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1 DOI: /NPLANTS All references numbered in this document are listed below. Further Discussion of Biogeochemistry The long term fate of the P tax in P-fixing soils deserves increased attention by researchers. One limitation of our survey data is that variability from farm to farm can potentially mask underlying trends of increasing soil P availability that would only be apparent from detailed experiments on the same soil. Such data remain scarce. However, a recent study based on long-term trials in the Brazilian Cerrado showed that large increases in soil total P over 3-4 decades of high inorganic fertilizer inputs were mostly accounted for within soil P pools unavailable to plants or difficult to access 1. Evidence from that study, other studies in Brazil, western Kenya, and southeast Asia suggests that P added to P-fixing soils and not harvested in crops largely accumulates as inorganic P held by chemisorption to Fe and Al components of soil surfaces 2-4. This inorganic P pool (extracted by 0.1 M NaOH in the sequential Hedley P fractionation scheme) can potentially be a source of P to readily plant-available pools over time 5, but immobilization in other forms is also possible 6. Studies of P-fixing soils in the southeastern U.S. and western Kenya have shown that once fertilization ceases the release rate of P from soil P pools not readily plant-available does not match the kinetics of crop demand 3,5. Further experimentation is needed to increase our understanding of soil P movement in fertilized P- fixing soils, and the P tax range we use here for high-yielding systems (10-20 kg P ha -1 yr -1 ) can be interpreted to accommodate uncertainty in soil P dynamics. Management of soil organic carbon (SOC) in agricultural systems is vital for numerous reasons, including its effect on P availability. Over time SOC can potentially build up in surface soils under highly productive agriculture 7 and play a role in saturating P-fixation sites in soils 8. NATURE PLANTS 1

2 DOI: /NPLANTS.2016.X Evidence from Brazil and elsewhere in the tropics illustrates that SOC accumulation depends on management and climate 7,9. No-till management is more likely to promote SOC increase in croplands than full-till management 7, which can cause substantial SOC declines in some cases 9. Higher decomposition rates in wetter and hotter regions may counterbalance large SOC inputs from crop residues 7. It is therefore difficult to estimate what effect SOC dynamics will have on fertilization requirements for croplands atop tropical P-fixing soils over long time periods at the global scale. This is an important question for future research. We would also like to note that, in our state-level P flow analysis in Brazil, there was no correlation between P surpluses and the percentage of P harvested that was in soy as opposed to other crops (p = 0.46). This suggests soy s status as a high P demanding nitrogen fixer is not biasing our assessment (Supplementary Fig. 2c). 2 NATURE PLANTS

3 DOI: /NPLANTS.2016.X SUPPLEMENTARY INFORMATION Survey and Remote Sensing Methods We randomly selected farms on which to sample by using ArcGIS s fishnet tool to create a set of 5km² grid cells covering the entire state of Mato Grosso, Brazil. In total, this operation resulted in a pool of 36,145 grid cells. We then used a random selection process in Stata to take a 5% subsample of these cells. Finally, we selected all grid cells located within 120 minutes driving times from Sinop, Mato Grosso for visiting. This resulted in a sample of 109 interest areas. In 2014, we then sought to conduct a census of property owners in these areas, focusing on landowners possessing more than 250 ha. In total, we identified nearly 250 property owners, 108 of which we succeeded in interviewing. Not every owner provided answers regarding fertilizer applications. Our sample consists of the 49 farmers who provided this information. All data are provided in Supplementary Table 7. Fertilizer survey questions: Se sabe, na media, quantos quilogramas de fertilizantes sejam aplicado na lavoura por soja? o (Do you know, on average, how many kilograms of fertilizer you apply for soybeans?) Você sabe o porcentagem de N:P:K no adubo que usa por soja (e.g., )? o (Do you know what percentage of N:P:K for fertilizer you use for soybeans?) Porcentagem de N? (Percentage of N?) Porcentagem de P? (Percentage of P?) Porcentagem de K? (Percentage of K?) NATURE PLANTS 3

