Additive main effects and multiplicative interaction for grain yield of rice (Oryza sativa) genotypes for general and specific adaptation to salt stress locations

Introduction

Soil health degradation has a direct negative impact on agricultural production across the globe. The GSASmap (Global Salt Affected Soil map) reported that more than 424 million ha of topsoil (0–30 cm) and 833 million ha of subsoil (30–100 cm) are salt-affected (FAO and ITPS 2015). The rising problem of salt stress is a serious threat to the production in salt-sensitive crops like rice (Oryza sativa). Approximately one-third of the irrigated rice-growing areas encounter salinity issues. A recent study shows that each day around 2000 ha of cultivable land are losing their productivity due to salinization (Shahid et al. 2018). The ICAR-Central Soil Salinity Research Institute (CSSRI) has categorized 6.7 million ha (Mha) in India as salt-affected, with 3.8 Mha classified as alkali and 2.9 Mha as saline, posing a severe threat to the livelihood security of the farming community. According to Sharma et al. (2015), salt-affected soils cause India to lose 16.84 million tonnes of crop output (including cereals, oilseeds, pulses, and cash crops) annually, resulting in estimated economic losses of Indian Rupee (INR)230 billion. Salinity causes osmotic stress in rice plants by disrupting their morphological and physiological balance, especially at the seedling and reproductive stage, which results in poor growth and reduced grain yield. Grain yield reductions range from 27% to 50% at an electrical conductivity (ECe) of 8 dS m⁻¹ across various rice cultivars (Mohammadi et al. 2013). It is estimated that for every increase of one unit in electrical conductivity (ECe) beyond the threshold of 4 dS m⁻¹, there is a 12% reduction in grain yield, and under extreme saline conditions, yields can plummet to zero, leading to plant death. Farm income declines with rising salt levels, with annual potential and actual losses per hectare reaching INR10,714 and INR7737, respectively, due to the adverse effects of salt. Therefore, continuous efforts are underway to tackle this issue using various approaches like soil reclamation and the adoption of more tolerant crop species. However, these methods face constraints due to economic factors associated with reclamation, nutritional requirements, and the marketability of alternative crops. The problem of salinity and alkalinity has been addressed through better management practices and by introducing salt-tolerant varieties that harvestable performance in soils with variable salt concentrations (Krishnamurthy et al. 2021). Globally, numerous salt-tolerant rice varieties have been developed and released for cultivation to address the challenges posed by saline soils. The pioneering variety, Pokkalli, was introduced in 1939 from Ceylon (now Sri Lanka), marking the beginning of efforts to breed rice capable of thriving in saline conditions. India and the Philippines have made significant contributions by developing several salt-tolerant rice varieties, including Kala Rata 1–24, Nona Bokra, Bhura Rata, SR 26B, Chin.13, and 349 Jhona. Additionally, Bangladesh, Thailand, Japan, the United States, South Korea, and Russia have each developed various salt-tolerant rice varieties (Qin et al. 2020). In India, the ICAR-Central Soil Salinity Research Institute (CSSRI) in Karnal has been exclusively focused on the development of salt-tolerant rice varieties. Their efforts have resulted in the release of approximately 13 such varieties including CSR 10, CSR 13, CSR 23, CSR 27, Basmati CSR 30, CSR 36, CSR 43, CSR 46, CSR 49, CSR 52, CSR 56, CSR 60, and CSR 76, which have significantly contributed to agricultural productivity in the country’s saline regions (Krishnamurthy et al. 2024).

Rice yield is a complex trait influenced by genotypes, environment, and the interaction of both. Hence, the evaluation of lines for grain yield across the different ranges of salt stress environments is crucial for the development of farmers’ accepted salt-tolerant varieties (Krishnamurthy et al. 2017). These kinds of trials are called multi-environmental trials (METs) and they help in quantifying Genotype × Environment interaction (GEI) with the help of various statistical methods (Sa’diyah and Hadi 2016). These trials are very informative as all the components of variability viz genotype, environment, and their interaction effect can be studied. In addition, GEI leads ranking of different genotypes across the environments (de Leon et al. 2016). Earlier biometricians explained GEI in a single dimension with the help of ANOVA and linear regression (Finlay and Wilkinson 1963; Eberhart and Russell 1966; Perkins and Jinks 1968). However, complex GEI occurs in nature, which can now be explained by biplot-based methods; namely, genotype main effect, genotype × environment (GGE) (Yan et al. 2000; Yan and Rajcan 2002), and Additive Main effects and Multiplicative Interactions (AMMI) (Gauch 1992).

