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# Spatial frameworks for robust estimation of yield gaps

## Abstract

Food security interventions and policies need reliable estimates of crop production and the scope to enhance production on existing cropland. Here we assess the performance of two widely used ‘top-down’ gridded frameworks (Global Agro-ecological Zones and Agricultural Model Intercomparison and Improvement Project) versus an alternative ‘bottom-up’ approach (Global Yield Gap Atlas). The Global Yield Gap Atlas estimates extra production potential locally for a number of sites representing major breadbaskets and then upscales the results to larger spatial scales. We find that estimates from top-down frameworks are alarmingly unlikely, with estimated potential production being lower than current farm production at some locations. The consequences of using these coarse estimates to predict food security are illustrated by an example for sub-Saharan Africa, where using different approaches would lead to different prognoses about future cereal self-sufficiency. Our study shows that foresight about food security and associated agriculture research priority setting based on yield potential and yield gaps derived from top-down approaches are subject to a high degree of uncertainty and would benefit from incorporating estimates from bottom-up approaches.

## Main

Meeting food demand on existing cropland, without further encroachment of natural ecosystems such as forests, wetlands and savannahs, is one of the greatest challenges of our time1. Orienting investments on agricultural research and development (AR&D) to meet that challenge requires information about where the largest opportunities to increase crop yields exist within the current cultivated area2,3,4,5. The yield gap, defined as the difference between actual farm yield and the yield potential with good management that minimizes yield losses from biotic and abiotic stresses, is a key biophysical indicator of the available room for crop production increase with current land and water resources6. Global assessments of future food security and land-use change published in high-profile journals have followed a ‘top-down’ approach that relies on crudely calibrated crop models and a gridded spatial framework to organize coarse data on climate, soil, and cropping systems to estimate yield potential and associated yield gaps7,8,9,10 (Fig. 1 and Supplementary Table 1). Recent assessments for specific countries suggest, however, that top-down approaches provide estimates of yield potential and yield gaps that are not useful for effective prioritization of AR&D investments11,12.

An alternative to the use of top-down spatial frameworks is to follow a ‘bottom-up’ approach that estimates yield potential and yield gap for a number of sites explicitly chosen to best represent the spatial distribution of crop production area and then upscales the yield potential estimated at those sites to larger spatial scales13 (Fig. 1 and Supplementary Table 1). While both spatial frameworks (that is, top down and bottom up) can eventually reach complete coverage of the entire cultivated area, they differ in the means to achieve it and the resulting outcomes. Bottom-up approaches favour the use of measured data on weather, soil and cropping systems and the use of crop simulation models calibrated using data from well-managed experiments where yield-limiting and reducing factors were effectively minimized, which, altogether, should lead to more accurate estimates of yield potential and yield gaps11,14 (Extended Data Fig. 1). The spatial granularity of the bottom-up approach, in terms of estimating yield potential for a specific combination of climate, soil and cropping systems, allows results to be validated by local experts. Moreover, results for specific locations can be aggregated to regional, national and continental scales by weighting contributions to larger-scale spatial units based on crop production area represented by soil, climate and cropping systems at each location. By contrast, outcomes produced by top-down approaches are difficult to validate because results are necessarily aggregated to the grid level, without differentiating amongst soil types and cropping systems that may exist within the grid. Weather data are also aggregated at the grid scale and may be interpolated from distant weather stations or remotely sensed data.

Yield potential and yield gaps are routinely used as inputs in studies dealing with global food security, biodiversity, land use and climate change6,15,16,17. However, despite the existence of two very different approaches to estimate these two indicators, there has been no explicit attempt to evaluate the performance of top-down versus bottom-up spatial frameworks for estimating yield potential and yield gaps at a local to global scale. We report here a global comparison of the two methods and discuss implications for informing AR&D investments. Our study includes outcomes from two of the most cited studies that utilize top-down approaches: (1) the Global Agro-ecological Zones (GAEZ) model developed by the International Institute for Applied Systems Analysis and the Food and Agricultural Organization of the United Nations (FAO; http://www.fao.org/nr/gaez/en/; refs. 18,19) and (2) the median of the model ensemble of the Agricultural Model Intercomparison and Improvement Project (AgMIP) (https://agmip.org/; refs. 20,21). Yield potential, yield gaps and extra production potential reported in these studies are compared against those derived from the bottom-up approach followed by the Global Yield Gap Atlas (GYGA; www.yieldgap.org; refs. 11,13,14).

