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In the version of this article initially published, there were errors in equations and notations in the Methods “Model development” subsection which arose during manuscript preparation; the errors affect presentation of the study but not the analysis, results, or code provided with the article. Clarifications to text and equations follow.In Equation (1), “N” replaces “Normal”; in Equations (2), (3), (7) and in text directly below Equations (3), (5) and (7), “ys,i,z” now replaces “Δxs,t1, t2.” In the two paragraphs below Equation (2), “t2 = 2016” and “t1 = 2001” now replace “2016” and “2001” in five instances. Further, Equations (5)–(7) have been revised as follows:$$begin{array}{ll}fleft( {x_{s,t}} right) = {{{mathrm{exp}}}} & left( {beta _0 + mathop {sum }limits_{i = 1}^{I = 5} beta _{1,i} x_{s,i,t} + mathop {sum }limits_{i = 1}^{I = 5} mathop {sum }limits_{k = i}^{K = 5} beta _{2,i,k}x_{s,i,t}x_{k,s,t}}right. \ & quad quad left. {+ mathop {sum }limits_{i = 1}^{I = 5} mathop {sum }limits_{k = 1, k neq i}^{K = 5} beta _{3,i,k}x_{s,i,t}x_{k,s,t}} right)end{array} {rm{Revised}} {rm{Eq}}. (5)$$$$begin{array}{ll}fleft( {x_{s,t}} right) \ = expleft( {beta _0 + mathop {sum }limits_{i = 1}^{I = 5} mathop {sum }limits_{j = 1}^{J = 2} beta _{0,i,j,}x_{i,s,t}^j + mathop {sum }limits_{i = 1}^{I = 5} mathop {sum }limits_{k = i + 1}^{K = 6} beta _{1,i,k}x_{i,s,t}x_{k,s,t}} right) {mathrm{Original}} {rm{Eq}}. (5)end{array}$$$$y_{s,i,z} = left{ {begin{array}{*{20}{l}} {y_{s,i,1} = left| {Delta x_{s,i}} right|,} hfill & {y_{s,i,2} = 0,} hfill & {{{{mathrm{if}}}},Delta x_{s,i} < 0} hfill \ {y_{s,i,1} = 0,} hfill & {y_{s,i,2} = Delta x_{s,i}} hfill & {{{{mathrm{otherwise}}}}} hfill end{array}} right. {rm{Revised}} {rm{Eq}}. (6)$$$$x_{i,s,} = left{ {begin{array}{*{20}{l}} {x_{1,i,s} = left| {Delta x_{i,s}} right|,} hfill & {x_{2,i,s} = 0,} hfill & {if,Delta x_{i,s} < 0} hfill \ {x_{1,i,s} = 0,} hfill & {x_{2,i,s} = Delta x_{i,s},} hfill & {otherwise} hfill end{array}} right. {rm{Original}} {rm{Eq}}. (6)$$$$omega left( {y_{s,i,z};gamma } right) = {{{mathrm{exp}}}}left( {mathop {sum }limits_{i = 1}^{I = 5} mathop {sum }limits_{z = 1}^{Z = 2} - gamma _{i,z} y_{s,i,z}} right) {rm{Revised}} {rm{Eq}}. (7)$$$$omega left( {Delta x_{s,t_1,t_2};gamma } right) = expleft( {mathop {sum }limits_{i = 1}^{I = 5} - gamma _{i,z}Delta x_{z,s,i}} right) {rm{Original}} {rm{Eq}}. (7)$$All changes have been made in the HTML and PDF versions of the article. More

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Study regions and recent trends in land use changeOur analysis focuses on four biomes (referred to as regions in the rest of the text), accounting for nearly all soybean area in Brazil: the Pampa, the Atlantic Forest, the Cerrado and the Amazon (Supplementary Section 1). Soybean production is negligible in the Pantanal and the Caatinga, so these two regions were excluded from our analysis. We focused on soybean-based systems in Brazil, either those that include one crop per year (single soybean) or those including a second-crop maize. In the latter system, soybean is sown in September–October, and maize is sown right after the soybean harvest in late January–February. Single soybean is common in the Pampa, where the drier climate does not allow double cropping. In contrast, higher precipitation allows double cropping in the Amazon, the Cerrado and most of the Atlantic Forest (Supplementary Section 2).Recent trends in yield, area and production for soybean and second-crop maize were derived from official statistics for the 2007–2019 period16. We fitted linear models to derive the annual rate of yield improvement and harvested area for soybean and second-crop maize, separately for each region (Fig. 1 and Extended Data Fig. 1). Land use change arising from soybean expansion was estimated using data from the MapBiomas project (v.5.0)10 (Supplementary Table 1). Our estimation of land use change accounted for the time lag between land conversion and the beginning of soybean production, which can include transitional stages such as the cultivation of upland rice or short-term pasture-based livestock systems42. To account for this, we looked at the new land brought into soybean production during the 2008–2019 period, and we analysed how much of this land was under a different land use type (forest, savannah, grassland, pasture or other crops) in 2000 (Extended Data Fig. 2).Estimation of yield potential and yield gapsWe used results on yield potential for Brazil that we generated through the Global Yield Gap Atlas project43 using well-validated process-based crop models and the