AMMI analysis serves as a more accurate model to understand genotype-environment interactions. It combines the univariate technique of ANOVA with PCA-based multivariate analysis to find out GEI thereby significantly improving the probability of successful identification of stable genotypes. In the case of METs related to salt tolerance in rice, several researchers have successfully used AMMI analysis in pursuit of identifying stable salt-tolerant genotypes (Krishnamurthy et al. 2015, 2016a; Islam et al. 2016). In this study, the AMMI model was used to analyze the data generated from screening of 19 rice genotypes across nine salt-affected environments to identify stable rice genotypes for salt stress and to process the delineation of environments into mega-environments.

Materials and methods

Results

Predictive accuracy, model diagnosis, and AMMI analysis of variance

Yield data from two seasons across nine environmental conditions subjected to AMMI analyses through yield-stability statistics (Yge). In this study, available variability in grain yield was partitioned into various components using ANOVA of the AMMI model (Table 4). About 85.16% of the total variability among genotypes for grain yield explained the variations in the treatment, and the rest was an experimental error due to residual error. Total treatment variations were classified into three key causative components: (1) genotype (G); (2) environment (E); and (3) their interaction (GEI). All three components differed significantly at a probability level of P ≤ 0.001 and the maximum proportion variation was explained by environment (32%). Contribution from G and GEI accounted for 27% and 26% of the total treatment variation, respectively. The GEI component was further subdivided into seven Interaction Principal Components (IPC1–IPC7), the first four of which (IPC1–IPC4) were determined to be significant. A total of 93% of the GEI for grain yield was supplied by the first four IPCs, with the IPC1 (48%) making the largest contribution. The results of this model demonstrated that 80% of total treatment variations were due to GEI_S (GEI signal), whereas the remaining 20% was attributable to GEI_N (GEI noise). Components E and GEI_N account for approximately 44% of the variation in this data, which is inconsequential to a breeder. Only the remaining 57% variation, represented by G and GEIS, is meaningful from a practical point of view. Sum of squares of component G was 1.3 and 5.4 times larger than that of GEI_S and GEI_N, respectively. Results from model diagnosis through cross-validation identified the AMMI-4 model as having the smallest RMS PD, indicating the highest predictive accuracy for grain yield (Table 5). This model is closer to the true means compared to the raw data (AMMI-F model). The AMMI gain factor for grain yield was 1.3. To determine the best model for this data, both the FR-test (at P < 0.01) and Gollob’s F-test were employed, as AMMI analysis relies on family diagnosis rather than a single model. The only discrepancy between the two F-tests was that six IPCAs were identified as significant by Gollob’s F-test, while only four IPCAs were selected by the FR test. The results indicated that IPC1 and IPC2, representing AMMI families AMMI1 and AMMI2, respectively, accounted for 72% and 90% of the GEI_S variations. AMMI biplot1 was used to demonstrate the principal additive influence of genotypes and environment on the x-axis, as well as the multiplicative effect of GEI on the y-axis in terms of mean and IPC1 (Fig. 1). AMMI biplot2 was created by combining IPC1 and IPC2, and it may be used to identify genotypes or environments with low, medium, or large interaction effects (Fig. 2).

Table 4.ANOVA for grain yield in rice genotypes across saline and sodic condition (2017 and 2018).