Because effective AR&D requires interventions at different spatial scales, we performed a comparison between top-down and bottom-up approaches at three levels, local, subnational (‘climate zone’) and national or subcontinental, with a respective average size of nearly 9,500, 60,000 and 1,000,000 km2. Climate zones are geographic areas with similar temperature and water regimes21. We focus on cereal crops, which account for 45% of global calorie intake (https://ourworldindata.org/food-supply). We compare top-down and bottom-up estimates for major cereal crop-producing areas in North and South America, Europe, Asia, Africa and Australia (Extended Data Fig. 2). For simplicity, we show examples on four geographic regions and three crops (maize, rice and wheat). The four regions were selected for being important food exporters and/or importers. As examples of regions with favourable climate and fertile soils (that is, favourable production environments), we include maize in the US Corn Belt, which produces 35% of global maize output, and lowland irrigated and rainfed rice in Asia, which accounts for about 90% of global rice production and about 80% of rice consumption during the 2014–2018 period22. As an example of a harsh production environment (less favourable climate and generally infertile soils), we include wheat in Australia, which accounts for 10% of global wheat exports. Maize in sub-Saharan Africa is also included, as this region has rapid population growth rates and domestic cereal demand is projected to increase threefold over the next 30 years23.

## Results

### Yield potential and yield gap comparison

Comparison of yield potential derived from top-down (GAEZ and AgMIP) versus bottom-up (GYGA) approaches reveals large discrepancies across all spatial levels. On average, yield potential estimated by AgMIP is 60% lower compared with GYGA across the four case studies (Fig. 2), which is consistent with the findings for other crop-producing regions (Supplementary Tables 2 and 3). As a result, AgMIP gives much more conservative estimates of extra crop production potential on existing cropland compared with GYGA across all spatial scales. Agreement between GYGA and GAEZ was better at national and subcontinental scales, although there were still large discrepancies between the two approaches, ranging from −50% to +30%. These differences were even larger at smaller spatial scales and for specific regions and crops, with GAEZ estimates differing from GYGA by −95% to 480% at local levels (Supplementary Tables 2 and 3). In some cases, yield potential derived from bottom-up and top-down approaches follows the same trend across locations and climate zones, but there remain several substantial disagreements on the absolute level of yield potential. That was the case for maize in the US Corn Belt, where GYGA estimates a yield potential that is 8% and 63% higher than that estimated by GAEZ and AgMIP, respectively (Fig. 2a,f). Similarly, estimated yield potential for rainfed wheat in Australia is 46% higher in GYGA than in AgMIP (Fig. 2g). Besides poor agreement at the national and continental levels in some cases, other cases show a complete lack of association between the yield potential derived from top-down and bottom-up approaches across locations and climate zones, as it is the case for lowland rainfed rice in Asia and maize in sub-Saharan Africa (Fig. 2b,d,f,h). In both regions, the range of yield potential across climate zones is very narrow as estimated following top-down approaches compared with much larger ranges from GYGA. In other words, some of the locations and climate zones reported by GYGA to have the highest yield potential are identified to be among the ones with lowest yield potential by GAEZ and AgMIP and vice versa.

In addition to evaluating the degree of agreement between top-down and bottom-up approaches, we also assess the quality of yield potential estimation per se by comparing the simulated yield potential against the average farm yield currently achieved in farmers’ fields (actual yields). By definition, the difference between the two, the so-called yield gap (yield potential minus actual yield), cannot be negative. If an estimated yield potential value is considerably lower than average farm yield, then yield potential is clearly underestimated. We find that the top-down approaches give negative yield gaps for a considerable number of cases worldwide (Fig. 3 and Extended Data Fig. 3). At local levels, yield gaps estimated by GAEZ are negative in 13%, 3% and 3% of the 582, 302 and 478 locations evaluated for maize, rice and wheat, respectively. In the case of AgMIP, yield-gap estimates are negative in 39% (maize), 45% (rice) and 25% (wheat) of the cases. In contrast, no negative yield gaps are estimated by GYGA. Because calculation of yield gaps relies on the same source of average actual yield data for both top-down and bottom-up methods (Methods), the substantial number of cases with negative yield gaps as estimated by top-down approaches can be seen as a strong indication of underestimation of yield potential.

