Introduction

Climate change is expected to directly impact agricultural production by reducing both crop yield and quality via changing patterns in temperature, water, gases and nutrients. Moreover, changing climate can also have indirect impacts on yields by altering impacts caused by pests, diseases and weeds. Statistical models of crop yield response to climate change can be estimated using data from controlled experiments. These models can be used to generate expectations of climate impacts in new settings such as future time periods or geographies with relatively scarce primary studies1,2,3,4,5,6,7. Predictions from such models are highly relevant to climate policy—climate yield response functions have been included in a number of Integrated Assessment Models (IAMs) and Intergovernmental Panel on Climate Change (IPCC) assessments of the impacts of climate change on food production4,8. However, it is difficult to validate the general usefulness of yield response functions applied to ‘out of sample’ settings. This difficulty is partly due to methodological challenges in estimating general relationships and transferring said relationships across settings, and partly because various sources of uncertainty throughout the modelling process can combine and propagate in confounding ways to modelled predictions. Estimating general relationships using data collected from studies—the technique of meta-analysis—is fraught with methodological challenges that can result in certain patterns in the data being over- or under-represented. A previous meta-analysis of climate impact estimates found strong evidence of duplication bias from between-study correlation, as well as within-study correlation from the inclusion of multiple estimates11. In the case of climate-yield responses, such challenges can lead to higher or lower yield responses than are warranted given the true structure of the data. Once general relationships have been estimated, how these estimates are transferred to new settings and interpreted in their context is also subject to many uncertainties. At a basic level, there is a large degree of variation across climate impact modelers’ data sampling strategies, choices to omit or impute missing values, and choices or assumptions related to the model specification and parameterization with input data. It is helpful for modellers to clarify these ambiguities, which we do in this study. Going further, the trajectory of global economic development and the effect of human emissions on earth systems and climate is often referred to as irreducibly uncertain, where more information may not necessarily reduce this uncertainty9. These ‘irreducible’ or ‘deep’ uncertainties cannot be collapsed, but we argue that impact modellers should aim to include inputs from a large range of climate models and emission scenarios, which will help users and policymakers better understand the range of possible impacts. The goal is to clarify the sources of uncertainty, making it easier to trust and use yield response predictions at policy-making levels.

Our study has three objectives: (1) to improve the estimation of yield responses to climatic factors such as temperature, precipitation and CO2, using data from an established crop yield response database (CGIAR data), (2) to decompose the range of uncertainty in resulting predictions into its separate sources, and (3) to provide policy-relevant estimates related to global food security. Our goal was to provide a comprehensive yet up to date estimation of global climate yield responses while also considering implications for food security and associated uncertainty under a greater set of emissions scenarios and time periods. First, we hypothesised that fitting mixed models to the CGIAR dataset would help to account for within-study correlation between multiple estimates in the dataset, resulting in better statistical model performance compared to pooled OLS models used in previous meta-analyses of the same dataset10,11. We could then compare general expectations of crop yield responses to climate change obtained by following this approach, to the expectations derived from these older meta-analyses12. Second, we used a bootstrap sampling technique repeated on the dataset across multiple dimensions of uncertainty, to see how different sources of uncertainty throughout the modelling process propagate through to estimated global yield responses. This allowed us to systematically quantify the share of variance that is attributable to data sampling, missing values, model specification, climate model input data from the sixth Coupled Model Intercomparison Project (CMIP6) multi-model ensemble of Global Circulation Models (GCMs). Finally, we estimated projected crop yield responses impacts using not only future projected temperatures but also future projected precipitation, which was not done in earlier meta-analyses fitted on the same dataset4,12. We applied the outputs of the preferred response model to calculate country-level calorie gaps and domestic food security status for three emissions scenarios of varying severity.

Results

Modelled yield response functions

We began by refreshing the CGIAR database with screening and imputation of missing data13. This database aggregates 74 studies related to maize, rice, soy and wheat (comprising 42% of calories consumed globally in 202014) containing over 8800 point estimates of changes in crop yield across varying temperature, precipitation, \(\hbox {CO}_2\) and other factors. We did not add studies to the database; it therefore remains a non-exhaustive collection of information on yield responses to climatic factors. The CGIAR database has a nested or hierarchical structure in which multiple estimates can come from a single study; these estimates should be treated as correlated or non-independent. Similarly, many estimates are derived from the same region or country, and we also assume these to be correlated.

We fit statistical models for each crop separately (see “Methods” section for full specifications). Our five candidate models are: (1) Ordinary Least Squares (OLS) pooled model, (2) Generalised Linear Mixed Model (GLMM) with random intercepts, (3) GLMM with random intercepts and random slopes, (4) Generalised Additive Mixed Model (GAMM) with random intercepts and (5) GAMM with random intercepts and random slopes, plotted in Fig. 1. Model 1 is a pooled OLS model which treats point estimates from the same study and country as though they are independent, and are similar to the OLS models used in previous published meta-analysis on the same CGIAR dataset12 except that our response functions are separately estimated for each of the four crops, and do not include an interaction term between quadratic temperature change and baseline temperature (see “Methods” section). Models 2 and 4 include random intercepts for studies and countries in the dataset, where study random intercepts account for correlation among multiple estimates from the same study, and country random intercepts accounts for correlation between studies that include estimates for the same country15. Including country random intercepts helps to capture non-weather factors associated with location, such as pest and disease susceptibility, soil fertility, and farming behaviour, and also allows for fitted estimates to be predicted on new countries not included in the CGIAR data. Models 3 and 5 include random intercepts for studies and countries but also random slopes for countries, which allows temperature, precipitation and CO2 functions to vary for each country (i.e. estimates a separate function for each country). Random effects allow for residual variance to partitioned among the hierarchical levels of countries and studies in the data. GAMMs are a non-parametric type of generalised linear model which allows the response variable (here yield change) to depend on smooth functions of model terms. Model terms were chosen following earlier literature and relevance to crop growth (see “Methods” section)16,17,18,19,20,21,22,23,24,25,26. Response functions were calibrated to changes in mean temperature, precipitation and CO2 conditions, and thus, do not represent impacts from extreme and variable temperatures and rainfall events including floods and droughts nor do they capture long term soil and nutrient fluctuations.

