Genotype by environment interactions (GxE)

and climate change Jacob van Etten Alberto Labarga

G x E

P = G + E + G*E

P = Production G = Genotype E = Environment

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)

Purely genetic difference

P = β1Gi + β2E + β3GiE β1 ≠ 0 β2 = 0 β3 = 0

Purely additive interaction

P = β1Gi + β2E + β3GiE β1 ≠ 0 β2 ≠ 0 β3 = 0

Non-additive interaction

P = β1Gi + β2E + β3GiE β1 ≠ 0 β2 ≠ 0 β3 ≠ 0

Cross-over: When does another variety take over?

climate change →

Lobell et al. (2011) study Weather variables

Yield

Ecophysiological variables

Weather variables

Yield

Ecophysiological variables

+ 1 °C

Estimate statistical

model Calculate

Recalculate Predict using

estimated model

Lobell et al. (2011)

Climate change impact maps

GxE: OPV vs hybrid

GxE: duration

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.)

Example of AMMI Biplot

Stress

Normal

RDA: adding environmental variables

Variety adaptation zones

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