NRPU8983: Complementing Food Security through selection of Superior & Stable genotypes of major crops

Introduction

Pakistan is an agricultural country and agricultural industry plays a vital role in the economic growth and development of the country, providing a significant contribution to the GDP and employment opportunities for a large portion of the population. This growth in the agriculture sector is crucial for the country’s food security and nutrition, as well as for the protection and enhancement of the environment and natural resources. To sustain this growth in the agriculture sector, it is essential to continue investing in research and development, modernizing the agricultural infrastructure, promoting innovative and sustainable farming practices, and providing access to credit and insurance facilities for small farmers. Additionally, there is a need to address the challenges faced by the agriculture sector, such as climate change, water scarcity, and soil degradation, through policy interventions and technological advancements. (Pakistan Economic Survey, 2022). In Pakistan, two distinct growing seasons are observed. The first season, known as “Kharif,” begins in April and concludes in June, with harvest occurring in December. This season encompasses a range of crops, including rice, sugarcane, cotton, maize, moong, mash, bajra, and jowar. The second season, referred to as “Rabi,” involves sowing from October to December, and harvesting takes place from April to May. The primary crops during the Rabi season are wheat, gram, lentil (masoor), tobacco, rapeseed, barley, and mustard. The agricultural sector in Pakistan comprises five subsectors: major crops, minor crops, livestock, fisheries, and forestry. Significant food grain crops within the agricultural sector include wheat, rice, maize, bajra, jowar, and barley (Raza et al., 2012; Anwer et al., 2015; Jiang and China, 2016; Khan et al., 2021).

The demand for food is experiencing rapid growth worldwide due to the expanding global population and rising average income levels. This issue is particularly severe in Pakistan, where 47% of the population is currently classified as food insecure (Kirby et al., 2017; Khaliq et al., 2019). Historically, Pakistan has seen parallel growth in population and agricultural production, driven by expansions in irrigated areas and yield improvements. However, future projections suggest significant challenges ahead. With Pakistan’s population projected to reach 270 million by 2050, maintaining the same level of agricultural production growth becomes highly challenging due to increasing water scarcity and urbanization encroaching on productive irrigated lands. Addressing these challenges will require innovative approaches to sustain agricultural productivity amidst limited water resources and urban development pressures (Kirby et al., 2017). A key strategy to meet the projected increase in future food demand of 60% by the year 2050 (Alexandratos and Bruinsma, 2012) is to maximize agricultural production on existing agricultural land. Hence, Pakistan can pursue the viable option of increasing water productivity and narrowing the crop yield gap on currently irrigated lands (Khaliq et al., 2019).

Based on the 6th Population and Housing Census of Pakistan conducted in 2017, the country is currently experiencing a population growth rate of 2.4% per annum (GoP 2017-2018). Projections indicate that Pakistan’s population is expected to reach 228.9 million by 2025 and 250.2 million by 2050. This rapid population growth has resulted in increased food demand, urbanization, and a decrease in available land resources, particularly arable land. In terms of global food security, Pakistan has an overall score of 52.2 and an affordability index of 59.8, according to the global food security index of 2022. This ranking places Pakistan at the 75th position globally. It is worth noting that 23% of the population in Pakistan is classified as undernourished (Unit 2021). To address these challenges and meet the growing demands of the expanding population for food and fiber, the agricultural sectors in Pakistan must focus on maximizing their potential productivity. Analyzing the increasing potential for food productivity serves as a reference for formulating food policies and implementing strategies to protect arable land. This analysis involves comparing potential food productivity with actual food production, providing valuable insights into the country’s agricultural productivity, and guiding decision-making processes to ensure food security and sustainable resource management. (Khaliq et al., 2019).

To address food insecurity, Pakistan should focus on reducing yield gaps in major food crops and expanding wheat cultivation in Balochistan Province’s moorlands. This requires considering agricultural management in the context of projected climate change impacts on agricultural productivity (Lobell et al., 2009) and bring on adaptation management (Tubiello et al., 2007). Specifically, a critical issue arises from the potential conflicts between water availability variations and the irrigation requirements necessary for closing yield gaps (Mueller et al., 2012). Previous studies have consistently shown that global food demand is experiencing rapid growth, while the current farmland production worldwide is significantly below its potential capacity (Tilman et al., 2002; Khan et al., 2021). However, the average yield of all major crops in Pakistan is still lower than that of many other countries, mainly due to the lack of modern farming technologies, inadequate irrigation facilities, and low-quality seeds. To increase yield of all Major crops in Pakistan, the government has launched various initiatives, and focused on the introduction of high-yielding varieties, subsidies on inputs such as fertilizers and pesticides, and the promotion of modern farming practices. In order to produce high-yielding varieties Plant breeders continuously work on new varieties and for evaluating the performance of these newly developed varieties multi-environment trials plays important role. Multi-environment trials (METs) play a crucial role in plant breeding programs as they enable the evaluation of crop productivity and adaptability across a wide range of environments.