We found that fitted temperature-yield response functions are downward sloping for maize, rice and wheat, suggesting that temperature effects in isolation tend to have a yield-reducing effect on crops (Fig. 1a). This response is not seen in soybean. Precipitation-response functions describe a positive relationship between changes in rainfall and yields for all crops except rice, the latter may be due to rice being mostly irrigated (Fig. 1b). For visualisation purposes, these plots show response functions at the median baseline levels of temperature and precipitation, but do not show interactions between changes in temperature and precipitation, or combinations of different baseline levels with changes. What can also be seen from the plotted data points are multiple estimates from the same study, which may represent unique experiments testing responses to combinations of temperature, precipitation and CO2. These multi-estimate studies raise the need for mixed effects modelling to account for correlation bias within-study.

Fig. 1
Fig. 1
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Marginal mean response functions (± 95% CI) for temperature change (a) and precipitation change (b), conditional on median baseline temperature, median baseline precipitation, and the absence of changes in precipitation (a) or changes in temperature (b), changes in \(\hbox {CO}_2\) and on-farm adaptation. Points depict study estimates derived from the CGIAR data. Error bars show 95% confidence interval pooling variance within and between 5 imputation-augmented fit estimates. Legend: GLM RI, Generalised Linear Mixed Model (GLMM) with random intercepts; GLM RS, GLMM with random intercepts and slopes; GAM RI, Generalised Additive Mixed Model (GAMM) with random intercepts; GAM RS, GAMM with random intercepts and slopes; LM, pooled Ordinary Least Squares (OLS) model. Supplementary Figure 3 shows some out-of-sample comparisons that were not included in the CGIAR database3,8,106,107.

Sources of uncertainty

We systematically quantified uncertainty by block-bootstrapping 100 samples of the data and comparing the resulting average standard deviation of estimated global yield responses across five dimensions. These dimensions span: (1) 100 block-bootstrap samples, blocking by study where a different set of studies are selected in each sample (i.e. uncertainty regarding the sampling strategy to compile the CGIAR dataset), (2) five different imputations of the CGIAR dataset to fill in missing values, using Multiple Imputation Chained Equations (MICE, see “Methods” section) (i.e. uncertainty regarding treatment of missing data), (3) five statistical models (i.e. uncertainty regarding the econometric specification), (4) 23 sets of temperature, precipitation and CO2 input data from the CMIP6 ensemble of 23 GCMs, for each of three emissions scenario (i.e. uncertainty regarding the effect of human emissions on the climate system) (see “Methods” section).

We found that uncertainty from model choice is equal to between 10 and 20% of global agricultural yields for maize, rice and wheat and over 50% for soybean (Table 1). All types of uncertainty and combined uncertainty are highest in soybean, followed by rice, wheat and maize. This roughly reflects the different sample sizes of non-imputed CGIAR point estimates related to each crop (maize: 3426; rice: 2776; soy: 788; wheat: 1972). High uncertainty around soybean results reflects the low sample size and considerable variation in these estimates. Variations across GCMs are lowest compared to other types of uncertainty across all crops. Figure 2 shows 575 model distributions of 2081–2100 impact estimates (pooling distributions across GCMs for better legibility). The pooled OLS model generates a narrower distribution of estimated responses compared to both GLMMs for maize, soy and wheat, and compared to GAM models for rice. This suggests that not accounting for study- and country-related correlations in the data may result in underestimates of prediction uncertainty.

Table 1 Sources of uncertainty attributable to model choice, sampling, GCMs and imputation-augmented datasets (missing data), as measured by the average standard deviation of global production-weighted yield change (%).
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Fig. 2
Fig. 2
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Distributions of predicted global production-weighted mean yield change in 2081–2100 from 575 model combinations for each crop (5 model specifications \(\times\) 5 imputed datasets \(\times\) 23 GCMs), pooled by GCM to represent only differences across model choice and imputation-augmented dataset. Legend: GLM_RI, Generalised Linear Mixed Model (GLMM) with random intercepts; GLM_RS, GLMM with random intercepts and slopes; GAM_RI, Generalised Additive Mixed Model (GAMM) with random intercepts; GAM_RS, GAMM with random intercepts and slopes; LM, pooled OLS model.

Model performance

We evaluated model predictive performance by running k-fold cross validation with tenfolds. We found the GAMM and GLMM with random intercepts and random slopes performed best as measured by Root Mean Squared Error (RMSE), and the pooled OLS model performed the worst. Figure 3 shows this alongside explained deviance for each of the five model specifications (each pooled across five imputed fit estimates). The pooled OLS model fit performed the worst, with the highest mean model RMSE and least explained deviance across all five model specifications.

