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.