best available sources of weather, soil and management data. Briefly, we selected 32 sites to portray the distribution of the soybean harvested area within the country, following protocols that ensure representativeness and a reasonable coverage of the national crop area44. The 32 sites collectively accounted for half of the soybean harvested area in Brazil. These sites were located within agro-climatic zones accounting for 86% of the national soybean production and accounted for 72–92% of the soybean area in each region. Following protocols that gave preference to measured data at a high level of spatial and temporal resolution45, we collected databases on weather, soil, management and crop yields for soybean for each site, and also for second-crop maize at those sites where double-cropping is practised (Supplementary Tables 2 and 3 and Supplementary Section 3).Yield potential was simulated for widespread cultivars in each region using the CROPGRO soybean model embedded in DSSAT v.4.546 and the Hybrid-Maize model47. Both models simulate crop growth and development on a daily time step. Growth rates are determined by simulating both CO2 assimilation and respiration, with partitioning coefficients to different organs dependent on developmental stage. The model phenological coefficients were calibrated to portray the crop cycle of the most dominant cultivars in each region in Brazil. We used generic default coefficients for growth-related model internal parameters such as photosynthesis, respiration, leaf area expansion, light interception, biomass partitioning and grain filling. In all cases, simulations of yield potential assumed the absence of insect pests, weeds and diseases and no nutrient limitations. In simulating yield potential, both models account for solar radiation, photoperiod, temperature, and the timing and amount of rainfall as well as soil properties influencing crop water balance.We first evaluated the CROPGRO and Hybrid-Maize models on the ability to reproduce measured phenology and yields across 40 well-managed experiments located across the four regions. The models showed satisfactory performance at reproducing the measured values (Extended Data Fig. 3). We then simulated soybean yield potential for the dominant agricultural soils at each site (usually two or three), as determined from the soil maps generated by the Radambrasil project48. The simulations were based on long-term (1999–2018) measured daily weather data retrieved from the Brazilian Institute of Meteorology49. Soybean yield potential was simulated for each year of the time series. We also simulated yield potential for second-crop maize for those sites where double-cropping is practised. To do so, we used sowing dates and cultivar maturities that maximize the overall productivity of the soybean–maize system; these sowing dates and cultivar maturities are within the current ranges in each region21,28. To estimate the average yield potential for each site, we weighted the simulated values for each soil type by soil area fraction at each site. In all cases, the simulations assumed no limitations to crop growth due to nutrient deficiencies or incidence of biotic stresses such as weeds, insect pests and pathogens. The results were upscaled from site to region and then to country following van Bussel et al.44. Briefly, the average yield potential for each region was estimated by averaging the simulated yields across the sites located within each region, weighing sites according to their share of the soybean area within each region. A similar approach was followed to upscale yield potential from region to the national level. Details on crop modelling, data sources and upscaling are provided in Supplementary Section 3.The average farmer yield was calculated separately for soybean and second-crop maize on the basis of the average yield reported over the 2012–2017 period for the municipalities that overlap with each site, weighing municipalities on the basis of their share of the soybean or maize area within each site16. Including more years before 2012 would have led to a biased estimate of average actual yield due to the technological yield trend in Brazil. Average farmer yields were estimated at the region and country levels following the same upscaling approach as for yield potential. Finally, the exploitable yield gap was calculated as the difference between attainable yield and average farmer yield. The attainable yield was calculated as 80% of the simulated yield potential, which is considered a reasonable yield for farmers with adequate access to inputs, markets and technical information (Supplementary Section 