Fig. 3
Fig. 3
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Model root mean squared error (RMSE) from tenfold cross validation (top) and deviance explained by each model (bottom) across 5 imputed dataset fit estimates. Black circles show model-specific mean RMSE and explained deviance, calculated across imputed datasets. Legend: GLM RI, Generalised Linear Mixed Model (GLMM) with random intercepts; GLM RS, GLMM with random intercepts and slopes; GAM RI, Generalised Additive Mixed Model (GAMM) with random intercepts; GAM RS, GAMM with random intercepts and slopes; LM, pooled OLS model.

GLMM and GAMM models with random intercepts and slopes performed better compared to all the GLMM and GAMM models with random intercepts only. This is unsurprising given the structural variation in studies across the CGIAR database; allowing climate variables (temperature, precipitation and \(\hbox {CO}_2\) change) to vary randomly for each study helps extract ‘true’ relationships from each study. Yet the flexible nature of the non-parametric GAMM models (we do not restrict the number of knots in splines) and the shape of their response functions suggest that the GAMM with random intercepts and slopes could overfit the data. Of the five models, we prefer the GLMM model with random intercepts and slopes as it has a lower tendency to overfit the data compared to the GAMM model despite having similarly good predictive performance.

Global future projected yield changes

We used fitted estimates from the preferred model (GLMM with random intercepts and slopes) to estimate future projected yield changes on a 0.5\(^\circ\) grid (\(\sim\) 50 km at the equator) and converted these impacts into calorie measures. We used these measures to analyse risks of food insecurity at the country level from 2021 to 2100. We consider three emissions scenarios using the combinations of Shared Socioeconomic Pathways (SSPs) in CMIP6: : SSP1–2.6, SSP2–4.5 and SSP5–8.5. In line with the IPCC’s Sixth Assessment Report27,28, SSP1–2.6 illustrates a scenario of sustainability with relatively low growth in population, consumption, and concentration of greenhouse gases (GHG), with a best estimate of 1.8 \(^\circ\)C average global surface temperature warming by 2081–2100 relative to the period 1850–1900. SSP2–4.5 is moderate population scenario, with medium challenges to mitigation and adaptation and 2.8 \(^\circ\)C warming by 2081–2100. SSP5–8.5 is a scenario of rapid economic growth alongside continued globalisation and fossil-fuelled development combined with high greenhouse gas concentrations, with 4.4 \(^\circ\)C warming by 2081–2100.

Table 2 Global production-weighted mean yield change (%) projections from Generalised Linear Mixed Model (GLMM) for SSP1–2.6 (top), SSP2–4.5 (middle) and SSP5–8.5 (bottom), central estimates bolded [95% confidence interval].
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Table 3 Production-weighted mean yield change projections for 2081–2100 from generalised linear mixed model (GLMM) random intercepts and slopes model for largest producers (%) for SSP1–2.6, SS2–4.5 and SS5–8.5, central estimates bolded [95% confidence interval].
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We show CMIP6-ensembled global predictions for the preferred model for SSP5–8.5 in Fig. 4 and for SSP1–2.6 and SSP2–4.5 in Supp. Fig. 5 and 6. The largest yield reductions are seen in maize, with losses of 3.8% under SSP1–2.6 and 22.2% under SSP5–8.5 in 2081–2100 (Tables 2, 3), which is consistent with other studies not included in the CGIAR dataset 8,46. Of the major global maize producers, the US and China are expected to suffer the largest yield reductions of 26% and 24.7% respectively (Table 3). Declining rice yields are expected in the Middle East, South America, and South/South East Asia, worsening over the century with a global weighted mean yield loss of 2.7% under SSP1–2.6 and by 9.0% under SSP5–8.5 by 2081–2100. Rice yields are expected to decline in India and Bangladesh by around 21%, while these losses are smaller in China (− 9.8%) and Indonesia (− 6.5%) (Table 3). Soy yields face considerable uncertainty with projections showing areas of net negative and positive change across regions of Brazil (− 5.6%) and the US (− 30.9%), while global mean yields show a net increase of 1.4% under SSP1–2.6 but a net decrease of 15.4% under SSP5–8.5. Wheat shows relatively small global yield decline of 1.5% under SSP1–2.6 by 2081–2100, but large losses are expected globally (14.1%), in India (− 21.7%) and the US (− 14.4%) under SSP5–8.5 (Table 3).

Fig. 4
Fig. 4
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Predicted yield changes derived from Generalised Linear Mixed Model (GLMM) with random intercepts and slopes pooled across 5 imputation models and 23 GCM prediction datasets for SSP5–8.5, shading indicates spatial distribution of crop production c. 200092.

Global projected food calorie gap

We converted projected global yield change estimates into national calorie supply and compared them to estimates of national calorie demand using data from the FAO and other literature14,29,30,31,32. The calorie gap represents future national calorie demand that cannot be met by production and imports. Our results show reduced calorie supply in many countries in south and southeast Asia, sub-Saharan Africa, with most severe losses expected under SSP5–8.5 relative to baseline calories supplied in 2015 (Fig. 5a,b, Supp. Fig. 7a). In addition to these countries, North America and Oceania could become at risk of not being able to meet national food demand under SSP5–8.5 (Fig. 5c,d). We took a deliberately simple approach to illustrate the potential implications of estimated yield responses on global food security. This approach treats many dynamic factors as fixed, such as harvested areas, average daily energy requirements, the share of each country’s production going to each export partner, and non-staple crops’ share of a country’s diet. We thus assumed static patterns for crop distribution, harvest frequency, total standing cropland area, nations’ demographic compositions, export patterns and dietary patterns33,34,35 (see “Methods” section).

