The experiment was conducted in 2004–2005. A total of 40 rice germplasm composed of 32 local aromatic, five exotic and three non-aromatic rice varieties as standard checks, were selected for this research (Table 1). Among the three non-aromatic varieties, BR28 was a modern Boro, BR39 was a modern T. Aman variety and the third one, Nizersail was used as a standard photoperiod sensitive genotype [17]. Exotic genotypes were collected from Pakistan (Basmati PNR346), Nepal (Sarwati and Sugandha-1) and Iran (Khazar and Neimat). The rest of the rice genotypes represented their distribution throughout Bangladesh. Forty rice genotypes formed the treatment variables and were assigned randomly to each unit plot of $5\text{m}\times 2\text{m}$ dimension. Thirty-day-old seedlings were transplanted in three sets of Aman season and 45 day-old seedlings in Boro season with a spacing of $20\text{cm}\times 20\text{cm}$. A fertilizer rate of 25–35–10–3 kg ha⁻¹ of P–K–S–Zn in the form of triple super phosphate, muriate of potash, gypsum and zinc sulfate, respectively, was applied as basal dose at final land preparation. Because of wide genotypic variation in phenological development and yield potential, varieties differed enormously in attaining panicle initiation (PI) stage and in the requirement of nutrient elements. For this reason, nitrogen was top-dressed as urea in 2–3 splits to the contrary of a common practice with fixed dose and time routine. The amount of urea and time of application were determined with the help of a leaf colour chart [18]. Crop duration was counted as the time interval from the day of seed bed sowing to the day of 50% flowering.

The four locations were:

B = Benarpota Farm, BRRI Regional Station, Satkhira (22.72° N, 89.08° E).

C = Charchandia Farm, BRRI Regional Station, Sonagazi, Feni (22.84° N, 91.39° E).

D = Domar Seed Production Farm, BADC, Sonaroy, Domar, Nilphamari (26.10° N, 88.84° E).

H = Headquarter Farm, Bangladesh Rice Research Institute (BRRI), Gazipur (24.00° N, 90.42° E).

Seed sowing was done in four dates. Three dates were in T. Aman (with an interval of 20 days) and one date was in Boro season.

1 = 1st planting in T. Aman (sowing in seedbed on 16th July 2004).

2 = 2nd planting in T. Aman (sowing in seedbed on 5th August 2004).

3 = 3rd planting in T. Aman (sowing in seedbed on 25th August 2004).

4 = Planting in Boro season (sowing in seedbed on 5th November 2004).

The combination of two factors (locations × planting times) resulted a total of 16 environments viz. B1, B2, B3, B4, C1, C2, C3, C4, D1, D2, D3, D4, H1, H2, H3 and H4.

Stability analysis was done according to the regression model of Eberhart and Russel [19]. The stability parameters viz. phenotypic index ($P_i$), regression coefficient ($b_i$) and deviation from regression $(S_{di}^2)$ were calculated to interpret the results [20]. Additive Main Effect Multiplicative Interaction (AMMI) model was used to quantify the effect of different factors (genotype, location, planting time) of the experiment. The AMMI statistical model is most appropriately termed as a hybrid model. It makes use of standard ANOVA procedures to separate the additive variance from multiplicative variance (genotype by environment interaction). Then it uses a multiplicative procedure – Principal Components Analysis (PCA) – to extract the pattern from the $\text{G}\times \text{E}$ portion of the ANOVA [21].

There were high genetic variability among the genotypes. Differences among the environments were also highly pronounced and influence on environmental differences on crop duration was immense. The genotype × environment interactions were also highly significant (Table 2). Thus the data were extended for analysis of stability indices. Significant genetic and environmental variability and significant genotype × environment interactions were reported for different characters in rice by several workers [22,23].

The response and stability parameters along with mean performance and phenotypic index for crop duration (days to flowering) are presented in Table 1. The range of genotypic means over the environments was found between 96 to 166 days. The lowest crop duration was obtained for V8 (96 days) followed by V4 (98 days) and V29 (102 days). The environment means were in the range of 91–155 days (see Supplementary Material Appendix I).

Twenty-seven genotypes had negative phenotypic indices ($P_i$) indicating shorter duration and 13 showed positive $P_i$ signifying to longer crop duration. The regression coefficients of V6 and V16 were significantly higher than 1.0 indicating extreme responsiveness to changes in environments, and lower adaptability. The $b_i$ values of 17 genotypes viz. V9, V12, V13, V14, V17, V21, V22, V23, V25, V27, V28, V32, V33, V34, V36, V38 and V39 were significantly lower than unity. Therefore, these varieties showed more resistance or stable crop duration due to environmental changes. However, non-linear component ($S_{di}^2$) for V27 and V38 showed significant values. Therefore, the prediction of stability for these two genotypes might be hampered. On the other hand, V4, V8, V29 and V37 showed only nonlinear sensitivity. It indicated that these four varieties were affected by environmental fluctuations i.e. linear prediction of these genotypes might not always correct. These results supported the findings of several researchers where they found significant linear and nonlinear sensitivity for growth duration in upland rice [24,25]. Insignificant values for both linear and nonlinear components in the remaining 17 genotypes indicated their average performance over the environments. Aromatic rices in Bangladesh are normally photoperiod sensitive, having flexible length of life span. The short duration genotypes (minimum $P_i$ values) with minimum $b_i$ values and smaller $S_{di}^2$ estimates would be desirable. In all these considerations, the genotypes V17, V21, V22, V25, V27, V32 and V39 were found to be more stable over the environments. The nature of response and stability of some genotypes were shown with regression lines (Fig. 1). Gandho kasturi (V16) showed the maximum slope indicating the highest sensitivity to environmental changes. Thus the crop duration of V16 is mostly variable in different environments. On the contrary, the lowest slope obtained for V23 (Kalijira Tapli-73) indicated its minimum vulnerability in wider environmental ranges.

