Stability Parameters
In stability analysis, relevant biometrical methods cited in the standard texts were followed (Singh and Chaudhury, 1985; Dabhokar, 1992).The analysis of variance (ANOVA) was used and the G-E interaction was estimated by the AMMI model (Zobel et al., 1988; Durate and Zimmermann, 1991). In this procedure, the contribution of each genotype and each environment to the G-E interaction is assessed by use of the bi-plot graph display in which yield means are plotted against the scores of the first principle component of the interaction (IPCA 1). The computational program for AMMI analysis is supplied by Durate and Zimmermann (1991). The stability parameters, regression coefficient (bi) and deviation from regression (S2di) were estimated according to Eberhart and Russell’s (1966) model. Significance of differences among bi value and unity was tested by t-test, between S2di and zero by F-test. The statistical approaches suggested by Eberhart and Russell (1966) were followed for genotype x environment interaction and estimating stability parameters. According to them, a stable genotype may be considered as one having high mean, average linear regression (bi=1) to environments of varying levels of productivity and deviation from regression as close to zero. According to Panwar et al., (1995), during data analysis, seasons are considered as separate environment in each season. Luthra et al., (1974) recommended Eberhart and Russell’s for stability analysis considered its simplicity. Eberhart and Russell’s (1966) used the following models to study the stability of genotypes under different environments,
Yij = m + biIj + Sij (i = 1, 2………g and j = 1, 2……….e)
Where,
M = Overall mean
Yij =Mean of the ith genotype over all the environments
bi = The regression coefficient of the ith genotype on the environmental index which measures the response of these genotype to varying environments.
Ij = The environmental index which is defined as the deviation of the mean of all the genotypes at a given environment from the overall mean, i.e.
Ij = Y.j – Y… (Y.j= mean of the ith genotype in the jth environment, Y= overall mean)
The regression coefficient (bi) was calculated for each genotype as follows bi= [Σj Yij Ij / Σj I2]
Where, ∑ Yij Ij is the sum of product of environmental index (Ij) with the corresponding mean of that genotype of each environment.
Σ δ2ij= [δ2vij–jbijΣjYijIj] which is the variance of mean over different environments with regard to individual genotypes.
δ2vi = [ΣjYij2 – Yi2/e]
Where, e = no. of environment and Yi = sum of the ith genotype over environments.
Mean square deviation (S2di) from linear regression was calculated using the following formula-
S2di = [ Σj δ2ij /(e-2)- S2e/r]
Where, S2e = estimated pooled error and r = no. of replication
The phenotypic index (Ram et al., 1970) has been introduced in the Eberhart and Russell’s model for easy interpretation and quick conclusion. The formula of phenotypic index (Pi) is given below,
Pi = Yi.- Y…
Where,
Yi. = mean of the ith genotype over environment,
Y= overall mean
The hypothesis is that there is no response of genotype to different environment (Ho: bi=1) and there is no deviation from regression (Ho: S2di=1) were tested approximately by the F test.
Ho: bi = 1, F =
Ho: S2di = 0, F=
The individual genotypic response i.e. regression coefficient (bi) was tested by ‘t’- test using the standard error of the corresponding bi value against the hypothesis. The individual deviations from linear regression tested by F-test using pooled error and S2di did not differ significantly from zero in the genotypes.
t =
SE(b)= and F = [ Σ δ2ij /(n-2)]/Pooled error