Spatial frameworks for prioritization of agricultural research and development

Food security interventions and policies need reliable estimates of actual crop production and the scope to enhance production on existing cropland. We assess the performance of two widely used “top-down” gridded frameworks (GAEZ and AgMIP) versus an alternative “bottom-up” approach that estimates extra production potential locally, for a number of representative sites, and then upscales the results to larger spatial scales (GYGA). Our results show that estimates from top-down frameworks are alarmingly unlikely, with estimated potential production being lower than current production at some locations. The consequences of using these coarse estimates to predict food security are illustrated by an example from sub-Saharan Africa. Our study shows that current foresights on food security, land use, and climate change and associate priority setting on AR&D based on yield potential and yield gaps derived from top-down approaches are subject to a high degree of uncertainty and would benet from incorporating estimates from bottom-up approaches.

allows results to be validated by local experts; in the case of top-down approaches, outcomes are di cult to validate because results are necessarily aggregated to grid level, without distinction by soil type and cropping system, and based on coarse weather data.
Yield potential and yield gaps are routinely used as inputs in studies dealing with global food security, biodiversity, land use, and climate changee.g., 5,14,15,16 . 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 approaches at estimating yield potential and yield gaps at local to global scale. We report here the rst global comparison of the two methods, and discuss implications at informing AR&D investments. Our study includes outcomes from two of the most cited studies following top-down approaches: (i) 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 http://www.fao.org/nr/gaez/en/; 17,18 and (ii) the median of the model ensemble of the Agricultural Model Inter-comparison and Improvement Project AgMIP; https://agmip.org/; 19,20 . 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). Because effective AR&D requires interventions at different spatial scales, we performed the comparison between top-down and bottom-up approaches at three spatial scales: local sub-national ('climate zone'), and national or sub-continental, with a respective average size of nearly 9,500, 60,000 and 1,000,000 km 2 .
The climate zones are geographic areas with similar temperature and water regimes 21 . We focus on cereal crops, which account for 45% of global calories 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. 1). 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 producing and / or demanding regions. As examples of regions with favorable climate and fertile soils (i.e. favorable 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 account for about 90% of global rice production and about 80% of rice consumption 2014-2018; 22 .
As an example of a harsh production environment (less favorable 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 exhibits fast population growth rates and domestic cereal demand is projected to increase three-fold over the next 30 years 23 .

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 ndings for other crop producing regions (Supplementary Table S1). As a result, AgMIP gives much more conservative estimates of extra crop production potential on existing cropland compared with GYGA across all spatial scales. In contrast, yield potential estimated at national and sub-continental scales by GAEZ and GYGA are fairly similar in most cases (except for rainfed US maize), with GAEZ estimates differing from GYGA by -50 to +30%. At smaller spatial scales, however, there are very large discrepancies for speci c regions and crops, with GAEZ estimates differing from GYGA by -95 to 480% at local levels (Supplementary Table S1). In some cases, yield potential derived from the bottom-up and top-down approaches follows the same trend across locations and climate zones but there is still an important disagreement 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 those estimated by GAEZ and AgMIP, respectively ( Fig. 2A, E). Similarly, estimated yield potential for rainfed wheat in Australia is 46% higher in GYGA than in AgMIP (Fig. 2G). Besides poor agreement at national and continental levels for some cases, there are cases in which there is 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 GYGA. In other words, some of the locations and climate zones reported by GYGA to have the highest yield potential are identi ed to be among the ones with lowest yield potential by GAEZ and AgMIP and vice versa.
Next to the (lack of) association between top-down and bottom-up approaches, we can also assess the quality of yield potential estimation by comparing the simulated yield potential against the average farm yield currently achieved (actual yields). By de nition 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. In our evaluation, we found that the top-down approaches exhibited negative yield gaps for a considerable number of cases worldwide (Fig. 3, Extended Data Fig. 2). At local level, yield gaps estimated by GAEZ were 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 were negative in 39% (maize), 45% (rice), and 25% (wheat) of the cases. In contrast, no negative yield gaps were estimated by GYGA. Because calculation of yield gaps relies on the same source of average actual yield data (see Methods, Section 3) for both topdown and bottom-up methods, the substantial number of cases with negative yield gaps as estimated by the top-down approaches can be seen as strong indication of underestimation of yield potential.
Implications for food self-su cient assessments. Although achieving food self-su ciency 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 e ciently 24 . A key indicator of food security is the self-su ciency ratio (SSR), which is the ratio between domestic production and total domestic consumption e.g., 25 . Comparison of SSR for different scenarios of yield gap closure can help assess the degree of food self-su ciency that a country or region can achieve by increasing productivity on existing cropland 23 . However, as we showed previously, such an assessment will be in uenced by the choice of top-down or bottom-up approach in calculating yield potential, yield gaps, and associated extra production potential. For example, self-su ciency 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 (Fig. 4). GAEZ forecasts that the region could become self-su cient for cereal grain by year 2050 by an ample margin via narrowing current yield gaps, with the potential production exceeding expected demand by 36% (i.e., SSR=1.36). In contrast, GYGA also estimates that the region could be self-su cient 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 su ciency, indicating that cropland expansion and/or increase in food imports will be needed to meet projected cereal demand by year 2050 (SSR=0.96). Discrepancies among approaches become larger when zooming in on speci c countries or regions. For example, while GAEZ predicts that yield gap closure would result in cereal surplus in seven of the 10 countries, outputs from GYGA and AgMIP suggest that most of the countries could not meet cereal demand by year 2050. And while SSR estimates at the sub-continental scale are similar from GYGA and AgMIP, there are large differences in estimated SSR at national scale, with AgMIP estimations differing from GYGA between -24 to 39%.

