The Stability of Sugar Yield in Promising Sugarcane Genotypes ( Saccharum officinarum L.)

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Introduction
A genotype has high consistency or stability when it has a high average yield, and at the same time, the yield also fuctuates slightly in diferent years and environments [1,2].To investigate the interaction between genotypes and the environment, researchers use various statistical methods, such as variance analysis, combined analysis, regression, and nonparametric and multivariate methods [3,4].To select and release high-yielding and stable varieties, yield comparison experiments are performed in several years and several environments.In these experiments, it is necessary to consider the compatibility of genotypes to diferent environments in addition to their yields [5,6].Te interaction between genotypes and environments is important in the releasing process of new lines.Tus, it is important to evaluate new lines in a series of uniform experiments to identify their degree of adaptation to diferent environmental conditions [7].
Yield stability refers to the ability of plant genotypes to show yield capacity in a wide range of environments [8].Cultivating genotypes in tested climates over the years and in diferent environments as a sample of the environments determines the stability of the yield and the genotypes with less genotype × environment interactions [9].Yield stability is also referred to as minimum damage caused by climatic changes, stress, or pests [10].
Sometimes, the term phenotypic fexibility is also used instead of yield stability.Yield stability depends on the genetic structure or reaction of individual or group genotypes [4].Stability is the result of the interaction between a variety and environmental factors, and the outcome of this reaction depends on the genetic structure of the variety and the intensity of environmental factors, especially limiting factors [11].
In plant breeding, breeders select plants based on their phenotypes, and as a result, the efect of selection largely depends on that part of the phenotype that is afected by the genotype.Terefore, the level of environmental infuence on quantitative traits is very important for plant breeders [12].
Romagosa and Fox [13] grouped agricultural sustainability evaluation methods into four groups, including variance analysis, regression, nonparametric, and multivariate methods.Lin et al. [10] also presented a similar grouping while comparing diferent methods of phenotypic stability and evaluating their efciency.
Te AMMI method is a combination of variance analysis and principal component analysis, which is used to analyze consistency studies [14,15].In this method, the main efect of genotypes and the environment is estimated (additive main efect) using variance analysis, and then the interaction efect of genotypes and the environment (multiplicative interaction efect) is analyzed using decomposition into principal components.Based on this method, stable genotypes are determined by plotting two main components that justify the most changes [7,13].
Najafan et al. [16] determined stable genotypes using the AMMI method and stated that this method could be used to determine the genotypes with general and special compatibility for diferent environments.
Cornelius [17] proposed two multiplicative methods in genotype and environment interaction studies, namely, a shifted multiplicative model (SHMM) and a spatial regression model (SREG).In the SHMM method, environments and genotypes are grouped based on the minimum and maximum probabilities, and stable genotypes can be determined based on the presented shape [17][18][19][20].
Tis study aimed to determine promising stable sugarcane genotypes for the sugarcane-growing areas of Khuzestan Province based on each of the stability analysis methods.
Since the program of improving and introducing new sugarcane varieties in Iran has been started for about 20 years and is quite young, the introduction of stable and suitable varieties in the mentioned areas clearly demonstrates the novelty and appropriateness of this research.

Experiment Implementation.
To evaluate the promising sugarcane genotypes, 26 promising sugarcane genotypes and four commercial varieties (CP57-614, CP69-1062, CP48-103, and NCo310) as controls in three environments of Khuzestan province (Amir Kabir, Imam Khomeini, and Mianab Agri-industry) were cultivated in a randomized complete block design (RCBD) with three replications for each experiment.Te genotypes in each experiment and each plot were cultivated in fve rows of 11 m long, with a distance of 183 cm between the rows.Te distance between each plot on the lines was 2 meters, and there was an empty farrow space between plots.Each genotype occupied an area equal to 87 m 2 .Te usual measurements were performed during the growth period.All agricultural operations, such as irrigation, fertilization, and the control of weeds, pests, diseases, etc., were carried out the same as commercial farms.
For the fnal analysis every year, quantitative and qualitative traits were measured by sampling 10 stalks of each genotype in each replication of each experiment.After measuring the sugar yield (SY) of the genotypes, all the obtained data were analyzed by simple and combined analyses using the SAS statistical program.

Te Geographical Environment of Khuzestan Province.
Khuzestan province is located in the extreme southwest of Iran.Te sugarcane area is located in the geographic latitude of 31-32 °N and the longitude of 48 °E with an altitude of 7-80 m above sea level.Te region extends from the vast plains of Mesopotamia to the Persian Gulf in the south of Iran.
Te geographical environment of the experimental site is in the Amir Kabir, Imam Khomeini, and Mianab agriindustry felds.