2).Assessing scenarios of intensification and land use changeWe explored three scenarios with different soybean and maize yields and areas by 2035 and assessed their outcomes in terms of production, land use change and GWP (Supplementary Table 4). A 15-year future timespan is long enough to facilitate the implementation of long-term policies, investments and technologies devoted to closing the exploitable yield gap and to implement land-use policies, but it is short enough to minimize long-term effects from climate change on crop yields and cropping systems. In the BAU scenario, historical (2007–2019) trends of soybean and second-crop maize area and yield (Extended Data Fig. 1) remain unchanged in all regions between the baseline year (2019) and the final year (2035). Likewise, soybean area expands following the same pattern of land use change observed during 2008–2019 (Extended Data Fig. 2).To explore the available opportunity for increasing production on the existing production area, we considered an NCE scenario in which there is no physical expansion of cropland while full closure of the exploitable yield gap occurs in the regions where the current yield gaps are small (the Pampa and the Atlantic Forest), and 50% closure of the exploitable yield gap takes place in regions where the current yield gaps are large (the Amazon and the Cerrado) (Supplementary Table 4). These rates are comparable to historical yield gains in the Pampa and the Atlantic Forest. A scenario of full yield closure in the Amazon and the Cerrado would have been unrealistic, as it would have required rates of yield improvement that are three to four times higher than historical rates, much higher than those in the Pampa and the Atlantic Forest, and well beyond those reported for main soybean-producing countries. In the case of second-crop maize, we assumed full closure of the exploitable yield gap by 2035 because historical rates of yield improvement are adequate to reach that yield level. Regarding second-crop maize area, we projected the proportion of double-cropping to increase from the current 47% (Amazon), 39% (Cerrado) and 31% (Atlantic Forest) to 100%, 70% and 50%, respectively, as determined on the basis of the degree of water limitation in each region (Supplementary Section 4).Finally, we explored a third scenario of intensification plus target area expansion (INT), in which identical yield gain rates and the adoption of double-cropping equivalent to those in the NCE scenario were assumed, but with physical expansion of the soybean–maize system allowed in low-C ecosystems (that is, pastures and grasslands). In this scenario, soybean expansion is limited to 5% of existing pastures and grasslands in the Pampa, the Atlantic Forest and the Cerrado (total of 5.7 Mha) as a result of a parallel intensification in the pasture-based livestock sector that frees up land for soybean production. The latter would require an increase of current stocking rates, not only for freeing up 5% of the area for soybean cultivation but also to meet the projected 7% beef production increase during the study period (2020–2035)17. Hence, an overall 12% increase in stocking rates would be required within our 15-year timeframe, which is a reasonable target as reported in previous studies and based on current trends in stocking rates16,29,32,33.Another assumption is that the yield potential of pasture and grasslands converted for soybean production is similar to that in existing soybean areas in each region. Cropland expansion into grassland and pastures was allowed in all regions except for the Amazon to prevent ‘leaking’ effects and the impact of road development on land clearing50,51. Similarly, the conversion of area cultivated with food crops for soybean production was not allowed to avoid the negative impact of indirect land use change52.Estimation of GWP and gross incomeWe estimated GHG emissions, including carbon dioxide (CO2), methane (CH4) and nitrous oxides (N2O), associated with land conversion (GHGLUC) and crop production (GHGPROD) for the baseline year (2019) and for the three scenarios by year 2035 (BAU, NCE and INT). GHGLUC includes emissions associated with changes in C stocks from aboveground and belowground biomass when land is converted for soybean production (GHGBIO), as well as GHG emissions derived from changes in soil organic C (GHGSOC). For each land use type, annual GHGBIO was estimated on the basis of the difference between C stocks of the land use type that was converted for production (Supplementary Table 5) and, depending on the scenario and region, the average C stocks of the new cropping system53,54,55:$${mathrm{GHG}}_{{mathrm{BIO}}} = {sum} {left( {{mathrm{TDM}}_i-{mathrm{TDM}}_{{mathrm{crop}}}} right) times A_i}$$
