AMMI and GGE Biplot Analyses for Mega Environment Identification and Selection of Some High-Yielding Cassava Genotypes for Multiple Environments

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Introduction
Cassava (Manihot esculenta Crantz) is grown across the tropics and subtropics for its thick and starchy storage roots [1][2][3]. Cassava is a woody herbaceous plant that thrives in low fertility and acidic soils and requires little labor demand than other major food crops [4]. It is estimated to be the major source of daily energy for over 800 million people worldwide, with over 500 million of these people living in Sub-Saharan Africa [2,5]. In 2019, global cassava production reached 304 million metric tons with an average fresh storage root yield of 11.13 t·ha −1 [2]. Te new genotype should be superior to the released genotype, and the productivity should be higher than the national productivity [6]. In Ethiopia, cassava is an essential food crop that provides food security and income as well as a signifcant percentage of the daily diet for humans [7,8]. Cassava is consumed as a boiled root and processed into four, which is mixed with cereals such as tef, barley, and wheat for bread or injera preparation [8,9].
A signifcant genotype by environment interaction for quantitative traits such as yield can reduce the usefulness of subsequent analyses, restrict the signifcance of inferences that would otherwise be valid, and severely restrict the possibility of choosing superior genotypes [10][11][12]. According to Rodrigues et al. [13] and Rodrigues [14], genotype environment interaction is defned by the change in the genetic ranking of genotypes with respect to the environment; for example, a genotype that performs well in wellwatered conditions may perform poorly in dry conditions. Te ultimate objective of plant breeders in a crop improvement program is to develop genotypes that can be adapted to a wide variety of diverse environments [15]. Yield stability analysis can be performed to fnd genotypes whose performance holds stable across a range of environments [15,16]. Hence, comparing performance across environments can assist in identifying the cassava genotypes that perform best in the target environments and those that are most adaptable to multiple environments.
Plant-breeding programs typically conduct rigorous genotype performance evaluations across environments [17]; the occurrence of genotype by environment interaction (GEI) is unavoidable in such multienvironment trials [18]. Te efects of genotype and environment interactions are statistically nonadditive, demonstrating that diferences in yield among genotypes depend on the environment [19]. As a result, selection strategies based on a genotype's mean yield in a particular environment are inefective [20]. Tis has resulted in a greater focus on phenotypic stability in breeding programs [21] as well as a better understanding and application of various stability approaches. According to Ssemakula and Dixon [22], signifcant GEI variation reduces the relationship between genotype and phenotypic values and lowers yield estimation accuracy. It is also one of the key reasons why formal breeding has not been able to help smallholder farmers in marginalized areas that have limited resources [18].
Plant breeders already have a number of statistical approaches for analyzing genotype-yield adaptability and stability, which can help them with the difcult task of discovering superior genotypes in the context of signifcant G × E interaction [23]. According to Agyeman et al. [24], AMMI and GGE biplot analyses are two widely used methods for overcoming the problems in multienvironment trial data analysis. Te AMMI and GGE biplot models are characterized as powerful tools for analyzing and commenting on multienvironment data structures in breeding operations [25,26]. Tese two statistical analyses (AMMI and GGE) are of more interest to agricultural researchers since they apply to any two-way data matrix, such as the number of genotypes tested in a number of locations, and such data can come from many trials [27]. Analysis of variance (ANOVA) and principal component analysis (PCA) are used in these analyses [28]. Te diference between GGE biplot analysis and AMMI biplot analysis is that the GGE biplot analysis is based on environment-centered PCA, whereas the AMMI biplot analysis is based on doublecentered PCA [29]. As a result, the AMMI and GGE biplot models facilitated visual comparison and identifcation of superior genotypes for widely adaptable environments and each target set of environments [17].
Despite the fact that cassava is usually adapted to a wide range of environmental conditions, most cultivars are reported to have narrow adaptability and large genotype by environment interaction (GEI) efects [30,31]. Tis highlighted the importance of extending research eforts to look at the diferences in storage root yield among cassava genotypes across environments. In Ethiopia, the so far evaluation of performance of cassava genotypes in contrasting environments is limited. Terefore, the objectives of this study were to (1) estimate the magnitude of genotype by environment interaction, (2) identify stable genotypes with high storage root yield, and (3) identify mega-environments to guide future testing strategies.