Climatic Conditions of the Experimental Site.
Average daily minimum and maximum temperatures in January and July are 1.5 and 45.1 °C, respectively.Te annual evaporation is about 3000 mm, and the relative humidity of the air is diferent depending on the environment of the sugarcane felds.Its amount was measured at 10-60% and 30-80% in the northern and southern areas, respectively, under sugarcane cultivation.Te main amount of rain falls between November and April, with an average of 240 mm in the center of the province.Due to the hot and dry climate of the region, sugarcane completely needs irrigation; hence, the cane yield is impressive with proper agricultural care.In Khuzestan province, sunlight is very variable throughout the year.Te amount of light in sugarcane-growing areas of the world, such as Florida and Hawaii, is compared with this exceptional area.1.Because the experiments were conducted in 3 years and three locations, each replicate in each experiment at each location was assumed to be one environment and, therefore, nine environments were considered in all the experiments.Due to the special method of sugarcane cultivation, the year and the environment were determined as random factors and genotypes as fxed factors.
Te parents and the number of genotypes selected from the progeny during the selection process are given in Table 2. Te seeds (cuttings) of the genotypes were planted in the mentioned stations in September 2016.
Te analyses of this study were performed according to the following steps: (1) Test of homogeneity of error variances [12].
Te condition for the correctness and performing the combined variance analysis is the homogeneity and uniformity of the variance of the experimental errors in the tested years and regions [12].Tere are several methods to test the homogeneity of experimental errors, one of which is the test of homogeneity of errors or Bartlett's test, which was used in this experiment [15,21].
In the combined analysis, MSE2 is the average (pooling) of all test errors, which is written in the following formula. (2) (3) C: It is a coefcient that is calculated as follows: Te value of C is always greater than 1.
To test homogeneity with Bartlett's test, a separate analysis of variance is frst performed for each year and environment.A simple analysis of variance was performed with nine experiments, as explained in the previous paragraph.(2) After the simple variance analysis for each year and Bartlett's test to examine the uniformity of error variance, the interaction efects of the genotype × the environment for diferent agronomic and phenological traits were estimated with the combined variance analysis to investigate the main efect and double/triple interactions.Te averages were compared by Duncan's test [15,21].(3) Te ecovalence [22] and Shukla [23] stability variance were determined for all genotypes.(4) Te stability analysis of the genotypes was performed using a nonparametric method based on the mean and standard deviation of the ranks for three cultivation years and their average values [8].For this purpose, the rank of each genotype was determined in terms of the average yield of all tested genotypes for each experiment, followed by calculating the average rank (R) and its standard deviation (Standard Deviation of Rank: SDR).Te Yield Index Ratio (YIR) was determined for each genotype and for all environments and years as another measure of yield stability.For this purpose, the average sugar yield of each genotype in all environments was divided by the average yield of all genotypes in all environments and expressed as a percentage [2,24].(5) Te stability of genotypes was also calculated based on the simultaneous selection method (Ysi) using the method proposed by Kang [25,26].(6) Te stability of genotypes was determined based on the AMMI model and by drawing related graphs (Cornelius).

International Journal of Agronomy
All statistical calculations of this study were performed using SPSS (Version 28), SAS (Version 9), MATLAB (Version 21.4), and GEST (Version 3.2.7)software.