Multi-environment trials (METs)

The main approach for evaluating genotypes involves the assessment of their agronomic performance, encompassing factors such as plant growth parameters, yield potential, disease resistance, and tolerance to various climatic conditions like drought, cold, and flooding. These evaluations are typically carried out through field trials, which can be established using different methods. Conventional trials are often conducted in research stations, providing controlled conditions for assessment. Alternatively, trials can be set up directly on farms, involving varying degrees of farmer participation, ranging from observation to full participation as citizen scientists (Ceccarelli and Grando, 2007; Ceccarelli, 2012; Van Etten et al., 2019). It is also possible to combine different trial designs, such as on-station trials with different levels of farmer involvement. Regardless of the trial design, the primary objective is to establish trials across various locations and over multiple growing seasons. The combination of location and time is referred to as the “testing environment,” and these trials are known as “multi-environment trials” (METs). The primary purpose of conducting METs is to evaluate the adaptability and performance of crop genotypes under diverse agroecological conditions (van Eeuwijk et al., 2005; Brown et al., 2020). METs are widely utilized in agricultural research, yet researchers still encounter challenges in their design, management, and analysis. Furthermore, the principles and practices of effective METs are often not adequately covered in basic research methods courses. The challenges primarily arise from the multiple (M) aspect, such as determining the appropriate number of environments, and the selection of environments (E) to be included in the trial. Current trends in agricultural research, including the participatory paradigm, introduce additional complexity. The involvement of stakeholders in the research raises questions about the definition of ‘environment’ and the criteria for choosing environments to incorporate in the trial. Moreover, as research is often linked to development interventions aimed at driving agricultural changes, certain constraints and opportunities need to be considered when designing METs. Multi-environment trials (METs) are undertaken with specific objectives in mind. Firstly, METs aim to identify options that exhibit stability and consistent performance across diverse contexts. This involves evaluating the performance of different options under varying conditions to ascertain their reliability. Secondly, METs seek to discover locally-adapted options that excel in specific contexts, considering the unique environmental and agricultural conditions of particular regions. Thirdly, METs aim to define the range of contexts in which a specific option performs optimally. This concept, known as the breeder’s concept of mega-environment, involves mapping the results and exploring effective definitions of niche and typologies used to characterize socio-ecological niches. Moreover, METs are conducted to collect evidence that can be extrapolated beyond the locations included in the study, providing valuable insights into the performance of options in untested environments. Finally, METs strive to deepen the understanding of the underlying basis and mechanisms driving the observed interactions. This knowledge allows for the exploitation of these interactions to achieve further gains and learning in new contexts, contributing to the advancement of agricultural practices and breeding programs. METs play a critical role for plant breeders as they introduce complexities in the selection of promising genotypes by reducing the correlation between genotypic and phenotypic values (Ebdon and Gauch Jr, 2002; Anuradha et al., 2022; Lee et al., 2023). These trials allow for the identification of genotypes that exhibit minimal temporal variability, meeting the needs and benefiting growers. They also enable the identification of cultivars that demonstrate consistent performance across different locations, meeting the needs and benefiting seed companies and breeders (Yan and Kang, 2002; Olivoto et al., 2019b). These trials encompass a series of trials that investigate numerous genotypes and environments to assess their main effects and interactions. These trials enable the determination of the average response of the genotypes and the ranking of genotypes based on their distinct responses to varying environmental conditions (genotype-environment interactions, GEI) for traits like yield (Gauch Jr, 1992; Queme et al., 2007; Tena et al., 2019). This environment interaction poses a significant challenge for plant breeders, as it can diminish the effectiveness of selection and complicate the identification of superior cultivars Accurately measuring GEI is crucial for determining an optimal strategy for selecting genotypes that are well adapted to specific target environments (Nowosad et al., 2016). Significant genotype-environment interaction (GEI) in breeding programs necessitates a thorough examination of its causes, nature, and implications (Sandhu et al., 2012). In order to establish effective selection and evaluation networks, it is crucial to have a clear understanding of the causes underlying GEI. (Ramburan and Zhou, 2011). The evaluation of various genotypes in multi-environment and/or multi-year trials is essential not only for identifying high-yielding cultivars but also for identifying sites that accurately represent the target environment (Yan and Hunt, 2002). The successfully developed high-yielding cultivar should exhibit stable performance and broad adaptability across diverse environments. Stability refers to the ability of a genotype or cultivar to maintain consistent performance for an economically important trait in different environments. While the environmental component (E) accounts for a significant portion of variance in analyses, it is not directly relevant to cultivar selection. Instead, the genetic component (G) and genotype-environment interaction (GE) are the key factors that must be considered simultaneously to make informed selection decisions for cultivar evaluation (Yan and Kang, 2002). The multi-environment experiment plays a pivotal role in predicting cultivar performance. Multilocation trials are employed to enhance the consistency of yield across various locations for different crop varieties. While there is no universally accepted method that completely satisfies breeders for studying genotype by environment (G x E) interactions, several statistical analyses, both parametric and non-parametric, are currently utilized to investigate the nature of genotype-environment interactions (Kaya et al., 2006). In Pakistan, Multi-environment trials of all major crops are performed, known as the Punjab Uniform Yield Trial (PUWYT), are conducted in Punjab to assess the yield efficiency and adaptation of promising lines across the province’s many zones. To evaluation of genotypes obtained from national breeding programs plays a significant role in identifying acceptable genotypes for target environments by analyzing genotype × environment interaction (GEI) and determining genotypes adaptable to various environmental situations. There is a consensus among plant geneticists that significant genotype-by-environment interaction (GEI) plays a crucial role in breeding superior varieties. Researchers have shown a longstanding interest in developing objective techniques for the selection of superior genotypes in crop performance trials (Yaseen et al., 2022). Due to the significant genotype-by-environment interactions, multi-environment trials have earned considerable attention. Numerous methodologies have been developed for analyzing such trials. Unfortunately, the utilization of these advanced statistical techniques in agricultural research stations in Pakistan remains limited. Consequently, the present study aims to employ these statistical methods on multi-environment trial data of wheat, maize, and rice, cultivated in Pakistan. The objective is to identify superior and stable genotypes, which will be advantageous for farmers and contribute to enhancing the production of these essential cereal and staple crops. This, in turn, will have positive impacts on the economy and help address food security concerns. The specific objectives of the study are