4 DOI: /NPLANTS.2016.X Fertilizer data obtained from above questions: Kilograms per hectare of fertilizer applied for soybeans (e.g., commonly 500 kg/ha) N-P-K formula of fertilizer applied for soybeans (e.g., commonly ) Fertilizer_P_input calculation methods: N-P-K formula was used to determine the fraction of fertilizer mass that is P2O5. For example, indicates that 18% of the fertilizer added is P2O5 by mass (fraction = 0.18). Total kilograms of fertilizer per ha x Fraction P2O5 by mass = Kilograms of P2O5 applied per ha Fraction of P2O5 that is P = (2*30.974)/[(2*30.974)+(5*15.999)] = Kilograms of P applied per ha = Kilograms of P2O5 applied per ha * Below, Fertilizer_P_input = Kilograms of P applied per ha (units are kg P ha -1 y -1 ) Soybean yield survey questions: Na media, qual foi a produção (em sacas de soja) dessa fazenda, no ano passado? (On average, how many sacks of soybeans (per hectare) were produced on this farm last year?) Na media, quantas sacas de soja pretende produzir na fazenda, nesta safra? (On average, how many sacks of soybeans (per hectare) do you expect to produce on this farm this year?) In all cases but two, farmers answered the first question (past year s yield). This value was used as the soybean yield in these cases. For the two other cases, the expected yield this year was used. 4 NATURE PLANTS

5 DOI: /NPLANTS.2016.X SUPPLEMENTARY INFORMATION Soybean_P_harvest calculation methods: In Brazil, 1 sack of soybeans = 60 kg From (Ref. 10), fresh soybeans are 10.12% moisture and % of dry soybean is phosphorus. Dry soybean yield in kg per ha = Fresh soybean yield in kg per ha x [1 - (10.12/100)] Soybean_P_harvest = Dry soybean yield in kg per ha x ( /100) (units = kg P ha -1 y -1 ) P_residual = Fertilizer_P_input - Soybean_P_harvest (units = kg P ha -1 y -1 ) P_output:input = Soybean_P_harvest / Fertilizer_P_input For Farm_size: Survey questions: o Qual é o tamanho da propriedade, em total (ha)? (What is the size of the property in total in hectares?) o Quantos hectares de lavoura foram plantados aqui no ano passado (em ha)? (How many hectares did you plant on this farm last year?) In all cases but one, farmers answered the second question. Farm_size used for the regression with P data was set equal to the number of hectares planted in these cases. In the one case where this information was not available, the total property size was used. To estimate Farm_age: We define Farm_age as the number of years a farm has been producing soybeans. This was estimated using a remote sensing approach. We identified farm boundaries by talking with farmers on site and using spatial data from the Cadastro Ambiental Rural (CAR) database NATURE PLANTS 5

6 DOI: /NPLANTS.2016.X managed by the Brazilian government ( if available. For each surveyed farm, Farm_age was estimated using Landsat 5 and Landsat 7 images collected during over Mato Grosso. Scenes were classified both statistically and visually. For each growing season from , two Landsat images were stacked: an early dry season scene (from September or October) and mid-wet season scene (from December or January). For , unstacked mid-wet season images for Landsat 7 were used, which agreed with classifications using stacked Landsat 5 images. Using soy, cloud, pasture, and forest training classes, we ran each growing-season stacked image through a maximum likelihood classifier. Cloud cover, however, sometimes limited the availability of algorithm-classifiable data. Where intense cloud cover corrupted our algorithmic classifications, visual classification was attempted. To visually classify a soy-cultivated field, Landsat scenes from each growing season were displayed as falsecolor images (RGB: Band 4, Band 5, Band 3) 11. Using this band combination, soy fields appear bright orange, while pasture and natural vegetation appear as textured green and brown. If the soy field was visible through clouds, the site was designated accordingly (less than 10 images were classified in this manner). If clouds obstructed the field throughout the entire growing season, it was not classified. All data were processed using Exelis ENVI / IDL 5.1 software. The performance of this remote sensing approach was tested by re-surveying a subset (n = 11) of the sample group in July Farmers were asked what year soy was first harvested on their property (regardless of proprietor). We were particularly interested in the older aged farms, and were able to make contacts for two additional farms that have been in soybean production for more than two decades. These do not fit our original criteria of random selection (i.e., they are not located within one of the randomly generated grids), but they do help us understand the accuracy of the remote sensing method (results for these farms are distinguished below and in 6 NATURE PLANTS

