Lecture GxE interactions

Transcription

1 Lecture GxE interactions Lynch and Walsh Ch 24 Reference Muir, W. M., Y. Nyquist and S. Xu Alternative partitioning of the genotype by environment interaction. Theor. and Appl. Gen. 84: Vince Matassa: 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 Quantitative characterization of malting barleys for consistency in grain protein concentration (in handouts) Lecture 16 1

2 An Early Study on Fitness of Drosophila In Natural Setting Wright et. al one of the first molecular genetics experiments Lecture 16 2

3 Andres Canyon Keen Pinon Flat Lecture 16 3

4 Lecture 16 4 Observed Numbers of Chromosome Arrangements () Andres Canyon Pinon Flat Keen Camp TOT CH/ TL AR/ TL AR/ CH ST/ TL ST/ CH ST/ AR TL/ TL CH/ CH AR/ AR ST/ ST Location

5 Andres Canyon Keen *** *** NS Pinon Flat Lecture 16 5

6 Statistical Definition GxE Interactions 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

7 The Basic Model Y = G + i i E i G 2 Breed B Genotype Effect G 1 Breed A E 1 Hot E 2 Cold Environment Effect The response of a genotype to a change in an environmental factor is sometimes called a reaction norm Lecture 16 7

8 GxE May Cause Changes in Rankings Y = G + E + i i i GxE i Change in rank There is no universal best genotype A specific breed is bred to each environment G 2 Breed B G 1 Breed A E 1 Hot E 2 Cold Lecture 16 8

9 GxE May Cause Changes in Scale Y = G + E + i i i GxE i Change in Scale Breed B is more environmentally sensitive G 2 Breed B G 1 Breed A Breed A is Environmentally Insensitive E 1 Hot E 2 Cold Lecture 16 9

10 GxE May Cause Both Changes in Scale and Rank Y i = G i + E j + GxE ij + ε ( ij) k Change in Scale Breed B is more environmentally sensitive and Better Suited to Cold G 2 Breed B G 1 Breed A Breed A is Environmentally Insensitive and Better Suited to Hot E 1 Hot E 2 Cold Lecture 16 10

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 11

12 Alternative Situations Where GxE Can Occur Impacts How to Analyze and Interpret Genotypes Environments Fixed Random Fixed Random Lecture 16 12

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 13

14 Naked Neck (courtesy A. Cahaner) Normal Lecture 16 14

15 Genotypes Random Individual Sires or Sire Lines Sampled From A Population of Sires Lecture 16 15

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 16

17 Environments Random Herd Year Season Effects Not Controllable Outdoor housing usually Lecture 16 17

18 Importance of GxE in Alternative Situations Combinations of Genotypes (F vs.r) Environments (F vs. R) Lecture 16 18

19 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

20 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

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 21

22 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

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 23

24 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

25 Analysis of Variance Lecture 16 25

26 Partitioning of GxE Method 1: Re-Ranking of Genotypes Important Determination of Heterogeneity of Variances G 1 G 1 G 1 G 2 G 4 G 2 G 4 G2 G 4 G 3 G 3 G 3 E 1 E 2 E n Standard Deviation of Genotypes in E 1 Z = V1( 1 G ) Standard Deviation of Genotypes in E 2 Z = V2( 2 G ) Standard Deviation of Genotypes in E n V (G) Lecture Z n = n

27 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

28 Partitioning of GxE Method 2: Environmental Sensitivity Important Determination of Heterogeneity of Variances E 1 E 1 E 1 E 2 E 4 E 2 E 4 E2 E 4 E 3 E 3 E 3 G 1 G 2 G n Standard Deviation Among Environments For G 1 S 1 = V E) 1( Standard Deviation Among Environments For G 2 2 V E) Standard Deviation Among Environments For G n Sn = Vn (E S = 2( ) Lecture 16 28

29 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

30 Example Data Lecture 16 30

31 Program For Partitioning GxE data a1; input gen env y; cards; 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

32 Source of Variation Overall ANOV Degrees of Freedom Sums of Squares Environments (E) 4 0 Genotypes (G) 1 40 GxE 4 20 Lecture 16 32

33 Re-ranking does not occur in the first case but does in the second Both Genotypes were Equally response to the Environment Lecture 16 33

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. Lecture 16 34