• To Implement cutting-edge statistical techniques to enhance the accuracy of multi-environment trials on major crops.
• To identify stable genotypes through the effective implementation and interpretation of these statistical techniques.
• To provide guidance and support to enhance the data handling and analysis capabilities of scientists working with multi-environment trial data.

Review Literature

Conventional Genotype \(\times\) Environment Interaction (GEI) and its Stability Measures

Yates and Cochran (1938) have applied joint regression analysis to study the average genotypes yield behavior in the presence of genotype and environment interaction. Moreover, they also studied the linear response of genotype changes in different environments with the hypothesis that all genotypes performed similarly in all environments. The best genotype is selected by calculating stability measure based on the mean performance of all genotypes, by giving weight to each genotype average with the inverse of its predictable variance. The environment with largest residual mean square environment assigned. They concluded that yield responses of the environment is correlated with given weights.

Wricke (1962) proposed method for measuring the stability of genotype also known as the coefficient of determination (COD), which used to assess the stability of treatment effects in a multi-environment trial (MET). It provides an indication of the consistency of treatment performance across different environments. A higher value of COD indicates greater stability, meaning that treatment effects explain a larger proportion of the total variation observed in the data.

Finlay and Wilkinson (1963) proposed a stability measure, also known as the regression coefficient (bi), which studying a grain yields data of a randomly selected group of 277 varieties of barley from a world selection cultivated. This measure assesses the stability of treatment effects in a multi-environment trial (MET) and quantifies the genotype by environment interaction by estimating the slope of the regression line for each treatment. The lower value of bi indicates greater stability, meaning that the treatments performance is less affected by GEI.