### Implications for food self-sufficiency assessments

Although achieving food self-sufficiency is not an essential precondition for food security, it can be highly relevant for developing countries with limited capacity to purchase food imports and infrastructure to store and distribute it efficiently24. A key indicator of food security is the self-sufficiency ratio (SSR), which is the ratio between domestic production and total domestic consumption25. Comparison of SSR for different scenarios of yield-gap closure can help assess the degree of food self-sufficiency that a country or region can achieve by increasing productivity on existing cropland26. However, as we showed previously, such an assessment will be influenced by the choice of top-down or bottom-up approach in calculating yield potential, yield gaps and associated extra production potential. For example, self-sufficiency estimates for major cereal crops (maize, sorghum, millet, rice and wheat) vary widely across SSA countries, assuming a production scenario in which average cereal crop yields reach 80% of the yield potential by year 2050 without changes in cropland area (Fig. 4). GAEZ forecasts that the region could become self-sufficient for cereal grain by 2050 by an ample margin via narrowing current yield gaps, with the potential production exceeding expected demand by 36% (that is, SSR = 1.36). In contrast, GYGA also estimates that the region could be self-sufficient in cereals if yield gaps are closed, but with production levels very close to the expected demand by 2050 (SSR = 1.03). In the case of AgMIP, estimates of crop production potential fall short of sufficiency, indicating that cropland expansion and/or increase in food imports will be needed to meet projected cereal demand by 2050 (SSR = 0.96). Discrepancies among approaches become larger when zooming in on specific countries or regions. For example, while GAEZ predicts that yield-gap closure would result in cereal surplus in seven of the ten countries, outputs from GYGA and AgMIP suggest that most of the countries could not meet cereal demand by 2050. While SSR estimates at the subcontinental scale are similar for GYGA and AgMIP, there are large differences in estimated SSR at the national scale, with AgMIP estimations differing from GYGA between −24% and 39%.

## Discussion

A key question for AR&D is where to invest in terms of crops and regions to maximize the return on investment. While yield gap alone is not sufficient to answer this question, together with other biophysical and socioeconomic factors that influence technology adoption, it is an important parameter to guide public and private investments in agriculture, because it specifies where and how much crop production can be increased. Here we show that the choice of spatial framework to make such assessments (that is, top down or bottom up) has important implications for projecting the return on investment. For example, different approaches lead to contrasting answers about the prognosis of a given country to reach a desired level of food self-sufficiency. Even in those cases in which both approaches give similar yield-gap estimates at the subcontinental level, there are large discrepancies when looking at specific countries or regions within each country. The considerable number of locations with a negative yield gap estimated by top-down approaches raises important questions about the accuracy of these approaches in estimating yield potential and gives caution to their use for effective prioritization of AR&D investments. While we focused on extra production potential and food availability, the uncertainty associated with top-down analysis will also apply to other studies focusing on land use, climate change and biodiversity that follow a similar approach to estimate crop production potential7,8.

Causes of inaccurate estimation of yield gaps following top-down approaches have been investigated elsewhere26,27; here we point out some of them. Top-down approaches are based on secondary (unmeasured) gridded data and coarse global soil maps and cropping systems data (Table 1 and Supplementary Data Table 1), which give a false sense of data quality and availability in spatial grids that are typically 0.5–2.0° (ca. 3,000–50,000 km2 at the Equator). Indeed, previous studies have shown important biases when simulating yield potential using coarse gridded weather data compared with simulations based on measured data27,28,29 or without proper selection of the dominant soil types within an agricultural area30,31. Similarly, the cropping-system context, including cropping intensity (that is, number of crops per year), crop calendar (sowing window and crop cycle duration) and water regime (irrigated or rainfed), is critical for the estimation of yield potential. While GYGA works with local experts to obtain reliable information about the cropping system context, the two top-down approaches rely on an in silico optimization of the cropping system (GAEZ) or coarse global crop calendars (AgMIP), predicting in many cases crop systems that do not match the dominant existing systems or even systems that simply do not exist (Table 1). For example, in the US Corn Belt, the global dataset MIRCA 200032 employed by AgMIP sets a maize-sowing window between April and October, but, in reality, producers typically do not sow beyond June to prevent crop loss due to fall frost33. Likewise, top-down approaches generally use generic crop model coefficients that do not account for the specificity of crop cultivars in terms of responses to temperature and photoperiod21,34,35; these models are also rarely validated for their ability to estimate yield potential based on data collected from well-managed crops where yield-limiting and yield-reducing factors have been effectively controlled. In summary, estimates of yield potential and yield gaps derived from top-down approaches are subject to a high degree of uncertainty considering the errors associated with the underpinning data.