7 DOI: /NPLANTS.2016.X SUPPLEMENTARY INFORMATION Supplementary Fig. 7). Two approaches were taken to compare the years in soy estimated by remote sensing versus farmer surveys. First, each farm (n = 13) was treated as a single unit and the earliest year of soy harvest reported by farmers was compared to the first year when soy was identified using remote sensing. Second, field-level comparisons were made. On many of these large farms, soy production began at different times for different fields. Each field was defined as an area of the farm where the farmer identified a unique first harvest date. In cases where there was not heterogeneity within a farm (either reported by the farmer or observed using remote sensing), the entire farm was considered a single field. In total, 27 fields were investigated. There was generally good agreement between the years of soybean production estimated using remote sensing and the information reported by farmers for the farm-level comparison (Supplementary Fig. 7a). All farms (n = 13): r 2 = 0.78, p<0.001 Only farms within survey grids (n = 11): r 2 = 0.71, p=0.001 The remote sensing method agreed within 1 year for survey data from 7 farms, identified a first harvest date >1 year earlier than the survey data for 2 farms (mean = 7 years earlier), and identified a first harvest date >1 year later than the survey data for 4 farms (mean = 5 years later). The remote sensing method most likely underestimates Farm_age for older farms because of data gaps due to cloud cover (Supplementary Fig. 7a). The field-level comparison also yielded strong correlations between survey data and remote sensing estimates (Supplementary Fig. 7b): All fields (n = 27): r 2 = 0.85, p<0.001 Only fields within survey grids (n = 24): r 2 = 0.81, p<0.001 NATURE PLANTS 7

8 DOI: /NPLANTS.2016.X We concluded that acceptable estimates of Farm_age could be made using the remote sensing method in cases where property boundaries were known and statistical or visual classification of soy was possible between 1985 and In total, 35 farms from our random survey met these criteria. Methods for Identifying Extreme Values: Upon visual inspection of the data, one survey response was discarded as an outlier. This farmer reported applying fertilizer equivalent to 654 kg P ha -1 y -1, which is 16-fold greater than the median value reported (39.3 kg P ha -1 y -1 ). Histograms for the remaining data (n = 48) are shown in Supplementary Figure 3a. In order to examine the effects of additional extreme values on the results, a series of three statistical analyses were undertaken: one for the mean values reported in main text for Fertilizer_P_input, Soybean_P_harvest, P_residual, and P_output:input; one for the regression between P_output:input and Farm_age; and one for the regression between P_output:input and Farm_size. [1] For mean values reported in main text for Fertilizer_P_input, Soybean_P_harvest, P_residual, and P_output:input: Boxplots were examined in SPSS for the first three of these (Supplementary Figure 3b). SPSS identifies far outliers ( ) as Q1 (3.0 x IQR) or Q3 + (3.0 x IQR), and outliers ( ) as Q1 (1.5 x IQR) or Q3 + (1.5 x IQR). The boxplot and far outlier identification for P_residual was used to examine the effect of excluding extreme values on the mean ± 1 S.D. values of Fertilizer_P_input, 8 NATURE PLANTS

