Models for g x e analysis

Models for G x E Analysis
Course code : GPB 733
Course title : Principles of Quantitative genetics
Year / Semester : 2nd year / 1st semester
Submitted to :
Dr. G. R Lavanya
Associate Professor
Submitted by :
Shruthi H.B
13 MSCGPB035
SAM HIGGINBOTTOM INSTITUTE OF AGRICULTURE, TECHNOLOGY AND SCIENCES
ALLAHABAD

INTRODUCTION
Definition:
The interaction between the genotype and
environment that produces the phenotype is
called and Genotype x Environmental
Interaction.
• Genotypes respond differently across a range
of environments i.e., the relative performance
of varieties depends on the environment

• GXE, GEI, G by E, GE
P = G + E + GE
2
GE
2
E
2
G
2
P  
• Genotype by environment interactions are common
for most quantitative traits of economic importance
•Advanced breeding materials must be evaluated in
multiple locations for more than one year

TYPES OF G X E
A
B
No interaction
A
B
Environments
No rank changes,
but interaction
A
B
Rank changes and
interaction
Response
A
B
No interaction
A
B
Environments
No rank changes,
but interaction
A
B
Rank changes and
interaction
A
B
No interaction
A
B
Environments
No rank changes,
but interaction
A
B
Rank changes and
interaction
Response
• Interaction may be due to:
– heterogeneity of genotypic variance across environments
– imperfect correlation of genotypic performance across
environments
Non crossover crossover

CHALLENGES OF G X E
• Environmental effect is the greatest, but is irrelevant to
selection (remember 70-20-10 rule, E: GE: G)
• Many statistical approaches consider all of the
phenotypic variation (i.e., means across environments),
which may be misleading
• Need analyses that will help you to characterize GEI
• "GE Interaction is not merely a problem, it is also an
opportunity" (Simmonds, 1991). Specific adaptations can
make the difference between a good variety and a superb
variety

• Some environmental variation is predictable
– can be attributed to specific, characteristic features
of the environment
– e.g., soil type, soil fertility, plant density
• Some variation is unpredictable
– e.g., rainfall, temperature, humidity

Strategies for coping with GXE
• Broad adaptation - develop a variety that performs
consistently well across a range of environments
(high mean across environments)
– this is equivalent to selection for multiple traits,
which may reduce the rate of progress from
selection
– will not necessarily identify the best genotype for a
specific environment

• Specific adaptation - subdivide environments into
groups so that there is little GEI within each group.
Breed varieties that perform consistently well in each
environment
– you have to carry out multiple breeding programs,
which means you have fewer resources for each,
and hence reduced progress from selection
• Evaluate a common set of breeding material across
environments, but make specific recommendations
for each environment

Models of G x E
• Additive Main Effects and Multiplicative
Interaction Model (AMMI) .
• GGE or SREG (Sites Regression) Model.
• Linear-Bilinear Mixed Model.

Additive Main Effects and Multiplicative
Interaction Model (AMMI) .
• 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

AMMI Model
Yijl =  + Gi + Ej + (kikjk) + dij + eijl
k = kth eigenvalue
ik = principal component score for the ith
genotype for the kth principal component
axis
jk = principal component score for the jth
environment for the kth principal
component axis
dij = residual GXE not explained by model

Interpretation
• 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?
– Rule of thumb - discard higher order IPCAs until
total SS due to discarded IPCA's ~ SSE.
– 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

GGE or SREG (Sites Regression) Model
• Another fixed effect, linear-bilinear model that is
similar to AMMI
• Only the environmental effects are removed before
PCA
• The bilinear term includes both the main effects of
genotype and GXE effects
• Several recent papers compare AMMI and GGE (e.g.
Gauch et al., 2008)
• May be used to evaluate test environments (Yan and
Holland, 2010)
Yijl =  + Ej + (kikjk) + dij + eijl

Steps involved:
• recommended pretreatment (transformation) –
scale the data by removing environment main
effects and adjust scale by dividing by the
phenotypic standard deviation at each site.
• use a classification procedure to identify
environments which show similar
discrimination among the genotypes.
• use an ordination procedure (singular value
decomposition) – similar to AMMI except that
it uses transformed data
• use biplots to show relationships between
genotypes and environments

Partial Least Squares Regression (PLS)
• PLS is a type of bilinear model that can utilize
information about environmental factors (covariables)
– rainfall, temperature, and soil type
• PLS can accommodate additional genotypic data
– disease reaction
– molecular marker scores
• Analysis indicates which environmental factors or
genotypic traits can be used to predict GEI for grain
yield

Factorial Regression (FR)
• A fixed effect, linear model
• Can incorporate additional genotypic and
environmental covariables into the model
• Similar to stepwise multiple regression, where
additional variables are added to the model in
sequence until sufficient variability due to GEI
can be explained
• FR is easier to interpret than PLS, but may give
misleading results when there are correlations
among the explanatory variables in the model

Linear-Bilinear Mixed Models
• Have become widely accepted for analysis of GEI
• Lead to Factor Analytic form of the genetic
variance-covariance for environments
• Has desirable statistical properties
• When genotypes are random, coancestries can be
accommodated in the model

• Assumptions for linear models
– homoscedasticity (errors homogeneous = common
variance)
– normal distribution of residuals
– errors are independent (e.g. no relationship
between mean and variance)
• Generalized linear models can be used when
assumptions are not met
– SAS PROC GENMOD, PROC NLMIXED, PROC
GLIMMIX
• Nonparametric approaches
– Smoothing spline genotype analysis

GEI - Conclusions
• An active area of research
• Need to synthesize information
– performance data and stability analyses
– understanding of crop physiology, crop models
– disease and pest incidence
– molecular genetics
– agroclimatology, GIS

Models for g x e analysis

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Models for g x e analysis