The shifted multiplicative model was developed by Cornelius and Seyedsadr in 1992. SHMM is used to analyze the complete separability, genotypic separability, environmental separability, and inseparability of environment effects and genotypic effects. Gregorius and Namkoong (1986) defined Separability as the property which is that cultivar effect is separable from environmental effect so that there is no rank. The shifted multiplicative model (SHMM) is used in an exploratory step-down method for identifying subsets of environments in which genotypic effects are "separable" from environmental effects. Subsets of environments are chosen on the basis of a SHMM analysis of the entire data set. SHMM analyses of the subsets may indicate a need for further subdivision and/or suggest that a different subdivision at the previous stage should be tried. The process continues until SHMM analysis indicates that a SHMM with only one multiplicative term and its "point of concurrence" outside (left or right) of the cluster of data points adequately fits the data in all subsets.

1. SHIFTED
MULTIPLICATIVE MODEL
GP 602
Sanjay Kumar Sanadya
A-2019-40-019

2. GE interaction
Most of the economic traits in plant breeding are
quantitative nature.
Phenotypes values of the Cultivar/Genotypes are the
combination of genotype (G) and environment (E) values, and
their interactions (GE).
defined as the variation in relative performance of
genotypes in different environmental conditions.
In Crop Improvement program, because it complicates
identification and selection of superior genotypes thereby
reducing genetic progress.

4. Shifted multiplicative model was developed by Cornelius
and Seyedsadr in 1992
SHMM is used to analyze the complete separability,
genotypic separability, environmental separability, and
inseparability of environment effects and genotypic effects.
Gregorius and Namkoong (1986) defined Separability as the
property which is that cultivar effect is separable from
environmental effect so that there is no rank.

5. Cornelius et al. (1992) defined sufficient conditions for the
absence of statistically significant:
(1) SHMM1 is an adequate model for fitting the data and
(2) Primary effects of environments have the same sign.
Non-significant environmental rank-change interactions
is indicated when SHMM1 is an adequate model holds
and
(3) Primary effects of genotypes have the same sign.
The absence of significance of both environmental rank-
change interactions and genotypic rank-change
interactions occurs when (1), (2) and (3) all hold.

6. Hypothetical Response pattern of SHMM1 A. COMPLETE SEPARABILITY
B. GENOTYPIC SEPARABILITY

7. C. ENVIRONMENTAL SEPARABILITY
D. INSEPARABILITY

8. SHMM with t multiplicative terms (SHMMt) is represented
by:-
β= Shift parameter
γjk= ktheffects of jth genotype
λk= Scaling constant
αik= kth effects of ith environment
eij = residual error
Note: kth If SHMM is adequate in single multiplicative term (k=1), is
refers to primary effect of ith environment & jth genotype (αi1 & γj1)
respectively

9. ANOVA for SHMM
The SC and SC/SM tests are the only significance tests which are available to use.

17. AMMI model
AMMI is a combination of ANOVA for the main effects of the genotypes and the
environment together with principal components analysis (PCA) the genotype-
environment interaction.
AMMI first calculate genotype and environment environment additive effect using
analysis of variance (ANOVA) and then analyse residual from
these model using principal components analysis (PCA).
The AMMI analysis provided
1. A better understanding of the GEI through analysis of variance.
2. It facilitated identification of genotypes possessing stable yields as well as
discriminating environments through the biplot display.
3. Specificity in adaptability of the genotypes to specific environments.
4. The scientific information obtained, could be of considerable importance in
developing location specific breeding strategies and selecting stable genotypes in
breeding programme.
Conclusion
The AMMI analysis provided a better understanding of the GEI through analysis of
variance, facilitated identification of genotypes possessing stable yields as well as
discriminating environments through the biplot display and specificity in adaptability
of the genotypes to specific environments.