At the global level and focusing specifically on the potential effect size of SOC on yield, we found that the largest gains in yield occur between SOC concentrations of 0.1 % and 2.0 %. For instance, yields are 1.2 times higher at 1.0 % SOC than 0.5 % SOC (Fig. 1). Gains in yield leveled off at a concentration of approximately 2 % SOC (Fig. 1). Two percent SOC has previously been suggested as a critical threshold, with values below this concentration threatening the structure and, ultimately, the ability of a soil to function (Kemper and Koch, 1966). Importantly, the asymptotic relationship between SOC and yield lends support to the idea that building SOC will increase yields – at least to a certain extent – as opposed to simply being an outcome of higher yields. That is, if yield was an explanatory variable for SOC, we would expect greater yields to keep driving greater levels of SOC (i.e., the relationship would appear more linear) since we know that soils can accumulate concentrations much greater than 2 % (Castellano et al., 2015). However, our data do not display a linear pattern, suggesting that higher yields are not driving higher levels of SOC.

It has been suggested that there is no evidence for 2 % SOC being a critical threshold for productivity, as long as there is sufficient mineral fertilizer to support crop production (Edmeades, 2003; Loveland and Webb, 2003; Oelofse et al., 2015). Such conclusions deem the amount of SOM as substitutable by mineral fertilizers (at least for crop growth), but are inconsistent with the motivation for sustainable intensification to minimize environmental harm caused by mineral fertilizers in relation to emissions of greenhouse gases and eutrophication of waters (Vitousek et al., 2009). The same logic about substitutability also does not account for the other co-benefits associated with building SOM in agricultural lands, such as reductions in nutrient runoff, drought resistance, and yield stability (Robertson et al., 2014). Field- and regional-scale studies have shown a similar pattern as that observed from our global analysis: there exists a positive relationship between SOC and yield that starts to level off at ∼2 % SOC (Kravchenko and Bullock, 2000; Pan et al., 2009; Zvomuya et al., 2008). Our analysis suggests that this relationship holds on average at the global scale and when N fertilization is controlled for.

Ninety-one percent of the published studies used for our analysis were carried out in fields with less than 2 % SOC, with a mean of 1.1 %. To see whether these observations in SOC distribution reflected global patterns, we used globally gridded data on crop yield and SOC (to a depth of 15 cm) (Hengl et al., 2014; Monfreda et al., 2008). We found that, by both area and production, two-thirds of maize and wheat cultivation takes place on soils with less than 2 % SOC (Fig. 2). Indeed, a recent analysis estimates that agricultural land uses (including cropland and grazing) have resulted in a loss of 133 Pg of carbon over the past 12 000 years of human land use (Sanderman et al., 2017). There appears to be, therefore, significant opportunity to increase SOC on maize and wheat lands to improve crop yields.

One of the key goals of sustainable intensification is to reduce the environmental impacts of agriculture (Foley et al., 2011; Mueller et al., 2012). Nitrogen fertilization, while a boon to yields, can cause environmental damages, such as eutrophication of waters and increased soil emissions of nitrous oxide, a potent greenhouse gas (Vitousek et al., 2009). Using our regression model, we asked whether there might be target N fertilizer addition rates that suggest the possibility of maximizing yield per unit N applied by building SOC and reducing inorganic N inputs. We wanted to see if yields converge at higher levels of SOC, suggesting that crops are obtaining sufficient nutrients through SOM and excess mineral N is not necessary. Our analysis suggests that SOC is not directly substitutable for mineral fertilizer (Fig. 1); however, at lower rates of N input (≤50 kg N ha-1), we found that increasing SOC from 0.5 % to 1.0 % could potentially maintain current yields and reduce fertilizer inputs by approximately half (50 %). At higher rates of N input (≥200 kg N ha-1), an increase from 0.5 % to 2.0 % SOC could potentially reduce synthetic N inputs by up to 70 % per hectare (Fig. 3). Building SOC from 0.5 % to 2.0 % represents a very large increase, which would require a significant amount of inputs that may not be feasible due to inherent and logistical difficulties related to soil properties, climate, and farmer access to inputs. Furthermore, such an increase could take several years or decades to accomplish. For example, results from long-term field trials show a range of annual increases in SOC for temperate agricultural soils, which were as low as 0.3 % and as high as 18 % (Poulton et al., 2018). At the low end of this range, and starting at 0.5% SOC, it would take ∼47 years to build to 2 % SOC if the annual relative rate of increase was constant, and ∼9 years at the high end of the range. Admittedly, the range emerged as a result of a number of different inputs ranging from farmyard manure to sewage sludge to mineral fertilization, some of which may not be available to farmers given cost and/or access (Poulton et al., 2018). Feasibility aside, however, our results suggest that building SOM in agricultural lands may supply enough plant available nutrients to sustain crop yields while drastically cutting back on N fertilizer inputs.

