The potential of genotypes and stability of their performance can be judged by multi environment trials [1] . It is more practical to develop and release varieties which are adapted to more than a single environment and can be successfully grown over a range agro ecological regions. Agronomic zoning is used to stratify environments in sub regions within which the interactions are not significant [2] . These methods are dependent on the genotypes and environments under study and may not be much informative if linearity fails [3] . For quantitative traits like yield, the relative performance of different genotypes often varies from one environment to another. So, genotype × environment interaction does exist when phenotypic response made by a change in environment is not the same for all genotypes [4] .

Genotype × environment interaction is a valuable concept in plant breeding programme for the selection and improvement of genotypes that perform well across environments [5] . Several statistical approaches designed to measure genotypic stability. However, no single method is sufficient to measure the performance of genotypes across different environments. A genotype may be considered more stable and adaptive if its yield fluctuation is less when cultivated over different seasons [6] .

Yield of mustard and its component being quantitative in nature would be useful to gain knowledge about the nature and magnitude of genetic variability and its interaction with environment. Interactions between genotypes and environments are particularly interesting because they do reflect the fluctuations in environment if genetic makeup is known and in most cases prediction can be made well ahead [7] .

Therefore, estimating heritability including the genotype × environment interaction variation for the total variance is more appropriate for prediction of genetic advance due to selection. Genotypes that can adjust their phenotypic state in response to environmental vulnerability in such a way that they provide maximum stable economic return, can be termed “buffered” or stable [7] . So, it is necessary to identify the stable genotypes that are suitable for wide range of environments. Several authors conducted experiments for this purpose, which have been carried out by [8] - [11] .

Statistically, G × E interactions are detected as a significantly different pattern of response among the genotypes across environments and biologically, this will occur when the contributions (or level of expression) of the genes regulating the trait differ among environments [12] . Therefore, an ideal approach in plant breeding is to develop cultivars that have fairly uniform performance (low G × E) over a range of environments with the ability to utilize the resources in high yielding environment.

Rapeseed-mustard is a major oilseed crop in Bangladesh. It contributes a lion share to the total edible oil production in the country. Rapeseed and mustard cover 66.48% area of total oil crops [13] . Production of oilseed crops dramatically increased by many folds (14.9 times) from 64,000 MT in 1960 to 956,000 MT in 2019 although encountered a pitfall in 1975 (237,000 MT), 1980 (246,000 MT) and 2005 (274,000 MT). This increase of oilseed crops was attributed to the combined effect of area expansion and a massive yield increase from 0.18MT/ha in 1960 to 2.1 MT/ha in 2019 implying a significant adoption of high yielding varieties and improved management practices [14] . The Oilseed Research Centre of BARI has already developed 22 rapeseed and mustard varieties, which comprise 10 Brassica rapa, 7 B. juncea and 5 B. napus. Their adaptability across environments is needed to be justified. The experiment has been undertaken to observe the performance of some rapeseed-mustard genotypes in different agro ecological regions in Bangladesh and to select the best one(s) over locations.

Nine rapeseed-mustard genotypes such as BS-11, BS-16, BS-18, BS-19, BS-14, BAUS-01, BAUS-02, BHS-01 and BAUS-03 were grown in 2023-2024 at Gazipur, Satkhira, Khulna and Cox’s Bazar. Gazipur—Old Brahmaputra Floodplain (Agro Ecological Zone—9), organic matter low to medium, fertility level low. Satkhira—High Ganges River Floodplain (Agro Ecological Zone—11), organic matter and fertility status low. Khulna-Gopalganj Khulna Beels (Agro Ecological Zone—14), organic matter and fertility level is medium. Cox’s Bazar—Chittagong Coastal Plains (Agro Ecological Zone—23), organic matter low, fertility level medium. Unit plot size was 5 rows 3 m long and row to row distance 30 cm and plant to plant distance 5 cm after thinning. The experiment was conducted following RCB design with 3 replications and treatments were the nine genotypes. Fertilizers were applied @ 260, 170, 90, 160, 5 and 10 kg/ha of Urea, TSP, MOP, Gypsum, Zinc-oxide and Boric acid respectively [15] . Half of urea and all other fertilizers will be used as basal dose and rest half of urea just before flowering. Plant height (cm), no. of branches/plant, no. of siliqua/plant, no. of seeds/siliqua, days to 50% flowering, days to maturity 1000seed weight (g) and seed yield (kg/ha), disease and insect reaction were recorded. Data were annualized using cropstat 7.2. Yield stability was analyzed employing [16] .