We also replicated calorie gap maps using the pooled OLS model (Supp. Fig. 7b,d). This shows many countries experiencing less severe calorie reductions occurring later in the century compared to the preferred GLMM model with random intercepts and slopes. This could be because multi-estimate studies with less severe yield responses are biasing the pooled OLS results, or because negative yield responses are apparent within individual studies, but muted when data from those studies are combined (i.e. Simpson’s paradox).

Fig. 5
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Food security implications estimated from Generalised Linear Mixed Model (GLMM) with random intercepts and slopes. Top: Reduction in total supply of food in calories relative to 2015 baseline (%) for SSP2–4.5 (a) and SSP5–8.5 (b). Bottom: Change in risk of not meeting national calorie demand from production and imports for SSP2–4.5 (c) and SSP5–8.5 (d). Maps for SSP1–2.6 are in Supp. Fig. 7.

Discussion

We offer a brief review of our results in the context of the broad and deep scientific literature covering the changing phenology of grain crops in response to elevated heat and drought conditions36,37,38,39. Our results identify larger yield losses for maize and rice in many regions than previously estimated using the same CGIAR dataset, by roughly 5–10 percentage points compared to12. Wheat results are comparable to Ref.12 with a 5–10 percentage point difference in either direction for most regions. Results from Ref.12 show slightly larger yield losses over central Asia, northern Africa, South America and western Australia. We believe these differences flow from methodological treatments of the data and the inclusion of precipitation change in our estimation of global gridded yield losses.

Compared to previous meta-analyses of the same CGIAR dataset4,12, our inclusion of precipitation change and its interaction with temperature change and baseline precipitation levels resulted in larger global yield losses for maize and rice. This demonstrates the importance of including temperature and precipitation interactions in climate-agriculture impact modelling. High temperatures often co-occur with, or are caused by, low precipitation, and their interaction can create impacts not otherwise captured by considering temperature or precipitation in isolation from one another. Recent reviews of the interactions of combined heat and drought have found greater yield impacts on grain crops than individual stresses alone40,41, as well as in interaction with nutrient availability42. Rising mean temperatures cause more water to evaporate from the soil surface (evapotranspiration losses) and therefore higher crop water requirements43. Precipitation is more spatially variable than temperature, and there is major disagreement between GCMs on the direction of precipitation change in many regions44,45. This highlights the importance of including the range of variance in future rainfall projections as we have done here by using input data from 23 GCMs.

The relatively more severe yield losses for maize compared to wheat aligns with other comparative analyses in the literature. Reference37 also found maize to be more sensitive to drought compared to wheat, partially due to the lengthening Anthesis Silking Interval (ASI) leading to asynchrony of anthesis and silking which affects pollination and reproduction. They posited that differences in drought sensitivity could be attributed to the origins of maize in less water-limited regions compared to wheat originating in dryland regions. Wheat has thus acquired adaptability traits including delayed senescence which can be useful for late-season drought, as well as deeper root systems to access sub-surface soil water37. On the other hand, wheat has lower limit temperature thresholds (35 \(^\circ\)C) than maize (45 \(^\circ\)C) or soybean (40 \(^\circ\)C)46,47, so we would expect declines or losses where these thresholds are surpassed where it is currently grown (see “Methods” section). However, many areas currently too cold for wheat may become viable for wheat up to the point of optimal temperatures for grain filling. A previous meta-analysis of maize and wheat drought responses identified that yields are more drought sensitive if water limited during the reproductive stage than vegetative stage of plant growth37. Day and nighttime temperatures moving outside of the optimal temperature range for maximum grain yield is expected to directly affect grain yields (Supp. Table 1)23,47. However, detailed differences in changing temperature and precipitation throughout the growing season cannot be picked up by our response functions here. Of all staple crops, maize has the current largest cultivated area (\(\sim\) 205 M ha in 2021)46,48. Assuming maize is grown in areas where the growing season temperatures are below but near optimal temperatures for development and production, further warming may push these locations out of the optimal range of growing temperatures.

Rice yield losses are larger than what has been estimated in previous meta-analyses using the same CGIAR dataset, and here yields are expected to decline in Africa, South America and Australia through to the end of the century in response to higher temperatures. This aligns with scientific understanding of the impact of high temperature stress on rice pollen, fertility and grain yield36,49,50. Reference3 estimated yield declines at one degree of global warming for China (3.0%), Russia (4–7%), France (4.2–5.2%), Kansas in the US (7.3%), India (8.0%), comparable to our projections in 2041–2060 and 2061–2080 showing wheat yields declining by 1.2–5% in China, 1.7–8.3% in India, 4–8% in the US, 1–5.9% in Russia and rising by 1–5% in France. Like12, we also see rice yield increases in regions of high elevation and latitude (e.g. Tibetan Plateau, Greenland, Siberia, Andes). Our soy results are starkly different to those previously estimated using the same CGIAR dataset, in which12 project total crop failure in Africa and Brazil and southern Australia. Other studies have discussed the large degree of uncertainty surrounding soy yield climate responses, which may be due both to its higher critical temperature tolerance to heat stress around anthesis (compared to maize and wheat) but also its lower limit temperature tolerance. This can be seen in similar studies predicting as many areas with decreased yields as there are with increased yields, particularly in the USA and Brazil46. We also found a large band of uncertainty around soybean projections across all dimensions of model choice, sampling, GCMs and missing data.

