Quinoa (Chenopodium quinoa Willd.) is a crop plant from the Amaranthaceae family. The origin of this crop is the Andes regions in Bolivia, Chile and Peru (Stanschewski et al., 2021). Quinoa is a self-pollinated plant, but some cultivars may show cross-pollination of about 4-20% (Anchico-Jojoa et al., 2023). Quinoa can grow in hard and stressful conditions such as salinity and drought stresses (Anchico et al., 2020; Manjarres-Hernández et al., 2021). The grain yield of quinoa cultivars varies between 2.2-9.8 tons per hectare (Vásquez et al., 2024). Different cultivars have different stem diameter, plant height, and grain length and diameter (Manjarres-Hernández et al., 2021). The growth and development of quinoa is strongly influenced by day length and photoperiod, so that its growth period in different cultivars and environmental conditions is approximately 90-240 days (Apaza et al., 2015; González et al., 2015).

The main product of quinoa is its grain, which is called vegetable caviar because of its high nutritional value (Ng and Wang, 2021). Quinoa grains have a lower sodium content but higher levels of calcium, magnesium, potassium, iron, manganese, and zinc compared to common cereals such as wheat, barley, and maize (Singh, 2019; Ayaşan, 2020; Thiam et al., 2021; Abdelshafy et al., 2024). Quinoa contains 9.1-15.7 grams of protein, 4-7.6 grams of fat, and 8.8-14.1 grams of fiber per 100 grams of fresh weight (Nowak et al., 2016). In addition to quinoa grains, young quinoa leaves can be used as a fresh and cooked vegetable (Pathan et al., 2019). Therefore, due to the nutritional value and high production potential of quinoa, attention to this crop plant has increased worldwide to sustainably replace the nutrition of the growing world population (Gómez et al., 2021; Mohamed Ahmed et al., 2021).

Climate changes in the world along with drying and salinization of the soils have caused many problems such as the loss of large parts of suitable agricultural soils and, finally, the migration of farmers and villagers to the cities. Quinoa is a very valuable crop plant in terms of tolerance to many environmental stresses, including drought and salinity. It can be cultivated in hard conditions and may be able to solve a significant part of these problems. Since different quinoa varieties have a very different range of tolerance, from sensitive to resistance to environmental stresses, it is necessary to investigate their adaptability and stability under different environmental conditions and to identify and introduce compatible and stable varieties to each environment (Ruiz et al., 2014; Bazile et al., 2015).

Genotype × environment interaction is of particular importance for plant breeding researchers and one of the complex issues of breeding programs to identify high-yielding and stable genotypes (Dessie et al., 2020; Teressa et al., 2021). Evaluation of genotype × environment interaction is necessary to introduce genotypes with higher average grain yield and lower fluctuations (stable) in different environments (Tariku et al., 2013; Bocianowski et al., 2019). Powerful methods are needed to investigate genotype × environment interaction and determine the stability of genotypes. There are many different methods, including univariate and multivariate methods, to evaluate the stability of genotypes, which one or more methods can be used according to the experimental conditions. Among all stability analysis methods, it seems that two multivariate methods, additive main effects and multiplicative interactions or AMMI (Crossa et al., 1991; Gauch, 2006), and genotype plus genotype by environment interaction or GGE-biplot (Yan, 2001; Yan et al., 2010) are better and more successful methods to identify high-yielding and stable genotypes.

Kempton (1984) was the first researcher to use the AMMI model to analyze grain yield data. The AMMI method is a combination of analysis of variance and principal components analysis, in which analysis of variance is used to determine the main effects of genotype and environment, and principal components analysis is used to determine interaction effects. This analysis is an effective method to investigate the stability of genotypes in different environments because it calculates a large part of the sum of squares of the genotype × environment interaction and separates the main and interaction effects (Gauch, 2006). Considering that the effect of the environment is very large in most cases and cannot be used, removing the effect of environment and focusing on the main and genotype × environment interaction effects can be important (Yan and Kang, 2002; Gauch, 2006). Among the multivariate stability methods, the GGE-biplot graphical method, which is based on principal component analysis, is also a very useful tool for evaluating the role of genotypes, environments, and their interaction. To evaluate the stability of genotypes in this method, the effects of genotype and genotype × environment interaction are used to obtain more reliable results (Yan and Kang, 2002; Yan et al., 2007). The presence of different graphs in this method allows a better interpretation of the results, so that, it is possible to identify genotypes with higher grain yield and general stability for all environments, genotypes with specific stability for each of the target environments, and the best environments using the GGE-biplot tool (Yan and Kang, 2002; Yan et al., 2007; da Silva et al., 2021).