There was an interaction between SOC and N input, where at higher SOC concentrations N input had a greater impact on yield (Fig. 1, Table 1). This may be because higher SOC improves soil structure and water holding properties, resulting in improved crop growth at a given level of N input (Powlson et al., 2011). Higher levels of SOM could also provide more essential macro- and micronutrients that are limiting in soils with lower SOC concentrations. Additionally, soils receiving more N may have greater SOC because N increases crop yields, which can increase the return of plant residues into the soil and potentially build SOC (Powlson et al., 2011). However, if the relationship was simply an effect of greater inputs building SOC, we should not have seen an interaction between SOC and N on yields (because SOC should then just have been additively related to yield). Whatever the specific explanation, the SOC by N interaction we detect suggests that a combination of both building SOM and using targeted N applications could lead to potential increases in yield (Fig. 3). Practices such as cover cropping represent a strategy that can both increase N supply and build SOM through biological N fixation and the return of high-quality residues (narrow C:N ratios) to the soil (Drinkwater et al., 1998). Building SOM and reducing fertilizer N input would require a balance where SOM N mineralization accounts for any limitations in N supply that arise from reducing mineral fertilizer applications. The balance required will depend on the amount and C:N ratios of inputs used in specific agricultural systems and could prove challenging to achieve in some smallholder systems where low SOC concentrations might be compounded by a lack of access to and insufficient quality of organic inputs (Giller et al., 2009; Palm et al., 2001). As such, the combination of both SOM improvement and targeted fertilizer input will likely be especially important for degraded soils, which require a suite of organic and inorganic nutrients to help build SOM and improve crop yields (Palm et al., 1997).

Gains in yield from fertilizer input leveled off at about 200 kg N ha-1 yr-1 (Fig. 3), meaning that optimum yields appear achievable, at least on average, with this fertilizer input level and an SOC target concentration of 2 %. Using this target N input rate, we explored potential fertilizer reductions on agricultural lands using more than 200 kg N ha-1 yr-1. We found that for lands receiving more than 200 kg N ha-1 yr-1, current yields could be maintained while decreasing global N fertilizer inputs by 7 % for maize and 5 % for wheat. It is estimated that 25 % to 30 % of fertilizer N is exported to streams and rivers, resulting in eutrophication (Raymond et al., 2012). Targeted reductions in the application of fertilizer N on the order of magnitude our analysis suggests could then prevent the annual export of as much as 3.73 million tonnes of N into inland waters, which amounts to 10 % of mineral fertilizer applied to maize and wheat lands (see Methods for an explanation of how this percentage was obtained).

With a majority of cultivated lands containing less than 2 % SOC and a growing imperative to build, restore, and protect SOC in agricultural soils (NSTC, 2016; FAO, 2008; NRCS, 2012), we used global gridded datasets coupled with our regression model (Table 1) to examine the potential gains in yield and production if opportunities to increase SOC are realized (Table 2). We then calculated how these gains in production would impact global yield gaps of maize and wheat, the difference between observed and attainable yields (Mueller et al., 2012). Although our model identified 2 % as a global target for SOC, we created regionally specific SOC targets given the fact that achieving 2 % SOC in some soils (e.g., those of drylands) may be unachievable due to inherent constraints of physical soil properties and climate (see Methods). We found that increasing SOC concentrations to the defined targets has the potential capacity to increase average yields on a per hectare basis by 10±11 % (mean ± SD) for maize and 23±37 % for wheat. These gains in yield translate to a 5 % and 10 % increase in the global annual tonnes produced of maize and wheat, respectively (Table 2). These increases in production would close 32 % of the global yield gap for maize and 60 % of the gap for wheat (Fig. 4a, b).

