INTRODUCTION
Chickpea is the second most cultivated grain legume in the world after phaseolus bean (Rubio et al., 1998, 2004).
It is cultivated mostly in the Mediterranean basin, the near east, central and south Asia, east Africa, south America, north America and, more recently, in Australia. Iranian chickpea (Cicer arientinum) is cultivated in 33 countries of the world and 650 thousand hectors of Iran's area is under the cultivation of chickpea (Imamjomah, 1999; Yaghotipoor, 2002). It is apparent that the phenotype of chickpea is joint contribution of both genes as well as environment. The GE interaction reduces association between phenotypic and genotypic value. The existence of genotypeenvironment interaction call for the evaluation of genotypes in many environments to determine their true genetic potential (Roy, 2000; Chahal and Gosal, 2002; Farshadfsr and Sutka, 2003).
In many practical situations, the experimenter is not interested in a knowledge
of the numerical amount of GE interaction per se, but he is only interested
in the presence of GE that leads to different ordering of genotypes in different
environments. This concept of GE interaction is closely related to the concept
of selection in plant breeding. The breeder is mainly interested in rank orders
of genotypes in different environments and in changes of these rank orders.
Therefore it is an obvious idea to use rank information for a quantitative description
of these relationships (Kang, 1990; Huehn, 1990a; Yaghotipoor, 2002). The detection
and quantification of GE interaction has been attempted through parametric and
nonparametric methods. Sabaghnia et al. (2006) studied four statistical
methods for the analysis of GxE interaction and suggested that for analysis
of noncrossover interactions, the methods of Brdenkamp, Hildebrand and Kubinger
are closely connected with the ANOVA. If some of the necessary assumptions are
violated, the validity of the interferences obtained from the standard statistical
techniques, for example, ANOVA, may be questionable or lost. In such cases,
however, the results of nonparametric estimation and testing procedures, which
are based on ranks, can be more reliable (Truberg and Huehn, 2000).
Also parametric measures are relatively more sensitive to errors of measurements and addition or deletion of one or few observations causes great variation in the parametric stability measures. Thus it is worthwhile to go for a nonparametric measure for stability. Some essential advantages of nonparametric statistics compared to parametric ones are: reduction or even avoidance of the bias caused by outliers, no assumptions are needed about the distribution of the analyzed values, homogeneity of variances and additivity (linearity) of effects are not necessary requirements, statistics based on ranks and rankorders are often easy to use and to interpret (Kang, 1990; Huehn, 1990b, c; Huehn and Nassar, 1987, 1989; Farshadfar, 1998; Roy, 2000; Chahal and Gosal, 2002).
The objectives of the present investigation were (i) evaluation of phenotypic stability of chickpea genotypes under rainfed and irrigated conditions and (ii) determination of the contribution of yield components in the phenotypic stability.
MATERIALS AND METHODS
In order to evaluate phenotypic stability of 19 breeding lines and two local varieties of Iranian chickpeas, a randomized complete block design with three replications was carried out under two different conditions (rainfed and irrigated) across 4 years from 1997 to 2000 in the research station of the College of Agriculture, Razi University, Kermanshah, Iran.
Twenty one plots were projected for each replication, so that each plot had 1.5 m length and 0.5 m wide. The distance between two plots was 50 cm. Single seeds were sown in three rows with 10 cm distance. Each row consisted of 12 seeds.
Maximum and minimum temperature in the research station was 44 and 27°C and the average rain fall was 378 mm. Maximum and minimum rainfall distribution was in March and April, respectively and the region was semiarid.
After separation of border effects from each threerow plot, Number of Shrub Per Unit Area (NSPA), Number of Capsules in Shrub (NCIS), Number of Seeds Per Shrub (NSPS), Thousand Seed Weight (TSW) and Grain Yield (GY) were measured.
Statistical analysis
Nonparametric stability measures: The following concept of phenotypic
stability were calculated (Huehn, 1990a; Kang, 1990).