Discussion
A key question for AR&D is where to invest to maximize the return on investment (ROI). While yield gap alone is not su cient to answer this question, together with other biophysical and socio-economic factors that influence technology adoption, it is an important parameter to guide public and private investments in agriculture since it speci es where and how much crop production can be increased. Here we showed that the choice of top-down or bottom-up approach has important implications for projecting ROI. For example, different approaches lead to contrasting answers about the prognosis of a given country to reach a desired level of food self-su ciency. And even in those cases in which both approaches give similar yield gap estimates at sub-continental level, there are large discrepancies when looking at speci c countries or regions within each country. The considerable number of locations with negative yield gap estimated by top-down approaches raises important questions about the accuracy of these approaches in estimating yield potential, and urges caution about their use as it would result in less effective prioritization of R&D investments in agriculture and reduced ROI. And 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 potential.
Causes for inaccurate estimation of yield gaps following top-down approaches have been investigated elsewhere e.g., 26,27 ; here we point out some of them. The two top-down approaches included in this study rely on coarse gridded weather data and global soil maps (Supplementary Table S1). Previous studies have shown important biases when simulating yield potential using coarse gridded weather data compared with simulations based on measured data e.g., 27,28,29 or without proper selection of the dominant soil types within an agricultural area e.g., 30,31 . Similarly, the cropping-system context, in relation to crop intensity (i.e., 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 existing ones or simply do not exist. For example, in the US Corn Belt, the global dataset MIRCA 2000 32 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 frost 33 . Likewise, top-down approaches generally use generic crop model coe cients that do not account for the speci city of crop cultivars, in terms of responses to temperature and photoperiod 20,34,35 ; 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. To summarize, estimates of yield potential and yield gaps delivered via top-down approaches are subjected 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: (i) the bottom-up approach of GYGA and (ii) 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 USA, 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 subnationallevel administrative units covering the entire crop production area. Finally, Van Wart et al. (2013b) and van Bussel et al. (2015) 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 strati ed (instead of random) selection of sites and use of the climate zone framework as basis for upscaling results from location to region and country. Altogether, these studies provide evidence of the robust estimates of yield potential and yield gaps following the bottom-up approach of the Global Yield Gap Atlas.
Although estimating yield gaps following a bottom-up instead of a top-down approach requires more time and efforts, we argue from our experience at developing GYGA that a conscious effort to estimate yield gap for all major cropping systems in the world following a robust bottom-up approach, and to keep the platform updated over time, can be accomplished in a relatively short timeframe and with a modest investment. Another apparent trade-off of the bottom-up approach is related with its large data requirement, which would make, in principle, its application di cult in regions where these data are scarce or simply do not exist. Nevertheless, a bottom-up approach that is exible to accommodate different scenarios of data availability and quality, giving priority to best sources of data when these exist, can help identify 'data gaps' that should be lled in the future. Along these lines, GYGA follows a tier preference approach 31 that gives priority to the use of measured weather data and ne-scale soil maps, but allows the use of gridded weather data or global soil databases as a last resort for sites in which measured data do not exist, making these decisions in an explicit way so that these data gaps can eventually be lled with better data. In contrast, top-down approaches based on unmeasured gridded data or coarse global soil maps give a false sense of availability of quality data at ne spatial resolution, since their estimates are provided for the entire planet (or the entire cropland area) in spatial grids that are typically 0.5-2.0° (ca. 3,000 to 50,000 km 2 at the equator). Regardless of the means to do it, one thing is clear: current foresights on food security, land use, and climate change and associate priority setting on AR&D based on yield potential and yield gaps derived from top-down approaches is subject to a high degree of uncertainty and would bene t from incorporating estimates from bottom-up approaches to their decision making.

