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Yield definitionsYield 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 approachesWe 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 levelsComparison 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 analysisWe 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 SummaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

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