Introduction
Genotype-environment interaction poses a majour barrier to the breeder in the process of evolution of improved variety. Nadarajan et al, (2005) define environment as the sum total of physical, chemical and biological factors that influence the development of an organism. Environment may cause change in the genetic constitution of a population by pressure of selection it exercises on the population and in the long run may lead to evolutionary changes (Dabholkhar, 1992). Since genotype-environment interaction has masking effect on genotype, it is necessary to estimate the magnitude of this interaction variance to avoid over/ under estimation of genotypic variance in breeding programme. The importance of genotype-environment interaction is recognized by breeder/ geneticist and these are known to be heritable (Jink et al., 1955) and statistical techniques are available to estimate them, the main effort of breeder/ geneticist is to reduce them or scale them out.

Interaction of genotypes with environment contributes to the total phenotypic variation which can be isolated and tested for significance. Several methods and techniques have been developed to describe and interpret the response of genotypes to variation in the environment. Biologically, genotype with minimum total variance under different environments is considered stable (Hanson, 1970). An agronomically stable genotype has a minimum interaction with environments but responds favourably to improving environments (Eberhart et al., 1966). Stability analysis provides a general solution for the response of the genotypes to environmental change. Many parameters/ statistics have been used for analyzing stability as reviewed by Lin et al., (1986), Becker et al., (1988) and Crossa, (1990). Additive Main effect and multiplicative interaction (AMMI) analysis has been shown to be effective because it captures a large portion of the GE sum of squares and the model often provides agronomically meaningful interpretation of the data (Gauch, 1992). AMMI is a combination of ANOVA for the main effects of the genotypes and the environment together with principal components analysis (PCA) of the genotype-environment interaction (Zobel et al., 1998; Gauch, 1988). AMMI models are usually called AMMI (1), AMMI (2), to AMMI (n), depending on the number of principal components used to study the interaction. Graphic representations are obtained using bi-plots (Gabriel, 1971) that allow (1) the observation, in the same graph, of the genotypes (points) and the environments (vectors), and (2) the exploration of patterns attributable to the effects of G × E interaction. In the bi-plot, the angles between the vectors that represent genotypes and environments show the interaction, and the distances from the origin indicate the degree of interaction that the genotypes show throughout the environments or vice versa.

Performance of improved, high yielding varieties of rice over different agro ecological regions of India has been well documented by several workers (Vijayakumar et al., 2001). The occurrence of G x E interaction within target environments necessitates conduct of multi-environment trials to evaluate genotype adaptation. A lot of work has been done in rice for phenotypic stability and adaptability of varieties as far back as early 1970. Tang et al. (1975) tested eleven japonica lines in sixteen environments for one set and fourteen environments for second set and found that, average yields of the lines over environments were highly correlated between two environments. No linear response was observed for the stability performance of lines between sets. Naidu et al. (1980) identified IET-2730, a red grained variety stable in Karnataka state and in other 29 locations throughout India. In another study, RD 3 and IR 8 were recognized as satisfactorily stable varieties for yield among 14 lines tested over 22 localities by Poonyarth et al. (1980). Sudin (1985) observed that shorter the plant, the lower was the stability in his investigations on adaptability and stability.

In recent years, AMMI analysis has been applied to interpret GEI in rice (Wade et al., 1999; Vijayakumar et al., 2001; Lafitte et al., 2002; Stanley et al., 2005; Mall et al., 2005; Ouk et al., 2007). Vijayakumar et al., (2001) studied G × E interaction effects on yield of 16 rice hybrids evaluated over 11 locations in different agro ecological regions of India. They reported presence of significant GEI that influenced the relative ranking of hybrids across the locations. It was evident from AMMI analysis that, genotypes, environment and the first principal component of interaction effect accounts for 86.96% of treatment sum of squares and that the first five principal components of interaction effect were found to be significant. The usefulness of the AMMI in selecting genotypes for general or specific adaptation was depicted by these authors. Das et al., (2010) conducted multi location yield trials of 11 mid-early (110-125 days) rice genotypes at four locations in Odisha state, India, over 3 years- 2003~2005, during kharif season. According to Das and colleagues, AMMI-predicted yield showed that Lalat and OR 2006-12 were high yielders and possessed broad adaptation to most locations. Genotypes showing good adaptation to specific locations were OR 2200-5 for Ranital, OR 2172-7 and OR 1916-19 for Bhubaneswar, OR 1976-11 for Chiplima and Konark for Ranital.

