2. INTRODUCTION
Genotype x environment interaction (GEI) is the
variation caused by the joint effects of
genotypes and environments (Dickerson, 1962).
Distinction between cross over interactions
(COI) and Non cross over interactions (NCOI) is
failed due to GEI
Cross over interaction results in the rank
change of genotypes over different
environments.
GEI complicate identification of superior
genotype for range of environment
If GEI is high, Breeding gain is smaller.
3. IMPORTANCE OF GEI
Range Broad genetic background Narrow genetic
background
Maximizing genetic
Low heritability due to GEI and variation among
Wide range of unreliable ranking of environment s and
distinct environment genotypes across significant means between
environments testing environments
Maximizing genetic variation
Uniform and significant means between
Useless
environments testing genotypes
4. Shifted multiplicative model is developed by
Seyedsadr & Cornelius (1992)
It is a tool to analyze the separability of
Genotypic effects from environment
effects
Environment effects from genotypic
effects
Complete separabilty
Gregarious and Namkoong (1986) Separability
defined one property which is that if cultivar effect is
separable from environment effect than there are no rank
5. Mean of ith genotype in jth environment
Shift parameter
Scaling constant for axis k
Constraints for ith genotype
Constraint for jth environment
Residual error
K = 1 Primary effect (significant)
= 2 Secondary effect (non-
significant)
6. REQUIREMENTS OF SHMM
Condition for absence of significant
genotypic rank change interaction
SHMM adequate for fitting data
Primary effect should have same signs of
environments
Condition for absence of significant environment
rank change interaction
SHMM adequate for fitting data
Primary effects of genotypes should have same
signs
Condition for absence of significant genotypic
and environment rank change interaction
SHMM adequate for fitting data
Primary effects of genotype and environment should
7. ANALYSIS OF VARIANCE (ANOVA)
Source d.f.
1. Genotype g-1
2. Site s-1
3. Genotype X Site (g-1)(s-1)
4. Pooled error s(r-1)(g-1)
SHMM
5. Primary effects
6. Secondary effects
7. Tertiary effect
8. Remainder
8. SHMM STUDIES
Cornelius et al. (1993) used SHMM clustering to
group 41 winter wheat (Triticum aestivum L.)
genotypes into non-COI clusters from a multisite trial
data that included seven environments.
Crossa et al. (1993), using the SHMM model,
clustered 59 international sites into five non-COI
groups and concluded that the procedure appears
useful in identifying subsets of sites with negligible
genotypic COI.
Crossa et al. (1995) used the SHMM model for
clustering five irrigation levels in two years (10
environments) and results were compared with the
conventional cluster analysis using the Euclidean
distance as the criterion. The SHMM clustering
strategy formed more homogeneous non-COI
subsets of sites than the conventional clustering
9. CASE STUDY
Data of 41 wheat genotypes evaluated in randomized
complete block design in four replications in the year 1985
at each of the seven Locations at Kentucky
10. Clustering
First step of is to make
the dendrogram by
complete linkage with
distance defined as
Residual Sum of
Square
• Total 40 clusters
• Nine clusters
formed
• By fitting the SHMM1
• No or insignificant
COI
15. DIFFERENCES IN CLUSTERS
Parallel Point of
regression intersection
lines toward left
Constrained sol.
Point of
Pt. of intersection
intersection
moved towards left
toward right
18. IMPORTANCE OF SHMM
Categorization of locations with similar
environments helps breeders to efficiently utilize
resources and effectively target germplasm.
Useful tool to breeder in making decision on
release of cultivar
It helps in selection, testing and identifying
superior genotypes
Subsets of environments represent similar
selection environments facilitate the exchange
of germplasm