9 DOI: /NPLANTS.2016.X SUPPLEMENTARY INFORMATION Soybean_P_harvest, P_residual, and P_output:input. Eight far outliers (note: 3 are obscured by other far outliers in Supplementary Figure 3b) were identified for P_residual. The results with and without these outliers removed are shown in Supplementary Table 2. The results with extreme values removed (n = 40) are reported in the main text. Using the mean value of P_residual calculated after extreme values were removed ultimately produced a more conservative estimate of the phosphorus tax collected by soils each year per hectare (i.e., less P_residual). Boxplots showing the results for mean values with extreme values removed reported in the main text are shown in Supplementary Figure 3c. [2] For linear regression of P_output:input versus Farm_age: We started with the group of farms remaining following the removal of extreme values described directly above (n = 40). For seven of these 40 farms, the time in soybean production could not be estimated by the remote sensing method described above due to uncertainty in property boundaries or absence of cloud-free satellite imagery and were therefore excluded. P output:input ratios for these seven farms were 0.46, 0.45, 0.46, 0.42, 0.54, 0.36, and This resulted in an initial sample size for this regression of n = 33. Next, remaining outliers having a substantial influence on the regression were identified using a single examination of the Standardized DfBeta statistic in SPSS (SDB1). The cutoff value for SDB1 used to classify outliers was 2/sqrt(n) in absolute value, where n = the number of observations. One outlier was identified and removed based on NATURE PLANTS 9

10 DOI: /NPLANTS.2016.X Standardized DfBeta. The final regression with this outlier removed (final n = 32) corresponds to results presented in the main text. In Supplementary Figure 4a, all data points included in the regression are shown as shaded circles. Data points removed during either the initial boxplot screening for extreme values (n = 2) or the DfBeta procedure (n = 1) are shown as squares. Finally, data points for two additional older farms outside of the random survey that were contacted in July 2015 are shown as triangles. [3] For linear regression of P_output:input versus Farm_size: We again started with the group of farms remaining following the removal of extreme values described in section [1] above (n = 40). Next, remaining outliers having a substantial influence on the regression were identified using a single examination of the Standardized DfBeta statistic in SPSS (SDB1). The cutoff value for SDB1 used to classify outliers was 2/sqrt(n) in absolute value, where n = the number of observations. Three outliers were identified and removed based on Standardized DfBeta. The final regression with these outliers removed (final n = 37) corresponds to results presented in the main text. In Supplementary Figure 4b, all data points included in the regression are shown as shaded circles. Data points removed during either the initial boxplot screening for extreme values (n = 8) or the DfBeta procedure (n = 3) are shown as squares. Note that for both plots displayed in Supplementary Figure 4, data points not included in the regressions showed no patterns that could potentially influence the key findings, which were: (1) no correlation of P_output:input with Farm_size, and (2) no evidence of increased P_output:input with increasing Farm_age. 10 NATURE PLANTS

11 DOI: /NPLANTS.2016.X SUPPLEMENTARY INFORMATION Geoprocessing Methods All geoprocessing was performed in ESRI ArcMap Two methods were used to estimate the % of cropland in cells with P-fixing soils present. Method 1 The first method follows the classification of P-retention capacity by Batjes 12 for dominant soil units in the FAO-UNESCO Digital Soil Map of the World (DSMW). We applied the P-retention classes of Batjes 12 to the revision of the DSMW, version 3.6 (ref. 13) with the exception of humic soil units high in organic matter (Supplementary Table 6). The dominant soil value field of the DSMW polygon was converted to a raster with identical resolution (~1 km 2 ) and alignment to the cropland layer. A binary raster was created that identified the presence (=1) or absence (=0) of soils with high or very high P-retention capacity using the definitions by Batjes 12, with all humic soil units set to 0. Method 2 The second method followed the identification in the Fertility Capability Soil Classification System (FCC) of high P fixation by Fe and Al oxides (>100 mg kg -1 P added to achieve adequate soil test levels) (the i modifier) and high P fixation by allophane in amorphous volcanic soils (> 200 mg kg -1 P added to achieve adequate test levels) (the x modifier) 14. See Sanchez et al. 14 for detailed descriptions of the identifying criteria for each modifier. As in the previous method, we filtered out cells overlying humic soil units from the layer for each modifier (cell size = approximately 1 km 2 ; ref. 15) using the DSMW 13. A binary raster was created to identify the presence (=1) or absence (=0) of soils with the i or x modifier, with all humic soil units in the DSMW set to 0. NATURE PLANTS 11