The main objectives of the present investigation is to determine the GEl effects on grain yield of Superior BILs derived from Swarna × WAB 450 inter cross and to select genotypes that are widely adapted across upland rice growing rainfed areas in North Karnataka, India.

1 Results and Discussion
Table 1 presents result of Additive Main Effects and Multiplicative Interaction (AMMI) analysis of variance for grain yield (kg/ha) of 19 BILs with 3 check varieties (Swarna, Pasanna and MGD 101) tested at 3 locations in six environments. Table 2 presents mean grain yield (kg/ha) of 19 BILs with three checks grown in 6 environments and the PCA scores for the GE Interaction effect as derived from AMMI analysis. The means of the genotypes and the environments along with the first principal component (PCAI) scores of corresponding genotypes are also presented. The genotype mean yields ranged from 3935.79 kg/ha to 5917.02 kg/ha (Table 2).

Table 1 AMMI analysis of variance for grain yield of 19 BILs and three check varieties tested at 3 locations in six environments

Table 2 Mean of grain yield (kg/ha) of 19 BILs and three checks grown in 6 environments and the PCA scores for the GE Interaction effect as derived from AMMI analysis

 
Result showed that genotypes, environments and GEI components were significant. The GEI were partitioned into four interactive principal components namely PCA I, PCA II, PCA III and PCA IV with contribution of 50.09, 36.84, 8.03 and 4.15 per cent, respectively, to the total GEI variance. The first two PCA components (PCA I and PCA II) for this model were significant and explained 86.93% of the data variability; however, PCA I explained the largest percentage (50.09%) of the variability. PCA III, PCA IV and the residual which accounted for 13.07% of the interaction were not significant (Table 1).

Figures 1 and Figure 2 presented bi-plot assays of the AMMI results. Figure 1 showed the main effects [genotype means and environment means] on the abscissa (x-axis), and the ordinate (y-axis) representing the first PCA. Both main effects and interaction component are shown clearly in the figure. Favourable environment is represented by positive PCA and unfavourable environment was represented by negative PCA. Result showed that six genotypes [genotypes 3, 21, 11, 2, 12 and 14 (Figure 1)] have PCA near to zero indicating small effect of GE interaction, these genotypes have differences only in main (additive) effect. Three out of these 6 genotypes (2, 12 and 14) have mean yield level between 5000 and 5650 kg/ha with genotype no 14 being the highest (Figure 1). Genotype 18 recorded very high yields and high PCA score in favourable environment whereas genotypes 5 and 13 recorded high mean yield level and had high PCA scores in unfavourable environment (Figure 1). Whereas genotypes 18, 5 and 13 had differences only in interaction effect, genotypes 3, 21, 11, 2, 12 and 14 have differences only in main effect.

Figure 1 Bi-plot graph for 22 selected genotypes mean and interaction principal component-1 (IPCA1)

Figure 2 Projection of 22 selected genotypes on the first two principal components of GEI effect

