Soybean and maize yield residuals in the Cerrado Biome

Based on the available information from the Municipal Agricultural Production Survey provided by the Brazilian Institute of Geography and Statistics [45], we obtained the average yield of soy-maize double cropping system (ton/ha) at the municipal level between 2006 and 2019. The tabular data were also converted into time-series maps with a gridcell resolution of 28×28 km using the Inverse Distance Weighting interpolation.The calculation of the Soybean and maize yield residuals is needed to eliminate the influence of other factors, such as technological advancements, which could bias our analyses. To achieve this, we calculated soybean and second-crop maize yield residuals using a three-step procedure (Section S1.8). Firstly, we applied generalized additive models (GAM) [29] to fit mathematical equations to the historical series of each grid cell as a function of time. Soybean and maize yields (Yst and Ymt, in kg/ha) were the dependent variables, and time (t, in years) was the independent variable. Here, we assume that the yields follow a Poisson distribution. This is based on the consideration that the probability of a series of events occurring over a specific period is calculated assuming that these events are independent of the time of the last event. In the second step, the angular coefficients of the fitted equations were used to estimate the yield values (̂Yst 𝑒 ̂Ymt), representing the trend for Yst and Ymt. In the third step, we subtracted the fitted yield values from the observed values (Equations 2, 3).Y′st = Yst − ̂Yst𝑡 (Eq. 2)Y′mt = Ymt − ̂Ymt (Eq. 3)The resulting values are considered the yield residual, isolating the influence of other climate factors.