Nine rapeseed-mustard genotypes such as BS-11, BS-16, BS-18, BS-19, BS-14, BAUS-01, BAUS-02, BHS-01 and BAUS-03 were evaluated in four agro ecological regions for eight characters. The combined analysis of variance for eight characters were presented in Table 1 . The mean sum of square for genotypes were highly significant for most of the characters studied except thousand seed weight (g) and yield (kg/ha). Similarly, environmental variances were also highly significant for those characters including thousand seed weight (g). Variances due to genotype × environment interaction were highly significant for four traits such as plant height, no. of seeds per siliqua, days to 50% flowering and days to maturity. Significant genotype and environmental variances recorded in the study of [17] - [20] . AMMI Component 1 and 2 showed variation for plant height, no. of seeds per siliqua, days to 50% flowering and days to maturity except days to 50% flowering in AMMI Component 2. G × E (Linear) revealed insignificant variation for all the characters except no. of seeds per siliqua and days to maturity. The pooled deviation (nonlinear portion of variance) which is unpredictable portion of G × E interaction was significant for only four characters such as plant height, no. of seeds per siliqua, days to 50% flowering and days to maturity.

Plant height (PH) (cm), no. of branches/plant (NBP), no. of siliqua/plant (NSP), no. of seeds/siliqua (NSS), days to 50% flowering (DFF), days to maturity (DM), 1000seed weight (TSW) and seed yield/ha (kg/ha). * indicates significance at 5% level of probability; ** indicates significance at 1% level of probability, the same below.

The PH (cm) along with the value of phenotypic indices (Pi), regression coefficient (bi) and deviation from regression (S²di) were presented in Table 2 . The environmental mean and genotypic mean ranged from 111.3 to 144.0 and 85.21 to 149.2, respectively. The regression coefficient (bi), deviation from regression (S²di) values of these genotypes ranged from −0.27 to 1.73 and 7.66 to 258.45, respectively. The lowest overall mean for PH was recorded in BS-14 (85.21 cm) followed by BS-18 (116.1), BS-19 (120.0) and BAUS-02 (121.0) indicating dwarf varieties. The highest PH was found in BS-16 (149.2).

Five entries showed negative phenotypic index while the other four had positive phenotypic index for PH (cm). Again, negative and positive phenotypic index (Pi) reflects the short statured and tallness for this character, respectively. The negative and positive environmental index (Ij) reflected the early maturing and late maturing environments for this character, respectively. The environment Gazipur (Ij = −5.140), Satkhira (Ij = −11.52*) and Cox’s Bazar (Ij = −4.570) were favourable for dwarf varieties while Khulna (Ij = 21.23**) environment was suitable for long staturedness. The three genotypes such as BS-18, BS-14 and BAUS-02 having negative phenotypic index, coupled with near unit regression co-efficient and non significant deviation from regression recorded stable.

The NBP along with the value of phenotypic indices (Pi), regression coefficient (bi) and deviation from regression (S²di) were presented in Table 3 . The environmental mean and genotypic mean ranged from 4.08 to 5.64 and 4.76 to 5.73, respectively.

In Gazipur, the highest NBP was found from BAUS-03 (5.37) followed by BS-16 (4.77) and BS-18 (4.20) and the lowest in BHS-01 (2.70). The maximum NBP was recorded in BS-11 (5.93), the lowest in BS-14 (4.07) in Satkhira. BAUS-01 (6.44) and BHS-01 (5.90) showed the maximum NBP in Khulna and Cox’s Bazar, respectively.

Four genotypes showed positive phenotypic index while the other five genotypes had negative phenotypic index for yield. Thus, positive phenotypic index represented the higher yield and negative represents the lower yield among the genotypes. Again, positive and negative environmental index (Ij) reflected the rich or favourable and poor or unfavourable environments for this character, respectively. Thus the environment of Gazipur was poor whereas Satkhira, Khulna, and Cox’s Bazar was favourable environments for mustard production.