Description of Study Area.
Te feld experiment was conducted at six environments in the 2020-2021 main growing season. Tese locations were diferent in soil type, altitude, and mean annual rainfall (Table 1). Hence, each location was considered as an individual environment.

Experimental Materials.
Twenty fve cassava genotypes were used in the study. From the total genotypes, 4, 16, and 5 were landraces, promising and released, respectively ( Table 2).

Experimental Design and Management.
Te experiment was laid out in 5 × 5 simple lattice designs. Mature cassava cuttings, measuring 25-30 cm long, were planted in a single row plot of 7 m long with an interrow spacing of 1 m and intrarow spacing of 1 m (7 m 2 ) on the top of the ridge at an angle of 45°to the ground surface. All cultural practices were conducted as recommended by Markos et al. [33] and farmers' practices in the area. Te middle fve plants within a row were marked and sampled for the root yield data collection. Te fresh storage root yield per plot was weighed and then converted to tons per hectare (t·ha −1 ).

Data Analysis.
Statistical analyses were conducted using GenStat [34] and GEA-R described by Angela and Vargas [35]. Prior to doing the combined analysis of variance across environments, each environment's data were subjected to the analysis of variance (ANOVA) and normality test. Bartlett's tests of homogeneity of variances were used to determine the homogeneity of the error variances of the individual location experiments, and then the combined analysis of variance across sites was performed after confrming the homogeneity of the variances. Te AMMI model was used to generate a combined ANOVA with genotypes as fxed factors and environments as random variables.

AMMI Analysis.
A fresh storage root yield analysis was performed for the additive main efect and multiplicative interaction (AMMI) model. In the validity test, the simple lattice design MS component of the block within replication is less than the residual error in all locations; therefore, the analysis of variance was a combined analysis based on the randomized complete block design (RCBD). As described by Gauch [36], the AMMI analysis was used to adjust the main or additive genotype and environmental efects by analysis of variance and the multiplicative efects of the GE interaction by the principal component analysis. Gauch [36] suggested the following model for the AMMI analysis of variance (ANOVA).
where Y ij � is the yield of the i th genotype in the j th environment; μ � is the grand mean; G i and E j are the genotype and environment deviations from the grand mean, respectively; λ k � is the eigenvalue of the PCA analysis axis k; α ik and c jk � are the genotype and environment principal component scores for axis k; n is the number of principal components retained in the model, and e ij is the error term.

AMMI Stability Value (ASV) Analysis.
Purchase et al. [37] suggested an ASV measure to quantify and classify genotypes according to their yield stability because the AMMI analysis does not provide a quantitative measure of stability. Te ASV is a measure of a genotype's stability. Te lower the value, the stronger the stability, according to weighted IPCA1 and IPCA2 scores [37]. Te ASV was determined using the following formula: where (IPCA1 sum square/IPCA2 sum square) is the weight given to the IPCA1 value by dividing the IPCA1 sum of squares by the IPCA2 sum of squares.

Genotype Selection Index (GSI) Analysis.
Using the formula GSI � RASV + RY, the genotype selection index was computed [38]. Here, RASV stands for AMMI stability value  ranking and RY stands for genotype mean yield ranking across environments. According to the author, GSI combines mean yield and stability into a single criterion, with a low score indicating stable genotypes with a high mean yield. As a result, the GSI with the lowest value is thought to be the most stable, with the highest storage root yield. Te higher the IPCA score, either positive or negative, the better suited a genotype is to specifc environments.