Results and Discussion
Te operations performed to calculate X 2 and Bartlett's test steps for the sugar yield trait are summarized as follows.Table 3 summarizes the operations performed to perform Bartlett's test and the homogeneity of variances in experiments for the sugar yield traits (S1).Te table indicates that X 2 value of 7.95 for the sugar yield trait, which is less than that in table (20.15).Tus, the variance of the errors of A test for this trait is homogeneous in diferent experiments [27].
Te results of the three-year combined variance analysis of sugar yield in the studied areas showed that the efects of year, location, year × location, and genotype were signifcant at the probability level of 1%, and the interaction efect of genotype × location was signifcant at the probability level of 5%.However, the triple interaction efect of genotype × environment × year was not signifcant (Table 4).
Te signifcance of the genotypes and the year × location interaction showed the diference between genotypes and locations from year to year.Tis result suggests a diference between the yields of diferent genotypes during diferent years and in each of the studied environments.Te MS of the genotype × year and genotype × year × location was not signifcant, showing that the yields of the tested genotypes were not signifcantly diferent from each other in diferent regions and years (S2).
Considering the signifcant interaction efect of the environment × year and genotype × environment, it can be concluded that the yield of genotypes is diferent in the investigated environments and the stability of genotypes should be analyzed for diferent stations of this study.
Table 5 shows the mean values and standard deviations of genotypes ranked in nine environments and three crop years 2017-2018.Te g 6 was the most stable genotype among the studied genotypes, with the lowest average rank and standard deviation in this method.Genotypes g 21 , g 15 , g 7 , g 22 , and g 17 were ranked after genotype g 6 with their means and standard deviations, respectively.In this method, the genotypes, g 12 , g 8 , g 16 , and the commercial variety CP48-103 showed less sugar yield stability by assigning the highest average rank and standard deviation (S3).
Table 5 lists the YIR values calculated based on the average results of three crop years, which is another nonparametric criterion, based on which genotype g 15 was the best genotype with the highest YIR among the studied  Genotypes g 16 , g 4 , and g 8 with low YIRs were considered unstable.Tis index, which groups genotypes exclusively based on the average yield, can complement the two criteria of the average rank and its standard deviation in the selection of stable genotypes.In the total of three criteria, genotypes g 6 , g 15 , g 17 , g 22 , and g 21 were included in the group of stable genotypes.
In the nonparametric method, genotypes cannot be grouped for general and special adaptations and this issue is considered the main problem of this method.However, the simplicity of this method makes it possible to be used in such experiments as genotype × year or genotype × environment to select stable genotypes.Becker and Leon [28,29] presented experiments for the interaction efect of ranks and determined a stable genotype when its rank is stable in diferent environments.
Te results of the mean square analysis based on Eberhart and Russell's regression method showed a signifcant F for genotypes, which indicated the existence of wide genetic variation among the genotypes.Moreover, the signifcance of F for the linear environment efect indicated a signifcant linear regression between the yield of each environment and the environmental index.
Te signifcant interaction efect of the genotype × linear environment showed that the response of genotypes is lower in more uniform environments.Considering the signifcance of the mean square deviation from the regression line (S2di), it can be claimed that the mentioned method can efectively select stable genotypes.Based on this method, genotypes g 2 and g 11 with an average yield of 7.65 and 7.71 tons/ha and a regression coefcient of 1 were determined as stable genotypes.Genotypes g 5 , g 7 , and g 14 were in the next ranks in the next environments.
Tis method was also used by Yates and Cochran [30], who introduced stable genotypes with high yields (Table 6) (S3).
According to Wrick's ecovalence method, genotypes g 27 , g 23 , g 16 , g 12 , g 5 , g 4 , g 7 , and g 21 , with the lowest coefcient of equivalence and, as a result, less contribution to the value of the genotype × environment interaction, were considered stable in this method [9].Te ecovalence coefcients of these genotypes were calculated at 0.75, 0.8, 1.16, 1.31, 1.69, 1.73, 1.89, and 1.9, respectively.Among these stable cultivars, the g 21 genotype was higher than the others with the average yield of 8.308 tons/ ha.Genotypes g 6 , g 15 , g 28 , g 8 , g 22 , g 30 , g 29 , and g 10 were unstable with the highest ecovalence coefcients and, as a result, greater contribution to the value of the genotype × environment interaction.Te variance of genotype × environment interaction related to Shukla's stability method also showed that genotypes g 23 , g 27 , g 16 , g 12 , g 5 , g 4 , g 7 , and g 21 with the lowest variance of genotype × environment interaction were the most stable genotypes.Genotypes g 6 , g 15 , g 28 , g 8 , g 22 , g 30 , g 29 , and g 10 did not show high stability due to their highest stability variance (Table 6).Te comparison of two criteria shows that the selection of genotypes based on these two criteria is similar to a signifcant extent, and there is a high correlation between these two criteria.Comparing the results of Wrick's ecovalence and Shukla's stability variance with the results based on the nonparametric criteria of the average rank and its standard deviation and the YIR indicated no high correlation between the results of these methods [26].
Based on the simultaneous selection for sugar yield and stability (Ysi), commercial varieties and genotypes g 30 , g 28 , g 26 , g 24 , g 23 , g 27 , and g 19 with Ysi values equal to 29, 29, 27, 23, 22, 21, and 20, respectively, were the most stable genotypes (Table 7).Te stable genotypes based on this method were relatively similar to those of Eberhart and Russell regression methods, Wrick's ecovalence, Shukla stability variance, and the nonparametric mean and standard deviation method [9,27].
Te mean square analysis based on the AMMI stability method showed that the frst component of the interaction efect was signifcant at the 1% probability level.Tis component and the second component with 26.59% and 19.03%, respectively, accounted for a total of about 45.62% of the total square of the interaction efect (Table 8).Based on the AMMI method, stable genotypes are determined as those with positive and lower values for the main components that account for most of the changes in the nonlinear efect of genotype × environment.
In addition to calculating the simple additive efect in the AMMI method, which was used in the previous methods, the main multiplicative efect (decomposition into the main components) can also be calculated to investigate the interaction efect of genotype × environment in more detail (Table 9).
Considering the importance of genotype × environment interaction, the analysis based on this method showed that the genotypes g 14 , g 20 , g 29 , g 28 , and g 30 with the least efect and high average yield are the most stable genotypes.Te distribution of genotypes in diferent environments was determined using AMMI's biplot, based on which the frst and second main components shown in Figure 1 indicate the distribution of the genotypes in terms of genotype × environment interactions.Genotypes that are close to the center of the coordinate axis are important in terms of general stability.Accordingly, genotypes g 27 , g 29 , and g 16 , respectively, with the highest average yields and the lowest genotype × environment interactions, were among the most stable genotypes based on the AMMI method [31].
Te frst group included genotypes with average yields in the stable group, and in terms of the values of the frst and second main components, they had small and positive values for the frst component and small and negative values for the second component, respectively [32,33].
In the second group, there were genotypes with average yields, in which the values of the two components were close to zero or negative.Te third group included genotypes that gained high and negative values in terms of the frst and second components.AMMI's biplot based on the yield and frst main components is shown in Figure 2 [32].
Tis diagram shows that genotypes g 14 , g 27 , g 28 , and g 29 have the least genotype × environment interactions, and g 28 and g 29 with IPC1 close to zero and higher yields were identifed as the most stable high-yielding genotypes [14].Tese genotypes maintained their yield stability in the three studied locations.
Terefore, all the studied environments have a high contribution to creating genotype × environment interactions, and the second environment had the largest contribution to creating large interactions.Accordingly, genotype g 6 can be considered to have special adaptation to the frst (Imam Khomeini) location, genotypes g 8 and g 15 to have special adaptation to the second location (Amir Kabir), and genotypes g 10 , g 17 , and g 22 were found to have special adaptation to the third location (Mianab) [6,14].
In this research, several statistical methods were used to determine and introduce the stable genotypes of sugarcane for commercial cultivation.As stated in the results of each statistical method, some of the genotypes were introduced as stable, which are summarized in Table 10.      Figure 1: Genotype × environment interaction and distribution of the genotypes (AMMI biplot).In this fgure, numbers 1 to 30 are genotype number and are equivalent to g 1 to g 30 .According to the AMMI biplot, genotype g 6 was considered to have a special adaptation to the frst location (Imam Khomeini), genotypes g 8 and g 15 to have a special adaptation to the second location (Amir Kabir), and genotypes g 10 , g 17 , and g 22 were found to have a special adaptation to the second location (Mianab).Terefore, these genotypes are introduced for commercial cultivation in the mentioned locations.
According to the results of this research, it is suggested to introduce genotype g 14 , with high stability based on the AMMI method, as a new variety for commercial cultivation in the studied locations.
Due to the importance of investigating environmental stresses in agricultural production, it is recommended to investigate the reaction of the introduced genotypes, especially the g 14 genotype, to environmental stresses in the future.