Source of variance	d.f.	MSS	Gollob’s F-test	Proportion of variation
				Total variation (%)	Main and interaction variation (%)	GEI variation (%)	GEIS variation (%)
Treatment	170	4223251.1***		85.1
Genotype	18	12845039.6***			27.4
Environment	8	33751438.5***			32.0
Interaction (G × E)	144	1505072.7***			25.7
IPC1	25	4161852.7***	120.6***			48.0	59.9
IPC2	23	2257536.2***	65.4***			24.00	29.9
IPC3	21	1246629.2***	36.1***			12.1	15.1
IPC4	19	986072.5**	28.6***			8.6	10.8
IPC5	17	449794.1	13.0***			3.5	4.4
IPC6	15	442937.7	12.8***			3.1	0.00
IPC7	13	90468.9	2.6			0.5	0.00
Residual	11	34506.1				0.2	0.00
Error	342	365793.2		14.8
Blocks/Env	18	1573170.6***			3.4
Pure Error	324	298716.8			11.5
Total	512	1646589.8		100	100	100

MSS, Mean sum of squares; GEI, genotype × environment Interaction; GEI_s, genotype × environment Interaction of signal; IPC, interaction principal component tested based on F_R.

**P < 0.01; ***P < 0.001.

Table 5.AMMI model and root mean square predictive difference (RMS PD) of 19 rice genotypes in nine salt stress environments for grain yield.

Model	d.f.	RMS PD
AMMI1	25	751.5
AMMI2	23	735.6
AMMI3	21	734.9
AMMI4	19	722.2*
AMMI5	17	730.0
AMMIF	170	751.4

AMMI additive main effects and multiplicative interaction.

Fig. 1.

2D representation of 19 rice genotypes and nine salt stress environments presented in AMMI biplot1 with average yield (kg ha⁻¹) on the abscissa and interaction principal component 1 scores (IPC1) on the ordinate

Fig. 2.

The scattered distribution patterns of 19 rice genotypes and nine salt stress environments presented in AMMI biplot2 showing the interaction principal component 1 scores (IPC1) on the on the abscissa and interaction principal component 2 scores (IPC2) on the ordinate.

Delineation of mega-environments based on AMMI1

The AMMI1 model family with the highest GEIS and the least amount of GEIN gives a better understanding of the suitability of different genotypes in different environments. The nine settings in the current investigation were listed in decreasing order of their IPC1 value (Table 7). According to the AMMI1 model, the current study divided nine environments into two mega-environments: (1) Mega-envrionment I that contains six environments; and (2) Mega-environment II that contains just three habitats (Fig. 3). The environments with the highest IPC1 values (E9, E7, and E6) are defined in Mega-environment II, while the remaining six environments (E1, E2, E3, E4, E5, and E8) are grouped in Mega-environment I. According to the AMMI1 model, genotype RP 5989-2-4-8-15-139-62-6-9 (GN14) yielded the best in all six environments of Mega-environment I, whereas CSR 23 (CHK2) yielded the best in the three environments of Mega-environment II, followed by RP 5989-2-4-8-15-139-62-6-9 (GN14), which ranked second place in Mega-environment II. Three genotypes, CSR-2748-4441-195 (GN05), CSR-2748-4441-193 (GN11), and CSR 2711-17(GN01), placed third, fourth, and fifth in Mega-environment II. The raw data-based AMMIF algorithm identified seven mega-environments with seven ‘winning’ genotypes.

Table 7.A ranking table showing the top five genotypes according to AMMI1 and AMMIF model family for 19 rice genotypes under salt-affected conditions.

Mega-environment	Environment code	IPC1 score	Ratio	AMMI1 Ranks					AMMIF Ranks
				1	2	3	4	5	1	2	3	4	5
II	E09	31.61	1.010	CHK2	GN14	GN05	GN11	GN01	GN14	GN01	GN10	CHK2	GN05
	E07	30.25	1.006	CHK2	GN14	GN05	GN11	GN01	GN11	GN14	GN03	GN01	GN05
	E06	28.68	1.002	CHK2	GN14	GN05	GN11	GN01	GN03	GN01	GN11	GN05	GN14
I	E05	19.38	1.000	GN14	GN05	GN11	GN1	CHK2	GN10	GN11	GN05	GN14	CHK2
	E08	−5.06	1.000	GN14	GN05	GN11	GN03	GN01	GN12	GN10	CHK5	GN05	GN13
	E03	−25.62	1.000	GN14	GN10	GN11	GN05	GN03	GN14	GN11	GN10	GN01	GN03
	E04	−25.69	1.000	GN14	GN10	GN11	GN05	GN03	GN08	CHK3	GN07	GN14	GN12
	E01	−26.50	1.000	GN14	GN10	GN11	GN05	GN03	GN01	GN11	GN10	GN05	GN03
	E02	−27.06	1.000	GN14	GN10	GN11	GN05	GN03	GN03	GN01	GN05	GN10	GN11

