Extended Data Fig. 1: Ranking, by importance, of predictors included in the causal forest model used to predict the maize yield response to fertilizer, estimated using the grf package in R ⁷⁵.

Importance is quantified as a weighted sum of the number of times that variable was used to split the data at each depth in the forest. The climate variables include: total precipitation in the 1st and 2nd months of the growing season (precip p1), during the 3rd month (precip p2), and during the 4th and 5th months (precip p3), average daily temperature during the 1st and 2nd months of the growing season (temp p1), during the 3rd month (temp p2), and during the 4th and 5th months (temp p3). The soil variables include: soil cation exchange capacity in centimol charge per kg soil (soilcec), soil pH as determined in a soil/water mixture (soilph), soil clay content share by volume (claypct), soil silt content share by volume (siltpct), soil bulk density in kg per cubic decimeter (bulkdens) soil exchangeable acidity in centimols charge per kg soil (acidity), soil organic matter in g per kg soil (soilom), soil nitrogen content in g per kg soil (soiln), the site’s elevation (elevm), and a binary variable indicating whether the soil is characterized as having poor drainage (poordrain). The management variables include an indicator for whether a hybrid variety was used (compared with an open populated variety) and an indicator for whether the data come from the OFRA trial (wortmann, ¹⁵) rather than the CIMMYT-supervised trials ^15,52. All continuous variables are standardized prior to estimation to a mean of zero and standard deviation of 1.