These yield gap results represent an exploration of potential best-case impacts of increasing SOC concentrations. We recognize there are inherent and logistical challenges to building SOM in agricultural soils; and when managing for and building SOM, it is important to account for its dynamic nature. For instance, to derive some of the nutrient benefits of SOM, it must be mineralized and used (Janzen, 2006), and so frequent additions of organic inputs may be necessary to sustain SOM levels. Furthermore, soil characteristics such as texture can have a large effect on SOC content because sandier (rather than more clay rich) soils have less surface area to stabilize SOC (Rasmussen et al., 2018) and so hold much less water and nutrients than clay-rich soils (Johnston et al., 2009). Maintaining SOC contents in sandy soils may require more frequent additions of organic amendments because these soils do not have the surface area to retain nutrients, moisture, and to stabilize SOC (Lehmann and Kleber, 2015).

Different regions and climate types also face different imperatives for building SOM. In the midwestern United States, for instance, building SOM may be a good strategy to reduce fertilizer inputs and irrigation needs, whereas in sub-Saharan Africa, building SOM may be critical for drought protection and nutrient provision. Notably, high SOM values are not common in dryland environments (for our dataset, mean SOC = 0.9 % for dryland climates versus 1.4 % SOC for mesic soils), and building and maintaining SOM in arid zones is typically hindered by the lack of organic matter to return to soils (Rasmussen et al., 1980). On a positive note, however, our analysis suggests that increases in SOC in drylands, for example, from 0.5 % to 0.8 %, could potentially increase yields by 10 %, likely due to impacts on water retention as well as improved nutrient supply.

The goal of our analysis was to establish a global, average relationship between SOC and yield. Whereas we did use lower SOC targets (ranging from 1.0 % to 1.5 %) for the arid agroecological zones (AEZs) in our analysis, the majority of data used for our analysis are from the more temperate and tropical humid zones (Fig. S2 in the Supplement) and a large proportion of our data comes from China (Fig. 5). We recognize that the distribution of our data could potentially bias our results. As such, we explored the SOM–yield relationship in the absence of data from China and also for Chinese observations only. While the effect size of SOC changes depending on the subset of data analyzed (Table S2 in the Supplement), the qualitative patterns of this relationship remain the same. That is, SOC leads to gains in yield that are most pronounced at lower SOC concentrations and decline in their magnitude as ∼2 % SOC is reached (Fig. S3). Notably, when exploring the subset of data from China, the effect size of SOC was higher than that from the entire dataset (Table S2). However, China only had 10 observations above 2 % SOC, and so the modeled relationship for China captures the part of the SOM–yield relationship where an increase in SOC leads to the largest gains in yield (i.e., where the modeled slope is the steepest). Our analysis then highlights both the need for studies to come evenly from systems where maize and wheat are grown and also the importance of analyzing regional datasets that capture the observed range of SOC values in order to quantify a regionally specific relationship between SOC and yield to more directly inform practice.

Moving from the global relationship presented in our paper to bolstering and/or refining SOC targets, our correlative analysis needs to be supplemented with well-replicated experimental studies incorporating different management strategies across multiple soil and climate types to develop SOC–yield relationships that can be applied to the specific set of local farm conditions. Further, these studies should ideally report data related to soil texture and mineralogy, nutrient management, and paired SOC–yield observations with SOC taken to meaningful depths, such as those that represent plant-rooting depth. These experimental studies will help generate information that practitioners can use to inform management by taking into account the potential benefits of SOC, compared against the inherent and logistical challenges to building SOC to target levels.