 
Figure 2 is the projections of the genotypes on the environmental vector. Result also indicated that only one environmental E5 (Gangavati, Kharif 2012) had PCA near to zero. Whereas environmental mean E1 (Mugad Kharif 2011) and E4 (Gangavati summer 2011) had positive PCA the environments E2 (Mugad summer 2011), E3 (Mugad summer 2012), E5 (Gangavati Kharif 2012) and E6 (Sirsi Kharif 2012) had negative PCA (Figure 1). Interactions of environments were highly varied; whereas E5 has low interaction, E4 and E6 were highly interactive. Figure 2 presents the spatial pattern of the first two PCA axes of the interaction effect corresponding to the genotypes. These bi-plots help in visual interpretation of the GE patterns and identify genotypes or locations that exhibit low, medium or high levels of interaction effects (Vijayakumar et al., 2001). We can infer from the result of this study that genotypes 11, 2, 12 and 14 had mean yield levels higher than that of local check (Prasanna-genotype 21), and were less influenced by the GEl effect and when compared to check were more widely adaptable. The bi-plot showed that genotypes 12 and 21 were more stable as they were located near the origin (Figure 2). It can be inferred from the result of this investigation that genotypes 5, 6, 2, 14, 15 and 19 are specifically adapted to environment E6 while genotype 13 is adaptable to three environments [E2, E3 and E6 (Figure 2)]. This inference is in agreement with other workers who used the same AMMI model for their analysis. Vijayakumar et al., (2001) used bi-plot (AMMI) assay and identified two hybrids viz., IR58025A/Swarna and IR58025A/IR21567 as having general adaptability at all locations. They also reported that hybrids ORI 161 and IR58025N1R54742 were identified as specifically adapted to favourable locations. Several authors have used AMMI to evaluate multi-environment experiments to distinguish the effects of the genotype and the environment and then assess the G × E interaction in a reduced dimensional space with minimum error (Kandus et. al., 2010).

2 Material and Methods
The breeding material for this study was inter-varietal backcross inbred lines (BILs) of Swarna × WAB 450 developed at Barwale Foundation, Hyderabad. Swarna is a mega rice variety from India whereas WAB 450 is an inter-specific derivative of NERICA lines from Africa. Multi-location yield trials of 19 superior BILs (BC1F8) selected for earliness, productivity, reaction to blast diseases and grain size were conducted at 3 locations-Mugad, Gangavati and Sirsi during kharif and summer seasons in 2011 and 2012, respectively. The selected BILs including recurrent parent (Swarna) and 2 released local varieties (Prasanna and MGD 101) were evaluated for yield in six environments of which 3 environments were in Kharif and 3 in summer season, respectively. All trials were laid out in randomized block design with 2 replications. In each trial, 25~30 days old seedlings were transplanted in 20 cm × 15 cm spacing and one seedling per hill. Normal cultural practices and plant protection measures were followed in each trial according to package of practice developed by University of Agricultural Sciences Dharwad (UAS Dharwad, 2009). In all trials, data were recorded on net plot for grain yield. Grain yield data of the six environments was analyzed for G × E interaction using AMMI model (Zobel et al., 1988) to identify genotypes adapted to specific environments.

3 Conclusion
Six genotypes [genotypes 3, 21, 11, 2, 12 and 14] were found to be indicating small effect of GE interaction in the present study; three out of these six genotypes (2, 12 and 14) had mean yield level between 5000 and 5650 kg/ha reflecting greater breeding advances and hence they are recommended for all environments. Genotype 18 with high mean yield level and positive IPCA 1 is recommended for favourable environment whereas genotypes 5 and 13 with high mean yield level and negative IPCA 1 are recommended for unfavourable environment. It can be concluded based on the values of mean and ICPA 1 for all 22 genotypes evaluated in this study that 6 genotypes were found suitable for all environments, 6 genotypes for favourable environments while 10 genotypes were identified as suitable for unfavorable environments.

References
Becker H.C. and J. Leon, 1988, Stability analysis in Plant Breeding, Plant Breeding, 101: 1-23
http://dx.doi.org/10.1111/j.1439-0523.1988.tb00261.x

Crossa H.M., 1990, Statistical analyses of multi-location trials, Advances in Agronomy, 44: 55-85
http://dx.doi.org/10.1016/S0065-2113(08)60818-4

Das S., Misra R.C., Patnaik M.C. and Das S.R., 2010, G × E interaction, adaptability and yield stability of mid-early rice genotypes, Indian J. Agric. Res., 44(2): 104-111

Dabholkar A.R., 1992, Elements of Bio Metrical Genetics, Concept publishing Company. New Delhi, pp.379-421
Eberhart S.A. and Russell W.A., 1966, Stability parameters for comparing varieties, Crop Science, 6: 36-40
http://dx.doi.org/10.2135/cropsci1966.0011183X000600010011x