Fig. 3.

AMMI1 mega-environment display for 19 rice genotypes evaluated under nine environments of saline and sodic condition. Environment means are shown on the abscissa and interaction principal component (IPC1) scores on the ordinate.

The primary purpose of all multi-environment experiments is to identify stable genotypes. In this experiment, the nominal yield of several genotypes was plotted against the environmental IPC1 score, indicating that RP 5989-2-4-8-15-139-62-6-9 (GN14), with an average grain production of 3353 kg ha⁻¹, demonstrated broad adaptability for all of the environments of mega-environment I (Fig. 4). The ratio of the grain yield of a ‘winner’ genotype in a particular environment to the yield of the overall ‘winner’ is used to identify genotypes with specific or general adaptability. In our experiment, CSR 23 (CHK2) with an average yield of 3008 kg ha⁻¹ yielded the best in all the environments of mega-environment II with yield ratios larger than one, indicating limited adaptation. The genotype CHK2 had a yield advantage of 3353 × 1.01 = 3386 kg ha⁻¹; i.e. 3386–3008 = 378 kg ha⁻¹ (13%) yield advantage over broad adaption under environment E09.

Fig. 4.

Adaptive responses for rice genotype according to AMMI1 model. Interaction principal component 1 (IPC1) scores for the nine environments are shown on the abscissa and nominal yields for the 19 genotypes on the ordinate.

Discussion

Utilizing waste and degraded land represents a viable strategy for increasing agricultural yield. Most waste and degraded soils result from the accumulation of salt in the upper soil layers, rendering them unsuitable for agricultural use. Consequently, it is crucial to develop cultivars capable of thriving under various conditions, including those involving degraded soils. GEI is a significant challenge for plant breeders (Lin and Binns 1988). Agricultural traits are frequently affected by external conditions throughout a plant’s life cycle (Kumar et al. 2015). To effectively evaluate genotype performance, it is crucial to test them in various environments. If genotypes are only assessed in one environment during early breeding stages, there is a risk of overlooking beneficial genetic variations that might perform better under different conditions. This limited testing approach can lead to the loss of valuable genes. Integrating GEI analysis into the breeding process can therefore improve genotype selection and enhance cultivation outcomes in specific target environments (Hassani et al. 2018).

Yield is a highly complex variable that is influenced by genetic and environmental factors as well as their interactions. Special statistical methods such as G main effect plus GGE and AMMI are necessary for the analysis of complicated environmental data that may draw valid inferences under variable environments. However, researchers prefer the latter strategy because of its ability to extract the signal component from noise (Gauch 2006; Yan et al. 2007; Gauch et al. 2008; Yang et al. 2009; Yan and Holland 2010). The main factor that makes the AMMI model more accurate than the GGE biplot analysis is the division of the treatment variation into G, E, and G × E components, followed by the application of singular value decomposition (SVD) to G × E. AMMI-based analysis is also better than linear regression model due to its accuracy in partitioning of interaction sum of squares into component variables (Nachit et al. 1992).

