use of ammi model for stability analysis of crop.

SEMINAR TOPIC :
USE OF AMMI MODEL FOR STABILITY ANALYSIS OF
DIFFERENT CROPS
Name – CHAVAN MAHADEO RAJARAM
REG NO.- ADPM/15/ 2419

 Factors that are of economic relevance
may be related to complex or polygenic
characteristics, and show a high influence
of the environment. Because of this, in
breeding programs, various experiments
are conducted in several locations to
evaluate grain yield
Introduction

 In these experiments, changes in the relative
behaviour of the genotype in different
environments are usually observed. This
phenomenon is called genotype by
environment interaction (GxE).
 It is the rule in most quantitative
characteristics (Bernardo, 2002). The GxE
interaction makes it difficult to select
genotypes that produce high yields and that
are more stable in breeding programs. This, of
course, reduces the selection progress (Yan &
Hunt, 1998).

 Genotypes respond differently across a
range of environments i.e., the relative
performance of varieties depends on the
environment
 Simmonds (1991): "GE Interaction is not
merely a problem, it is also an
opportunity”

 the term stability refers to the ability of
the genotypes to be consistent, both
with high or low yield levels in various
environments.
 Static – performance of a genotype does
not change under different environmental
conditions.
 Dynamic – Response to environment is
parallel to mean response of all genotypes
in the trial .
Stability

 Adaptability refers to the adjustment of an
organism to its environment, e.g., a
genotype that produces high yields in
specific environmental conditions and poor
yields in another environment (Balzariniet
al., 2005).
Adaptability

 combined ANOVA,
 multivariate methods
 Stability analysis :An analysis to estimate the
adaptability of a genotype. It included two
model:
Different model for stability analysis are
given below :
Statistical methods to analyse the GxE interaction :

A.Con ventional model :
1.stability factor model.
2.ecovalence model
3.stability variance model
4.lin and binns model.
B. Regression coefficient model :
1. finley and wilkinson model.
2.Eberhart and russell model.
3.perkins and jinks model.
4.freeman and perkins model
5.genotypic stability model.
C. Principal component analysis :
1.Additive Main effect and
Multiplicative Interaction (AMMI)
model (Gauch 1992)

AMMI is a combination of ANOVA for the main
effects of the genotypes and the environment
together with principal components analysis (ACP)
of the genotype-environment interaction (Zobel et
al., 1998; Gauch, 1988).
AMMI models are usually called AMMI(1),
AMMI(2), ….,AMMI(n), depending on the number
of principal components used to study the
interaction and Graphical representations are
obtained using biplots (Gabriel, 1971)
AMMI Model

The Additive Main effect and Multiplicative
Interaction (AMMI) method proposed by Gauch
(1992) is a statistical tool which leads to
identification of stable genotypes with their
adaptation behaviour in an easy manner.
In this method main effects are initially
accounted for a regular analysis of variance and
then the interaction is analysed through
principal component analysis.

AMMI is applicable and usefull for data:
1.Stuctured in two way factorial , with at least three
row and three columns.
2.Containing one kind of data , quntitative rather
than categorical .
3.Fitted by AMMI model reasonabaly well ,
as ordinarily happens when main
effect and intraction are both singnificant

Yijl =  + Gi + Ej + (kikjk) + eijl
Where,
•Yij is the observed mean yield of the ith genotype in jth environmt
•μ is the general mean
•Gi and Ej represent the effects of the genotype and environment
•λk is the singular value of the kth axis in the PCA
•αik is the eigenvector of the ith genotype for the kth axis
•γjk is the eigenvector of the jth environment for the kth axis
•n is the number of principal components in the model
•eij is the average of the corresponding random errors
AMMI Model

source df SS MS F
TOTAL (ger- 1)
Tretment (ge -1)
Genotype (g -1)
Environment (e-1)
Interaction
IPCA 1
IPCA 2
Residual
(g-1) (e-1)
blocks (r-1)
error (r-1) (ge -1)
Analysis of variance for stability – AMMI Model

usually the first principal component (CP1) represents
responses of the genotypes that are proportional to the
environments, which are associated with the GxE
interactionwithout change of the range.
The second principal component
(CP2) provides information about cultivation locations
that are not proportional to the environments,
indicating that those are responsible of the GxE
crossover interaction.
Principal components

Feature of PCA :
1. It computes a genoty[ score and an environment
score whose product estimate yeild
For that genotype in that environment .
2. Usually grand mean is removed before calculating PCA.

Biplot allow the observation, in the same graph,
of the genotypes (points) and the environments
(vectors), and (2) the exploration of patterns
attributable to the effects of GxE interaction.
In the biplot, the angles between the vectors that
represent genotypes and environments show the
interaction, and the distances from the origin
indicate the degree of interaction that the
genotypes show throughout the environments or
vice versa.
BIPLOTS

 Graphical representation of numerical results
often allows a straight forward interpretation
of GEI
 The angles between the vectors that represent
genotypes and environments show the
interaction
 Distances from the origin indicate the degree of
interaction that the genotypes show
throughout the environments

Interpretation
EXAMPLE : Eight lines and 28 hybrids maiz.

Code used in the biplot analyses for each
location and year :

AMMI biplot for “BLS” and “Normal” lines Points represent lines
and vectors represent environments

Result
General interpretation
 Genotypes that occur close to particular
environments on the IPCA2 vs IPCA1
biplot show specific adaptation to those
environments
 A genotype that falls near the center of
the biplot (small IPCA1 and IPCA2
values) may have broader adaptation

• How many IPCAs (interaction principal
component axes) are needed to adequately
explain patterns in the data?
–Usually need only the first 2 PC axes to
adequately explain the data (IPCA1 and
IPCA2). This model is referred to as
AMMI2.
• Approach is most useful when G x location
effects are more important than G x year
effects

Main feature of AMMI Model .
• Method for analyzing GEI to identify patterns
of interaction and reduce background noise
• Combines conventional ANOVA with principal
component analysis
• May provide more reliable estimates of
genotype performance than the mean across
sites

• Biplots help to visualize relationships among
genotypes and environments; show both main
and interaction effects.
• Enables you to identify target breeding
environments and to choose representative
testing sites in those environments.
• Enables you to select varieties with good
adaptation to target breeding environments.

• Can be used to identify key agroclimatic
factors, disease and insect pests, and
physiological traits that determine
adaptation to environments
• A type of fixed effect, Linear-Bilinear Model

use of ammi model for stability analysis of crop.

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