GGE Biplot Analysis.
Te model for a GGE biplot [25], based on singular value decomposition of the frst two principal components, is where Y ij � is the measured mean of genotype i in the environment j, μ � is the grand mean,âj � is the main efect of environment j, μ −âj � is the mean yield across all genotypes in the environment j,ë1 andë2 � are the singular values for the frst and second principal components, respectively, ıi1 andîi2 � are eigenvectors of genotype i for the frst and second principal components, respectively, çj1 + çj2 � are eigenvectors of environment j for the frst and second principal components, respectively, and εij � is the residual associated with genotype i in the environment j.

Results and Discussion
3.1. AMMI ANOVA. Te AMMI model's analysis of variance for twenty-fve cassava genotypes evaluated in six environments were found that environments (E), genotypes (G), and genotype environment interaction (GEI) had a signifcant (P ≤ 0.001) infuence on the cassava fresh storage root yield (t·ha −1 ) (Table 3). Additionally, the analysis of variance of the AMMI model indicated that the frst two AMMI (IPCA1 to IPCA2) were very highly signifcant (P ≤ 0.001). Tis demonstrated that there was a signifcant variation in yield performance among the cassava genotypes across the tested environments due to the presence of strong genotype by environment (G × E) interaction. As a result, stable genotypes or entries for a specifc environment may be possible. Tis fnding is in line with several studies that have identifed signifcant interactions between cassava genotypes and the environment [16,30,[39][40][41][42][43]. Te total sum of squares factors explained (%) showed that cassava storage root yield was infuenced by genotype by the environment (G × E) interaction efect (61.36%), environment efect (28.16%), and genotype efect (10.48%) ( Table 3). Te GEI sum of squares factor was roughly 6 times larger than the genotype sum of squares factor, indicating that genotypic response varied signifcantly across environments. Terefore, there is a high possibility of cultivar development for a specifc environment since the GE interaction, the sum of squares, contributed more to the total variation. In agreement with these results, Hmwe et al. [43] reported that the genotype by the environment interaction efect accounted for the largest total sum of square, followed by genotype and environment. However, this was contrary to fndings from Noerwijati and Prajitno [40], who reported that the environment is the most contributing, followed by the genotype by the environment interaction efect and the genotype efect, while Adjebeng-Danquah et al. [16] reported that the environment contributed a greater proportion of the treatment sum of squares, followed by the genotype efect and genotype by the environment interaction. Both studies reported that the cassava storage root yield was strongly infuenced by environmental factors. Tis indicates that there is a large diference in storage root yield in diferent environments. However, the large environmental infuence is irrelevant to genotype evaluation, while genotype (G) and genotype-by-environment interaction (GEI) are relevant to genotype evaluation [40].
For crossvalidation of the yield variation explained by the GEI, the AMMI with IPCA1 and IPCA2 is the best predictive model [20]. In this study, IPCA1 (33.42%) and IPCA2 (23.5%) each explained a signifcant portion of the G × E interaction. Te IPCA1 and IPCA2 sums of squares combined to contribute 57.17% of the overall GEI, with the frst two terms having a sum of squares greater than genotypes. Te model explained the entire genotype by environment interaction component well enough [44]. Tis indicates that the AMMI model with the IPCA1 and IPCA2 was acceptable for crossvalidation of the root yield variation loaded by GEI in the current data set, as it eliminates the majority of the actual variation.