Where, S_{i}^{(1)} is the mean of the absolute rank differences of a genotype I over the N environments.
can be interpreted to be the expectation of each r_{ij} under the hypothesis
of maximum stability (= equal ranks). Where S_{i}^{(2)} is the
common variance of the ranks.
(= sum of the absolute deviations of the r_{ij}'s from maximum stability
expressed in units).
Tests of significance for stability of a single genotype and stability comparisons between certain genotypes was done using the following formula:
where Z_{i}^{(m) }have an approximate chisquared distribution with one degree of freedom and, similarly, the statistic
may be approximated by a chisquared distribution with k degrees of freedom with E (S_{i}^{(m)}) = Expectation (= mean) of S_{i}^{(m)} and V (S_{i}^{(m)}) = variance of S_{i}^{(m)}.
Under the null hypothesis that all genotypes are equally stable. The means E (S_{i}^{(m)}) and variance V (S_{i}^{(m)}) may be computed from the discrete uniform distribution (1, 2, …, k). The following formula are used:
The contribution of yield components in the phenotypic stability was calculated as:
Where, Y is the grain yield and X_{1}.X_{2}.X_{3}...X_{n}
are the yield components.
Log (Y) = log (X_{1}) + log (X_{2})
+ … + log (X_{n}) 
Where log (Y) denotes the natural logarithm of Y.
C_{i} = cov (log (Y), log (X_{i})
) 
Where, C_{i} (coefficient of variation) is the measure for the contribution of the Ith yield components to the phenotypic stability of yield (Piepho, 1995).
Combined analysis of variance, mean comparison using Duncan's Multiple Rang Test (DMRT) were carried out using MSTATC and SPSS softwares. Nonparametric analysis of phenotypic stability and component analysis were done by the biometrical genetic in plant breeding software provided by Farshadfar (1998).
RESULTS AND DISCUSSION
Genotypes of annual crops evaluated for grain yield on a multilocational, multiyear basis frequently show genotypeenvironment interactions that complicate the selection or recommendation of materials. Coping with GenotypeYear (GY) and GenotypeLocationYear (GLY) interaction effects is possible only by selection for yield stability across environment defined as locationyear combinations (Annicchiarico, 1997).
There are two possible strategies for developing genotypes with low GxE interactions. The first is subdivision or stratification of a heterogeneous area into smaller, more homogeneous subregions, with breeding programs aimed at developing genotypes for specific subregions. However, even with this refinement, the level of interaction can remain high, because breeding area does not reduce the interaction of genotypes with locations on years (Eberhart and Russell, 1966; Tai, 1971). The second strategy for reducing GxE interaction involves selecting genotypes with a better stability across a wide range of environments in order to better predict behavior (Eberhart and Russell, 1966; Tai, 1971). Various methods use the GxE interaction to facilitate genotype characterization and as a selection index together with the mean yield of the genotypes. Accordingly, genotypes with a minimal variance for yield across different environments are considered stable. This idea of stability may be considered as a biological or static concept of stability (Becker and Leon, 1988). This concept of stability is not acceptable to most breeders and agronomists, who prefer genotypes with high mean yields and the potential to respond to agronomic inputs or better environmental conditions (Becker, 1981). The high yield performance of released varieties is one of the most important targets of breeders; therefore, they prefer a dynamic concept of stability (Becker and Leon, 1988).
According to Huehn (1990a) the nonparametric procedures have some advantages over the parametric stability methods. They reduce the bias caused by outliers and no assumptions are needed about the distribution of the observed values. They are easy to use and interpret and additions or deletions of one or few genotypes don't cause much variation of results. Even, we can use nonparametric methods for balance data with normal distributions because they are relatively simple. Stability estimates from nonparametric models based on the relative classification of the genotypes in a given set of environments do not require previous assumptions and a good alternative for parametric measurements (Nassar and Huehn, 1987; Huehn and Nassar, 1989). The interaction concepts of the classification they represent are strongly related to that of selection in which breeders are interested i.e., whether the best genotype in one environment is also the best in other environment and they can define static and dynamic concepts of stability.