Many researchers have used AMMI and GGE-biplot methods to investigate the adaptability and stability of cultivars and genotypes in quinoa (Ali et al., 2018; Thiam et al., 2021; Al-Naggar et al., 2022; Anchico-Jojoa et al., 2023), maize (Al-Naggar et al., 2021; Patel et al., 2023; Greveniotis et al., 2023a), wheat (Mohamed et al., 2022; Omrani et al., 2022; Gupta et al., 2023), rice (Hasan et al., 2022; Abebe et al., 2023) and sorghum (Al-Naggar et al., 2018a, b). Ali et al. (2018) used univariate and multivariate methods to evaluate the stability of five quinoa genotypes in ten different environments in Egypt during two crop years, 2016 and 2017. They reported that the stability parameters and AMMI method were similar in identifying stable genotypes. Thiam et al. (2021) used the AMMI method to evaluate the stability of 14 quinoa genotypes in five different environments in Morocco, and classified the genotypes into three groups, stable, relatively stable and unstable. Al-Naggar et al. (2022) studied the stability and adaptability of 37 quinoa genotypes in 12 environments under different nitrogen fertilizer sources and level conditions in Egypt. They reported that the results obtained from both AMMI and GGE-biplot methods were different and each method introduced three different genotypes as stable and adaptable genotypes. Anchico-Jojoa et al. (2023) reported a significant difference between environments, genotypes, and genotype × environment interaction using the AMMI method to evaluate the stability and adaptability of eight quinoa genotypes in Brazil and Colombia during 2018 and 2019 and introduced four quinoa genotypes with high grain yield and general adaptability.

A few studies have been conducted in Iran on the adaptability and stability of quinoa. Bagheri et al. (2021) studied the stability and adaptability of ten different quinoa genotypes in four environments in cold and temperate locations of Iran during the 2017 and 2018 crop years, and introduced the stable and adaptable genotypes using the AMMI method. Also, Etaati et al. (2023) evaluated the adaptability and stability of ten quinoa genotypes in different locations of Iran using different parametric and non-parametric methods, and identified a high-yielding, stable and adaptable genotype.

Iran is a vast country located in the Asian continent and in the Middle East region and has a very diverse climate but with an average annual temperature of 17.6°C and an average rainfall of 266 mm (Abbasi et al., 2019), it is generally classified as a hot and dry climate. Therefore, it will be successful to cultivate plants that can tolerate the hard conditions caused by drought and heat stresses in most regions of Iran. It seems that the cultivation of quinoa as a valuable crop, especially in terms of tolerance to environmental stresses such as drought, can be successful in these conditions. Quinoa is a new crop plant in Iran, and suitable genotypes for different locations have not been introduced. The objective of the current study was to identify high-yielding and stable genotypes for the study regions, as well as to compare multivariate AMMI and GGE-biplot methods and introduce the best method for identifying stable and high-yielding genotypes.

Quinoa is known as a key crop for food security in many countries of the world, which can produce products in more than 120 countries, but on the one hand, the high climatic diversity in different regions and, on the other hand, the existence of environment × genotype interaction, requires the introduction and cultivation of stable and adapted genotypes to these areas (Alandia et al., 2020). There are various statistical methods to study genotype × environment interaction and identify stable genotypes, among which AMMI and GGE-biplot provide better and more interpretable results (Gauch et al., 2008). In the AMMI method, the genotype × environment interaction is separated from the environment and genotype effects, and then this interaction is analyzed using PCA (Zobel et al., 1988), While in the GGE-biplot method, only the environment effect is removed, and the total effects of genotype and genotype × environment interaction are used to identify stable genotypes, and by presenting different biplot, ideal and stable environments and genotypes are introduced (Yan et al., 2007).

The variance analysis of the data in this study showed that the effects of genotype, environment, and genotype × environment interaction were significant. The significant genotype × environment interaction indicates the fluctuation of the grain yield of the genotypes from one environment to another (Thiam et al., 2021; Allaoui et al., 2023; Ruswandi et al., 2023). This means that the grain yield of the genotypes was affected by environmental conditions and produced different grain yields in different environments. The separation of the contribution of each factor also showed that genotype, environment, and genotype × environment interaction justified 63.0%, 4.3%, and 29.7% of the total variation, respectively. Describing 30% of the total grain yield variation by genotype × environment interaction makes the necessity of stability analysis and identification of stable genotypes unavoidable. The results of this study were consistent with the results of many researchers who reported the contribution of the effects of genotype and genotype × environment interaction more than the environment effect (Hmwe et al., 2018; Katsenios et al., 2021; Hossain et al., 2023; Wodebo et al., 2023). On the other hand, some researchers also estimated the environmental effect is more than the effects of genotype and genotype × environment interaction (Ali et al., 2018; Wardofa et al., 2019; Thiam et al., 2021; Al-Naggar et al., 2022).

