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 change Jacob van Etten

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

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

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

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

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

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

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

10. Lobell et al. (2011)

11. Climate change impact maps

12. GxE: OPV vs hybrid

13. GxE: duration

14. 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.)

15. Example of AMMI Biplot Stress Normal

16. RDA: adding environmental variables

17. Variety adaptation zones

19. Get an estimate of the error

20. Link to daily plant breeding practice!Package weatherData to get weather data for trial locations and derive ecophysiological variables