Eberhart and Russell (1966) have used regression techniques for measuring stability and this measure is known as the Eberhart and Russell’s regression coefficient (bi). This measure estimates the slope of the regression line for each treatment and asses the stability of treatment effects in a MET. This method was very popular in 1966 because it improved the method for the selection of stable genotypes by dividing the GEI into two portions. First, the slope of the line, and the second deviation from the regression line. The value of bi equal to 1 indicates perfect stability, meaning that the treatments performance is not influenced by GEI. Values of bi less than 1 indicate increasing levels of instability, with lower values indicating greater sensitivity to GEI.

Perkins and Jinks (1968) introduced two methods for assessing the performance of genotypes across multiple environments: the AMMI (Additive Main effects and Multiplicative Interaction) stability analysis and the GGE (Genotype plus Genotype x Environment interaction) biplot analysis. The AMMI stability analysis combines analysis of variance (ANOVA) with principal component analysis (PCA) to evaluate stability, while the GGE biplot analysis provides a graphical assessment of stability. The analysis using these methods is more complex compared to the Eberhart and Russell Model. Both the AMMI stability analysis and the GGE biplot analysis serve as valuable tools for breeders and researchers in identifying genotypes that consistently perform well across diverse environments.

Freeman and Perkins (1971) introduced the two stability measures based on the concept of regression analysis namely regression coefficient (bi) and the deviation from regression (S2di). The (bi) measures the genotypes stability by quantifying the slope of its regression line across different environments. On the other hand S2di measures the deviation of the observed yield of a genotype in a particular environment from its predicted value based on the regression line. Both measures provide insights into genotype stability helps in identifying genotypes with consistent performance and minimal deviations from expected values.

Tai (1971) proposed a stability measure known as Tai’s stability measure while studying regional variety trials of potato. This measure provides a comprehensive evaluation of genotypes by considering both mean performance and stability across environments. He applied a different method of fitting, estimating a structural relationship using maximum likelihood estimation with a suitable joint normal distribution expected. Shukla, (1972) has suggested a stability measure known as Shukla’s stability variance (σ2), which quantifies the stability of genotypes by considering both their mean performance and the interaction effects with the environments. A lower value of σ2 indicates greater stability, meaning that the genotypes performance is less influenced by GEI.

The Analysis of AMMI model and its biplots

Gabriel, (1971) proposed that biplot is a powerful data analysis tool that allows to see the structure of big data matrices graphically. The biplot illustrates inter-unit reserves and suggest a gathering of units, as well as present variances and correlations of the variables, which is particularly useful in principal component analysis (PCA).

Zobel et al. (1988) have described the improvement in experimental techniques. They suggested that a large number of replications and well-organized statistical analysis can help to increase the accuracy of a yield trial. For accuracy of yield AMMI model, combined ANOVA for additive properties of genotype-by-environment (GE) with principal component analysis (PCA) are recommended along with stability measures.

Gauch and Zobel (1988) have reviewed three traditional models to identify the significance of main effects for genotype and environment and their interaction. The results showed that both ANOVA and PCA failed to identify the main effects for genotype and environment. All these problems are covered by the AMMI model. This model divides the non-additivity into further modules that have a clear benefit on these two models and have significance resolution. AMMI model does not require a specific design, it only needs a two-way data structure. Yan et al. (2007) suggested that plant breeders, as well as other agricultural scientists, have increased their yield trials efficiency by evaluating genotype (G) plus GE interaction along with biplot analysis. They compared AMMI analysis with GGE biplot analysis covering three aspects. It covers genotype evaluation then analyze G+GE interaction and lastly evaluate environment analysis and test environment. Genotype evaluation means genotype with high average performance and high stability measures within the environment. Evaluation of test environment means testing the environments that identify effectively superior genotype. In these three aspects of GED research, they examine whether G and GE should also be combined or separated also explained about model diagnosis importance in the analysis of the biplot of GED. For these reasons, they must be treated G and GE simultaneously. For mega environment analysis, the GGE biplot performed better than AMMI1 graph.

Gauch Jr et al. (2008) suggested that AMMI1 model was considered superior among others because it describes the major effects of genotype, the leading impacts of location, and the interactions between genotype and environment. All these variations are very important so, agricultural researchers face a variety of challenges and opportunities as a result of these three types of variation. AMMI model is best for gaining yield performance as well as getting more accuracy for complex datasets than the GGE biplot.