Combined analysis of variance: The results of combined analysis of variance for yield and yield components over 7 different environments (Table 1) showed high significant differences for genotypes and genotypeenvironment interaction indicating the presence of genetic variation and possibility of selection for stable genotypes. As G*E interaction was significant, therefore we can further proceed and calculate the phenotypic stability of varieties (Farshadfar and Sutka, 2003). Chandra et al. (1974) observed that G*E interaction with location is more important than G*E interaction with year.
Mean comparison: Mean performance (Table 2) of Grain Yield (GY) and yield components over 7 different irrigated and rainfed conditions ranged from 55.59 g for genotype number 2 to 100.3 g for genotype number 12. The same performance was observed for genotypes number 2 for Number of Shrub per Unit Area (NSPA), Number of Capsules in Shrub (NCIS) and Number of Seed per Shrub (NSPS) but maximum NSPA was attributed to genotype number 14 and NCIS to genotype number 20, NSPS to genotype number 15 and TSW to genotype number 12.
ChiSquare values with l1 (for genotype), m1 (for environment) and (l1)
(m1) (for GxE interaction) degrees of freedom for the methods of Brdenkamp
and Van der Leende Kroon at the levels probability were tested. The null hypothesis
for Bredenkamp is no noncrossover GxE interactions and for van der Laande Kroon
is no crossover GxE interaction. The results indicated that both significant
noncrossover and crossover interaction [Gx (E) and Ex(G)] were found according
to Brdenkamp (for non crossover) and the van der Laande Kroon (for crossover)
methods.
Table 1: 
Combined analysis of variance using nonparametric method 

**Significant at the 0.01 probability level 
Table 2: 
Mean comparisons of yield and yield components using Duncan's
multiple range test 

Mean values with different letters are not statistically significant 
In comparison the result of ANOVA with nonparametric analysis procedures,
We found that both methods were in agreement with each other, but nonparametric
analysis provide more specific information about the presence of crossover and
noncrossover GxE interaction (Truberg and Huehn, 2000).
The overall consideration of yield and yield components introduced line 12 as the most outstanding genotype for grain yield with no significant difference with bivanich a landrace of kermanshah but better performance of genotype 12.
Nonparametric phenotypic stability measures: The statistics S_{i}^{(1)}, S_{i}^{(2)}, Z_{i}^{(1)} and Z_{i}^{(2)} were calculated for 21 genotypes over 7 different environments (Table 3). The significant tests for S_{i}^{(1)} and S_{i}^{(2)} were developed by Nassar and Huehn (1987). For each genotype, Z_{i}^{(1)} and Z_{i}^{(2)} values were calculated based on the ranks of adjusted data and summed over genotype to obtain Z values (Table 3). It is seen that Z_{i}^{(1)} sum = 68.61 and Z_{i}^{(2)} sum = 881.5. Since both of these statistics were less than the critical value χ^{2}_{0.05,df = 20} = 37.7, no significant differences in rank stability were found among the 21 genotypes grown in 7 environment. In the original data the null hypothesis that all the genotypes have equal genotypic stability is rejected at 5% level of probability because
This statistic indicates that genotypes have different adaptability for irrigated
and rainfed conditions. On inspecting the individual Z values, it was found
that the genotype were significantly unstable relative to others, because they
showed large Z values, in comparison with the critical value χ^{2}_{0.05,
df = 1} = 3.84.
Table 3: 
Nonparametric measure of phenotypic stability over rainfed
and irrigated conditions 

S_{i}^{(1)} is the mean of the absolute rank
differences of a genotype I over the N environments. S_{i}^{(2)}
is the common variance of the ranks. Z_{i}^{(m)} have an
approximate chisquared distribution with one degree of freedom 
The S_{i}^{(1)} and S_{i}^{(2) }statistics are based on ranks of genotypes across environments and they give equal weight to each environment. Genotypes with fewer changes in rank are considered to be more stable (Becker and Leon, 1988). The S_{i}^{(1)} estimates based on all possible pairwise rank differences across environments for each genotype, whereas S_{i}^{(2)} is based on variance of ranks for each genotype accroach environments (Nassar and Huehn, 1987). These two statistics ranked genotypes similarity for stability. Nassar and Huehn (1987) reported that the S_{i}^{(1)} and S_{i}^{(2)} are associated with the static (biological) concept of stability, as they define stability in the sense of homeostasis. The stability statistics of S_{i}^{(1)} and S_{i}^{(2)} represent a static concept of stability and were correlated neither positively nor negatively with mean yield. Therefore, these stability statistics could be used as compromise methods that select genotypes with moderate yield and high stability.