AMMI Biplot.
Te AMMI 1 biplot space ( Figure 1) is divided into four sections, ranging from low-yielding environments in Sections 1 (upper left) and 4 (low left) to high-  AMMI PCA1 Score vs Yield from a Lattice yielding environments in Sections 2 (upper right) and 3 (low right). Figure 1's biplot clearly demonstrates that the points for the environment are more scattered than the points for genotypes, showing that variability due to environments is greater than variability due to genotype diferences, which is in line with ANOVA (Table 3). Te points for the usually adapted genotypes on the biplot would be on the right hand side of the grand mean levels (suggesting high mean performance) and near to the IPCA � 0 line (this suggests negligible or no GE interaction). In this regard, thirteen cassava genotypes, for example, G4 and four environments such as Tarcha, were positioned on the right side of the perpendicular vertical line in the AMMI biplot ( Figure 1). According to the current study, these genotypes and environments were considered as high-yielding genotypes and environments. Tese results are supported by previous studies by Tumuhimbise et al. [31], Morais et al. [42], Hmwe et al. [43], and Esuma et al. [45] who reported that yield stability among genotypes was evaluated using mean performance and the IPCA score by graphically constructing the AMMI-1 biplot into four quadrants. Tey also discovered that genotypes and environments ranging from low to high yield were distributed in four quadrants.
Te X-coordinate denotes the main efects (genotype and environment means), whereas the Y-coordinate denotes the interaction efects (IPCA1) in the AMMI 1 biplot (Figure 1). Te diferences between genotypes in terms of direction and magnitude along the X-axis (yield) and Y-axis (IPCA 1 scores) are signifcant in the AMMI 1 biplot. A biplot assay is interpreted, and if main efects have an IPCA score near to zero, it implies negligible interaction efects (stable), but a greater score (absolute value) shows instability and is specifcally adapted to certain environments [46]. When a genotype and its environment have the same sign on the IPCA axis, their interaction is positive; when they have diferent signs, it is negative [47]. According to the AMMI model, genotypes with root mean yield greater than the grand mean and an IPCA score of virtually zero are generally adaptable to all environments. However, genotypes with a high mean performance and a high IPCA score are thought to be more adaptable to their environments [44].
According to Figure 1, G18, G19, and G25 (adaptive group 1 or characterized by low-yielding environments with stable genotypes) showed specifc adaptability for Disa environment having a fresh storage root mean yield below the grand mean. Te frst adaptive group's genotypes and environments have the same sign on the IPCA axis, indicating that their interaction is positive. G4, G8, G9, G11, G12, and G17 (adaptive group 2 or characterized by high yielding/ ideal environment with an unstable genotype) were found to have specifc adaptability for environments such as Tarcha, Wara, and Areka, with a higher fresh storage root mean yield than the grand mean and high positive interaction. Genotypes G5, G6, G7, and G16 were in adaptive group 3 (characterized by a high-yielding environment). Tey revealed a specifc adaptation for the Bonbe environment with a higher fresh storage root yield than the grand mean yield and positive interaction. Te genotypes, G1, G2, G3, G15, and G22 (adaptive group 4, or defning a low-yielding environment with an unstable genotype), were identifed as having sole adaptability for the environment of Jimma. At IPCA = 0, the genotypes G10, G13, G14, G20, G21, G23, and G24 (adaptive group 5 or stable genotypes) showed high stability and general adaptability; G20, G21, G23, and G24 had fresh storage root yields close to the grand mean yield, while G10, G13, and G14 had higher storage root mean yields than the grand mean and negligible interaction. In general, genotype G10 was screened with general adaptability for all environments (close to IPCA = 0 or insignifcant interaction) with a high fresh storage root yield of more than the grand mean yield and was the overall winner with less variable yield across the environments, suggesting its eligibility as one of the leading genotypes for the current study. Agyeman et al. [24], Morais et al. [42], and Hmwe et al. [43] supported this study by discovering that genotypes with high yield were least interactive with the environment (low IPCA score), indicating that they were broadly adapted genotypes with high yield in all environments, whereas unstable genotypes with high yield were adapted to specifc environments. Similarly, several studies for diferent crops reported that genotype-adaptive grouping in four quadrants was estimated on the basis of mean yield and the magnitude of IPCA1 scores [48][49][50][51]. Also, they observed the stable, unstable, and overall winning genotypes.
On the other hand, some environments stood out as having a small contribution to the interaction (Wara); a moderate contribution (Disa, Areka, and Bonbe); and a large contribution (Tarcha and Jimma) ( Figure 1). Tarcha, Wara, and Bonbe environments, produced a higher mean storage root yield than the grand mean (47.01 t·ha −1 ), indicating that these were ideal sites to acquire high means. With a high positive IPCA 1 score, the environments with the most potential (Tarcha, Wara, and Areka) demonstrated diferential performance of genotypes for fresh storage root yield ( Figure 1). Te low-yielding environment (Jimma) had the lowest yield but a negative IPCA1 score, indicating that all genotypes performed poorly in this environment. Similar observations were reported by Kadhem and Baktash [49], Erdemci [50], and Wardofa et al. [51], who observed highyielding and low-yielding environments with varied contribution interactions.