Farshadfar (2008) has performed a research to identify the best genotype of wheat based on yield data as a single parameter. ASV was used as a stability measure to select best performed genotypes of bread wheat with high grain yield. The experiment was conducted in four different years with twenty genotypes of bread wheat in irrigated and rained conditions. The outcomes of combined ANOVA showed highly significant dissimilarities for GE interaction. AMMI explained 10% variability and 83% variation explained by the first three IPC’s. Based on ASV, six genotypes out of twenty were recommended as most stabled for rainfed and irrigated conditions.

Mohammadi et al. (2015) have conducted a study to determine the performance of twenty wheat genotypes in five different locations during growing seasons. The experiment used a four-replication under RCB design. The results of combined ANOVA revealed that genotypes respond differently to different environments and that stability analysis is required. In the AMMI model first four IPCS calculated for 78.32 percent of GE interaction, while the first two IPCs accounted for only 52 percent variability. For the selection of stable genotypes depending on the largest contribution of GE interaction, the MASV index was used, there were six genotypes were selected that recommend as the most stable based on MASV.

Kendal et al. (2016) have examined the effects of two different seasons, one is a normal season and the second is the late spring season on the grain yield using GGE and AMMI model. The results revealed that two different seasons affect the grain yield, in two seasons yield is largely exaggerated by the changes in the environmental situations. The GGE biplot analysis indicated only two genotypes performed stably in both seasons and based on AMMI more than two genotypes were superior and higher-yielding genotypes.

Sa’diyah and Hadi (2016) compared the predictive accuracy of AMMI model with the BLUP model by analyzing multi-environment trials data. AMMI is the popular method for MET with fixed effect, when the sample size is large, the large number of genotypes, then the effects of genotype observed as random may be appropriate then the mixed model is very useful. Both methods are applied for comparing the predictive accuracy using the rice dataset under the RCB design. Comparison of AMMI and BLUP were performed using root mean square error prediction (RMSEP). The outcomes of the analysis indicated that RMSEP is minimum for AMMI 10 as compared to the BLUP model. It means the estimation of AMMI is near to the accurate cost of yield than BLUP predictions. So, AMMI is the best method to estimate the mean yield of the genotype of the crop in diverse locations. Sharifi et al. (2017) found that AMMI model outperformed other methods in identifying the best rice genotypes when analyzing multi-environment trials. The experiment involved seven promising rice genotypes and two control varieties, following a randomized complete block design with three replications conducted over three consecutive years in nine different environments. The combined analysis of variance (ANOVA) revealed significant influences of environment, genotype, and genotype-environment interactions on grain yield. The substantial impact of genotype-environment interactions was evident in the varying responses of genotypes across diverse environments. The Gollob’s F-test indicated that only the first two components of the AMMI model were statistically significant. The cumulative scores of the first two interaction principal components could be used to assess genotype stability. Genotype six (G6) was identified as the most stable genotype based on the AMMI stability value, exhibiting high productivity and stability according to the AMMI biplot approach. The study concluded that genotype-environment interactions played a crucial role in rice yield variation, and AMMI biplots proved to be effective tools for visualizing these interactions.

Koundinya et al. (2019) have looked at the phenotypic stability of eggplant genotypes for yield components and fruit quality measures over the course of four seasons. Modern statistical tools such as the AMMI model, GGE model, and Cluster Analysis were used to analyze the data. For sum of fruits per plant, the combined contribution of IPC-1 and IPC-Il to the overall GE variation was 95.72 percent. According to the AMMI-I biplot, eight genotypes suggested for common cultivation in the spring-summer and autumn-winter seasons to attain the best production. In terms of response to the location, cluster analysis revealed a significant degree of similarity between genotypes.

Alizadeh et al. (2020) have performed an experiment to determine the stability of yield of rapeseed in winter cold temperate. This study was conducted with twenty-five rapeseed lines under RCB design with three replicates. In this experiment, five different environments were used during the period of two years of cultivation. AMMI model and stability index based on AMMI model was applied for yield stability and comparing different lines. The results of the AMMI model revealed that three IPC’s were statistically significant out of four. ASV is used for the selection of more stable rapeseed lines. The lowest value of ASV indicated more stability of yield, only one rapeseed line had the highest stability of genotypes.