The most adaptable genotype is that with the least S_{i}^{(1)} and S_{i}^{(2)} over environments. As S_{i}^{(1)} = S_{i}^{(2)} = 0 means maximum stability therefore, the variety filip929c (number 8) showed the highest stability for rainfed and irrigated conditions followed by genotypes 10, 12, 14, 17 and 19. It is to be mentioned that stability of chickpea is highly associated with location (Dani and murty, 1982) and stability of grain yield is correlated with number of capsule and seed weight (Yaghotipoor, 2002).
Component analysis: Component analysis is a simple method of analysing
yield components. It allows quantification of the contribution of each component
to the variability of final yield (Sparuaaij and Bos, 1993; Piepho, 1995). Ci
assesses the joint effect of the variability of the ith yield components, quantified
by σi^{2} as well as the compensating (or sometimes mutually enhancing)
relation with other components, quantified by σij. Thus meets with empirical
finding that high variability in yield may be associated with high variability
in the yield components if there is little compensation among the components.
If, on the contrary, the crop under investigation shows a high plasticity in
its yield structure, increments in one component may be offset by decreases
in other components, which implies a negative covariance between the components.
Thus, a component that is highly variable (large variance), but is well compensated
for by other components (negative covariance), will exert a small effect on
the variability of yield. This will be reflected by a low Civalue of the component.
In summary it can be stated that Ci is an aggregate measure of the ith component,
contribution to the variability in yield, which assess the variability of that
component as well as its interdependence with other yield components. The results
of components analysis (Table 4) revealed that for most of
the genotypes seed weight followed by number of seed per shrub exhibited more
Ci values indicating that instability is mainly caused by these components,
while the influence of number of shrub per unit area and number of capsule per
shrub was low. As number of shrub per unit area showed negative Ci this implies
that number of shrub can highly be compensated by other components (negative
covariation) and has a little effect on the instability of grain yield.
The overall judgement of the components analysis displayed that selection for
improvement of phenotypic stability must be apparently through the selection
of number of shrub per unit area followed by number of capsule per shrub (Sparnaaij
and Bos, 1993; Piepho, 1995).
Simultaneous consideration of yield and yield stability: Simultaneous consideration of yield and yield stability in only one parameter is of particular interest and importance.
The parameter
has been proposed by Huehn (1979) and applied by Leon (1986) and Huehn (1990).
This parameter realizes a confounding and simultaneous evaluation of yield
stability and yield since the numerator measures the stability (= variability
of the ranks r_{ij}), while the denominator reflects the yield level
(= mean of the ranks r_{ij}). Another method based on ranks for combining
yield and stability has been proposed by Schuster and Zchoche (1981) and by
Kang (1990) : Ranks were assigned for mean yield (highest yield = lowest rank
of one) as well as for the stability variance (Kang, 1990) or ecovalence (Schuster
and Zchoche, 1981) (lowest variance or ecovalence = lowest rank of one) and
both ranks were summed (Kang, 1990) or multiplied (Schuster and Zchoche, 1981).
The lowest ranksum or rankproduct would be the most desirable. Using the above
mentioned parameters (Table 5) genotype number 8 was the most
desirable for both yield and yield stability.
Table 5: 
Simultaneous consideration of yield and yield stability in
one parameter using Kang and Schuster methods 

Consequently, nonparametric stability measurements to be useful alternative to parametric measurements (Yue et al., 1997). Many parametric and nonparametric measures of stability have been presented and compared with Lin et al. (1986) and Flores et al. (1998). For making recommendations, it is essential to investigate the relationship among these parametric and compare their powers for different stability models. This topic will be considered in details a subsequent study.