In the first stage of our approach, we searched the database Web of Science (Thomson Reuters) in January 2016 and again in October 2016 using the following topic search terms: soil organic matter, soil organic carbon, soil carbon, or soil c; and yield, crop yield, productivity, and agricult*. We restricted the initial search to articles published in English between 1980 and December 2015 and excluded conference proceedings; the second search captured articles published in 2016. The initial search resulted in 1384 articles and the second in 169 articles (Fig. S1). For each citation, we reviewed titles and abstracts to select articles that met the following criteria: experimental field studies whose abstract included information on yield and SOC for systems growing wheat and/or maize. This initial screening resulted in 523 records for which we assessed the full text. We assessed these records for eligibility based on inclusion of data on crop yield, SOC, and N fertilizer rates for each observation. For inclusion within our analysis, it was essential that studies reported paired SOC and yield data. Furthermore, we required SOC concentrations (as opposed to stocks). Studies did not meet our criteria for inclusion if they reported SOC stocks with no corresponding data on bulk density to convert into concentrations and also if they reported baseline SOC concentrations as opposed to experimental SOC concentrations that we could pair with yield data. In addition to our literature search, we also contacted authors to see if they were willing to include raw data within our database. This resulted in three datasets (Adiku et al., 2009; Birkhofer et al., 2008; Kautz et al., 2010). Finally, we consulted the recently published database by the Swedish Board of Agriculture that is a key repository of peer-reviewed literature focusing specifically on studies (735 in total) related to the effects of agricultural management on soil organic carbon (Haddaway et al., 2015). We explored this database to find studies from regions that were underrepresented within our literature search (e.g., the Southern Hemisphere). This resulted in a search of 55 studies to see if they met our criteria for inclusion. We scanned each paper to see if they included SOC data paired with matching yield data. From these papers, we extracted data from 12 studies, which resulted in an additional 52 data points. We encountered limitations similar to our initial search: namely, SOC and yield data were not paired, studies included only baseline SOC concentrations, or SOC stocks were reported without any corresponding bulk density data to convert into concentrations. Overall, our dataset included 840 individual observations from 90 articles covering sites across the globe (Adiku et al., 2009; Agegnehu et al., 2016; Albizua et al., 2015; Alijani et al., 2012; Araya et al., 2012; Atreya et al., 2006; Bai et al., 2009; Bedada et al., 2014; Bhardwaj et al., 2011; Bhattacharyya et al., 2015; Birkhofer et al., 2008; Boddey et al., 2010; Boulal et al., 2012; Bremer et al., 1994; Calegari et al., 2008; Campbell et al., 2007; Castellanos-Navarrete et al., 2012; Celik et al., 2010; Chen et al., 2015; Chirinda et al., 2010; Cid et al., 2014; Costa et al., 2010; D'Hose et al., 2014; Datta et al., 2010; DeMaria et al., 1999; Diacono et al., 2012; Grandy et al., 2006; Guo et al., 2012, 2009; He et al., 2011; Hossain et al., 2016; Hu et al., 2015, 2014; Kaihura et al., 1999; Karbozova Saljnikov et al., 2004; Kautz et al., 2010; Kazemeini et al., 2014; Kucharik et al., 2001; Larsen et al., 2014; Lebbink et al., 1994; Leogrande et al., 2016; Li et al., 2015; E. K. Liu et al., 2014; X. E. Liu et al., 2014; X. Y. Liu et al., 2014; Liu et al., 2016; López-Garrido et al., 2014; Lu et al., 2016; Ma et al., 2012, 2016; Madejón et al., 2001; Mandal et al., 2013; Masto et al., 2007; Mikanová et al., 2012; Mishra et al., 2015; Mupangwa et al., 2013; N'Dayegamiye, 2006; Niu et al., 2011; Njoku and Mbah, 2012; Paul et al., 2013; Qin et al., 2015; Quiroga et al., 2009; Sadeghi and Bahrani, 2009; Saikia et al., 2015; Scalise et al., 2015; Seremesic et al., 2011; Singh and Dwivedi, 2006; Singh et al., 2016; Sisti et al., 2004; Soldevilla-Martinez et al., 2013; Spargo et al., 2011; Šimon et al., 2015; Tejada et al., 2016; Tiecher et al., 2012; van Groenigen et al., 2011; Vieira et al., 2007, 2009; Wang et al., 2015; Q. J. Wang et al., 2014; Z. G. Wang et al., 2014; Wortman et al., 2012; Wu et al., 2015; Yang et al., 2013; J. Yang et al., 2015; Z. C. Yang et al., 2015; Yeboah et al., 2016; Zhang et al., 2015, 2009, 2016; Zhao et al., 2016). Where necessary, we extracted data from manuscript figures using GraphClick software (version 3.0.3, http://www.arizona-software.ch/graphclick/, last access: January, 2018).