ÖZATA (2021) has performed an experiment, to study the stability of waxy maize genotypes and promising the yield and quality characteristics of different maize genotypes. AMMI biplot and GGE analysis were used for stability purposes. Ten waxy maize and two dent corn (control) genotypes were used in this experiment under RCB design with three replicates. Combined ANOVA, normality and equality of variances test were applied that indicated the genotype, year and their interactions had statistically significant. The effect of AMMI analysis revealed that grain yield of genotypes is mostly precious by the environmental belongings which contribute to the 95.15% variation in the performance of yield while GE interaction contributes 4.15% only. AMMI and GGE biplots showed the contrast of waxy maize genotypes with dent com varieties. Dent corn varieties had more average yield than the waxy maize genotypes. Alizadeh et al. (2022) used eleven new advanced genotypes and two cultivars to discover high-yielding stable rapeseed genotypes using multiple parametric and nonparametric statistics during the 2015–2017 growing seasons. The selected genotypes were tested using an RCBD design across twelve settings. The findings demonstrated that the factors of G +GE interaction have a considerable impact on seed production. Moreover, it is concluded that the genotypes respond differently in diverse environments. The genome G13, which shows the best and most stable yield was recommended for commercial growing in Iran’s cold and moderately cold regions.

Momotaz et al. (2021) analyzed multi-environment experiments using sugarcane data. GEI has an effect on crop growth and cane yield, as well as making genotype selection more difficult. The goal of the research was to evaluate GEI for grain yields and stalk weight to select high-yielding and stable genotype. On the Florida organic soils, thirteen Passage Point sugarcane emulations in addition to three check cultivars were assessed in five different sites (environments) over three crop cycles using RCBD with six replications. The AMMI and genotype significant GEI, i.e. GGE biplot, were applied to evaluate data on mean stalk weight and cane yield. The results of the study showed that using the GGE biplot in sugarcane testing method can support discovering clones that are best suited to specific areas and improve selection productivity.

Teressa et al. (2021) introduced the differential reactions of genotypes over a wide range of settings are known as genotype by environment interaction. Plant breeders’ primary goal in crop development is to maintain high agricultural production by developing varieties with high yield potential. Plant breeders are quite concerned when genetic variation by environmental (G×E) interactions arise since these interactions can greatly lower selection advantages and make it more difficult to identify superior cultivars. These models, known as factorial regression models, link genotype sensitivity to observable environmental variables. One of the first implementations of this method was the AMMI model. It is also of major concern to crop breeders, as a phenotypic response to environmental transformation differs among genotypes.

Verma and Singh (2021) have studied stability analysis for wheat genotypes using AMMI and best linear unbiased prediction (BLUP) in rainfed well-timed seeded judgments in India’s Northern Hills Zone. Analysis was performed two times for two different years. During two cropping seasons, sixteen wheat genotypes were tested in field trials at eight locations and sixteen wheat genotypes at nine sites. Around 53 percent of the sum of squares connected to treatments in the first year were accounted for by the environment, 30.5% by the GE interaction, and only 5.4% by genotypes. For 16 wheat genotypes evaluated across nine locations in the second year, AMMI analysis revealed that 7.8% of the total sum of squares (SS) was ascribed to genotypes (G), 48.6% to environments (E), and 3.4% to GE interaction effects. For the selection of stable genotype in the AMMI model depends on the ranking of Modified Ammi Stability Value (MASV) and in the BLUP model on the ranking of Weighted Average of Absolute Scores (WAASB). The key advantages of AMMI and BLUP were merged in this study to improve the reliability of multilocation trials analysis.

Sholihin (2021) has used GGE and AMMI biplot methods to test the stability of yield for releasing a new genotype. For promoting new variety, the experiments were done with eight environments and eight promising genotypes of Cassava were tested under RCB design with three times repeated. The effects of the analysis showed that there were significant differences amongst yields in each environment. By GGE analysis seven IPC were identified, where the first four were statistically significant and the first two had contributed 76% to the total variation. GGE visualization is very important to find the most stable variety among others. The results of the AMMI biplot and GGE biplot showed the same conclusion, both methods select the same genotypes which were more stable.

Mehareb and El-Bakary (2021) have performed an experiment to study the GE interaction in sugar beet genotypes. In two different locations and in two seasons, twenty varieties of sugar beet were applied. The experiment was performed under Randomized Complete Block Design in all locations with 3 replications. For stability analysis of the genotype of sugar beet AMMI model was used. The results of AMMI analysis revealed that there are large differences among different environments, genotypes, and their interactions. The results of the analysis indicated that AMMI is the best instructive model for sugar beet genotypes because in AMMI contributions of two IPCA are 96.53% whereas IPCAI and IPCA2 contribute 69.6% and 27.03% of total variations. For defining the relationship among different genotypes of sugar beet Cluster analysis was performed, according to the cluster analysis, twenty genotypes were grouped into five different clusters based on their similarity and interrelationship.