The accuracy of the spatial sampling framework of the GYGA bottom-up approach has been validated for regions where high-quality and spatially detailed data are available. Hochman et al.36 conducted a study on yield gaps of rainfed wheat in Australia following two approaches: (1) the bottom-up approach of GYGA and (2) a data-rich method using high-density data available in the Australian grain zone (both relying on measured weather data). These researchers reported that the two approaches gave similar estimates of yield potential and yield gaps at climate zone and national levels. Similarly, Aramburu Merlos et al.37 and Morell et al.38 show that national average actual yield estimates for Argentina and the United States, calculated using a limited number of selected locations following the GYGA protocols, were remarkably similar to the reported national average yield based on data from hundreds of subnational-level administrative units covering the entire crop production area. Finally, Van Wart et al.39 and van Bussel et al.13 showed that variability in weather and simulated yield potential was relatively low for sites located within the same climate zones, which provides further support for a stratified (instead of random) selection of sites and use of the climate zone framework as a basis for upscaling results from location to region and country. Altogether, these studies provide strong evidence of robust estimates of yield potential and yield gaps following the bottom-up approach of the GYGA.

Given the ‘global public goods’ nature of food self-sufficiency estimates across local to global scales, we see an urgent need for robust estimates of yield gaps for major cropping systems worldwide as input to a national and international dialogue on future global food security under climate change. Such a project can be accomplished with a modest investment on a bottom-up approach that gives priority to use primary measured weather data, finer-scale soil maps and accurate cropping systems data for a given location31. We still see a number of areas for complementarity between top-down and bottom-up approaches. For example, the bottom-up approach requires more granular and detailed data on climate, soils and cropping systems than the top-down approaches evaluated in this study, which makes its application difficult in regions where these data are scarce or simply do not exist. In these regions, it may be necessary to rely on top-down approaches that obtain the required data by interpolation and informed guesses using data from coarser spatial scales. Similarly, top-down modellers may benefit from using bottom-up estimates of yield potential, and underpinning weather and soil databases, to evaluate their model outcomes. We conclude that foresight studies of food security, land use and climate change and associated priority setting on AR&D based on yield potential and yield gaps would benefit from using a bottom-up spatial framework and good-quality data to reduce uncertainties in previously reported estimates of food production potential under current and future climates.

## Methods

### Yield definitions

Yield potential (Yp; megagrams per harvested hectare) is defined as the yield of a cultivar in an environment to which it is adapted, when grown with sufficient water and nutrients in the absence of abiotic and biotic stress40. In irrigated fields, Yp is determined by solar radiation, temperature, atmospheric CO2 concentration and management practices that influence crop cycle duration and light interception, such as sowing date, cultivar maturity and plant density. In rainfed systems where water supply from stored soil water at sowing and in-season precipitation is not enough to meet crop water requirements, water-limited Yp (Yw) is determined by water supply amount and its distribution during the growing season, as well as by soil properties influencing the crop–water balance, such as the rootable soil depth, texture and terrain slope. Actual yield is defined as the average grain yield (megagrams per harvested hectare) obtained by farmers for a given crop with a given water regime. The difference between Yp (or Yw) and farmer actual yield is known as the yield gap11. In the case of irrigated crops, Yp is the proper benchmark to estimate yield gaps, while Yw is the meaningful benchmark for rainfed crops. With good, cost-effective crop management, reaching 70–80% of Yp (or Yw) is a reasonable target for farmers with good access to markets, inputs and extension services, which is usually referred to as ‘attainable yield’41,42. Beyond this yield level, the small return to extra input requirement and labour does not justify the associated financial and environmental costs and level of sophistication in crop and soil management practices.

