This document discusses genotype by environment interactions (GxE) and how climate change may impact them. It presents different statistical models that can be used to analyze GxE, including regression models that account for additive and non-additive interactions between genotypes and environments. Specific studies are mentioned, such as one analyzing how increased temperatures may impact crop yields based on estimated statistical models. The document also discusses various statistical analysis methods commonly used by breeders, such as AMMI analysis, and how including environmental data can help complement mechanistic models.

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