Adil et al. (2022) conducted a study to investigate the stability of yield and the influence of genotype-environment interactions on 101 wheat genotypes over a span of two years (2018-2020). The trials were conducted in the Khudwani and Wadura regions of Kashmir, which encompassed a significant altitudinal range, following established agronomic practices. Utilizing the additive main effect and multiplicative interaction (AMMI) model, the analysis of seed yield variance revealed noteworthy effects of genotype, environment, and genotype-environment interaction, with a significance level of p<0.01. Furthermore, employing the AMMI analysis based on three primary principal components, a significant proportion of the variation attributed to genotype-environment interaction was effectively explained. These findings enable the identification of specific genotypes with superior yield and other desirable characteristics, allowing for recommendations tailored to broader or niche-specific locations.

Agyeman and Ewool (2022) conducted research to find the improved genotypes with proper relief and profitable usage. The purpose of this research was to assess maize’s productivity. From 2016 to 2018, maize cultivars were tested in 11 different environments. To assess genotype GGE variance modules and forecast genetic principles, the linear mixed model study was done expanding restricted maximum likelihood then best linear unbiased prediction methodologies. To describe links across multiple environments, genetic correlations were estimated. BLUP estimates were used to do a biplot analysis by GGE. This cultivar stayed also supreme stable genotype beginning through 11 environs, allowing the GGE biplot study. The mixed model analysis permitted the selection of superior provitamin A maize genotype using ease.

Rao et al. (2022) concluded that genotype × environment interaction has a significant impact on breeding success and it is difficult to detect superior genotypes for a single location in multi-location trials. The magnitude of genotype by site interaction is typically larger than genotype by year interaction. In the staged development of variety, genotype assessment in multi-environment trials is required. During the kharif of 2019, nine elite pigeonpea genotypes of the mid-early period were tested in six different locations in a randomized complete block design (RCBD) using three replications to determine stable genotypes, locations discrimination, and genotype by environmental intersections using AMMI and GGE biplot stability simulations. According to the findings of this study, the first two main mechanisms clarified 73.4 percent of variation interaction, whereas the GGE biplot explained 80.50 percent.

Gupta et al. (2022) suggested that Genotype Environment Interaction (GEI) is a phenomenon characterized by inconsistent performance under a variety of environmental settings, and it plays a significant role in genotype performance in many environments.

Linear Mixed Model (LMM)

Gogel et al. (1995) have proposed LLM (Longitudinal Linear Mixed) model was put forward as an expansion of the F-W (Finlay-Wilkinson) model. To assess its effectiveness, an experiment was conducted involving ten different wheat varieties cultivated in eleven distinct environments across the United Kingdom. In this study, the effects of the environments were considered random, and the estimation of variance components was carried out using both the Maximum Likelihood (ML) and Restricted Maximum Likelihood (REML) methods. For the estimation of variance components in multi-environment trials (MET), the preference was given to the REML estimate. Kassa et al. (2006) have performed a linear mixed model for grain yield stability of genotypes, as an alternative approach for the previous method as Finlay and Wilkinson model, Eberhart and Russell model, and Shukla stability variance. Linear mixed model on MET data with thirteen genotypes of tef over twelve different environments was used, where locations were treated as random and genotypes were treated as permanent. The conventional analysis of variance across twelve environments found significant differences among the performance of genotypes, as well as interactions that had significant effects on grain yield. The significance of interaction suggested that genotypes respond or else to various environments. The likelihood ratio tests for different stability measures displayed that the stability of tef genotype was best considered by an Eberhart Russel model.

