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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)
Lecture 16 2
An Early Study on Fitness of Drosophila In Natural Setting
Wright et. al. 1942one of the first molecular genetics experiments
Lecture 16 3
Keen
Pinon Flat
Andres Canyon
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
Lecture 16 5
Keen
Pinon Flat
Andres Canyon
NS
******
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.
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
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
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
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
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
Lecture 16 12
Alternative Situations Where GxE Can OccurImpacts How to Analyze and Interpret
Random
Fixed
RandomFixedEnvironments
Genotypes
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
Lecture 16 14
Naked Neck (courtesy A. Cahaner)
Normal
Lecture 16 15
Genotypes RandomIndividual Sires or Sire Lines Sampled From A
Population of Sires
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
Lecture 16 17
Environments Random
• Herd• Year • Season • Effects
– Not Controllable– Outdoor housing
usually
Lecture 16 18
Importance of GxE in Alternative Situations
Combinations of Genotypes (F vs.R)
Environments (F vs. R)
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
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
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
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
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
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
Lecture 16 25
Analysis of Variance
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
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
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
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
Lecture 16 30
Example Data
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;
Lecture 16 32
Overall ANOV
204GxE
401Genotypes (G)
04Environments (E)
Sums of Squares
Degrees of Freedom
Source of Variation
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
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.