12 DOI: /NPLANTS.2016.X For both methods, the binary rasters produced were then multiplied by the cropland raster, resulting in rasters of cropland presence (0-100%) for the respective P-fixing soil definitions with all other pixels set to 0. These resulting rasters, along with the cropland raster, were then converted from floating point to integer and next projected using the Cylindrical Equal Area (World) projection with cell size set to 800 m by 800 m and the sampling technique set to nearest. Areas were then estimated using the data from the attribute tables of these projected rasters (see Supplementary Table 6 for full breakdown of results for each method). National- and state-level percent of cropland overlying P-fixing soils in Brazil using both methods were estimated using an algorithm where data from the equal area projected global rasters were extracted by mask using Brazilian state boundary rasters of the identical projection, cell size, and cell alignment (see Supplementary Table 1 for results). Using Method 1, we estimated that the phosphorus-fixing soil types that underlie cropland in Brazil represent three quarters of the phosphorus-fixing soils currently being used for crop production globally (see Supplementary Table 6). For more information on the source data and limitations of the DSMW, as well as the Harmonized World Soil Database (HWSD) used by Ahamed et al. 15 to map FCC modifiers, readers can refer to refs. 16 and 17 listed below. For 2050 scenarios Spatial data sets from Bouwman et al. 18 were obtained containing cropland layers for 2050 projections associated with three Millennium Ecosystem Assessment (MEA) scenarios 19,20 : Global Orchestration (GO), Order from Strength (OS), and Technogarden (TG). Data resolution 12 NATURE PLANTS

13 DOI: /NPLANTS.2016.X SUPPLEMENTARY INFORMATION is 0.5 by 0.5 degrees. In total, six data layers were utilized for each 2050 scenario: 5 cropland layers showing 0-100% cropland for each cell (uc50 upland crops, wr50 wetland rice, ce50 crops within pastoral systems, ci50 dominant crops and crops in mixed systems, leg50 legumes = pulses and soybeans) and 1 layer (garealand) containing the land area of each cell ( km 2 ). Overlap exists between some of the cropland layers. The Cell Statistics function (overlay statistic = maximum) was used to create a layer containing the maximum value (0-100% cropland) for each cell from the 5 cropland layers (resulting layer = max_of_5_crop_layers). Raster calculator was then used to create a new layer where each cell contained the maximum area of cropland ( km 2 ): max_of_5_crop_layers_area (km 2 ) = garealand (km 2 ) * [max_of_5_crop_layers (%) / 100] This resulting layer (floating point) was then converted to integer (result = Int_ max_of_5_crop_layers_area). Next, the 3 binary rasters developed in Methods 1 and 2 as described above were loaded. These 3 rasters identify the presence (=1) of absence (=0) of: (i) soils with high or very high P-retention capacity using the definitions by Batjes 12, with all humic soil units in the DSMW set to 0; (ii) soils with the i modifier of the FCC 14, with all humic soil units in the DSMW set to 0; and (iii) soils with the x modifier of the FCC 14, with all humic soil units in the DSMW set to 0. The resolution of these rasters is approximately 1 km 2 at the equator. These 3 rasters were then resampled to produce rasters with the same resolution as Int_max_of_5_crop_layers_area (0.5 by 0.5 degrees). The Resample tool (resampling technique = nearest; snap raster = Int_max_of_5_crop_layers_area) was used (resulting rasters referred to collectively here as P_fixing_soil_binary_resampled). Then, these resampled binary rasters were multiplied by the integer raster containing the cropland area of each cell: NATURE PLANTS 13

