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Text S1 Crop-specific grid net primary productivity.

Text S2 Probability of historical changes in yields.

Figure S1 Location of grid cells in which subnational yield data were used.

Figure S2 Relationships between the extent of harvested area in a grid cell and the correlation coefficients and root-mean-square errors calculated between modelled yields and subnational yield statistics in 1982–2006.

Figure S3 Relationships between the extent of harvested area in a grid cell and mean errors of annual rates of change in yields between the modelled yields and subnational yield statistics in 1982–2006.

Figure S4 Agreement between mean modelled yields in 1990–96 and M3-Crops data and that between mean modelled yields in 1999–2001 and MapSPAM data.

Figure S5 Means, coefficients of variation and annual rates of change in soybean yields in the periods 1982–93 and 1994–2006 and the differences between the two periods.

Figure S6 Means, coefficients of variation and annual rates of change in rice yields in the periods 1982–93 and 1994–2006 and the differences between the two periods.

Figure S7 Means, coefficients of variation and annual rates of change in wheat yields in the periods 1982–93 and 1994–2006 and the differences between the two periods.

Figure S8 Empirical cumulative distribution functions of crop production at the grid cell level versus the extent of harvested area in a grid cell.

Figure S9 Geographic harvested area distributions in 2000 for maize, soybean, rice and wheat.

Figure S10 Derivation of crop-specific grid net primary productivity.

Table S1 Subnational yield statistics used for this study.

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