AMMI Stability Value (ASV).
To determine the genotypes' stability, an AMMI stability value was calculated (Table 5). In a two-dimensional scatter graph of IPCA1 (interaction principal component analysis axis 1) scores against IPCA2 scores, ASV is the distance from zero. Te proportional diference between the IPCAs (1 : 2) can be used to compensate for the diference in stability measurements of the two principal components, which can then be computed using the Pythagorean theorem to the efect of the AMMI stability value [37]. According to Purchase [52], the AMMI stability value (ASV) does not give a quantitative stability metric but rather quantifes and ranks genotypes based on their yield stability. In this sense, genotypes with lower ASV values are thought to be more stable, while those with higher ASV values are thought to be unstable. Genotype G14 was the most stable, with an ASV value of 0.58, followed by genotypes G24 and G21 with ASV values of 0.78 and 0.88 in fresh storage root yield, respectively, and the genotypes G9, G16, G22, and G25 were the most unstable, with ASV values of 4.23, 5.74, 5.49, and 5.78, respectively (Table 5). A similar procedure was used by Adjebeng-Danquah et al. [16], Tumuhimbise et al. [31], and Esuma et al. [45], who found a more stable genotype with a lower ASV value.

Genotype Selection Index (GSI) Analysis.
Stability is not the only parameter for selection because the most stable genotypes would not necessarily give the best yield performance. Te term "high stability" only has signifcance if it is linked to average performance [53]. Hence, there is a need for approaches that incorporate both mean yield and stability into a single index [38]. Te lowest GSI value is considered the most stable, with a high mean yield. Terefore, G14 and G10, with a GSI value of 12, were the most stable genotypes with a high fresh storage root yield, followed by G4, G11, and G8, with GSI values of 14, 14, and 16, respectively, indicating that they were stable (widely adaptable) and high-yielding. Based on the value of the genotype selection index, the genotypes G2, G3, G17, G22, and G25 were unstable genotypes (Table 5). Tis fnding is in line with previous studies, which stated that stable genotypes with high yields were identifed by analysis of the genotype selection index based on the ranking mean yield and ranking AMMI stability value [31,45,54].