This study aimed to assess the environmental stability of grain yield under salt stress conditions. The experiment was conducted across nine salt stress environments, which were combinations of different locations and years. Descriptive statistics for grain yields indicated the presence of significant variation in this trait among the genotypes. The ANOVA of AMMI divides the treatment variation from residual error or variations caused by unknown factors. The sum of squares of G, E, and G × E significance is used to evaluate the appropriateness of the AMMI model. At a P-value of ≤0.001, all three components are highly significant. The environment is the most important component in this variability, but both G and GEI contribute approximately equally. Likewise, several studies have reported that environmental components contribute the most to the total variation (Ghaed-Rahimi et al. 2014; Islam et al. 2016; Hassani et al. 2018; Shahriari et al. 2018; Krishnamurthy et al. 2021). Both signal (GEI_S) and noise (GEI_N) are present in the GEI component. The degree of freedom of GEI is multiplied by the mean sum of squares of the experimental error to generate the SS for GEIN. To get GEIS, GEIN is then subtracted from SS of GEI (Gauch 2013). As compared to the genotypic main effect, the SS for GEIS and GEIN is 0.8 and 0.2 times higher, respectively. The current findings are consistent with earlier studies in which evaluations of rice genotypes were carried out under various salt-affected soil conditions and significant contributions of G, E, and GEI for grain yield were discovered (Anandan et al. 2009; Krishnamurthy et al. 2015, 2021; Islam et al. 2016).

Model families ranging from AMMI0 to AMMIF are produced during AMMI analysis. Because the AMMI0 family lacks both GEIS and GEI, the genotypes were compared in the original set of mega-environments. In contrast, the AMMIF family keeps all of the GEIS and GEIN as this model uses the original set of data or raw data. The model family in between these two extremes can be used for a particular set of data. The selection of the best model family depends on three parameters: (1) statistical significance; (2) interpretability; and (3) accuracy (Gauch 2013). In this study, the seven IPCs (IPC1–IPC7) accounted for 76% of the total GEI distribution, with the remaining 24% attributable to residual effects on grain yield. Of these seven IPCs, only the first four were statistically significant according to FR statistics, while the Gollob F-test identified six out of the seven IPCs as significant. A similar contrast result was observed by Hassani et al. (2018) in root and sugar yield. The F-test methods depend on distributional assumptions and data normality, with some tests like FR being either liberal (Akbarpour et al. 2014) or conservative in detecting significant IPCs (Annicchiarico 1997). In our study, data normality was confirmed by Shapiro–Wilk (1965) tests (Table S2). Model diagnosis is essential to determine the most suitable model family for a given dataset and research objective. Two primary approaches for model diagnosis are cross-validation and hypothesis testing about the number of components, which help in identifying the optimal number of multiplicative terms for dissecting GEI mean squares (Cornelius 1993; Gauch 2013). Both approaches were employed in this study to enhance the predictive accuracy of AMMI model families. In our study, the AMMI model accounted for 80% of the GEI sum of squares (GEI_S) and 20% of the GEI_N. Cross-validation results identified AMMI4 as the most predictive and accurate model, as indicated by its low root mean square predictive differences (RMS PD) value. Therefore, AMMI4 is recommended for the current model to maximize prediction accuracy (Agahi et al. 2020). Similarly, other researchers have used RMS PD to assess the predictive accuracy of AMMI models (Ghaed-Rahimi et al. 2014; Hassani et al. 2018; Shahriari et al. 2018). Krishnamurthy et al. (2021) found that IPC1, IPC2, and IPC3 together explained 60.5% of the GEI variation and 67% of the GEIS variation for rice under salt stress conditions. Studies on GEI often show significant discrepancies between the results of different diagnostic methods and predictive accuracy (Hassani et al. 2018). Practical constraints typically limit the number of feasible mega-environments to two or three, or possibly a few more, which often requires a simpler AMMI model (AMMI-1 or AMMI-2) rather than a more complex one determined solely by statistical criteria (Gauch 2013). This highlights a trade-off between statistical and practical considerations that can guide the selection of appropriate and parsimonious models in GEI studies.

