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Lecture 16 1
Lecture GxE interactionsReference
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 genotype-by-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)
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Lecture 16 2
An Early Study on Fitness of Drosophila In Natural Setting
Wright et. al. 1942one of the first molecular genetics experiments
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Lecture 16 3
Keen
Pinon Flat
Andres Canyon
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Lecture 16 4
Observed Numbers of Chromosome Arrangements
()
2842420124787141889Andres Canyon.
2087337553400211131PinonFlat
2646348366530441130Keen Camp
TOTCH/TL
AR/TL
AR/CH
ST/TL
ST/CH
ST/AR
TL/TL
CH/CH
AR/AR
ST/ST
Location
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Lecture 16 5
Keen
Pinon Flat
Andres Canyon
NS
******
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Lecture 16 6
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.
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Lecture 16 7
The Basic Model
iii EGY +=
E1Hot
E2Cold
G1Breed A
G2Breed B
Genotype Effect
EnvironmentEffect
The response of a genotype to a change in an environmental factor is sometimes called a reaction norm
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Lecture 16 8
GxE May Cause Changes in Rankings
iiii GxEEGY ++=
E1Hot
E2Cold
G1Breed A
G2Breed B
Change in rank
There is no universal best genotype
A specific breed is bred to each environment
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Lecture 16 9
GxE May Cause Changes in Scale
iiii GxEEGY ++=
E1Hot
E2Cold
G1Breed A
G2Breed B
Change in Scale
Breed B is more environmentally sensitive
Breed A is Environmentally Insensitive
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Lecture 16 10
GxE May Cause Both Changes in Scale and Rank
kijijjii GxEEGY )(ε+++=
E1Hot
E2Cold
G1Breed A
G2Breed BChange in Scale
Breed B is more environmentally sensitive and Better Suited to Cold
Breed A is Environmentally Insensitive and Better Suited to Hot
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Lecture 16 11
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
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Lecture 16 12
Alternative Situations Where GxE Can OccurImpacts How to Analyze and Interpret
Random
Fixed
RandomFixedEnvironments
Genotypes
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Lecture 16 13
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
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Lecture 16 14
Naked Neck (courtesy A. Cahaner)
Normal
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Lecture 16 15
Genotypes RandomIndividual Sires or Sire Lines Sampled From A
Population of Sires
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Lecture 16 16
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
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Lecture 16 17
Environments Random
• Herd• Year • Season • Effects
– Not Controllable– Outdoor housing
usually
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Lecture 16 18
Importance of GxE in Alternative Situations
Combinations of Genotypes (F vs.R)
Environments (F vs. R)
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Lecture 16 19
Genotypes FixedEnvironments 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
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Lecture 16 20
Genotypes RandomEnvironments 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
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Lecture 16 21
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
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Lecture 16 22
Genotypes RandomEnvironments 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
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Lecture 16 23
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
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Lecture 16 24
SummaryGxE 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
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Lecture 16 25
Analysis of Variance
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Lecture 16 26
Partitioning of GxEMethod 1: Re-Ranking of Genotypes Important
G2
G3
G4
G1
Standard Deviation of Genotypes in E1
G2
G3
G4
G1
G2
G3
G4
G1
E1E2 En
…
)(11 GVZ =
Standard Deviation of Genotypes in E2
Standard Deviation of Genotypes in En
)(22 GVZ = )(GVZ nn =
Determination of Heterogeneity of Variances
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Lecture 16 27
Sub-partitioning of GxE: Method 1Fixed or Random Genotypes; Fixed Environments
Issue: Re-ranking
Degree of interaction due to scale correlation of same genotype
across environments
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Lecture 16 28
Partitioning of GxEMethod 2: Environmental Sensitivity Important
E2
E3
E4
E1
Standard Deviation Among Environments For G1
E2
E3
E4
E1
E2
E3
E4
E1
G1G2 Gn
…
)(11 EVS =
Standard Deviation Among Environments For G2
Standard Deviation Among Environments For Gn
)(22 EVS = )(EVS nn =
Determination of Heterogeneity of Variances
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Lecture 16 29
Sub-partitioning of GxE: Method 2Fixed Genotypes, Random Environments,
Issue: Stability
Differential Environmental Sensitivity Among Entries
Differences in Correlations Among Pairs of Entries
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Lecture 16 30
Example Data
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Lecture 16 31
Program For Partitioning GxE
data a1;input gen env y;cards;1 1 81 2 91 3 101 4 111 5 122 1 122 2 112 3 102 4 92 5 8proc 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;
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Lecture 16 32
Overall ANOV
204GxE
401Genotypes (G)
04Environments (E)
Sums of Squares
Degrees of Freedom
Source of Variation
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Lecture 16 33
Both Genotypes were Equally response to the Environment
Re-ranking does not occur in the first case but does in the second
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Lecture 16 34
Lab Problem• From the Following Barley Data, Each Group Chose 2
different genotypes. Partition the GxE interaction for the pair and interpret the results.