1 Figure 2 :
Figure2: Te biplot obtained from the average sugar yield and IPC1 stability parameter (oval and rectangular shapes, respectively, shows the groupings resulting from the cluster analysis of genotypes and environments based on the IPC1 stability parameter.Horizontal and vertical lines, respectively, pass the points of average yield and IPC1 � 0).In this fgure, numbers 1 to 30 are genotype number and are equivalent to g 1 to g 30 .

Table 2 :
Parents and the number of selected genotypes from among their progeny in diferent stages of selection.
genotypes.Genotypes g 6 , g 22 , g 21 , and g 17 were ranked after genotype g 15 in terms of yield stability.

Table 3 :
Homogeneity test of error variance of experiments (Bartlett's error variance test) for sugar yield (Sy).

Table 4 :
Combined analysis variance of sugar yield of promising sugarcane genotypes.

Table 5 :
Sugar yield Stability of sugarcane genotypes based on nonparametric methods.27 , g 11 , g 16 , g 3 , and g 23 had moderate genotype × environment interactions and occurred in the group of genotypes with low stability.

Table 6 :
Yield stability of sugarcane genotypes based on ecovalence and Shukla's stability variance.

Table 7 :
Sugar yield stability of sugarcane genotypes based on the simultaneous selection method (Ysi).

Table 8 :
Variance analysis of genotype × environment interaction using AMMI's method.

Table 9 :
Quantities related to the two main components of sugarcane genotypes in the AMMI model.