Our maps of projected global gridded yield changes show expanding suitability for rice and wheat in the northern latitudes and elevations and declining suitability nearly everywhere else (see Fig. 4). This accords with other studies showing growing suitability in northern Europe for rainfed wheat crops due to changes in rainfall and temperature51. The reduction of frost occurrence has also been observed to benefit crop yields17. From the perspectives of climate adaptation, water saving and nutrient pollution, the regional scale production basket and optimal crop distribution may need to be significantly reconsidered52,53,54. Our approach assumes that crops are fed by rainwater, yet almost 20% of cultivated land and 40% of global crop production occurs under irrigated conditions55. Going forward, freshwater limitations mean that irrigated croplands in some regions may need to revert to rainfed management56 while expanding in others57. Irrigation plays an important role in supporting crop production in drier regions, though weather-driven variability in global irrigation withdrawals has been modest at a global scale (\(\sim\) 10%) to date58,59. Various studies have projected scenarios of future water stress and growing demand from competing industries and changing land use, which will likely constrain expansion of irrigation and diminish the reliability of blue water resources60,61. The climate response of rainfed versus irrigated farms is not well understood on a global scale and deserves further study especially in the context of adaptation to climate change and mitigation of losses62,63. Blue water availability for irrigated crops should also be integrated into future work on this topic64.

Our results shed light on shifting crop distributions due to changing temperature and precipitation patterns, however it misses the effects of sea level rise, salinity and water stress from competing land uses60,61. For their global analyses of climate change damages, Ref.1 estimate the percentage loss of arable coastal land by metre of sea level rise for 140 regions, finding that the physical effects of sea level rise are concentrated among small island states of Oceania and the Pacific. This may lead to increased salinity of inland and coastal arable soils, a significant abiotic stress for crop plants—currently greater than 20% of global croplands are adversely affected by salt stress65,66,67.

Our estimates, which consider changes in multi-decadal norms, also do not fully capture the effects of variable and extreme temperatures and rainfall events. There is evidence suggesting that crops may be more sensitive to a highly variable climate on a warmer planet on average than to a climate that changes gradually17. In South Asia the summer monsoon rainfall is responsible for almost 50% of the variability in total food grain production anomalies in the region68. Stochastic weather generators have also been used to show that increased variability in temperature or precipitation in the UK and France sometimes had a larger effect on wheat yields than changes in averages, especially when combined with warmer mean seasonal temperature18,21.

We have found that reductions in calorie supply of between 15 and 30% are possible in 2081–2100 under the worst case emissions scenario of SSP5–8.5 (Fig. 5). Many countries in sub-Saharan Africa, south Asia, North America and Oceania are at heightened risk of being unable to meet domestic food demand through production and imports. Thus adaptation measures including sustainable intensification, expanding areas of cultivation, changing trade patterns or emissions mitigation should all be considered. Indeed, our results for SSP1–2.6 and SSP2–4.5 representing lower emissions scenarios (Supp. Fig. 7) show much smaller calorie deficits for many countries. It bears repeating that we have not assumed any trends in harvest frequency nor total standing cropland area, even though global harvested land area grew roughly four times faster than the total standing cropland area between 2000 and 201135. In reality we would expect harvest frequency and total standing cropland area to continue changing, though not in the same direction across all regions (e.g. crop harvest frequency increased from 1961 to 2011 in Brazil, India and China but decreased in many places in Africa35). Expansion of suitable areas for cultivation may offset some of the yield losses modelled here. However, we believe our estimates of yield losses and damages to be conservative as we have not considered the indirect effects of climate change on food security such as through extreme rainfall, floods, wildfires, pests and diseases.

Nutrient quality is highly likely to be affected by climate change, but was not possible to include in this analysis. Research shows mixed effects of elevated CO2, temperature, salinity, waterlogging and drought stress on nutrient accumulation in soils, with effects being highly dependent on the nutrient, crop plant and intensity level of change69. Moving forward, sustainable nutrient and irrigation management underpins farmers’ ability to close yield gaps while maintaining or increasing nutrient quality70,71,72,73,74,75,76,77,78. Another factor affecting future food security are crop losses from pests and diseases. Climate change is already affecting the range distributions, pest status and synchrony of economically important pests and diseases with host plants79,80. These impacts should be integrated in future modelling of yield responses.

Finally, we have interrogated the sources of uncertainty contributing to variance around estimated global yield responses. We found that uncertainty from model choice is most significant compared to uncertainty from sampling, missing data and GCMs. Regarding model choice uncertainty, ensembling model predictions may not be the best way to represent this variation since some models were shown to outperform others. We have chosen the mixed effects model specification that we believe best achieves the trade-off between predictive performance and over-fitting the data. We are comforted by seeing full model agreement across many regions in the mean sign of future yield projections for all crops except for soy, though these areas of agreement do not necessarily overlap with where crops are currently grown (Supp. Fig. 9). Uncertainty from GCMs reflects uncertainty about the effect of human emissions on the climate system. While this deep uncertainty can be clarified by including a range of CMIP6 models as inputs to climate impact modelling, model ensembles may not represent the complete or systematic sample of the climate response9,80. Other studies have shown that for GCM-based projections of climate response, uncertainty attributable to GCMs and the internal variability of the climate system tends to dominate other sources of uncertainty in the near-term, whereas in the late-century scenario uncertainty dominates (though GCM uncertainty remains significant)81,82. In our analysis of late-century projections for a single scenario, GCM uncertainty is dominated by model uncertainty and sampling uncertainty. For future meta-analyses, we recommend expanding the set of studies and sample size where possible, or to take a bootstrapping approach to characterise uncertainty from data sampling strategy.