GGE Biplot
3.5.1. Which Won Where View of GGE Biplot. Te polygon view of the GGE biplot graphic analysis is presented (Figure 2) for the identifcation of winning genotypes by visualizing the interaction patterns between genotypes and environments [55]. It is helpful in identifying crossover and noncrossover genotypeby-environment interactions as well as the possible existence of diferent mega-environments in multilocation yield trials [19,56]. As displayed by (Figure 2) genotypes, G3, G5, G13, G16, G17, G22, and G25 were the vertex genotypes. Tese genotypes perform best or worse in some or all environments because they are the furthest from the biplot's commencement [55], and they are regarded as specifcally suited genotypes since they are more responsive to environmental change. Tey thrive in environments that are part of their specifc sector in the GGE's polygon view-biplot [55]. At Tarcha and Disa, G25 was the most successful genotype, while G16 at Bonbe and Jimma and G17 at Wara and Areka. As a result, G25 won in Tarcha and Disa environments, while G16 and G17 won in Bonbe and Jimma and Wara and Areka environments, respectively. On the other hand, the vertex genotypes G3, G5, G13, and G22 were the poorest genotypes in almost the entire test environments because they were the furthest from the biplot's origin on the opposite side of the environments. Similar results were reported by Agyeman et al. [24], Akinwale et al. [30], Noerwijati and Prajitno [40], and Sholihin [57], who characterized genotypes' which-won-where patterns. Tey found that some genotypes performed better in a specifc environment than others and that some genotypes performed worst in some environments.
Te biplot was divided into seven sections by the equality lines in Figure 2. Te environments were distributed across three sectoral areas, whereas the genotypes were distributed throughout all the seven. Te three mega-environments were, namely, frst (Tarcha and Disa), second (Wara and Areka), and third (Jimma and Bonbe). Tis suggests that comparable genotypes do better in a homogeneous environment. Terefore, the identifed mega-environments could be useful in managing the genotype-byenvironment interactions and then generalizing the results to similar agroclimatic locations. Te genotypes that are located near the sector's vertex are the most yielding genotypes in that sector [56]. Two environments (Tarcha and Disa) were found in the frst sector (I). Tis sector encompassed nine genotypes: G4, G9, G11, G12, G14, G15, G19, G20, and G25 ( Figure 2). Te frst sector's vertex genotype was G25, indicating that this was the better genotype for these two environments and that environments within the same sector had the same winning genotype, while it was not clearly separated since G4 and G9 were also very near to the side of that vertex, the second sector (II) contained fve genotypes without any environment, and G5 was the vertex genotype ( Figure 2). Te third sector (III) contained two environments (Jimma and Bonbe) and two genotypes, G7 and G16. Te vertex and best-yielding genotype for this Key: RY � ranking mean storage root yield, ASV � AMMI stability value, GSI � -genotype selection index, and RASV � AMMI stability value ranking.
International Journal of Agronomy 7 section was G16. Without any environment, the fourth (IV), the ffth (V), and the sixth (VI) sectors contained one, four, and two genotypes, respectively ( Figure 2). Under these sectors, the vertex genotypes were G3, G13, and G22. However, these were not the highest yielding genotypes in any environment; rather, they were the poorest genotypes in all or some environments. As a result, these genotypes are thought to be well suited to their environment. Te last sector (VII) comprised two environments (Wara and Areka) and one (G17) vertex genotype. GEI variation was lower in the genotypes near the origin than in the vertex genotypes. Tus, the G8, G11, G14, G21, and G24 genotypes were close to the biplot origin, indicating roughly average performance, and their GEI variation was lower than that of the vertex genotypes. Tis fnding was similar to that of Noerwijati and Prajitno [40], Esuma et al. [45], Sholihin [57], Akter et al. [58], and Bakare et al. [59], who reported that the testing environment was delineated into diferent megaenvironments with winning genotypes and sectors containing various numbers of genotypes. Figure 3 that the frst (PC1) and second (PC2) principal components combined explained 51.67 percent of the total variation, indicating that this biplot can be used to separate interrelationships across the environments. Te angle between the biplot origin and the markers of test environments is connected to the correlation coefcient [25]. Furthermore, the length of an environmental vector confers a high level of genotype discrimination [19].

Relationship among Environments. Te GGE biplot demonstrates in
In the present study, environments Tarcha and Jimma were the most discriminating (holding more information) about the genotypes having the longest vectors from the origin, followed by Disa and Areka, which were medium discriminating, and environments Bonbe and Wara, little or no discriminating about the genotype diferences ( Figure 3). Nondiscriminating (noninformative) test environments provide minimal information about genotypes and should not be used as test environments [53]. Furthermore, the biplot vector view is primarily used to fnd test environments with acute, obtuse, and right-angle relationships, respectively, with positive, negative, and zero correlation between environments [56]. Based on the angle test between environment vectors, the six environments were clustered into three groups. Te frst group was discovered to have a small angle between environments Jimma and Bonbe, Tarcha with Disa and Wara, and Areka with Disa and Wara, that there was a highly positive correlation between them and that they provided similar information on genotypes (Figure 3). It implies that the environment provides unnecessary information on their ability to discriminate between genotypes. Obtaining reliable information on environment similarity and clustering should allow breeders to employ fewer test environments, reducing testing costs and enhancing breeding efciency. Te second group possesses the large angle revealed between the environments of Jimma and Tarcha, Disa, Wara, Areka, and Bonbe with Tarcha, Disa, Wara, and Areka. Hence, they were negatively correlated. Te presence of wide obtuse angles among the test environments is an indication of strong crossover GE, and the largest angle is slightly larger than 90°, implying that the GE is moderately large. Te third group, which had the right angle, was formed between Disa and Areka. Tis indicates that these two environments have little or no correlation between them and the genotype performing diferently. Akter et al. [58], Lule et al. [60], and Baraki   8 International Journal of Agronomy among environments characterized based on the angle method. Tey found that some environments between them had large angles or low or negative correlations, whereas the associations with small angles had strong positive correlations and ofered similar data on genotypes.

