This document discusses genotype by environment interactions (GxE) and how climate change can impact them. It presents equations to model production (P) as a function of genotype (G), environment (E), and their interaction (G*E). Different values for the coefficients β1, β2, and β3 represent purely genetic differences, additive interactions, and non-additive interactions between G and E. Methods like AMMI and RDA are described that use statistical models to analyze GxE, predict impacts of climate change, and define variety adaptation zones.

1. Genotype by environment interactions (GxE) and climate changeJacob van Etten

2. G x EP = G + E + G*EP = ProductionG = GenotypeE = Environment

3. In other words...Suppose we have a continuous environmental variable

4. two different genotypes i = {1,2}Now the regression equation becomes:P = (β0 +) β1Gi + β2E + β3GiE (+ e)

5. Purely genetic differenceP = β1Gi + β2E + β3GiEβ1≠ 0β2 = 0β3 = 0

6. Purely additive interactionP = β1Gi + β2E + β3GiEβ1≠ 0β2≠ 0β3 = 0

7. Non-additive interactionP = β1Gi + β2E + β3GiEβ1 ≠ 0β2 ≠ 0β3 ≠ 0

8. Cross-over: When does another variety take over?climate change ->

9. Lobell et al. (2011) studyWeather variablesYieldEcophysiological variablesWeather variablesYieldEcophysiological variablesEstimate statistical modelCalculate+ 1 °CPredict using estimated modelRecalculate

10. Lobell et al. (2011)

11. Climate change impact maps

12. GxE: OPV vs hybrid

13. GxE: duration

14. What breeders usually do: AMMIAdditive Main Effects and Multiplicative InteractionProduction = G + E + residualsThen do a PCA on residuals to visualize the GxE interactions.(An alternative is to only remove G – known as GGE.)

15. Example of AMMI BiplotStressNormal

16. RDA: adding environmental variables

17. Variety adaptation zones