The description of nearly 50% of the variance of the genotype × environment interaction by the first component and nearly 71% of this variance by the first two components indicates the existence of a strong interaction between the studied genotypes and environments. Tekdal and Kendal (2018) also investigated the stability of 122 different durum wheat genotypes in two environments using the AMMI model, and they reported that genotype, environment, and genotype × environment interaction explained 59.8%, 3.5%, and 36.7% of the data variation, respectively. Other researchers also reported a high percentage of the first and second principal components in the AMMI method (El-Sadek, 2017; Ali et al., 2018; Allaoui et al., 2023; Hossain et al., 2023). The studied environments were located far from the origin of the AMMI biplot, which indicated strong interaction forces with the genotype, and the angles between the studied environments ( Figure 2 ) indicate the distinctiveness in the selection of genotypes (Balakrishnan et al., 2016; Jain et al., 2019). Therefore, using the values of the first principal component, the mean grain yield of the genotypes ( Figure 1 ), and the values of the first and second principal components ( Figure 2 ), the AMMI diagram was drawn to show the effects of genotypes and environments and the distribution of genotypes in the eight studied environments. The results showed that the genotypes located on the right side of the AMMI1 diagram ( Figure 1 ) had higher grain yield than the total mean. Among these genotypes, genotypes G16, G19, G17, and G35 produced the highest grain yield with 4977, 4901, 4418 and 4263 kg.ha^-1, respectively. According to Figure 2 , genotypes G25, G28, G31, G9, and G23 with Buin Zahra and Takestan environments in 2022 and 2023 (E1, E2, E3, and E4) and genotypes G34, G12, G14, and G5 with Kuhdasht and Poldokhtar environments in 2022 and 2023 (E5, E6, E7 and E8) were adaptable. Thiam et al. (2021) also identified the genotypes adapted to each environment using the graph obtained from the first two components in the AMMI model according to the proximity of the genotype to the environment vector. The difference in grain yield between Lorestan province (Kuhdasht and Poldokhtar) and Qazvin province (Takestan and Buin Zahra) can be attributed to several factors. Sparrow (Passer domesticus) infestation during the flowering and harvesting of quinoa had a greater impact on yield in Lorestan province due to the absence of fields or cover crops to deter sparrow attacks, while in Qazvin province, the cultivation of sunflowers alongside quinoa helped reduce the impact of sparrows. Additionally, the soil in Qazvin province was more suitable for quinoa cultivation, with a lighter texture compared to Lorestan province. Furthermore, high temperatures during flowering and physiological maturity in Lorestan province led to a decrease in the number of seeds and ultimately a decrease in grain yield.

The IPCA_g index is one of the parameters that is calculated to determine the degree of interaction of each genotype with the environment and to identify stable genotypes in the AMMI method. Based on this, genotypes with a large IPCA_g1 Score (positive or negative) have a high interaction with the environment, and on the contrary, genotypes with an IPCA_g1 score close to zero have a low interaction and are stable genotypes (Purchase et al., 2000). Investigation of the IPCA_g1 values showed that genotypes G15, G16, G18, G6, G12, G19, G11, G24, G26, and G4 were the most stable studied genotypes in this experiment with the lowest IPCA_g1 score, respectively. The AMMI stability value (ASV) is another parameter of the AMMI method that expresses the variation between genotypes so that genotypes with less ASV and close to zero are considered stable (Mohammadi and Amri, 2008; Kebede and Getahun, 2017). The ASV index, like the IPCA_g1 index, identifies similar and identical stable genotypes. Considering that genotypes must be introduced that have high grain yield in addition to stability and fewer yield fluctuations in different environments, the examination of the grain yield of these genotypes showed that only genotypes G16, G19, G35, G30, G39, G24, and G18 had higher grain yield than the population means. These genotypes were also placed at the origin of the AMMI biplot ( Figure 2 ) and as a result, stable genotypes with high general adaptability were introduced.