Evaluation of Genotypes Based on the Ideal Genotype.
Te GGE biplot model is an interesting application for the evaluation of genotypes relative to an ideal genotype. Several authors Diriba [53], Yan and Tinker [56], and Farshadfar et al. [62] described that an ideal genotype has a high mean performance as well as high stability across environments. According to Nimlamai et al. [63], the ideal genotype with high mean performance and high stability was identifed by using the ideal position (the center of the concentric circle).
An ideal genotype has large PC1 scores (high mean yield) and small (absolute) PC2 scores (high stability). Even though such an "ideal" genotype may not be present in reality, it might be used as a benchmark for genotype evaluation [64]. Concentric circles were formed in a GGE biplot graph based on genotype-focused scaling to better visualize the distance between genotypes and the ideal genotype [56,65]. In early breeding cycles, genotypes that are far from the ideal genotype can be ruled out, while genotypes that are close to it can be considered in subsequent tests [55]. A genotype is more desirable if it is closer to the "ideal" genotype, which is located in the frst concentric circle of the GGE biplot graphic [64,66]. According to the GGE biplot graph (Figure 4), genotype G10 was positioned in the frst concentric circle. Terefore, G10 was the ideal genotype position, followed by G15, G4, G20 G19, G14, and G11, making it more desirable than other cassava genotypes. In spite of this, G1, G2, and G3 improved cultivars were more undesirable than other cassava genotypes, and they were adapted to specifc environments. G14, G21, and G24 were placed near the biplot origin, and they were less sensitive to an environmental change. Tis is similar to what Akinwale et al. [30], Erdemci [50], and Naheif and Alaa [67] reported as one ideal genotype and some other desirable genotypes located in the frst and next concentric circles, respectively. Similarly, Noerwijati and Prajitno [40] identifed ideal genotypes using diferent approaches; their criteria were that an ideal genotype should have large PC1 scores (high mean yield) and a small absolute PC2 score (high stability), but this approach was not able to identify desirable genotypes.