Significant caveats remain on the approach we have taken to statistical modelling here. Perhaps most significantly, function transfer implicitly assumes that estimated function parameters at study sites transfer across time and space83. Since only a subset of all countries is represented in the CGIAR data (see Supp. Fig. 1), this assumption obviously may not hold. For example, Australia has exceptionally nutrient poor soils from undergoing a much longer period of weathering and drying than other continents, and a large proportion of crop production takes place under semi-arid and drought conditions. Australian average rainfed yields of key grain crops since the 1960s severely lag the rest of the world with the exception of yields in Africa84. Compared to zones with higher baseline rainfall, rainfed crops in Australia generally display higher yield sensitivity to rainfall, meaning that a small increase in rainfall results in relatively higher increases in yield. This suggests that transferring global parameters for yield response to precipitation change may not predict local responses well, even though our models account for interactions between baseline levels and level changes in rainfall, and we used estimated country random effects to predict local yield changes. Factors such as nutrient availability and their interactions with climatic factors have not been captured here as mentioned earlier. Thus transferring model parameters to settings in which nutrient deficiencies are particularly acute requires extra care. We maintain that the use of mixed effects models is preferrable to OLS models, as the inclusion of random country effects helps to calibrate the estimation of responses for those countries. Moreover, we show that the use of mixed effects models leads to estimates showing more severe calorie reductions and larger ranges of uncertainty compared to the original OLS model. We contend that choosing the right model to fit the data has important implications for estimating climate responses on agricultural productivity. We have not given much attention to how these results compare to crop process models, however a recent review of process and statistical models found that the two methods generate similar crop yield sensitivities to changes in climate85. Further, although individual predictions often deviate widely, the ensembled average of process models tends to correlate well with statistical model predictions85.

Conclusion

In this study, we used statistical meta-analysis to fit mixed effects models of crop yield responses to climate change using an established database. We fit five model specifications and estimated future yield changes using temperature and precipitation projections to 2100 from a CMIP6 ensemble of 23 GCMs. We used these estimates to calculate national calorie supply and compared them to measures of calorie demand to understand their implications for global food security. Our preferred model estimates that global yields may change from 2015 levels by − 22% (maize), − 9% (rice), − 15% (soy) and − 14% (wheat) in 2080–2100 under the business-as-usual scenario of SSP5–8.5, but reduce to − 3.8%, − 2.7%, 1.4% and − 1.5% respectively under the lower emissions scenario of SSP1–2.6. We argue that this demonstrates substantial benefits from emissions mitigation. We quantified uncertainty across five dimensions and found that despite a wide range for projected soybean yield changes, our results offer overall validation of changing patterns for rice and wheat crop distributions under climate change. For some crop species and regions, such as the soybean-producing nations of US, China, Brazil and Argentina, uncertainty regarding future yield changes is so large that decision-makers should adopt a precautionary principle to invest in climate change adaptation in the agricultural sector. In the absence of local validation we believe these estimates provide a general expectation of future staple crop yield changes under climate change. Amidst considerable uncertainty, the signal is sufficiently clear on the need for national and intergovernmental policies to anticipate national food security risks. As empirical data on yields, changing crop calendars and cropping systems become available at higher resolutions and time frequencies, it is critical to validate impact estimates and update IAM projections used in policymaking5,86. Systematic evaluations of uncertainty such as these will help food security policymakers and researchers understand the drivers of variation and biases in similar large-scale modelling exercises.

Methods

Objectives and scope

We performed statistical meta-analysis to understand potential climate impacts on crop yields and thus obtain estimates of potential calorie deficits under three emissions scenarios to the end of the century. To do this we fitted five model specifications including mixed effects models to account for correlation within and between studies, and quantified the relative magnitude of uncertainty attributable to model choice, sampling, missing data and GCMs from the CMIP6 ensemble. We converted projected yield change estimated by the preferred mixed model into measures of national calorie supply and compared them against measures of calorie demand to understand future impacts on food security.

Data, extraction and screening

CGIAR data includes 13,890 point estimates of yield change, temperature change, \(\hbox {CO}_2\) change, on-farm adaptation, and other variables extracted from 89 studies with varied methodologies that can be broadly categorised into either statistical regression models or crop biophysical process models13. Reviews of the strengths and weaknesses of the two different methodologies show that the results are comparable when aggregated85,87,88. We first reviewed and validated each of the 8846 estimates from 74 studies that are related to the four major crops maize, rice, soy, and wheat by reviewing the original studies (full list in Supplementary Information). We built a validation and cleaning database to manually record values identified from this review process as missing or mis-entered, and replaced them with correct values from the studies. We also verified that any missing values recorded in the CGIAR dataset were true missing values (i.e., not zero values).

Baseline growing-season temperatures and precipitation

To estimate location-specific baseline growing-season temperatures, we drew on global monthly 0.5\(^{\circ }\) degree gridded temperature data from the Climatic Research Unit (CRU TS v4.05) from 1950 to 201589. We then applied 0.5\(^{\circ }\) degree gridded crop calendar information on planting and harvesting dates in 2000 for the four crops from two complementary data sets circa 2000 on global crop planting dates90 and global monthly irrigated and rain-fed crop areas91. Crop baseline growing-season temperature was calculated for each grid cell location by first identifying the growing-season months for each crop, and then calculating average annual historical growing-season temperatures for each year from 1950 to 2015, and then calculating average growing-season temperatures across all years in the baseline period specified for each CGIAR estimate (a subset of the 1950–2015 period). Finally, crop baseline growing-season temperatures were aggregated to the country level, by taking a crop production-weighted average of grid cell values in each country. To do this we used a 0.5\(^{\circ }\) degree gridded data set on crop production circa 200092.

