1. Genotype by environment
interactions (GxE)
and climate change
Jacob van Etten
Alberto Labarga

2. GxE
P = G + E + G*E
P = Production
G = Genotype
E = Environment

3. In other words...
Suppose we have
 a continuous environmental variable
 two different genotypes i = {1,2}
Now the regression equation becomes:
P = (β0 +) β1Gi + β2E + β3GiE (+ e)

4. Purely genetic difference
P = β1Gi + β2E + β3GiE
β1 ≠ 0
β2 = 0
β3 = 0

5. Purely additive interaction
P = β1Gi + β2E + β3GiE
β1 ≠ 0
β2 ≠ 0
β3 = 0

6. Non-additive interaction
P = β1Gi + β2E + β3GiE
β1 ≠ 0
β2 ≠ 0
β3 ≠ 0

7. Cross-over:
When does another variety take over?
climate change →

8. Lobell et al. (2011) study
Weather Ecophysiological Yield
variables variables
Estimate
Calculate statistical
model
Weather Ecophysiological Yield
variables variables
+ 1 °C
Predict using
Recalculate estimated
model

9. Lobell et al. (2011)

10. Climate change impact maps

11. GxE: OPV vs hybrid

12. GxE: duration

13. What breeders usually do: AMMI
Additive Main Effects and Multiplicative Interaction
Production = G + E + residuals
Then do a PCA on residuals to visualize the GxE
interactions.
(An alternative is to only remove G – known as GGE.)

14. Example of AMMI Biplot
Stress
Normal

15. RDA: adding environmental variables

16. Variety adaptation zones

17. Final remarks
Statistical models complement mechanistic
models
 Use real data for places where mechanistic models
have not been calibrated
 Get an estimate of the error
 Link to daily plant breeding practice!
Package weatherData to get weather data for trial
locations and derive ecophysiological variables