Studies that presented individual data points recorded over multiple years were included as well as studies that averaged both yield and SOC data over multiple years. To avoid overrepresentation of studies that included data points recorded for both yield and SOC over multiple years (>10 years), we took observations from the beginning, middle, and last year of the study.

For each extracted observation, we compiled the following information: latitude, longitude, year of data collection, crop type, yield, SOC or SOM, depth of SOC or SOM measurement, N fertilization rate, P fertilization rate, soil pH, texture, and whether or not crops were irrigated. We used SOC (as opposed to SOM) for our analysis given that SOC is a common proxy for SOM. Carbon, as an element that is easily identified and measured within soil, is thought to comprise ∼50 %–60 % of SOM and is commonly reported in the literature (Pribyl, 2010). When SOM was reported, we converted it to SOC by dividing the value by 1.724 (Cambardella et al., 2001). Different studies reported SOC concentrations to different depths, which ranged from 0–5 to 0–30 cm, with the majority of studies reporting SOC to 0–20 cm. When studies reported SOC to multiple depths, we averaged SOC values across depths to 30 cm. If no information on irrigation was provided, we scored the observation as rain fed. Soil texture and pH were not reported for every study; 79 % of included studies reported pH, and so we used the study's latitude and longitude to extract these data using ISRIC SoilGrids (Hengl et al., 2014) to fill in the missing pH values. Texture was reported for about half (49 %) of included studies, and so we used coordinates to pull these data from SoilGrids as well (Hengl et al., 2014). We also used latitude and longitude to obtain an aridity index through the CGIAR-CSI database (Zomer et al., 2008). We chose to use aridity as our primary climatic variable since it is expressed as a function of precipitation, temperature, and potential evapotranspiration (Trabucco, 2009).

We used a linear mixed model (LMM) to analyze the observations we extracted from the literature. Our model included SOC, N fertilizer rate, crop type (maize or wheat, coded as a binary variable), irrigation (coded as a binary variable), aridity index, latitude, pH, and texture (% clay) as fixed effects. The differences in soil carbon observed in our dataset are from experimental plots capturing long-term differences in SOC within a given site. Specifically, our data capture differences within SOC largely driven by management interventions related to inputs (e.g., compost, fertilizer, manure, crop residues) and tillage (e.g., no till versus till). Site-specific differences in management as well as spatial and temporal correlation among the studies were accounted for by nesting year within study as random effects (Bolker et al., 2009). The LMMs were fit with a Gaussian error distribution in the “lme4” package for the R statistical program (version 3.3.1), using the “lmer” function. The first stage of our data analysis was to test the data distributions. We removed data points with N fertilization rates >600 kg N ha-1 (four data points) and yields >18 t ha-1 (two data points) since these represented outliers for our dataset (being beyond 3 times the interquartile range of the meta-dataset) and are not representative of on-farm management practices or outcomes. Our final model was based on 834 observations across 90 studies. We added quadratic terms for both SOC and N input rate since these variables exhibited a nonlinear relationship with yield. The square root of the variance inflation factors (vif) was <2 for all factors when included as main effects, indicating that collinearity was low among all variables. As would be expected, there was a correlation between SOC and its quadratic term and between N input rate and its quadratic term. We reran our regression after removing four seemingly influential data points (those that had high SOC concentrations with low yields; see Fig. 1) and model coefficients remained essentially the same. We calculated the r2 values for our model following Nakagawa and Schielzeth (Nakagawa and Schielzeth, 2013) to retain the random effects structure. The r2 of our model was 83 % for the full model, with the fixed effects explaining 42 % of observed variance within our dataset.