The regression coefficient (bi), deviation from regression (S²di) values of these genotypes ranged from 0.39* to 1.59 and 0.01 to 1.78, respectively. These differences in bi values indicated that all the genotypes responded differently to different environments. Considering the mean, bi and S²di, it was evident that all the genotypes showed different response of adaptability under different environmental conditions. Among the genotypes, BAUS-03, BS-16, BS-11 and BS-19 exhibited the higher grain yield, bi~1 and S²di~0 indicated that the hybrids were stable across the environment. Regression co-efficient and deviation from regression showed insignificant values for all the genotypes except BAUS-03.

The NSP along with the value of phenotypic indices (Pi), regression coefficient (bi) and deviation from regression (S²di) were presented in Table 4 . The environmental mean and genotypic mean ranged from 79.75 to 183.4 and 70.69 to 168.6, respectively.

Six genotypes showed positive phenotypic index while the other three genotypes had negative phenotypic index for yield. Thus, positive phenotypic index represented the higher yield and negative represents the lower yield among the genotypes. Again, positive and negative environmental index (Ij) reflected the rich or favourable and poor or unfavourable environments for this character, respectively. Thus all the three environments were favourable for mustard production except Gazipur.

The regression coefficient (bi), deviation from regression (S²di) values of these genotypes ranged from 0.34 to 1.48 and 5.72 to 205.42, respectively. These differences in bi values indicated that all the genotypes responded differently to different environments. Considering the mean, bi and S²di, it was evident that all the genotypes showed different response of adaptability under different environmental conditions. Among the genotypes, BAUS-01, BHS-01 and BS-11 exhibited the higher grain yield, bi~1 and S²di~0 indicated that the hybrids are stable across the environment. None of the genotypes showed significant values for regression co-efficient and also deviation from regression.

The NSS along with the value of phenotypic indices (Pi), regression coefficient (bi) and deviation from regression (S²di) were presented in Table 5 . The environmental mean and genotypic mean ranged from 15.56 to 18.78 and 12.61 to 27.55, respectively.

In Gazipur, the highest NSS was found from BS-14 (29.10) followed by BS-18 (23.73) and BHS-01 (18.33). In Satkhira, BS-14 produced the highest yield (30.00) followed by BAUS-02 (24.28) and BS-16 (20.93). The maximum production recorded in BS-14 (29.67) in Khulna which was followed by BHS-01 (26.67), BS-18 (24.33). In Cox’s Bazar the maximum yield recorded in the genotype BAUS-02 (21.67) followed by BS-14 (21.43) and BS-18 (16.97).

Four genotypes showed positive phenotypic index while the other five genotypes had negative phenotypic index for yield. The positive phenotypic index represented the higher yield and negative represents the lower yield among the genotypes. Again, positive and negative environmental index (Ij) reflected the rich or favourable and poor or unfavourable environments for this character, respectively. The environment of Khulna was favourable environments and the rest three were unfafourable for mustard production.

The regression coefficient (bi), deviation from regression (S²di) values of these genotypes ranged from −0.15 to 0.90 and 0.48 to 54.61, respectively. These differences in bi values indicated that all the genotypes responded differently to different environments. Considering the mean, bi and S²di, it was evident that all the genotypes showed different response of adaptability under different environmental conditions. Among the genotypes, BS-14, BS-18 and BHS-01 exhibited the higher grain yield, bi~1 and S²di~0 indicated that the hybrids are stable across the environment. All the genotypes showed insignificant values for regression co-efficient and also deviation from regression.

The DFF along with the value of phenotypic indices (Pi), regression coefficient (bi) and deviation from regression (S²di) were presented in Table 6 . The environmental mean and genotypic mean ranged from 40.22 to 43.44 and 41.08 to 44.83, respectively. The regression coefficient (bi), deviation from regression (S²di) values of these genotypes ranged from 0.26 to 2.06 and 0.73 to 33.31, respectively.

The minimum DFF recorded in BS-14 (32.67) which was followed by BHS-01 (36.33) in Gazipur. The maximum DFF recorded in BS-18 (43.33). The minimum DFF were recorded minimum in rest three locations such as Satkhira (36.67), Khulna (35.67) and Cox’s Bazar (39.33).

Two entries showed negative phenotypic index while the other seven had positive phenotypic index for DFF. Positive phenotypic index represented the late maturing and negative represented the early maturing genotypes. The negative and positive environmental index (Ij) reflected the early maturing and late maturing environments for this character, respectively. The environment of Satkhira (Ij = −0.583) and Gazipur (Ij = −1.398) were early maturing whereas Cox’s Bazar (Ij = 1.824) and Khulna (Ij = 0.157) was late maturing environments for this character. Two varieties such as BS-14, BHS-01 having negative phenotypic index, near unit regression co-efficient and non significant deviation from regression recorded stable.