The results of the GGE-biplot method also showed that the first two principal components, explained 68.1% and 15.2%, respectively, and in total about 83% of the variation of the genotype and genotype × environment interaction. According to many researchers, the GGE-biplot method is one of the most appropriate methods to investigate the stability of genotypes (Chandrashekhar et al., 2020; Haile and Kebede, 2021; Greveniotis et al., 2023b) because in this method, by removing the environment effect as an uncontrollable source, the sum of the effects of genotype and the interaction of genotype × environment are used, and as a result, the total controllable effects are used to study the response of genotypes and identify stable genotypes. Many researchers have reported the high contribution of the first principal component in explaining diversity of the genotype and genotype × environment interaction in different plants, including quinoa (Afiah et al., 2018; Thiam et al., 2021; Hafeez et al., 2022), rice (Hasan et al., 2022; Ghazy et al., 2023), maize (Shojaei et al., 2022; Ninou et al., 2023), wheat (Elfanah et al., 2023; Han et al., 2024), barley (Akan et al., 2023) and sorghum (Wang et al., 2023) which was consistent with the results of this study.

Considering that about 83% of the variance of the genotype and genotype × environment interaction in this study were described by the first and second components, therefore, different biplot diagrams can be drawn to study the distribution of genotypes in different environments and to choose the best genotypes and environments. One of these diagrams is the polygon biplot which is presented in Figure 3 , and it can be used to identify superior genotypes adapted to any environment (Gao et al., 2022; Esan et al., 2023). In this diagram, vertical lines are drawn from the origin of the biplot to each side of the polygon, and the studied genotypes and environments are divided into several sections so that the genotypes placed in each part of the polygon diagram have high specific adaptability with the environment of that part, especially the genotypes located at the vertices of the polygon, which have the highest specific adaptability with the respective environment (Bojtor et al., 2021; Sissoko et al., 2024). Based on the study, it was found that Poldokhtar was the most unfavorable environment for grain yield, while Takestan was the most favorable. Several genotypes were identified as superior in each environment, with some performing well in one region but not in another. This information can be valuable for selecting appropriate genotypes for different environmental conditions to optimize grain yield. In addition to the stable and high-yielding genotypes introduced in all locations, genotypes G7, G30, G33, and G34 can be introduced as superior genotypes in the Poldokhtar environment, which did not provide optimal yield in the Takestan environment. Also, genotypes G25, G31, and G39 had optimal grain yield in the Takestan environment, but produced low grain yield in the Poldokhtar environment.

Another diagram that is drawn in the GGE-biplot method is the biplot diagram to investigate the relationships between the studied environments. The cosine of the angle between the environment vectors in this diagram shows the correlation between environments. A zero-degree angle means +1 correlation, a 90-degree angle means no correlation, an acute angle means positive correlation and an obtuse angle means negative correlation (Yan and Tinker, 2006). In addition, based on the length of the environment vectors in this diagram, the studied environments can also be examined in terms of the power of distinguishing genotypes, so that the environments with a longer vector length have more power and the ability to differentiate (Esan et al., 2023; Kebede et al., 2023). Correlation between the eight studied environments in this experiment showed that the angle between the vector of Buin Zahra and Takestan environments in both cropping years (E1, E2, E3, and E4) and Kuhdasht and Poldokhtar in both cropping years (E5, E6, E7, and E8) is smaller, which means that these environments are more similar to each other and there is a high correlation between them, while the angle between the environment vectors of Buin Zahra and Takestan with the vectors of Kuhdasht and Poldokhtar environments in both cropping years (E1, E2, E3, and E4 with E1, E2, E3, and E4) is larger and indicates the greater difference between these environments and less correlation between them. Considering that the information obtained from environments with high correlation is similar and identical, therefore, to increase the efficiency of the experiments, one of the environments with high correlation can be selected and future experiments can be performed in this environment and eliminate other environments and finally reduce the costs of performing experiments (Sharma et al., 2020; Karuniawan et al., 2021; Ruswandi et al., 2021; Taleghani et al., 2023). The investigation of the length vector of the environment also showed that all the eight studied environments in this experiment had large length vectors, which meant a high discrimination power in all the experiment environments, However, the vector length of Takestan and Buin Zahra environments in 2023 (E2 and E4) was more than the other six environments, which indicated the greater impact of these environments in differentiating genotypes compared to other studied environments ( Figure 4 ). In other words, Takestan and Buin Zahra environments in 2023 (E2 and E4) had a greater contribution to the formation of the genotype × environment interaction than the other six environments. Therefore, the length of the environment vectors is a measure to determine the stability of environments and there is an inverse relationship between them, so that an environment with a smaller environment vector size is more stable (Esan et al., 2023; Kebede et al., 2023). Taking into account that the length of the vectors of the Kuhdasht environment in both cropping years (E5 and E6) was smaller than the vectors of other environments, these environments had higher stability and the grain yield fluctuation of quinoa genotypes in these environments was less than in other environments. This environment can be used for planning to select superior quinoa genotypes (Ansarifard et al., 2020).