We based the choice of factors for inclusion in our model on the approach of Hobbs and Hilborn (2006), by only investigating factors where biological mechanism as to their influence on yield is firmly established and where we were interested in their effect sizes relative to one another. Also following Hobbs and Hilborn (2006), we did not carry out model selection. Operationally, there is substantial subjectivity and lack of agreement in model selection approaches, with different decisions leading to markedly different conclusions as to the influence of different factors. Instead, coefficients are generally most robust when all terms are retained in a model, assuming that the inclusion of each is biologically justified. We decided to include an SOC by N interaction to explore potential reductions in N fertilizer with increased SOC concentrations. This was an effort to see if there is a level of SOC that can compensate for N input. We acknowledge that there are a number of interactions we could have included within our statistical model, and we did run our regression model with additional interactions to include SOC by irrigation, SOC by clay, and SOC by aridity. Including these interactions, however, did not offer any additional explanatory power and our main results between SOC, N inputs, and yield were essentially unchanged with these additional interactions (Table S3). As such, we chose to present our analysis including only the SOC × N interaction.

To examine the effect sizes of the factors on yield, we took two approaches. First, we compared the size of the standardized coefficients, where standardizing involved subtracting the mean of the factor from each observed value and dividing by 2 standard deviations (Gelman, 2008). Dividing by 2 standard deviations is useful when binary predictors are included within regression models (in our case, crop type and irrigation are coded as binary predictors). This way, continuous and binary variables all have a mean of 0 and a standard deviation of 0.5 (Gelman, 2008). This accounts for the fact that the factors were measured on different unit scales (Table 1). Second, we examined the influence of changing SOC concentration or N fertilization rates on yield. To do this, we used the regression relationship derived from our statistical model, held all other factors at a constant value (e.g., the mean of all observations for that factor), and systematically varied SOC or N fertilization across the range of values we extracted from the literature. For SOC, this meant varying SOC values from 0.1 % to 3.5 % to estimate changing yield of rain-fed maize or wheat as SOC concentrations were increased (Fig. 1). For N fertilization, we varied N input rates from 0 to 300 kg N ha-1 for rain-fed maize or wheat at different SOC concentrations (Fig. 3). When these factor–yield relationships were plotted, we identified threshold values where yield became minimally responsive to SOC or N fertilization as the point where the slope of the relationship became <0.25 (for SOC) and <0.002 (for N fertilization).

We used the regression relationship developed in the first stage of our approach to predict how building SOC concentrations would potentially affect global crop yield averages. To obtain values for each of the factors in our regression model at a global scale, we used globally gridded data products. Global SOC, pH, and texture data were taken from ISRIC SoilGrids (Hengl et al., 2014) at a 10 km grid cell resolution to match the spatial grain for maize and wheat yields and N fertilization data, which we obtained from the EarthStat product (Monfreda et al., 2008; Mueller et al., 2012). SoilGrids has multiple layers for SOC concentrations, so we used the 0–15 cm layer because the average depth to which SOC was reported for our dataset was 0–20 cm. The aridity index was obtained from the CGIAR-CSI database (Zomer et al., 2008). We used the resulting global dataset to explore the potential impact of increasing SOC (up to regionally identified threshold levels ranging from 1 % to 2 %) on yield for lands across the globe where maize and wheat are produced.

To establish regionally appropriate SOC targets, we classified maize- and wheat-producing areas by their agroecological zones. The Food and Agricultural Organization has 18 zones defined on the basis of combinations of soil, landform, and climatic characteristics (Ramankutty et al., 2007). For each AEZ, we examined the distribution of SOC in areas classified as naturally vegetated (e.g., not in urban or agricultural land uses). We did this by stacking two GIS raster layers of SOC (SoilGrids) and land use (Friedl et al., 2010), excluding agricultural and urban land use classifications. We then extracted SOC data for each AEZ using a shape file outlining the geographical extent of each AEZ (Ramankutty et al., 2007). Examining the distribution of SOC across each AEZ, we identified targets based on the mean SOC value within each zone. All but four zones had means greater than 2 % SOC, so we set target values for those zones at 2 %. Mean SOC concentrations were lower for the more arid zones and so we set those targets to 1 % for AEZ 1 and 1.5 % for AEZ zones 2, 3, and 7. These targets were in line with recent quantitative assessments based on similar climatic classifications. For instance, recent analysis of global SOC concentrations across globally defined ecoregions shows mean values of SOC at or greater than 2 % for all regions except land classified as desert and xeric shrubland (Stockmann et al., 2015).