Days to maturity (DM) along with the value of phenotypic indices (Pi), regression coefficient (bi) and deviation from regression (S²di) were presented in Table 7 . The environmental mean and genotypic mean ranged from 88.85 to 95.93 and 80.50 to 98.42, respectively. The regression coefficient (bi), deviation from regression (S²di) values of these genotypes ranged from −0.130 to 2.12 and 0.36 to 30.06, respectively.

The minimum DM recorded in BS-14 (80.50) which was followed by BHS-01 (91.25), BAUS-01 (92.33). The maximum days for maturity recorded in BS-16 (98.42). Satkhira region was favourable for early maturity (88.85) followed by Khulna (90.11) and Gazipur (95.59). Three genotypes showed negative phenotypic index while the other six hybrids had positive phenotypic index for DM. Positive phenotypic index represented the late maturing and negative represented the early maturing genotypes. Again, negative and positive environmental index (Ij) reflected the early maturing and late maturing environments for this character, respectively. The environment of Satkhira (−3.769**) and Khulna (−2.509*) were early maturing whereas Gazipur (2.97) and Cox’s Bazar (3.306) was late maturing environments for this character. Three varieties such as BS-14, BHS-01, BAUS-01 having negative phenotypic index, near unit regression co-efficient and non significant deviation from regression recorded stable.

The TSW (g) along with the value of phenotypic indices (Pi), regression coefficient (bi) and deviation from regression (S²di) were presented in Table 8 . The environmental mean and genotypic mean ranged from 2.58 g to 4.18 g and 3.61 g to 3.98 g, respectively.

In Gazipur, the highest TSW was found from BHS-01 (4.58 g) followed by BAU-03 (4.53 g) and BS-11 (4.36 g). In Satkhira, BS-16 produced the highest yield (3.12 g) followed by BAUS-03 (3.09 g) and BS-14 (2.68 g). The maximum production recorded in BHS-01 (4.67 g) in Khulna which was identical with BS-11, BS-16, BS-18 (4.33g) and BS-14, BS-19, BAUS-03 (4.00g). In Cox’s Bazar the maximum yield recorded in the genotype BS-14 (4.43 g) followed by BS-11 (4.35 g) and BAUS-02 (4.24 g).

Three genotypes showed positive phenotypic index while the other six genotypes had negative phenotypic index for yield. Thus, positive phenotypic index represented the higher yield and negative represents the lower yield among the genotypes. Again, positive and negative environmental index (Ij) reflected the rich or favourable and poor or unfavourable environments for this character, respectively. Thus the environment of Satkhira was unsuitable whereas Khulna, Gazipur and Cox’s Bazar was suitable environments for mustard production.

The regression coefficient (bi), deviation from regression (S²di) values of these genotypes ranged from 0.53 to 1.34 and 0.01 to 0.71, respectively. These differences in bi values indicated that all the genotypes responded differently to different environments. Considering the mean, bi and S²di, it was evident that all the genotypes showed different response of adaptability under different environmental conditions. Among the genotypes, BS-16, BS-11 and BHS-01 exhibited the higher grain yield, bi~1 and S²di~0 indicated that the hybrids are stable across the environment. All the genotypes showed insignificant values for regression co-efficient and also deviation from regression.

The yield (kg/ha) along with the value of phenotypic indices (Pi), regression coefficient (bi) and deviation from regression (S²di) were presented in Table 9 . The environmental mean and genotypic mean ranged from 1020 kg/ha to 1889 kg/ha and 1119 kg/ha to 1629 kg/ha, respectively.

In Gazipur, the highest yield was found from BS-16 (1276 kg/ha) followed by BHS-01 (1273 kg/ha) and BAUS-03 (1164 kg/ha). In Satkhira, BAU-02 produced the highest yield (1904 kg/ha) followed by BAUS-03 (1866 kg/ha) and BAUS-01 (1751 kg/ha). The maximum production recorded in BS-18 (2150 kg/ha) in Khulna which was identical with BS-19 (2000 kg/ha) and BAUS-02 (1950 kg/ha). In Cox’s Bazar the maximum yield recorded in the genotype BS-16 (2146 kg/ha) followed by BS-18 (1797 kg/ha) and BAUS-02 (1715 kg/ha). But the variety BS-14 produced the lowest mean yield (1119 kg/ha) in all four locations.