### Sources of Yp data derived from top-down and bottom-up approaches

We retrieved data generated from two initiatives following a top-down approach: (1) the GAEZ (http://www.fao.org/nr/gaez/en/; refs. 18,19) and (2) the AgMIP (https://agmip.org/data-and-tools-updated/; refs. 20,21). As the bottom-up approach, we used results from the GYGA (www.yieldgap.org; refs. 11,31,43). The main features of these databases are summarized elsewhere (Supplementary Table 1 and Supplementary Section 1). In the process of selecting the specific dataset, we explicitly attempted to reduce biases in the comparisons to the extent this was possible. For example, in all cases, we used simulations that meet the yield definitions provided in the previous section. We also tried to be consistent in terms of the time period for which Yp (or Yw) was simulated; however, this was not always possible, because while GAEZ and AgMIP use weather datasets that cover the time period between 1961 and 1990 and between 1980 and 2010, respectively, GYGA uses more recent weather data (Supplementary Table 1). Similarly, comparisons between databases were limited to those regions for which there were estimates of Yp (or Yw) for each of the top-down and bottom-up approaches. More detailed information about the three approaches can be found in Supplementary Section 1. We acknowledge that, when assessing different approaches, it is conceivable that there would be an inherent bias depending on who performs it and his/her preference. Although the authors of this current study have all contributed to the development of GYGA, we have maintained neutrality when conducting the analysis and made inferences solely based on the results shown here, avoiding any inherent bias. Additionally, methods and data sources are fully documented and publicly accessible for other researchers who may be interested in replicating our comparison.

### Comparison of bottom-up and top-down approaches at different spatial levels

Comparison of the three databases needs to account for the different spatial resolution at which the data are reported (grid in GAEZ and AgMIP versus buffer in GYGA). In the present study, we compared Yp (or Yw) among the three databases at three spatial levels: local (also referred to as buffer), climate zone (CZ) and country (or subcontinent). An example of the three spatial levels evaluated in this study as well as the Yw estimated by each of the three databases for rainfed maize is shown in Extended Data Fig. 4. We note that buffer is the lowest spatial level at which Yp and Yw are reported in GYGA. For a country such as the United States, where maize production is concentrated on flat geographic areas, the average size of buffers and CZs selected by GYGA is 17,000 and 60,000 km2, respectively; the size is smaller for countries with greater terrain and climate heterogeneity, such as Ethiopia, where the average size of buffers and CZs selected for maize by GYGA is a respective 4,000 and 21,000 km2, or for smaller countries, such as in Europe.

The GYGA already provides estimates of Yp (or Yw) and yield gaps at those three spatial levels. Following a bottom-up approach, GYGA estimates the Yp (or Yw) at the buffer level based on the Yp (or Yw) simulated for each crop cycle and soil type (within a given buffer) and their associated harvested area (within that same buffer) using a weighted average. Subsequently, Yp (or Yw) at buffer levels are upscaled to CZ, national or subcontinental levels using a weighted average based on harvested area retrieved from the Spatial Production Allocation Model (SPAM) 201044. Details on the GYGA upscaling method can be found in van Bussel et al.13 In the case of top-down approaches, for comparison purposes, it was necessary to aggregate Yp (or Yw) reported for each individual grid into buffers, CZs and countries in order to make them comparable to those reported by GYGA. To do so, Yp (or Yw) from GAEZ and AgMIP was scaled up to buffer, climate zone and country (or subnational levels) considering the crop-specific area within each pixel, as reported by SPAM 201044. For example, for a given buffer, the average Yp (or Yw) was estimated using a weighted average, in which the value of Yp (or Yw) reported for each of the GAEZ or AgMIP grids located within the GYGA buffer was ‘weighted’ according to the SPAM crop-specific area within that grid. The same approach was used to estimate average Yp (or Yw) at the CZ and country (or subcontinental) levels for GAEZ and AgMIP.

