ha⁻¹), so these two genotypes are included in the selected category. In addition, in another study, Filio et al. (2023) revealed that genotypes with medium SI criteria and that had high average yields were included in the ideal category. Nine rice genotypes were in the medium SI category (40–60%) (Table 8), including G1, G3, G5, G8, G9, G10, G11, G14, and G15; however, only genotypes G5, G8, and G14 have a yield above the average overall yield (>4.18 t·ha⁻¹). Genotypes with low SI values indicate unstable yields for these three genotypes, so they are not recommended for further development [41,42].

To select superior (stable and high-yielding) rice genotypes, slices were taken from all measurements used. This has also been carried out by several researchers, including grass peas [45], sweet potatoes [7,66], soybeans [17,18], and maize [13,40,41]. The information on selected genotypes presented in Table 9 shows that AMMI, GGE biplot, and the SI each selected stable genotypes by 33.33%. In comparison, the combined stability (parametric and non-parametric) succeeded in selecting 26.67%. However, only one genotype was determined based on all measurements (6.67%), namely G4. Therefore, G4 is highly recommended to be used as a new superior, stable rice variety with a high yield.

5. Conclusions

The measurement results showed that the genotypes, environments, and GEIs significantly influenced Fe-tolerant rice yields with contributions of 13.30%, 35.78%, and 50.92%, respectively. Based on all measurements, G4 (B14316E-KA-4) was selected as a superior (stable and high yield) Fe-tolerant rice genotype. In this experiment, two mega-environments (MEs) were generated, i.e., Lampung and Banjar Baru and Bogor and West Papua. Lampung was identified as a representative environment for the development of superior genotypes based on AMMI and GGE biplots. The results of this study can be used as a consideration in the release and development of new superior varieties of Fe-tolerant rice in Indonesia.