Another diagram drawn in the GGE-biplot method is the Biplot diagram to compare genotypes with the ideal genotype. Based on this diagram, the genotypes are ranked and placed in concentric circles, and the genotypes placed in the center of these concentric circles are known as the ideal genotypes. In addition, the distance from the Average Environment Axis (AEA) is also an indicator to determine the stability of genotypes and has an inverse relationship with stability (Kebede et al., 2023; Ninou et al., 2023). The unique feature of the GGE-biplot is that it allows the comparison of genotypes with the ideal genotype. Examining the ‘Mean vs. stability’ pattern ( Figure 5 ) showed that the genotypes G16, G19, G17, G35, and G31 were placed in the center of the concentric circles, and in contrast, the genotypes G40, G4, G21, G27, G36, G38, and G32 were located farther away from the concentric circles. Genotypes G16, G19 and G17 had the highest mean and genotypes G40, G4, and G21 had the lowest mean in the environment. According to this figure, genotypes G16, G19, and G17 were recognized as ideal genotypes in this study. Following this, genotypes G35 and, G31 were identified as superior and stable genotypes. Finally, using Figure 6 ., ideal environments were identified. In this diagram, the smaller the angle of the environment vector with the Average Environment Axis (AEA) and the intended environment placed in concentric circles, the more ideal that environment is (Ye et al., 2019). Therefore, the Takestan environment in 2022 (E3) and then the Kuhdasht environments in 2022 and 2023 (E5 and E6) were recognized as ideal environments for cultivating the studied quinoa genotypes. Al-Naggar et al. (2022) also introduced ideal genotypes and ideal fertilizer environments for quinoa cultivation by evaluating 37 quinoa genotypes using this biplot. These environments can be used to improve quinoa genotypes because they consistently produce the highest grain yield. GGE-biplot diagrams allow the evaluation of environments and genotypes based on the power of differentiation and representation, so this method is more favorable than the AMMI method (Aktaş, 2016).

In this study, genotype × environment interaction and grain yield stability were investigated in 40 quinoa genotypes using AMMI and GGE-biplot methods. The variance analysis of the data in this study showed that the effects of genotype, environment, and genotype × environment interaction were significant. The significant genotype × environment interaction indicates the fluctuation of grain yield of genotypes from one environment to another due to the variation in climatic and edaphic factors. The breakdown of the contribution of each factor reveals that genotype accounts for 63.0% of the total variation, environment for 4.3%, and genotype × environment interaction for 29.7%. The fact that genotype × environment interaction explains 30% of the total grain yield variation underscores the importance of conducting stability analysis and identifying stable genotypes. The results of AMMI analysis showed that the six principal components explained of the variance of genotype × environment interaction. The description of nearly 50% of the variance of the genotype × environment interaction by the first component and nearly 71% of this variance by the first two components indicates the existence of a strong interaction between the studied genotypes and environments. Among the genotypes studied, genotypes G16, G19, G17, and G35 had the highest grain yield with 4977, 4901, 4418, and 4263 kg/ha respectively. Also, various statistical analyses showed that Pol Dokhtar was the most unfavorable and Takestan was the most favorable environment for grain yield. Based on AMMI graphs, genotypes G25, G28, G31, G9, and G23 were adaptable to the environments of Buin Zahra and Takestan, and genotypes G34, G12, G14, and G5 were adaptable to the environments of Kohdasht and Pol Dokhtar. The results of the GGE-biplot method also showed that the first two principal components, explained about 83% of the variation of the genotype and genotype × environment interaction. The polygon diagram ( Figure 3 ) separated the environments studied in this experiment into two mega-environments. The first mega-environment included the environments of Buin Zahra and Takestan, while the environments of Kuhdasht and Poldokhtar were placed in the second mega-environment. Among the studied genotypes, genotypes G16, G19, and G25 had the highest specific adaptability with the first mega-environment, and genotype G17 with the second mega-environment. The grain yield analysis of 40 studied quinoa genotypes in this experiment with both AMMI and GGE-biplot analysis methods identified genotypes G16 and G19 as stable and high-yielding genotypes. Also, both AMMI and GGE-biplot methods were beneficial in studying genotype × environment interaction and identifying stable and high-yielding genotypes. However, the GGE-biplot method, due to presenting different graphs, determining mega-environments, and identifying ideal genotypes, was a more useful tool for stability analysis. High-yielding and stable genotypes identified in this experiment can be introduced as suitable cultivars for the studied environments.