Within a mega-environment, the habitats exhibit similar characteristics, resulting in consistent responses from genotypes (Yan and Rajcan 2002). However, fluctuations in genotype rankings due to environmental factors can complicate the identification of the most stable genotype. AMMI analysis addresses this issue by separating noise from the true GEI component, thereby facilitating a more accurate comparison of genotypes. Modern model families like AMMI5, AMMI6, and AMMI7 capture more GEI_N, resulting in the formation of several mega-environments. In the current instance, AMMI6 and AMMI7 both recognized six mega-environments, but AMMIF detected seven mega-environments. The fraction of GEIS drops from AMMI1 to AMMI7, whereas the GEI_N component grows in the same way. Therefore, the AMMI1 family provides the finest foundation for the division of environments into mega-environments (Gauch 2006). Using the AMMI1 model family as a foundation, the original nine environments are divided into two mega-environments with two ‘winners’. RP 5989-2-4-8-15-139-62-6-9 (GN14) yielded the best in all six environments of Mega-environment I, while CSR 23 (CHK2) took first place in each of the three mega-environments of Mega-environment II. The primary additive effect of genotypes and environments is represented on 2D surfaces using the AMMI biplot1, which makes it simple to identify related genotypes and environments. The AMMI biplot1 groups together the environments that fall under the same mega-environments or the genotypes that exhibit a similar pattern of behavior. The AMMI2 model family also defined six mega-environments, like AMMI6 and AMMI7, but it caught a greater proportion of GEI_S than AMMI6 and AMMI7, which gives it a higher level of prediction accuracy for the current dataset. In the six mega-environments based on the AMMI2 model family, CSR RIL-01-IR 165 (GN10) and CSR 2711-17 (GN01), respectively, took first place in three and two environments. The first two IPC can be used to determine genotypes or locations with low, medium, or high GEI. The genotypes close to the biplot’s origin have a low IPC1 score and are more stable as a result of less environmental interaction. The IPC1 score grows in either a positive or negative direction as we approach away from the origin, and as a result, the interaction effect increases significantly (Anandan et al. 2009). Points nearer to a score of 1 suggest two environments or genotypes with comparable interaction patterns. According to Gauch (2013) the most reliable genotype in terms of stability across many conditions is one with a ratio of 1. In this instance, genotype RP 5989-2-4-8-15-139-62-6-9 (GN14) is the clear victor and is advised for widespread adaption. A genotype is suited for a limited range of environments when the ratio for that genotype approaches or exceeds 1. Because it produces better results in that environment. For narrow adaptation in this environment, the check genotype CSR 23 (CHK2), which has a yield advantage of 12% under E09, is advised (Kumar et al. 2010, 2011; Anandan et al. 2009; Ali et al. 2013; Krishnamurthy et al. 2014, 2016b, 2016c, 2017).

Conclusion

In response to increasing salt stress, this study aimed to assess potential salt-tolerant rice lines across nine environments, encompassing both saline and sodic stress conditions, using the AMMI stability model. Significant genetic variability in grain yield was observed, which could be leveraged in rice breeding programs. Genotypes RP 5989-2-4-8-15-139-62-6-9 (GN14) and CSR-2748-4441-195 (GN05) exhibited exceptional performance under sodic stress conditions. Conversely, CSR RIL-01-IR (GN10), CSR-2748-4441-193 (GN11), and CSR 2711-17 (GN01) demonstrated strong performance under saline stress conditions. According to the low RMS PD model diagnosis analysis, the AMMI-4 model emerged as the most predictive. In the AMMI-4 model, four ‘winning’ genotypes were identified across four mega-environments: (1) CSR 2711-17 (GN01); (2) CSR RIL-01-IR 165 (GN10); (3) RP 5989-2-4-8-15-139-62-6-9 (GN14)’ and (4) RP 5989-2-4-8-15-139-62-6-9 (GN14). Using the AMMI1 model family as a basis, the nine environments were categorized into two mega-environments, each featuring two top-performing genotypes: (1) RP 5989-2-4-8-15-139-62-6-9 (GN14); and (2) CSR 23 (CHK2). The superior performing and ‘winning’ genotypes can be recommended for cultivation in saline and alkaline soils and can also be utilized in breeding programs aimed at enhancing rice productivity in salt-affected areas, thereby contributing to increased rice production to meet the needs of the growing population.

Supplementary material

Supplementary material is available online.