For a given buffer, CZ or country (or subcontinent), the yield gap was calculated as the difference between Yp (or Yw) and the average farmer yield (actual yield, Ya). The Yp and Yw were taken as the appropriate benchmarks to estimate yield gaps for irrigated and rainfed crops, respectively. To avoid biases due to the source of average actual yield in the estimation of yield gap, we used the average actual yield dataset from GYGA, because it provides estimates of average actual yield disaggregated by water regime for the most recent time period. Actual yield data from GYGA were retrieved from official statistics available at subnational administrative units such as municipalities, counties, departments and subdistrict. The exact number of years of data to calculate average yield is determined by GYGA on a case-by-case basis, following the principle of including as many recent years of data as possible to account for weather variability while avoiding the bias due to a technological time trend and long-term climate change31. Using the GYGA database on average actual yield for estimation of yield gaps does not bias the results from our study, as GYGA favours the use of official sources of average yields at the finer available spatial resolution, which is the same source of actual yield data used by other databases such as FAO and SPAM22,44. In this study, we opted not to use actual yield data from GAEZ, because they derived from FAOSTAT statistics of the years 2000 and 2005, and thus, they could lead to an overestimation of the yield gap in those regions where actual yields have increased over the past two decades19. Finally, extra production potential was calculated based on the yield gap estimated by each approach and the SPAM crop-specific harvested area reported for each buffer, CZ and country (or subcontinent). The top-down and bottom-up approaches were compared in a total of 67 countries, which together account for 74%, 67% and 43% of global maize, rice and wheat harvested areas, respectively (Extended Data Fig. 2). Overall, our comparison included a total of 1,362 buffers located within 870 CZs, with 422 buffers (within 249 CZs) for rainfed maize, 160 buffers (116 CZs) for irrigated maize, 93 buffers (66 CZs) for rainfed rice, 209 buffers (114 CZs) for irrigated rice, 400 buffers (274 CZs) for rainfed wheat and 78 buffers (49 CZs) for irrigated wheat. In all cases, Yp (or Yw), yield gaps and extra production potential were expressed at standard commercial moisture content (that is, 15.5% for maize, 14% for rice and 13.5% for wheat).

We assessed the agreement in Yp (or Yw), yield gap, and extra production potential between GYGA and the two databases that follow a top-down approach (GAEZ and AgMIP) separately for each of the spatial levels (buffer, CZ, country or subcontinent) by calculating root-mean-square error (RMSE) and absolute mean error (ME):

$${\mathrm{RMSE}} = \sqrt {\frac{{{\sum} {(Y_{{\mathrm{TD}}} - Y_{{\mathrm{BU}}})^2} }}{n}}$$
(1)
$${\mathrm{ME}} = \frac{{{\sum} {\left( {Y_{{\mathrm{TD}}} - Y_{{\mathrm{BU}}}} \right)} }}{n}$$
(2)

where YTD and YBU are the estimated Yp (or Yw), yield gap, or extra production potential for database i following a top-down approach and for GYGA, respectively, and n is the number of paired YTD versus YBU comparisons at a given spatial scale for a given crop in a given country. Separate comparisons were performed for irrigated and rainfed crops.

### Impact of Yp estimates on food self-sufficiency analysis

We assessed the impact of discrepancies in Yp (or Yw) between top-down and bottom-up approaches on the SSR, which is an important indicator for food security. To do so, we focused on cereal crops in sub-Saharan Africa, and we calculated the SSR for the five main cereal crops in this region (that is, maize, millet, rice, sorghum and wheat) following van Ittersum et al.23. Millet and sorghum were included in the analysis of SSR in sub-Saharan Africa, because together they account for ca. 25% of the total cereal production and ca. 40% of the total cereal harvested area in this region (average over the 2015–2019 period)22. Briefly, we computed current national demand (assumed equal to the 2015 consumption) and the 2015 production of the five cereals to estimate the baseline SSR (that is, in 2015) in ten countries for which Yw (or Yp) data were available in GYGA. Current total cereal demand per country were calculated as the product of current population size derived from United Nations population prospects and cereal demand per capita based on the International Model for Policy Analysis of Agricultural Commodities and Trade (IMPACT)35,45. The annual per-capita demand for the five cereals was expressed in maize yield equivalents by using the crop-specific grain caloric contents, with caloric contents based on FAO food balances46. Current domestic grain production per cereal crop per country (approximately 2015) was calculated as mean actual crop yield (2003–2012) as estimated in GYGA times the 2015 harvested area per crop by FAO22. Total future annual cereal demand per capita (2050), for each of the five cereals and each country, was retrieved from IMPACT modelling results35 using the shared socioeconomic pathway (SSP2, no climate change) from the Intergovernmental Panel on Climate Change fifth assessment47. Total cereal demand per country in 2050 was calculated based on projected 2050 population (medium-fertility variant of United Nations population prospects; https://population.un.org/wpp/) multiplied by the per-capita cereal demand in 2050 from the SSP2 scenario. In our study, we assumed an attainable yield of 80% of Yw for rainfed crops, which is consistent with the original approach followed by van Ittersum et al.23, but, in our study, we also used 80% of Yp for irrigated crops as an estimate of the attainable yield, instead of 85% as in van Ittersum et al.23, to be slightly more conservative. Because the goal was to understand the level of SSR on existing cropland, we assumed no expansion of rainfed or irrigated cropland and no change in net planted area for each of the cereal crops. Our calculations for sub-Saharan Africa may be too pessimistic if genetic progress to increase Yp is achieved. Historically, genetic progress in Yp has contributed to progress in farm yields, although the magnitude of Yp increase is debatable. Progress in elevating Yp of the major cereals would imply, however, that even larger yield gaps need to be overcome than the already large gaps reported herein. Hence, we did not account for changes in genetic Yp in our calculation of SSR by 2050, also because climate change is likely to have a negative effect on Yp and Yw in sub-Saharan Africa.