Six genotypes showed positive phenotypic index while the other three genotypes had negative phenotypic index for yield. Thus, positive phenotypic index represented the higher yield and negative represents the lower yield among the genotypes. Again, positive and negative environmental index (Ij) reflected the rich or favourable and poor or unfavourable environments for this character, respectively. Thus the environment of Gazipur was poor whereas Khulna, Satkhira and Cox’s Bazar was favourable environments for mustard production. Khulna was highly suitable for mustard cultivation followed by Satkhira and Cox’s Bazar.

The regression coefficient (bi), deviation from regression (S²di) values of these genotypes ranged from 0.24 to 1.31 and 36.68 to 220.33, respectively. The differences in bi ( Table 9 ) values indicated that all the genotypes responded differently to different environments. Considering the mean, bi and S²di, it was evident that all the genotypes showed different response of adaptability under different environmental conditions. Among the genotypes, BS-16, BHS-01, BS-18 and BAUS-01 exhibited the higher grain yield, bi~1 and S²di~0 indicated that the hybrids are stable across the environment. All the genotypes showed insignificant values for regression co-efficient and also deviation from regression. [21] studied GxE of 71 Indian mustard varieties over 6 environment in two several years and selected one genotype well stable in all environment and one to a specific environment. [22] studied 25 mustard genotypes in 3 environment found 6 as stable. [17] studied 57 mustard over 3 environments selected 3 as stable. [18] conducted stability analysis in 11 genotypes, 2 seasons in 3 environment and found one genotype stable in case of yield. [23] studied GxE in mustard of 8 cultivars in 10 locations of different agro climate and selected 2 genotypes stable due to low deviations from egression coupled with b value near 1.

The AMMI model combines regular analysis of variance for additive effects with principal component analysis (PCA) for multiplicative structure within the interaction. AMMI also provides a visual representation patterns in the data through a biplot that makes use of the first interaction principal component axis (IPCA1) and the mean yields of both the genotypes and environments [24] .

The AMMI biplot provides a visual expression of the relationships between the first interaction principal component axis (IPCAI) and means of genotypes and environments ( Figure 1 ) with the biplot accounting up to 87.2% of the treatment sum of squares. The IPCA1 was highly significant and explained the interaction pattern better than other interaction axes. The mean genotypes or environments in AMMI biplot located on the same parallel line, relative to the ordinate, have similar yield, while those located on the right side of the center of the axis has higher yields than those on the left hand side ( Figure 1 ).

The biplot showed four grouping of genotypes having two of them such as 4 (BS-19), and 1 (BS-11) were low yielding and unstable. The genotype 5 (BS-14) was low yielding but moderately stable, 6 (BAUS-1), 3 (BS-18), 7 (BAUS-2), 2 (BS-16) were high yielding and stable hybrids. The genotype 8 (BHS-01) and 9 (BAUS-03) were high yielder but highly unstable.

Since the IPCA2 scores also play a significant role in explaining the GEI, so, the IPCA1 scores were plotted against the IPCA2 scores for further exploring adaptation ( Figure 2 ). According to Figure 2 , the entry 9 (BAUS-03), 2 (BS-16), 3 (BS-18), 8 (BHS-01) were unstable due to their dispersed position. The genotypes 6 (BAUS-1), 1 (BS-11), 7 (BAUS-2), 5 (BS-14), 4 (BS-19) showed to be more stable when plotting the IPCA1 and IPCA2 scores. Genotypes with IPCA1 scores having near zero showed little interaction across environments while genotypes with very high IPCA1 values had considerable interactions across environments. The underlying causes of the interaction observed can therefore be based on both the genetic differences between these genotypes and the different environments [25] .

Among the genotypes, BS-16, BHS-01, BS-18 and BAUS-01 exhibited the higher grain yield, bi~1 and S²di~0 indicated that they were stable across the environment. The environment of Gazipur was unsuitable whereas Khulna, Satkhira and Cox’s Bazar were favourable environments for mustard production in that season. Khulna was highly suitable for mustard cultivation followed by Satkhira and Cox’s Bazar. The experiment could be repeated further for final conclusion.