Rainfed lowland rice ecosystems are highly variable and unpredictable in nature (Yoshida 1977). Multiple abiotic stresses such as unfavorable soil conditions, regional weather patterns, topography, pests and weeds all contribute to the complexity of the ecosystem. The worldwide harvested area of rainfed lowland rice is estimated to be 46 to 48 million hectares. Of this, 90% is in South and Southeast Asia. Rice farming in these rainfed areas is risk-prone. Yields remain low, about 1.5 to 2.5 t ha^{-1} in most areas. The income of most farmers is low and they are challenged by erratic yields. In Asia, about 50% of all the rice land is rainfed and although rice yields in irrigated ecosystems have doubled and tripled over the past 30 years, only modest gains have occurred in rainfed rice systems (Fischer et al. 2003). The water supply in rainfed areas principally comes from rainfall. Uncertainty in the timing of rainfall and variability in its intensity and its distribution cause either flood or drought stress in rainfed lowland rice production ecosystem.

Drought is the major constraint to productivity and the cause of yield instability in rainfed lowlands. At least 23 million ha of rice area in Asia are estimated to be drought-prone (Pandey et al. 2005). Severe and regular droughts affect mainly eastern India, northeast Thailand and parts of Myanmar and Laos. In India, the rainfed lowland rice area is about 20.4 million hectares, which accounts for 32.4% of the total area under rice in the country. Out of the total of 20.4 million ha of rainfed rice area, approximately 7.3 million ha of lowland area are drought-prone (Pandey and Bhandari 2008). The timing of drought, early season, mid-season or terminal stage, has a major influence on how much yield loss occurs (Fischer et al. 2003). Drought patterns also differ among locations and among years, and in some years no drought occurs during the growing season. Therefore, poverty reduction strategies in rainfed areas must focus on stabilizing yields, that is, on breeding varieties with improved yield under drought stress as well as good response to irrigated conditions. To a farmer’s eyes, a drought-resistant cultivar is one that yields better than any other available cultivar particularly under water-limited conditions (Blum 2006). The objective of a drought-tolerance breeding program is to select varieties that outperform currently available varieties in the target population of environments (TPE). The TPE is the future set of drought-prone environments in which the varieties developed by the breeding program will be grown. The environments in the TPE vary in predictable ways such as annual rainfall patterns, toposequence, soil type and farmers practices and in unpredictable ways such as random drought or disease incidence (Fischer et al. 2003). Variability among environments within TPE (locations and seasons) is particularly common in rice.

The ability of crop cultivars to perform reasonably well in drought-stressed environments is paramount for stability of production. The relative yield performance of genotypes in drought-stressed and non-stressed environments can be used as an indicator to identify drought-resistant varieties in breeding for drought-prone environments. Several drought indices have been suggested on the basis of a mathematical relationship between yield under drought conditions and non-stressed conditions. These indices are based on either drought resistance or drought susceptibility of genotypes.

Let (*Y*_{
i
})_{
S
} denote the yield of the i^{th} genotype under stress, (*Y*_{
i
})_{
NS
} the yield of the i^{th} genotype under non-stress (i.e., irrigated) conditions and *y*_{
S
} and *y*_{
NS
} the mean yields of all genotypes evaluated under stress and non-stress conditions, respectively.Rosielle and Hamblin (1981) defined stress tolerance (TOL) as the differences in yield between the stress and non-stress environments, i.e., $TOL={\left({Y}_{i}\right)}_{\mathit{\text{NS}}}-{\left({Y}_{i}\right)}_{S}$. Higher values of TOL indicate susceptibility of a given cultivar.Hossain et al. (1990) defined mean productivity index (MPI) as the average of (*Y*_{
i
})_{
NS
} and (*Y*_{
i
})_{
S
}. This index has an upward bias when the differences between non-stress and stress conditions are large and it favors genotypes with higher yield potential and lower stress tolerance. Higher values mean a higher rate of productivity. Mean relative performance is calculated as $MRP=\frac{{\left({Y}_{i}\right)}_{S}}{{Y}_{S}}+\frac{{\left({Y}_{i}\right)}_{\mathit{\text{NS}}}}{{Y}_{\mathit{\text{NS}}}}$ and relative efficiency is given by $REI=\frac{{\left({Y}_{i}\right)}_{S}}{{Y}_{S}}*\frac{{\left({Y}_{i}\right)}_{\mathit{\text{NS}}}}{{Y}_{\mathit{\text{NS}}}}$,Ramirez Vallejo and Kelly (1998) computed the geometric mean of productivity (GMP), which is the square root of the product of yield under stress and yield under non-stress: $GMP=\sqrt{{\left({Y}_{i}\right)}_{S}*{\left({Y}_{i}\right)}_{\mathit{\text{NS}}}}$. This index is suitable when the breeding objective is directed toward testing performance under favorable and stress conditions, taking into consideration variability in drought intensity over environment and years.Fernandez (1992) defined a stress tolerance index as $STI=\frac{\left({\left({Y}_{i}\right)}_{\mathit{\text{NS}}}*{\left({Y}_{i}\right)}_{S}\right)}{{Y}_{\mathit{\text{NS}}}^{2}}$, which can be used to identify genotypes that produce high yield under both stress and non-stress conditions. A high value of STI implies higher tolerance of stress. A stress susceptibility index (SSI) that assesses the reduction in yield caused by unfavorable compared with favorable environments was suggested byFischer and Maurer (1978). SSI is expressed by $SSI=\frac{\left(1,-,\frac{{\left({Y}_{i}\right)}_{S}}{{\left({Y}_{i}\right)}_{\mathit{\text{NS}}}}\right)}{SI}$, SI, the stress intensity is estimated as $SI=1-\frac{{Y}_{S}}{{Y}_{\mathit{\text{NS}}}}$. Lower SSI values indicate lower differences in yield across stress levels, in other words, more resistance to drought. A modified formula for Schneider’s stress severity index (Schneider et al. 1997) is defined bySingh et al. (2011) as $SSSI=\left(1-\frac{{\left({Y}_{i}\right)}_{S}}{{\left({Y}_{i}\right)}_{\mathit{\text{NS}}}}\right)-\left(1-\frac{{Y}_{S}}{{Y}_{\mathit{\text{NS}}}}\right)$. The SSSI estimates the relative tolerance for yield reduction of a genotype relative to the population mean reduction in grain yield response due to stress. Selections based on these indices were carried out by many authors (Pantuwan et al. 2002,Ouk et al. 2006,Golabadi et al. 2006, Sio-SeMardeh et al. 2006,Talebi et al. 2009,Khayatnezhad et al. 2010,Nouri et al. 2011,Singh et al. 2011).