### Reporting Summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

## Data availability

Data on yield potential and actual yield from GYGA are available at www.yieldgap.org. Data on yield potential from AgMIP and GAEZ can be downloaded from www.fao.org/nr/gaez/en and https://agmip.org/data-and-tools-updated/, respectively. Source data are provided with this paper.

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## Acknowledgements

This study was supported by the Bill & Melinda Gates Foundation (grant to K.G.C., P.G. and M.K.v.I.), the National Institute of Food and Agriculture of the United States Department of Agriculture (grants Hatch NEB-22-373 & AFRI #12431808 to P.G.), Wageningen University & Research (grant to M.K.v.I.), the CGIAR research program on Climate Change, Agriculture, and Food Security (grant to M.K.v.I. and and M.P.v.L.) and the Senior Expert Programme of NWO-WOTRO Strategic Partnership NL-CGIAR (grant to M.K.v.I.).

## Author information

Authors

### Contributions

Research was conceived by J.I.R.E., P.G., K.G.C. and M.K.v.I. Data acquisition, data processing, and statistical analysis were performed by J.I.R.E., J.F.A. and M.P.v.L. The manuscript was written by J.I.R.E. and P.G. with input from all authors.

### Corresponding author

Correspondence to Patricio Grassini.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Food thanks Tony Fischer and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 Evaluation of crop simulation models used in GYGA.

Simulated yield potential plotted against measured yields in well-managed experiments conducted across a wide range of rainfed and irrigated environments. Details are provided elsewhere12,37,48,49,50,51,52. Number of data points (n), root mean square error (RMSE), RMSE as percentage of the average measured yield (RMSE%), and mean error (ME) are indicated. Diagonal dashed line indicates y = x.

### Extended Data Fig. 2 Target crops and countries.

Crop density of rainfed and irrigated maize, rice, and wheat, and countries included in the comparison shown in the present study (dark grey). Crop harvested area density was retrieved from SPAM 201044.

### Extended Data Fig. 3 Comparison of yield gap derived from top-down and bottom-up approaches.

Yield gap estimated following a bottom-up approach (GYGA) versus those derived from top-down GAEZ (upper panels) and AgMIP (bottom panels) for rainfed (R) and irrigated (I) maize, rice, and wheat in important producing regions and at three spatial scales: local, regional (climate zone), and national or subcontinental. Inside each panel, dashed areas indicate negative yield gaps. Each data point represents the average yield gap. The dashed line corresponds to x = y. Comparisons for other cropping systems are shown in the Supplementary Materials.

### Extended Data Fig. 4 Yield potential derived from top-down and bottom-up approaches.

Comparison of water-limited yield potential estimated for rainfed maize in the US Corn Belt following top-down (GAEZ and AgMIP) and bottom-up (GAEZ) approaches. Figures show three spatial resolutions: local (buffer with blue borders), subnational (climate zone with red borders), and national. For simplicity, only one buffer and one climate zone are shown.

## Supplementary information

### Supplementary Information

Supplementary Methods, Fig. 1, Tables 1–4 and References.

Raw data.

Raw data.

Raw data.

Raw data.

Raw data.

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Rattalino Edreira, J.I., Andrade, J.F., Cassman, K.G. et al. Spatial frameworks for robust estimation of yield gaps. Nat Food 2, 773–779 (2021). https://doi.org/10.1038/s43016-021-00365-y

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• DOI: https://doi.org/10.1038/s43016-021-00365-y

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