Models for G x E Analysis

Course code : GPB 733Course title : Principles of Quantitative geneticsYear / 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

2GE

2E

2G

2P

• 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

AB

Environments

No rank changes,but interaction

AB

Rank changes and interaction

Res

pons

e

A

B

No interaction

AB

Environments

No rank changes,but interaction

AB

Rank changes and interaction

A

B

No interaction

AB

Environments

No rank changes,but interaction

AB

Rank changes and interaction

Res

pons

e

• 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 + (kikjk) + dij + eijl

k = kth eigenvalueik= 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 + (kikjk) + 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

THANK YOU