Prior to our global extrapolations, we performed a suite of data checks. We wanted to ensure that global yields predicted using our regression model were comparable to those from EarthStat. These checks helped validate the strength of our extrapolations. Firstly, we explored the range of variation in variables from experimental data used to generate our model as well as the range of global variation in variables we project across. The range of our regressors encompasses the range of global variation, except for aridity, in which case 4.6 % percent of our projections fall in grids that have axis conditions outside of our range of measurements. These values fall in extremely arid systems, with aridity values of less than 0.1. In these extremely arid zones, we do make a point to use lower target SOC values, recognizing that achieving 2 % SOC in these very arid areas is not very likely. Secondly, using our regression model to predict global yields for both maize and wheat (separately), we first removed all values from the analysis that had predicted yields of less than 0 because negative yields are not possible. This amounted to 0.004 % of the total predictions for maize and 0.15 % for wheat. For clarification, we refer to predictions from our regression model as predicted or model predicted. We then calculated the proportional difference between model-predicted and globally gridded yield data from EarthStat. We dropped all cells for which the proportional difference between predicted and gridded data was >3 times. This threshold represents the mean ± half of the standard deviation for the distribution of the proportional difference between predicted and EarthStat yield data. This amounted to 14 % of cells for maize and 7 % for wheat. The mean proportional difference between predicted and gridded data was 0.85±0.91 for maize (Fig. S4b) and 0.45±0.87 for wheat (Fig. S5b). The correlation between predicted and gridded data was r=0.73 for maize (Fig. S4c) and r=0.38 for wheat (Fig. S5c). We also visualized an overlap in the distribution of model-predicted and gridded data. Model-predicted maize yield had a global mean of 4.66±1.84 t ha-1 and EarthStat had a global mean of 3.34±2.62 t ha-1 (Fig. S4a). Model-predicted wheat yield had a global mean of 3.18±1.66 t ha-1 and EarthStat had a global mean of 2.43±1.58 t ha-1 (Fig. S5a).

We also compared the distribution of EarthStat yield data with observed yield data from the studies included in our analysis. We found that the correlation (r values) between the gridded and collected data was 0.56 for maize and 0.39 for wheat. Average observed maize yield was 5.61±3.32 t ha-1 and wheat yield was 4.02±2.11 t ha-1 (mean ± SD). EarthStat maize yield, again, was 3.34±2.62 t ha-1 and wheat yield was 2.43±1.58 t ha-1. These differences between predicted and EarthStat yield averages are likely due to the fact that EarthStat data are based on regional census data, incorporating much more variability in terms of management practices and skill than experimental field studies.

After the data checks, we then used our model to extrapolate global yield potentials of maize and wheat given increases in SOC. We masked EarthStat production and cultivated area data layers for maize and wheat for cells that had SoilGrids SOC concentrations of >2 %. We compared the subsetted data (i.e., cultivated lands with <2 % SOC) with the original data layers to determine the fraction of global maize and wheat production and cropland that is on soils with less than 2 % SOC. We used this subsetted data along with our regression model to predict yields at current SOC levels. As stated above, we used EarthStat, ISRIC SoilGrids, and CGIAR-CSI data layers to fill in the values for each of the factors in our regression model. This new data layer was used as a baseline with which to compare to potential gains in yield with an increase to SOC target values. This created a second data layer with model-predicted yields given an increase in SOC. We calculated the percentage increase in yield between these two layers (the baseline and the improved-SOC layer) and multiplied this by EarthStat yield and production data to determine potential gains in maize and wheat yields and production (Table 2). We then used EarthStat yield gap data to see how such an increase in SOC would reduce projected yields gaps. Using the new yield data layer (with yields at SOC target values), we calculated the proportion of EarthStat yield gaps that was reduced for both maize and wheat.

Finally, we used data on global N use (EarthStat) to explore potential reductions in fertilizer use for both maize and wheat, separately. We used a value of 200 kg N ha-1 yr-1 as our N input threshold, as this is the value from our regression model at which gains in yields level off. We created a new data layer for those areas that have N input rates greater than 200 kg N ha-1 yr-1. We then calculated the potential N reductions, in tonnes, by multiplying this new data layer by EarthStat cultivated maize and wheat lands, separately. Finally, we divided the potential reduction in N input (in tonnes) by total N input (in tonnes) as provided through the EarthStat data product.