Declarations
Yield potential 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 stress 39 . In irrigated elds, yield potential (Yp) is determined by solar radiation, temperature, atmospheric CO 2 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 requirement, water-limited yield potential (Yw) is determined by water supply amount and its distribution during the growing season, and 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 (t per harvested ha) 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 gap 10 . 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 40,41 . Beyond this yield level, the small return to extra input requirement and labor does not justify the associated costs and level of sophistication in crop and soil management practices.

Sources of yield potential data derived from top-down and bottom-up approaches
We retrieved data generated from two initiatives following a top-down approach: (i) the Global Agro-Ecological Zones (GAEZ) http://www.fao.org/nr/gaez/en/; 17,18

and (ii) the Agricultural Model
Intercomparison and Improvement Project (AgMIP) https://agmip.org/; 19,20 . As an example of a bottomup approach, we used results from the Global Yield Gap Atlas GYGA; www.yieldgap.org; 10,31,42 . Main features of these databases are summarized in Table 1. In the process of selecting the speci c 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 de nitions provided in the previous section. We also try 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 data sets that cover the time period between 1961-1990 and 1980-2010, respectively, GYGA uses more recent weather data (Table 1). Similarly, comparison between databases where limited to those regions for which there were estimates of Yp (or Yw) for the each of the top-down and bottom-up approaches. More detailed information about the three approaches can be seen in Section 1 of the Supplementary Materials. Combination of (i) generic and cropspeci c, (ii) site-based process and ecosystem, and (iii) calibrated and noncalibrated models (Table S2).
Crop-speci c model, simulates crop growth on a daily step. To the extent it is possible, models are calibrated for each study region. For a given buffer, climate zone, or country (or sub-continent), 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 yield in the estimation of yield gap, we used the average yield dataset from GYGA because it provides estimates of average yield disaggregated by water regime and for the most recent time period. Actual yield data were retrieved from o cial statistics available at subnational administrative units such as municipalities, counties, departments, and sub-district. 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 whole avoiding the bias due to a technological time-trend and long-term climate change 31 .
Using GYGA database on average yield for estimation of yield gaps will not biased the results from our study as GYGA favors the use of o cial sources of average yields at the ner available spatial resolution, which is the same source of actual yield data used by other databases such as FAO and SPAM 22,44 . 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 decades 18 . Finally, extra production potential was calculated based on the yield gap estimated by each approach and the SPAM crop-speci c harvested area reported for each buffer, climate zone, and country (or sub-continent). 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. 1 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, climate zone, country or subcontinent) by calculating root mean square error (RMSE) and absolute mean error (ME): where Y i and Y GYGA 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 Y i versus Y BU 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 yield potential estimates on food security analysis
We assessed the impact of discrepancies in Yp (or Yw) between top-down and bottom-up approached on the self-su ciency ratio (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 ve main cereal crops in Sub-Saharan Africa (i.e., maize, millet, rice, sorghum, and wheat) following van Ittersum et al. (2016). Millet and sorghum were included in the analysis of SSR in sub-Saharan Africa because together they account for ca. 15% of the total cereal production and ca. 25% of the total cereal harvested area in this region. Brie y, we computed current national demand (assumed equal to the 2015 consumption) and the 2015 production of the ve cereals to estimate the baseline SSR (i.e., in year 2015) in ten countries for which Yw data were available in GYGA. Current total cereal demands per country were calculated as the product of current population size derived from UN population prospects and cereal demand per capita based on IMPACT 35,45 . The annual per capita demand for the ve cereals was expressed in maize yield equivalents by using the crop-speci c grain caloric contents, with caloric contents based on FAO food balances 46 .

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 download from www.fao.org/nr/gaez/en and www.agmip.org, respectively.