14 DOI: /NPLANTS.2016.X Final_cropland_on_P_fixing_soil (km 2 ) = P_fixing_soil_binary_resampled * Int_ max_of_5_crop_layers_area (km 2 ) This converted cells to 0 if no P-fixing soils were present for each respective P-fixing soil data layer. Finally, the attribute tables from the 3 final rasters, along with Int_ max_of_5_crop_layers_area, were used to estimate respective areas. Total cropland areas generated for the three MEA scenarios were inspected and matched those reported previously 18. See Supplementary Figs. 5 and 6 for results. References 1. Rodrigues, M. et al. Legacy phosphorus and no tillage agriculture in tropical oxisols of the Brazilian savanna. Sci. Tot. Environ. 542, (2016). 2. Riskin, S. H. et al. The fate of phosphorus fertilizer in Amazon soya bean fields. Philos. T. Roy. Soc. B 368, (2013). 3. Nziguheba, G., Merckx, R., & Palm, C. A. Soil phosphorus dynamics and maize response to different rates of phosphorus fertilizer applied to an Acrisol in western Kenya. Plant Soil 243, 1-10 (2002). 4. Dobermann, A., George, T., & Thevs, N. Phosphorus fertilizer effects on soil phosphorus pools in acid upland soils. Soil Sci. Soc. Am. J. 66, (2002). 5. McCollum, R. E. Buildup and decline in soil phosphorus: 30-year trends on a Typic Umprabuult. Agron. J. 83, (1991). 6. Guo, F., et al. Changes in phosphorus fractions in soils under intensive plant growth. Soil Sci. Soc. Am. J. 64, (2000). 7. Maia, S. M. F., et al. Changes in soil organic carbon storage under different agricultural management systems in the Southwest Amazon Region of Brazil. Soil Till. Res. 106, (2010). 8. Iyamuremye, F. & Dick. R. P. Organic amendments and phosphorus sorption by soils. Adv. Agron. 56, (1996). 9. Ogle, S. M., Breidt, F. J., & Paustian, K. Agricultural management impacts on soil organic carbon storage under moist and dry climatic conditions of temperate and tropical regions. Biogeochemistry 72, (2005). 10. United States Department of Agriculture. Crop nutrient tool. Natural Resources Conservation Service. (1 April 2015). 11. Spera, S.A., et al. Recent cropping frequency, expansion, and abandonment in Mato Grosso, Brazil had selective land characteristics. Environ. Res. Lett. 9, (2014). 12. Batjes, N. H. Global distribution of soil phosphorus retention potential. Report 2011/06 (ISRIC - World Soil Information, 2011). 14 NATURE PLANTS

15 DOI: /NPLANTS.2016.X SUPPLEMENTARY INFORMATION 13. FAO-UNESCO. Digital soil map of the world version 3.6. (2012). 14. Sanchez, P. A., Palm, C. A., & Buol, S. W. Fertility capability soil classification: a tool to help assess soil quality in the tropics. Geoderma 114, (2003). 15. Ahamed, S., Palm, C., & Sanchez, P. Updating Soil Functional Capacity Classification System. HarvestChoice. International Food Policy Research Institute and University of Minnesota. (2010). 16. FAO/UNESCO. Soil map of the world. Volume I. United Nations Educational, Scientific and Cultural Organization (1974). 17. FAO/IIASA/ISRIC/ISS-CAS/JRC. Harmonized world soil database. Version 1.1. FAO, Rome, Italy and IIASA, Laxenburg, Austria (2009). 18. Bouwman, A. F., Beusen, A. H. W., & Billen, G. Human alteration of the global nitrogen and phosphorus soil balances for the period Global Biogeochem. Cy. 23, GB0A04 (2009). 19. Alcamo, J., Van Vuuren, D., & Cramer, W. in Ecosystems and Human Well-being: Scenarios (ed Carpenter, S. R.) (Island Press, 2006). 20. Van Vuuren, D. P., Bouwman, A. F., & Beusen, A. H. W. Phosphorus demand for the period: a scenario analysis of resource depletion. Global Environ. Chang. 20, (2010). NATURE PLANTS 15