(1)
where i is the land cover type, TDM is the total dry matter (tC ha−1) in land cover type i and in cropland (crop), and Ai is the annual area converted from land use type i for soybean cultivation (Supplementary Table 4). C stocks for single soybean and soybean–second-crop maize systems were assumed at 2 and 5 tC ha−1, respectively53,54,55. Changes in SOC stocks were estimated following the Intergovernmental Panel on Climate Change 2019 guidelines54, available country-specific emission factors56 and the SOC values estimated for each region57,58:$${mathrm{GHG}}_{{mathrm{SOC}}} = {sum} {left( {{mathrm{SOC}}_{{mathrm{REF}},i} times F_{{mathrm{LU}}}} right) times A_i}$$
(2)
where SOCREF is the SOC stock for mineral soils in the upper 30 cm for the reference condition (tC ha−1)57 in land cover type i (Supplementary Table 5), and FLU is the stock change factor for SOC land-use systems for a particular land use (Supplementary Table 4). Because no-till is the predominant soil management strategy in Brazil59, we used FLU = 0.96 for natural vegetation converted to no-till annual crop production, and FLU = 1.16 for pasture and grassland converted to no-till annual crop production56. Because we wanted to assess the full impact of the three scenarios (BAU, NCE and INT) on GWP, we assigned all GHGBIO and GHGSOC derived from land conversion to the first year after land conversion and expressed them as CO2 equivalents by multiplying changes in C stocks by 3.67.Annual GHG emissions derived from soybean and second-crop maize production (GHGPROD) were calculated for each scenario and included those derived from manufacturing, packaging and transportation of agricultural inputs, fossil fuel use for field operations, soil N2O emissions derived from the application of nitrogen (N) fertilizer, and domestic grain transportation. For the baseline year (2019), annual GHG emissions from N, phosphorous (P) and potassium (K) fertilizers and other inputs (lime, pesticides and fuel) were calculated on the basis of current average input rates for soybean and second-crop maize in each region as derived from the crop management data collected for each region (Supplementary Table 6 and Supplementary Section 3.4). To calculate GHG emissions associated with manufacturing, packaging and transportation of N, P and K fertilizers and lime, we used specific updated emissions factors for South America60, selecting those fertilizer sources that are most commonly used for soybean and second-crop maize production: urea (N), monoammonium phosphate (P) and potassium chloride (K). Our calculations also included the extra lime application that is needed to correct soil acidity in converted areas. Emission factors associated with seed production, pesticides and diesel were derived from ref. 61. Soil N2O emissions derived from N fertilizer application were calculated assuming an N2O emission factor of 1% of the applied N fertilizer on the basis of the country-specific emission factor62. Emissions derived from domestic grain transportation for each region were estimated using the GHGs per ton of grain as reported by previous studies for each region63. We assumed that inputs other than nutrient fertilizer will not change relative to the baseline in the BAU scenario. In the INT scenario, applied inputs were calculated on the basis of those reported for current high-yield fields where the yield gap is small. We estimated fertilizer nutrient rates for the three scenarios following a nutrient-balance approach that depends on the projected yield for each scenario (Supplementary Table 6 and Supplementary Section 3.4).GHGPROD in the baseline year (2019) and for the three scenarios in 2035 (BAU, NCE and INT) was estimated for each region by multiplying the emissions per unit of area by the annual soybean harvested area, summing them to estimate GHG emissions at the national level. Overall 100-year GWP was estimated as the sum of GHGLUC and GHGPROD, both expressed as CO2e to account for the higher warming potential of CH4 and N2O, which are 25 and 298 times the intensity of CO2 on a per mass basis, respectively. The gross income was estimated for each scenario by multiplying the annual crop production by the average price for soybean and maize grain during the past ten years (US$453 and US$184 per t for soybean and maize, respectively1). Finally, to combine the environmental and economic impacts into one metric, we calculated the GWP intensity as the ratio between GWP and gross income.Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More