Lecture GxE interactions
Reference
Lynch and Walsh Ch 24
Muir, W. M., Y. Nyquist and S. Xu. 1992. Alternative partitioning of
the genotype by environment interaction. Theor. and Appl. Gen.
84:193-200
Vince Matassa: 2001. Statistical methods for partitioning genotypeby-environment interactions: an empirical evaluation of Muir's
method using a GenStat program (in handouts)
L.C. Emebiri and D.B. Moody. 2001. Quantitative characterization of
malting barleys for consistency in grain protein concentration (in
handouts)
Lecture 16
1
An Early Study on Fitness of Drosophila
In Natural Setting
Wright et. al. 1942
one of the first molecular genetics experiments
Lecture 16
2
Andres Canyon
Keen
Pinon Flat
Lecture 16
3
Observed Numbers of Chromosome
Arrangements
()
Location
ST/ AR/ CH/ TL/
ST AR CH TL
ST/ ST/ ST/ AR/ AR/ CH/
AR CH TL CH TL TL
TOT
Keen
Camp
30 11
44
0
53
66
3
48
3
6
264
Pinon
Flat
31 11
21
0
40
53
5
37
3
7
208
Andres
Canyon.
89 18
4
1
87
47 12
20
4
2
284
Lecture 16
4
Andres Canyon
Keen
***
***
NS
Lecture 16
Pinon Flat
5
GxE Interactions
• Statistical Definition
– Effects are not additive: the whole is greater
than the sum of the parts.
• Biological Definition
– One event impacts another in a chain of
events: The environment up and down
regulates genes, i.e. there is an interaction
between the genotype and environment that
produces the phenotype.
Lecture 16
6
The Basic Model
Yi = Gi + Ei
G2
Breed B
G1
Breed A
Genotype Effect
E1
Hot
E2
Cold
Environment
Effect
The response of a genotype to a change in an environmental
factor is sometimes called a reaction norm
Lecture 16
7
GxE May Cause Changes in Rankings
Yi = Gi + Ei + GxEi
G2
Breed B
Change in rank
There is no universal
best genotype
G1
Breed A
A specific breed is
bred to each
environment
E1
Hot
Lecture 16
E2
Cold
8
GxE May Cause Changes in Scale
Yi = Gi + Ei + GxEi
G2
Breed B
Change in Scale
Breed B is more
environmentally
sensitive
Breed A is
Environmentally
Insensitive
G1
Breed A
E1
Hot
Lecture 16
E2
Cold
9
GxE May Cause Both Changes in Scale and
Rank
Yi = Gi + E j + GxEij + ε ( ij ) k
G2
Breed B
Change in Scale
Breed B is more
environmentally
sensitive and Better
Suited to Cold
Breed A is
Environmentally
Insensitive and Better
Suited to Hot
G1
Breed A
E1
Hot
Lecture 16
E2
Cold
10
Detection and Interpretation of GxE
• Simple Analysis of Variance
– Genotypes (G)
– Environments (E)
– GxE
– Error
• Interpretation and determination of Nature
is more difficult and important
• Determination of Interactions Due To
Scale vs. Re-ranking is critical
Lecture 16
11
Alternative Situations Where GxE Can Occur
Impacts How to Analyze and Interpret
Genotypes
Environments
Fixed
Random
Fixed
Random
Lecture 16
12
Genotypes Fixed
• Elite Lines
• White Leghorn vs Barred Rock
• Angus vs Zebu
• Lines with specific genes of large effects
• Naked Neck vs Normal
• Dwarf vs Normal
• ESR vs Normal
Lecture 16
13
Naked Neck
(courtesy A. Cahaner)
Normal
Lecture 16
14
Genotypes Random
Individual Sires or Sire Lines Sampled From A
Population of Sires
Lecture 16
15
Environments Fixed
• Macro-environmental Differences
– Arctic vs Temperate vs Tropical
– Humid vs Dry
• Disease or pests vs not (ticks)
• Floors
– Cement
– Dirt
• Housing
– Floor pen
– Cages
Lecture 16
16
Environments Random
•
•
•
•
Herd
Year
Season
Effects
– Not Controllable
– Outdoor housing
usually
Lecture 16
17
Importance of GxE in
Alternative Situations
Combinations of
Genotypes (F vs.R)
Environments (F vs. R)
Lecture 16
18
Genotypes Fixed
Environments Random
• Breed x Herd, Year, Season (H-Y-S)
Interactions for a given trait
– Be aware that for this trait, it most likely is also
susceptible to GxE for Fixed environments too
– Suggests Caution to a breeder
• Particularly if breeds re-ranking in different H-Y-S
• Important question might be which breed
is most stable over environments because
cannot control environment
Lecture 16
19
Genotypes Random
Environments Fixed
• Issue: Is there genetic variability for
adaptability to specific environments
• Do you need to develop one breed or
many
– Will broiler breeds developed for the North
American market do well in South America?