16 DOI: /NPLANTS.2016.X Supplementary Figure 1 Phosphorus flows in Brazil ( ). Fertilizer P input to Brazilian cropland and silviculture soils has exceeded harvested P output since 1970, with approximately 50% of inputs being recovered in recent years (a). Soybeans have accounted for an increasingly large portion of the flow of harvested P from soils (b). 16 NATURE PLANTS

17 DOI: /NPLANTS.2016.X SUPPLEMENTARY INFORMATION Supplementary Figure 2 Linear regressions of positive P balance and measures capturing soil and crop production properties for the primary Brazilian agricultural states (n = 11). All data plotted are means. See Methods and Supplementary Information text above for descriptions of Method 1 vs. Method 2 for identifying P-fixing soils. Primary agricultural states were those with 1 million ha in production (evidence of large production extent) and areal fertilizer P input 10 kg P ha -1 yr -1 (evidence of intensive production) based on averages (Supplementary Table 1). NATURE PLANTS 17

18 DOI: /NPLANTS.2016.X Supplementary Figure 3 P balance results from survey of Mato Grosso soybean farmers. (a) Histograms of all survey data collected (n = 48) for fertilizer P input, soybean P harvest output, and the residual P retained by the soil post-harvest. (b) Boxplots for P balance results for all data (n = 48) with outliers and far outliers shown as circles and triangles, respectively. (c) Boxplots for P balance results following filtering of outliers (n = 40) that are presented in the main text. See Supplementary Information text above for details and Supplementary Table 2 for full results. 18 NATURE PLANTS

19 DOI: /NPLANTS.2016.X SUPPLEMENTARY INFORMATION Supplementary Figure 4 The efficiency of P recovery on Mato Grosso soybean farms does not increase with farm age and is independent of farm size. The ratio of soybean P harvest output to fertilizer P input (P output:input) is shown as a function of farm age (a), and as a function of farm size (b). Linear regressions shown in the plots correspond to results presented in the main text and only include data points displayed as shaded circles. Squares indicate data points identified as outliers, and triangles indicate data from farms not part of the random sample. See the Supplementary Information text above for methods. NATURE PLANTS 19

20 DOI: /NPLANTS.2016.X Supplementary Figure 5 Total global cropland areas (a), global cropland areas on P- fixing soils (b,c), and global P taxes imposed by soils for 2005 and 2050 scenarios (d-g). Total cropland and agriculture/p fertilizer dynamics for 2050 MEA scenarios were previously reported 18,20. We do not make specific assumptions about the tax rates likely to be paid, only those potentially imposed, using two estimates (10 and 20 kg P ha -1 yr -1 ) representing a range required for high yields on P-fixing soils. In reality, trade-offs exist. For example, not paying the P tax to establish high yields could lead to agricultural extensification. 20 NATURE PLANTS

21 DOI: /NPLANTS.2016.X SUPPLEMENTARY INFORMATION Supplementary Figure 6 Maps of cropland with (purple) and without (green) P-fixing soils for three scenarios of cropland extent based on the Millennium Ecosystem Assessment using two methods for identifying P-fixing soils. Resolution is 0.5 by 0.5 degree. Darker shade represents a greater area of cropland in a given cell (scale = 0 to 3077 km 2 ). For P-fixing soils, Methods 1 and 2 are described in the Methods text. See Supplementary Fig. 5 for aggregated results. NATURE PLANTS 21