Evaluation of Environments Relative to Ideal
Environments. According to Yan and Tinker [56], an ideal environment has the highest discriminating capability and representativeness, which are important properties of a test environment. Yan and Kang [55] defned an ideal environment as one that is highly diferentiating for the tested genotypes while at the same time representative of the target environments. In this regard, Tarcha had a smaller angle with the average environment axis (AEA), while Wara, Bonbe, and Areka had a large angle with the average environment axis ( Figure 5). Bonbe and Wara were close to the center with very short vectors ( Figure 5) and provided less helpful discriminating information about the genotypes. As a result, Tarcha was the most representative environment, whereas Wara, Bonbe, and Areka were the least representative. Also, Tarcha had the highest discriminating capability of the genotypes ( Figure 5). As a result, Tarcha is the most favorable environment for the selection of superior genotypes.
In the environment-focused GGE biplot, the ideal environment is positioned in the frst concentric circle, and the desired environments are defned as those that are closest to the ideal environment. In this regard, Tarcha is in the frst concentric circle and has been in the ideal environment ( Figure 6). Tarcha's PC1 score was high, while its PC2 score was low. Hence, genotype evaluation in the Tarcha environment maximized the observed genotypic variation among genotypes for the fresh storage root yield of the tested cassava genotypes and should be regarded as the most suitable to select widely adapted genotypes. Disa's environment was close to the ideal environment (Tarcha), and this environment has been identifed as a desirable environment ( Figure 6). On the other hand, the Jimma and Areka environments were located far away from ideal environments, so they might be regarded as undesirable environments (fewer representatives) for selecting widely adapted cultivars but can be used for selecting specifcally adapted cultivars. Tis variation among environments can be associated with soil fertility, rainfall, and other environmental variability across the environments. Te composition of genotypes afects a location's discriminating capacity, but the presence of GEI makes fnding an appropriate test location more difcult [25].  environments should have high PC1 scores to discriminate genotypes in terms of the genotypic main efect and low PC2 scores in an absolute value to be more representative of the overall locations [44]. As far as the testing environment is concerned, the environment obtained directly concurs with that described by [27,50,58,67]. In their study, they classifed the testing environment as ideal, desirable, discriminating, and representative, where the ideal environment was situated in the frst concentric circle, and the desirable or potential environment was closest to the ideal. In the same way, they reported that the ideal environment is the most discriminating and representative environment. Furthermore, they suggested that the most representative environments can be used for widely adapted genotype selection, while nonrepresenting environments can be useful for specifcally adapted genotype selection.

Ranking of Genotypes Based on Mean Yield and Stability Performance.
In the GGE biplot, the assessment of mean root yield and stability of genotypes (Figure 7) was conducted by using the average environment (tester) coordinate (AEC) methods [31,68]. Te average environmental (tester) coordinate (AEC) is defned by the average PC1 and PC2 scores for all the environments [55]. Te AEC X axis (PC1) line passes through the biplot origin with an arrow indicating the positive end of the axis and indicates the mean yield performance axis of genotypes. Te line, which passes through the origin and is perpendicular to the average environmental axis, measures the stability of genotypes (PC2) in either direction ( Figure 7). Stable genotypes had the smallest perpendicular lines and were close to AEC (PC1) with PC2 scores of almost zero. On the other hand, any direction on the axis away from the biplot origin suggests increased GE interaction and decreased stability. Te best genotypes for selection criteria are those with both    high mean yield and high stability. In this regard, in the present study (Figure 7), the single arrowed line was pointed to higher yield across environments. Terefore, genotype G5 had the highest mean yield, followed by G10 and G4. Genotype G18 had a mean yield similar to the grand mean, and G3 had the lowest mean yield. Furthermore, genotypes G14 and G10 were the most stable, while G22 and G16 were highly unstable. Mostly, genotype G22 was a highly unstable and poor-performing genotype in the environments where genotype G5 was the winner but not in the Areka environment. Te present study's fndings are in line with the report made by [24,30,[69][70][71]. Tey ranked genotypes based on mean performance and stability across environments. In this way, they found some genotypes to be the most stable with a high mean yield and some unstable high yielders, while some other genotypes were unstable with a poor yield and a stable low yielder.

Conclusions
According to the combined analysis of variance, the degree of GEI had the greatest infuence on cassava fresh storage root yield performance, followed by the environmental efect, while genotype had the least efect on the total treatment SS. Te AMMI and GGE biplot models were good tools for visual multienvironment trials data analysis and allowed the estimation of the interaction efects of a genotype in each environment. Te three mega-environments have been identifed that could be helpful for genotype evaluation and productive breeding. Te GGE biplot revealed that Tarcha was the ideal and the most representative environment, while G10 was the ideal genotype and overall winner. According to the AMMI, GGE biplot model, and GSI analysis genotypes, G10 and G14 were identifed as being the most stable, with a higher fresh storage root mean yield than other genotypes and the grand mean. As a result, G10 and G14 were selected as superior genotypes that could be exploited in a cultivar development program as widely adaptable genotypes for all environments.

Data Availability
Te datasets that support the fndings of this study are available from the corresponding author upon request.

Conflicts of Interest
Te authors declare that they have no conficts of interest.