Mendes et al. (2012) aimed to evaluate the performance, adaptability, and stability of maize cultivars in unbalanced experiments using the harmonic means procedure of relative performance of genetic variables. The experiment spanned two growing seasons and involved assessing the grain production of 45 cultivars, including hybrids and variations, across 49 locations. Statistical analyses were conducted using mixed models, treating genotypes as random factors and replications within environments as fixed factors. The combined analyses yielded highly precise experimental results, enabling the identification of maize hybrids and varieties with superior adaptation and stability. The findings indicated that the method of harmonic means of relative performance of genetic values is a valuable tool for maize breeding programs. Carvalho et al. (2016) have performed an experiment for improving the genetic program in cotton crops. They noted that the REML/BLUP method has been mostly used in changed crops like rice, sugarcane, eucalyptus, bean, and cashew for interpretation adaptability and genotypic stability of crops but research is limited with the cotton crop. The goal of this study was to use mixed models to choose cotton genotypes that are both adaptable & stable and to see if this methodology can be applied in cotton genetic improvement projects. Thirty-six strains were tested in a randomized block design with two replications in three trials. The genetic parameters were calculated using REML/BLUP methods, and the genetic values were chosen using the harmonic mean approach. Because of their high adaptability and productive stability, the two genotypes of cotton may be farmed in similar settings to those evaluated. Candido et al. (2018) conducted an analysis involving ten genotypes, seven cropping conditions, and two growing seasons. The objective of the research was to assess the stability and genotypic adaptation of advanced lines and cultivars of curled green-leaf lettuce across various growing situations and seasons, using the REML/BLUP mixed model. The Selegen REML/BLUP software was utilized for data analysis and evaluation of plant yield traits. Genotype stability and adaptation were assessed using the harmonic mean of genotypic values (HMGV) and the relative performance of genotypic values (RPGV). The harmonic mean of RPGV (HMRPGV) was employed to measure stability, adaptability, and yield of breeding lines or cultivars. Based on the comprehensive analysis of attributes from both time periods, the lines L6, L7, and L8 were identified as promising and recommended for planting. These breeding lines consistently demonstrated high yields across all seasons and were deemed superior to the commercial cultivars.

Buntaran et al. (2018) have tested the performance of BLUE and BLUP using genotypes of Swedish crops. The main objective of the experiment is to select a variety that is the best for their field conditions. For this purpose, MET was conducted to provide an accurate prediction. In this experiment yield of wheat and barley was used, the experiment was conducted under alpha design in three different environments, and genotypes were arranged under a balanced incomplete block design. Two-stage analysis was performed, in stage one, the effects of genotypes, environments, and their interaction as fixed and the effects of rep and block were random. In stage two, environments, genotypes, and years were random. The performance of BLUP and BLUE is dependent on the average mean squared error of prediction differences (MSEP). The results of the analysis indicated that the BLUE model performed poorly for both wheat and barley crops. BLUP model performed better than BLUE. So, the BLUP is more appropriate to predict the future performance of genotypes in plant variety trials.

dos Santos et al. (2019) have studied the performance of bean genotypes by using GGE and REML/BLUP methods. The experiment was conducted in four different locations with 32 common verities of bean which included /5 black bean genotypes and 17 carioca bean genotypes under RCB design with three replications. The selection of high yield stable genotype was consistent with both GGE and REML/BLUP methods. The conclusion indicated that four genotypes were most stable and widely adapted from black bean group and two genotypes were from carioca bean group by both methods.

Olivoto et al. (2019a) have performed the analysis to compare the yield stability and mean performance of genotypes by using the mix feature of the AMMI model and BLUP methods. Both techniques are very useful and popular in multi-environment trials for analyzing the GEI effect on the grain yield of crops. AMMI model is a useful visualization technique for modeling the GEI but fails when the random effect model is appropriate. In such a situation, BLUP provides reliable estimates. In this research multi-environment trials datasets of Maize, Soybean, Oat, and Wheat crops were used, there are a total of 118 genotypes where, 55 Maize, 13 Soybean, 10 Oat, and 40 wheat genotypes were tested in 47 environments to compare the predictive accuracy of AMMI and BLUP. in this article also proposed a quantitative stability index based on the singular value decomposition of BLUP’s matrix for GE effects, called WAASB stands for weighted Average of Absolute Scores. This index is very useful and applied when the contribution of IPCI is very low and the interpretation regarding the stability of genotypes may be biased, to deal with such a problem WAASB index is useful. The results of the analysis showed predictive accuracy of BLUP using the LM model was high for all four crops.

Bocianowski and Liersch (2021) have studied the performance of twenty-five oilseed rape varieties using a mixed model. Field experiments were conducted in five different locations under RCB design with four replicates. REML estimates were used for variance components in the mixed model, 8.91% of the total variation was explained by the GEI. Selection of the superior and stable varieties of oilseed rape was made by BLUP estimates in each location, then the harmonic mean was used for the overall relative performance of genotypes.