Extended Data Fig. 6: Irrigation modifies the influences of climatic factors on crop yield and validates empirical separation of water supply and temperature stresses.

Identical to Fig. 3 except that responses are estimated separately for each of the four crops rather than pooled. Grey backgrounds indicate models where either allowing for heterogeneity with respect to irrigation does not improve performance or where the response function is not significantly different from the null of zero effect at the p < 0.10 level (see Extended Data Table 1 for model performance when neither T nor S is interacted with irrigation or when both T and S are; when only T is interacted with irrigation, within-R² = 0.097 for maize, 0.141 for soybeans, 0.034 for sorghum and 0.028 for millet; when only S is interacted with irrigation, R² = 0.106 for maize, 0.136 for soybeans, 0.054 for sorghum and 0.022 for millet). Outliers are winsorized for display to their 0.5 and 99.5 percentiles for temperature and soil moisture and 1 and 99 percentiles for precipitation.