Data imputation

Of the 8846 point estimates in the CGIAR data, many values for key variables that were theoretically important for modelling crop yield responses to temperature change were missing. These included temperature change, precipitation change, \(\hbox {CO}_2\) change, yield change, and start and end years for the baseline period. We assume that missingness among the six key variables should be mostly missing at random, with possibly a few exceptions93,94. Listwise deletion of observations with missing values is one option, but fitting a model on complete cases only may bias the results. We therefore implemented a formal imputation procedure using Multiple Imputation by Chained Equations (MICE) to fill in missing values for five variables: baseline average growing-season temperature and precipitation, temperature change, yield change, precipitation change and \(\hbox {CO}_2\) change. MICE treats missing data as an explicit source of variation to be averaged over by Markov chain Monte Carlo (MCMC) simulation based on a fully conditional specification of probability distributions95,96,97. We adopted a multilevel Multiple Imputation approach that takes into account the clustered structure of our data98. We set the number of imputed datasets to five, and 30 iterations to be run in parallel, based on visual inspection of convergence patterns. We found that two-level predictive mean matching simulated observed values best (Supp. Fig. 2).

Model fitting

We fit 5 candidate models for each crop separately with percentage yield change as the response variable: OLS model, two GLMM and two GAMM models each fit with random intercepts only (RI) and with random intercepts and slopes (RS)99,100. These were estimated with Restricted Maximum Likelihood (REML) using the mgcv package in R99. We also tested models that weighted estimates by the inverse of variance in each study, as sometimes recommended in formal meta-analysis. However, study-wide variance can encompass meaningful variance across separate experiments (i.e. unique combinations of changes in temperature, precipitation and \(\hbox {CO}_2\)), and it was impractical to separate unique combinations of all three continuous variables into discrete categories.

The most complex model specification (that includes random intercepts and slopes) allows temperature change, precipitation change and \(\hbox {CO}_2\) change to vary randomly for each study. Model specifications for the response variable with an identity link function are written for GLMM with random intercepts and slopes in Eq. (2) (estimated with orthogonal polynomial terms) and for GAMM with random intercepts and slopes in Eq. (3). The distribution function is assumed normal based on inspection of fitted residuals in Supp. Fig. 10. The pooled OLS model specification is included in Eq. (4), and differs from earlier literature12 in two ways: response functions are separately estimated for each of the four crops, and do not include an interaction term between the quadratic temperature change term and baseline temperature.

Included parameters: \(\Delta Y_{ijk}\) is the percentage change in yield from point estimate i in country j and study k. \(\Delta T_{ijk}, \Delta CO_{2ijk}\) and \(\Delta P_{ijk}\) are the changes in temperature (degrees), \(\hbox {CO}_2\) concentration (ppm), and precipitation (%) for point estimate ijk, \(\bar{T}_{ji}\) and \(\bar{P}_{ji}\) are mean growing-season temperature and precipitation for country j over the baseline period specified for point estimate i, \(C_{3}\) and \(C_{4}\) are dummy variables indicating the crop photosynthetic metabolic pathway, and \(Adapt_{ijk}\) is a dummy variable indicating whether the point estimate includes on-farm adaptation (set to zero in all projections). As the response functions are estimated separately for each crop, \(C_3\) is equal to 1 and \(C_4\) equal to 0 for rice, soy and wheat, while \(C_4\) is equal to 1 and \(C_3\) equal to 0 for maize. Following12, we assume a concave function to account for the diminishing marginal positive effect of \(\hbox {CO}_2\) of the form \(f(\Delta CO_{2ijk}) = \frac{\Delta CO_{2ijk}}{\Delta CO_{2ijk}+A}\) where \(A=100\) for \(\hbox {C}_3\) crops (i.e. rice, soy wheat) and \(A=50\) for \(\hbox {C}_4\) crops (i.e. maize). Terms \(\Delta T_{k ^{:}}\), \(\Delta {P}_{k^{:}}\),Δ \(CO_{2k ^{:}}\) in the random slope terms represent the study-mean values. The term \(\nu _j\) is the random country intercept, \(\xi _{k0}\) is the random study intercept, \(\xi _{k1}\) is the random temperature slope varying by country, \(\xi _{k2}\) is the random precipitation slope varying by country, \(\xi _{k3}\) is the random \(\hbox {CO}_2\) slope varying by country, and \(\varepsilon _i\) is the residual error. Parameters \(f_{3}()\) and \(f_{4}()\) in Eq. (3) are smooth functions of \(\Delta T_{ijk}\) and \(\Delta P_{ijk}\) respectively. Each smooth function is a spline which is the sum of s smaller basis functions \(b_s\) with coefficient \(\beta _s\) evaluated at the values of x.