• Different Altitude, Nutrition, Disease
• Answer depends on if a re-rankings of genotypes
across environments occurs, not change in
variance
Lecture 16
20
Do a GxE experiment with Random
Sire Lines
• If GxE due to changes in scale
– Unimportant
• If GxE due to change in Rank
– Critical
– Must select animals in specific environment for
production in that environment
– Example Muir (1986)
• Sire line x (4 bird vs 1 bird) cage environment not significant
• Same Sires x (9 bird vs 1 bird) cage environment significant
• Implies that selection of birds in single bird cages will
improve production in 4 bird cages but not 9 bird cages
Lecture 16
21
Genotypes Random
Environments Random
• Sire x Herd, Year, Season (H-Y-S) Interactions
for a given trait
• Does the breeder need to measure performance
over several random uncontrollable
environments before a breeding decision can be
made
– If GxE Significant and sire lines are re-ranking in
different H-Y-S
• Be sure for that Offspring From a Sire are Measured Across
a large number of different Herds, Year, and Seasons
– Be aware that for this trait, it most likely is also
susceptible to GxE for Fixed environments too
– Suggests Caution to a breeder
Lecture 16
22
Genotypes Fixed
Environments Fixed
• Common Type of GxE experiment
• Do GxE Experiment
– Determine GxE due to
• Re-ranking
– Chose Specific Breed for Specific Environment
• Scale
– Unimportant
Lecture 16
23
Summary
GxE Interactions
• In Most Situations Need to determine if
GxE is due to re-ranking of genotypes
across environments
• Exception: if one wants a consistent
producer across environments
– change in scale important
Lecture 16
24
Analysis of Variance
Lecture 16
25
Partitioning of GxE
Method 1: Re-Ranking of Genotypes Important
Determination of Heterogeneity of Variances
G1
G2
G4
G3
G1
G2
G4
G3
E1
E2
Standard Deviation of
Genotypes in E1
Standard Deviation of
Genotypes in E2
Z1 = V1 (G )
Z 2 = V2 (G )
Lecture 16
G1
…
G2
G4
G3
En
Standard Deviation of
Genotypes in En
Z n = Vn (G )
26
Sub-partitioning of GxE: Method 1
Fixed or Random Genotypes; Fixed Environments
Issue: Re-ranking
Degree of interaction due to
scale
correlation of same genotype
across environments
Lecture 16
27
Partitioning of GxE
Method 2: Environmental Sensitivity Important
Determination of Heterogeneity of Variances
E1
E2
E4
E1
E2
E4
E3
E3
G1
G2
Standard Deviation
Among Environments
For G1
Standard Deviation
Among Environments
For G2
S1 = V1 ( E )
S 2 = V2 ( E )
Lecture 16
E1
…
E2
E4
E3
Gn
Standard Deviation
Among Environments
For Gn
S n = Vn (E )
28
Sub-partitioning of GxE: Method 2
Fixed Genotypes, Random Environments,
Issue: Stability
Differential Environmental
Sensitivity Among Entries
Differences in Correlations
Among Pairs of Entries
Lecture 16
29
Example Data
Lecture 16
30
Program For Partitioning GxE
data a1;
input gen env y;
cards;
118
129
1 3 10
1 4 11
1 5 12
2 1 12
2 2 11
2 3 10
249
258
proc glm; classes gen env;
model y=env gen env*gen/ss1;
proc sort data=a1;by env;
proc means noprint;by env;var y;
output out=m1 mean=my css=sy;
data m2;set m1; sy=sqrt(sy);
proc means noprint data=m2;var sy;
output css=scalee;
proc print;run;
proc sort data=a1; by gen;
proc means noprint;by gen;var y;
output out=m1 mean=my css=sy;
data m2;set m1; sy=sqrt(sy);
proc means noprint data=m2;var sy;
output css=scaleg;
proc print;run;quit;
Lecture 16
31
Overall ANOV
Source of
Variation
Degrees of
Freedom
Sums of
Squares
Environments (E)
4
0
Genotypes (G)
1
40
GxE
4
20
Lecture 16
32
Both Genotypes were
Equally response to the
Environment
Re-ranking does
not occur in the
first case but does
in the second
Lecture 16
33
Lab Problem
• From the Following Barley Data, Each Group Chose 2
different genotypes. Partition the GxE interaction for the
pair and interpret the results.
Lecture 16
34