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# Genotype by environment interactions gx e and climate change

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### Genotype by environment interactions gx e and climate change

1. 1. Genotype by environment interactions (GxE) and climate change Jacob van Etten Alberto Labarga
2. 2. GxE P = G + E + G*EP = ProductionG = GenotypeE = Environment
3. 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. 4. Purely genetic differenceP = β1Gi + β2E + β3GiEβ1 ≠ 0β2 = 0β3 = 0
5. 5. Purely additive interactionP = β1Gi + β2E + β3GiEβ1 ≠ 0β2 ≠ 0β3 = 0
6. 6. Non-additive interactionP = β1Gi + β2E + β3GiEβ1 ≠ 0β2 ≠ 0β3 ≠ 0
7. 7. Cross-over:When does another variety take over? climate change →
8. 8. Lobell et al. (2011) studyWeather Ecophysiological Yieldvariables variables Estimate Calculate statistical modelWeather Ecophysiological Yieldvariables variables+ 1 °C Predict using Recalculate estimated model
9. 9. Lobell et al. (2011)
10. 10. Climate change impact maps
11. 11. GxE: OPV vs hybrid
12. 12. GxE: duration
13. 13. What breeders usually do: AMMIAdditive Main Effects and Multiplicative Interaction Production = G + E + residualsThen do a PCA on residuals to visualize the GxEinteractions.(An alternative is to only remove G – known as GGE.)
14. 14. Example of AMMI Biplot Stress Normal
15. 15. RDA: adding environmental variables