The effect of genotype, environment and the components of $\text{G}\times \text{E}$ interactions were highly significant (Table 2). The environment SS was quite large. Also, the $\text{G}\times \text{E}$ interaction SS was about double as genotype SS. Most of the interaction SS was captured by the first IPCA axis. IPCA1 and IPCA2 together hold 97% of $\text{G}\times \text{E}$ SS. The root mean square (RMS) residuals were examined for model fit. The RMS residual for crop duration data in Table 2 was ${(1658/1920)}^{0.5}=0.93$ day following AMMI4 model. Similarly, the RMS residual for AMMI2 was 1.26 days and that for AMMI1 was 2.06 days, or 1.90% of the grand mean (108.48 days). Table 3 listed the additive parameters (deviations) and the multiplicative effects (IPCA scores). The first four axes have been computed in the present analysis, although only first one or two are usually considered for interpretation. Expected crop duration (response) could be calculated from the table by using the AMMI model equation. For example, the AMMI1 expected crop duration for V1 grown in B1 would be $108.48+(-0.18)+(-4.62)+[(-0.11)\times (-2.24)]=103.93$ days. The observed duration was 106.67 days (Appendix I). Thus the AMMI1 model leaved a residual of 2.74 days. Moreover, V40 under H4 environment had leaved a residual of 6.94 days in AMMI1 model. It was estimated that AMMI1 model accounted for 97.7% of the observed data.

Fig. 2 showed the expected crop duration considering mean duration on the abscissa and IPCA1 scores (for genotypes and environments) on the ordinate. Sixteen environments are shown with open circles. Filled tetragons denote the genotypes. The genotypes with similar positions were not shown in the graph. Eighteen genotypes out of 40 were presented in the AMMI biplot. Straight lines draw attention to the grand mean on the abscissa and to zero on the ordinate.

The genotypes V6, V8 and V37 showed more or less similar distances from the horizontal reference line. However, series of displacements along the abscissa indicated their differences due to only main effects. On the other hand, V6, V9, V15, V28 and V30 are being dispersed along the ordinate and apparently they differ only in interaction effects. The genotypes V8 and V28 differ in both; while V1, V10, V20, V27 and V38 are rather similar with respect to both main effects and interaction effects.

The main effect for genotypes reflects breeding advances and the main effect for environments characterize the site [21]. Considering these responses, the four environments viz. B4, C4, D4 and H4 had exhibited remarkably longer life span of rice plants (Table 3 and Fig. 3). On the other hand, environments B2, C2, H2, B3 and C3 were characterized by extremely short duration. In general, shorter duration of rice varieties produces inferior yield mainly because of lower amount of solar radiation received.

Direction and level of interactions of genotypes with environments could be determined from Fig. 2. For example, V16 had strong positive interactions with the environments B4, C4, D4 and H4, and strong negative interactions with all other 12 environments. In fact, this variety could not emerge panicle at all in the Boro season in all four locations. As a result, its duration was extended up to the next T. Aman crop. On the other hand, V9, V28 and V33 had strong positive interactions with D3, little interactions with B1 and H1, and strong negative interactions with B4, C4, D4 and H4. In general, local aromatic rice varieties possess photoperiod sensitivity at varying degrees. For this reason, life span might be flexible depending on planting time and season. Negative interaction for duration may be preferred up to a certain limit of grain yield reduction.

For further observation of interaction effects exclusively, a different type of biplot had been presented in Fig. 3. It held IPCA1 on the abscissa and IPCA2 on the ordinate. It captured 97% of the interaction as against 92% of Fig. 3. Figs. 2 and 3 together effectively captured 99% of the treatment SS in the AMMI2 model, leaving a RMS residual of only 1.26 day, or 1.16% of the grand mean (Table 2). Principles of biplot graph for IPCA1 and IPCA2 were described by Kempton where he proved efficiency of this type of graph in the explanation of interactions [26]. The genotypes V1, V3, V7, V9, V15, V20 and V33 and the environments B2, C2 and D2 are situated very near the origin. It indicated a little interaction for the entities (varieties and environments). Therefore the genotypes V1, V3, V7, V9, V15, V20 and V33 are stable over the environments and the environments B2, C2 and D2 are more stable environments for all the rice genotypes.

Note