Phenology is important in determining grain yield response also because quick maturing cultivars often escape from severe stress while late maturing cultivars may be affected by terminal stress (Singh et al. 1996). Research on genetic variation in grain yield of pearl millet under post flowering indicated that as much as 50% of the total variation in grain yield under stress is explained by yield potential and time of flowering.Bidinger et al. (1987) calculated a drought response index based on a regression model to quantify the remaining part of the variation associated with tolerance / susceptibility and to identify traits linked to tolerance. The following quadratic equations were used to develop stress indices for lines in advanced screening. Mid-season stress is defined by the regression equation ${\stackrel{\u02c6}{Y}}_{s}=a+{b}_{1}\left({Y}_{c}\right)+{b}_{2}\left(bl\right)+{b}_{3}\left(b{l}^{2}\right)$and terminal stress by ${\stackrel{\u02c6}{Y}}_{s}=a+{b}_{1}\left({Y}_{c}\right)+{b}_{2}\left(bl\right)$, where $\hat{{Y}_{s}}$is the regression estimate of the stress yield, *Y*_{
s
} is the measured stress yield, *Y*_{
c
} is the non-stress control yield, *bl* the days to flowering under non-stress, *a* the intercept and *b*_{1}, *b*_{2} and *b*_{3} the regression coefficients. The drought index is then given by $\frac{\left({Y}_{s}-{\stackrel{\u02c6}{Y}}_{s}\right)}{S.E.\left({\stackrel{\u02c6}{Y}}_{s}\right)}$, where *S*.*E*. indicates the standard error. Attention is focused only on those cultivars with indices of less than −1.3 or more than +1.3. These represent the upper and lower 10% of the normal distribution of the indices. FollowingBidinger et al. (1987),Slim and Saxena (1993) used a DRI to describe the response of individual chickpea genotypes to drought conditions and fitted multiple regression of stressed grain yield on unstressed grain yield and days to flowering: ${\stackrel{\u02c6}{Y}}_{0}\phantom{\rule{0.37em}{0ex}}=\phantom{\rule{0.37em}{0ex}}a\phantom{\rule{0.37em}{0ex}}-\phantom{\rule{0.37em}{0ex}}bF\phantom{\rule{0.37em}{0ex}}+\phantom{\rule{0.37em}{0ex}}C{Y}_{i}$. Here, $\hat{{Y}_{0}}$is the regression estimate of yield under drought, *Y*_{
i
} is the yield potential, *F* is the number of days to flowering under non-stress, *b* and *C* are the regression coefficients and *a* is the intercept. The drought response index is then given by $DRI=\frac{\left({Y}_{0}-{\stackrel{\u02c6}{Y}}_{0}\right)}{S.E.\left({\stackrel{\u02c6}{Y}}_{0}\right)}$, where S.E indicates the standard error. (Garrity and O’Toole 1995) proposed a field screening method for reproductive phase drought resistance in rice based on the drought index suggested byBidinger et al. (1982) to adjust for genotypic variation in phenlogy before genotypic difference in drought tolerance is estimated.

Under severe stress, yield reduction in rice is 65-85% compared with that in non-stress conditions (Kumar et al. 2008). Rice is particularly sensitive to drought stress during reproductive growth, even under moderate drought stress (Hsiao 1982,O’Toole 1982). In rice, moderate stress can be broadly characterized by a 31 to 64% loss in grain yield as compared with non-stress conditions (Kumar et al. 2008). The objective of our study is to develop a drought yield index (DYI) that takes into account yield under both moderate and severe drought stress for the identification of breeding lines with superior performance over current cultivated varieties. The mean yield index (MYI) is proposed for rainfed areas where, in different years or during different growth stages of the crop in the same year, water availability fluctuates between a normal supply of water due to favorable rain and the occurrence of mild and moderate to severe drought stress based on the duration of days without rain during the cropping season. The MYI enables breeders to identify breeding lines with superior performance over current varieties under all situations.