22 DOI: /NPLANTS.2016.X Supplementary Figure 7 Comparison of results from the remote sensing method used to estimate the number of years that a property has been producing soy with results from a July 2015 farmer survey. Comparisons were made at the farm-level (a) and field-level (b). Solid circles denote data from 11 farms located in grids sampled in Triangles denote data points from two additional farms surveyed in July 2015 that were not part of the 2014 random sample. Dashed lines indicate slope = 1. Methods and regression results are presented in the Supplementary Information text above. 22 NATURE PLANTS

23 DOI: /NPLANTS.2016.X SUPPLEMENTARY INFORMATION Supplementary Figure 8 Comparison of the two methods used to estimate the % of cropland in cells with P-fixing soils for all Brazilian states (n = 27). See Methods text for further details. Dashed line indicates slope = 1. NATURE PLANTS 23

24 DOI: /NPLANTS.2016.X State Fertilizer P input (Mg P yr -1 ) Total production area (cropland + silviculture) (ha) Areal fertilizer P input (kg P ha -1 yr -1 ) Total harvested P (Mg P yr -1 ) Total harvested P / Fertilizer P input % total P harvest in soybeans Areal P balance (kg P ha -1 yr -1 ) % cropland in cells with P- fixing soils using Method 1 % cropland in cells with P- fixing soils using Method 2 Acre , Alagoas 5, , , Amapá , Amazonas , Bahia* 77,223 5,419, , Ceará 1,116 1,900, , Distrito Federal 2, , , Espírito Santo 7, , , Goiás* 133,572 4,324, , Maranhão* 23,002 1,777, , Mato Grosso* 249,770 8,776, , Mato Grosso do Sul* 69,483 3,397, , Minas Gerais* 141,263 6,146, , Pará 7,020 1,303, , Paraíba 1, , , Paraná* 199,872 10,454, , Pernambuco 5,458 1,168, , Piauí* 11,606 1,212, , Rio de Janeiro 1, , , Rio Grande do Norte 1, , , Rio Grande do Sul* 164,229 8,457, , Rondônia 4, , , Roraima 1,138 52, Santa Catarina* 33,588 2,381, , São Paulo* 136,606 8,182, , Sergipe 2, , , Tocantins 12, , , bold* denotes primary agricultural state with 1 million ha in production (i.e., evidence of large production extent) and areal fertilizer P input 10 kg P ha -1 yr -1 (i.e., evidence of intensive production practices). Supplementary Table 1 Mean values ( ) of P flows and production areas, along with the proportions of cropland in cells with P-fixing soils, for Brazilian states. See Methods and Supplementary Information text above for further details. 24 NATURE PLANTS

25 DOI: /NPLANTS.2016.X SUPPLEMENTARY INFORMATION Without outliers removed n Median Min Max Mean Stdev Fertilizer P input (kg P ha -1 yr -1 ) Soybean P harvest (kg P ha -1 yr -1 ) P residual (kg P ha -1 yr -1 ) P output:input With outliers removed (reported in main text) n Median Min Max Mean Stdev Fertilizer P input (kg P ha -1 yr -1 ) Soybean P harvest (kg P ha -1 yr -1 ) P residual (kg P ha -1 yr -1 ) P output:input Supplementary Table 2 Soybean production P balance results from survey of Mato Grosso farmers. Results are shown without and with outliers removed. The latter are reported in the main text. See Supplementary Fig. 3 and the Supplementary Information text above for more details. NATURE PLANTS 25

26 DOI: /NPLANTS.2016.X Additional Supplementary Files Supplementary Table 3. P flows in Brazil at the national scale. (.xlsx, 66 KB) Supplementary Table 4. Crop moisture and P content data used to estimate P harvest. (.xlsx, 15 KB) Supplementary Table 5. Results from state-level P flow analysis. (.xlsx, 55 KB) Supplementary Table 6. Global cropland overlying P-fixing soils in (.xlsx, 13 KB) Supplementary Table 7. Data from farmer survey in Mato Grosso. (.xlsx, 18 KB) 26 NATURE PLANTS