Gauch H.G. Jr., 1988, Model selection and validation for yield trials with interaction, Biometrics, 44: 705-715
http://dx.doi.org/10.2307/2531585

Gauch H.G.Jr., 1992, Statistical Analysis of Regional Yield Trials: AMMI Analysis of Factorial Designs, Elsevier, Amsterdam, pp.1-278

Gabriel K.R., 1971, Bi-plot display of multivariate matrices with application to principal components analysis, Biometrika, 58: 453-467
http://dx.doi.org/10.1093/biomet/58.3.453

Hanson G.R., 1970, Genotypic stability, Theoretical and Applied Genetics, 40: 226-231
http://dx.doi.org/10.1007/BF00285245

Jink J.L. and Hayman B.I., 1955, The analysis of diallel crosses, Maize Genetics Coop, News Letter, 27: 48-54

Lafitte H.R. and Courtois B., 2002, Interpreting cultivar × Environment Interactions for yield in upland rice: Assigning value to drought adaptive traits, Crop Science, 42: 1409-1420
http://dx.doi.org/10.2135/cropsci2002.1409

Lin C.S., Binns M.R. and Lafkovitch L.P., 1986, Stability analysis: where do we stand? Crop Science, 26: 894-900
http://dx.doi.org/10.2135/cropsci1986.0011183X002600050012x

Mall C.N. and Sharma M.Ki., 2005, Genotype × environment interaction effects on yield of rainfed lowland rice, (Oryza sativa) varieties, Indian Journal of Genetics and Plant Breeding, 65(2): 125-126

Nadarajan N. and Gunasekaran L.M., 2005, Quantitative genetics and biometrical techniques in plant breeding, Kalyani publishers, New Delhi, pp.223-241

Naidu B.S., Joshi M.S., Badralah Khan T.A. and Jayakumar, 1980, IET 2490 and IET 2730 have high grain yield stability, Current Research, UAS, Bangalore, 9(9): 148-149

Poonyarth M., Sumantaradon K. and Aswasophenkul A., 1980, Yield stability of 14 rice (Oryza sativa L.) varieties and promising lines, Kasetsael Journal, 14(2): 7-16

Ouk M., Basnayake J., Tsubo M., Fukai S., Fischer K.S., Kang S., Men S., Thun V. and Cooper M., 2007, Genotype-by-environment interactions for grain yield associated with water availability at flowering in rainfed lowland rice, Field Crops Research, 101: 145-154
http://dx.doi.org/10.1016/j.fcr.2006.10.003

Stanley Omar, Samonte P.B., Wilson L.T., Mcclung A.M. and Medley J.C., 2005, Targeting cultivars onto Rice growing environments using AMMI and SREG GGE bi-plot analyses, Crop Science, 45: 2414-2424
http://dx.doi.org/10.2135/cropsci2004.0627

Sudin V.M., 1985, The Adaptability and Stability of Plant Height among Rice Varieties, Selethigai Semenovoditro, Ussr, 2: 11-12

Tang W.T., and Tai C.C., 1975, An analysis of stability of yield as breeding criterion of rice, Journal of Agricultural Association, 91: 1-6

UAS Dharwad, 2009, Package of Practice for Rice: University of Agricultural Sciences, Dharwad

Vijaykumar C.H.M., Ahmed Ilyas M., Viraktamath B.C., Balkrishnan R. and Ramesha M.S., 2001, Genotype × environment interaction effects on yield of rice hybrids in India, Indian Journal of Genetics and Plant Breeding, 61: 101-106

Wade L.J., 1999, Critical characteristics of rainfed rice environments and Implications for rice improvement, In: Ito O., O’Toole J., and Hardy B., (eds.), Genetic Improvement of Rice for Water-limited Environments, International Rice Research Institute, Philippines, pp.1-22

Zobel R.W., Wright M.J. and Gauch H.G., 1988, Statistical analysis of a yield trial, Agron J., 80: 388-393
http://dx.doi.org/10.2134/agronj1988.00021962008000030002x