$$\begin{aligned} \begin{aligned} \Delta Y_{ijk}&\sim \mathcal {N}(\mu _{ijk}, \sigma ^2), \\ \end{aligned} \end{aligned}$$
(1)
$$\begin{aligned} \begin{aligned} \mu _{ijk} =&\alpha + \beta _1 Adapt_{ijk} + \beta _2 \Delta T_{ijk} * Adapt_{ijk} + \beta _3 f_1(\Delta CO_{1ijk})*C3 + \beta _4 f_2(\Delta CO_{2ijk})*C4 \\&+ \beta _5 \Delta T_{ijk} + \beta _6 \Delta P_{ijk} + \beta _7 \Delta T_{ijk} * \bar{T}_{ij} + \beta _8 \Delta P_{ijk} * \bar{P}_{ij} + \beta _9 \Delta T_{ijk} * \Delta P_{ijk} + \Delta T_{ijk}^2 + \Delta P_{ijk}^2 + \nu _j \\&+ \xi _{k0} + \xi _{k1}(\Delta T_{ijk} - \Delta T_{k ^{:}}) + \xi _{k2}(\Delta P_{ijk} - \Delta P_{k ^{:}}) + \xi _{k3}(f_1 (\Delta CO_{2ijk}) - f_1(\Delta CO_{2k ^{:}})) + \varepsilon _i, \end{aligned} \end{aligned}$$
(2)
$$\begin{aligned} \begin{aligned} \mu _{ijk} =&\alpha + \beta _1 Adapt_{ijk} + \beta _2 \Delta T_{ijk} * Adapt_{ijk} + \beta _3 f_1(\Delta CO_{2ijk})*C3 + \beta _4 f_2(\Delta CO_{2ijk})*C4 \\&+ \beta _5 \Delta T_{ijk} * \bar{T}_{ij} + \beta _6 \Delta P_{ijk} * \bar{P}_{ij} + \beta _7 \Delta T_{ijk} * \Delta P_{ijk} + f_3 (\Delta T_{ijk}) + f_4 (\Delta P_{ijk}) + \nu _j \\&+ \xi _{k0} + \xi _{k1}(\Delta T_{ijk} - \Delta T_{k ^{:}}) + \xi _{k2}(\Delta P_{ijk} - \Delta P_{k ^{:}}) + \xi _{k3}(f_1 (\Delta CO_{2ijk}) - f_1(\Delta CO_{2k ^{:}})) + \varepsilon _i, \end{aligned} \end{aligned}$$
(3)
$$\begin{aligned} \begin{aligned} \mu _{ijk} =&\alpha + \beta _1 Adapt_{ijk} + \beta _2 \Delta T_{ijk} * Adapt_{ijk} + \beta _3 f_1(\Delta CO_{2ijk})*C3 + \beta _4 f_2(\Delta CO_{2ijk})*C4 \\&+ \beta _5 \Delta T_{ijk} + \beta _6 \Delta T_{ijk}^2 + \beta _7 \Delta T_{ijk} * \bar{T}_{ij} + \beta _8 \Delta P_{ijk} + \varepsilon _i. \end{aligned} \end{aligned}$$
(4)

We ran these five different model specifications on each of the five imputed datasets, yielding 25 combinations of fitted estimates per crop. We then fit these to 23 sets of prediction data containing all model terms, including temperature, precipitation and \(\hbox {CO}_2\) change variables calculated from the CMIP6 ensemble of 23 GCMs provided by WorldClim for four future time periods: 2021–2040, 2041–2060, 2061–2080, 2081–2100101.

Model prediction

We created prediction data for each of the model terms. Baseline growing-season temperatures and precipitation were estimated using the same approach used to calculate the variable in the main data set, but for 2015 (Supp. Fig. 4). Gridded temperature and precipitation values for 2021–2040, 2041–2060, 2061–2080 and 2081–2100 were retrieved from 23 WorldClim bias-corrected CMIP6 GCM datasets for SSP1–2.6, SSP2–4.5 and SSP5–8.5 at a 10-min spatial resolution101. We estimated projected yields on each of the 23 GCM datasets individually. The 23 GCMs from the CMIP6 ensemble were: ACCESSCM2, ACCESS-ESM1-5, CanESM5, CanESM5-CanOE, CMCC-ESM2, CNRM-CM6-1, CNRM-CM6-1-HR, CNRM-ESM2-1, EC-Earth3-Veg, EC-Earth3-Veg-LR, FIO-ESM-2-0, GISS-E2-1-G, GISS-E2-1-H, HadGEM3-GC31-LL, INM-CM4-8, INM-CM5-0, IPSL-CM6A-LR, MIROC-ES2L, MIROC6, MPI-ESM1-2-HR, MPI-ESM1-2-LR, MRI-ESM2-0 and UKESM1-0-LL. The same 23 GCMs was used for scenario SSP1-2.6 but with the addition of GFDL-ESM4. We used the bioclimatic variables for annual mean temperature (BIO1) and annual precipitation (BIO12) converted to average monthly precipitation.

For global \(\hbox {CO}_2\) change, we used data on annual global \(\hbox {CO}_2\) concentrations calculated from the multi-model CMIP5 ensemble mean of 39 GCMs retrieved from Climate Explorer102, converted to changes in concentrations from 2015 levels. Historical \(\hbox {CO}_2\) levels were drawn from global observations103.

We predicted global gridded yield impacts across each of the four time periods using 5 imputed fit estimates \(\times\) 5 model specifications \(\times\) 4 crops (i.e. 100 model combinations), and on each of the 23 GCM outputs (i.e. 575 prediction combinations per crop, or 2300 prediction combinations in total). To obtain pooled results in Fig. 4, Supp. Figs. 5, 6 and 9, we pooled prediction fit and standard error estimates sequentially across each crop model specification’s imputation-specific model predictions and GCM-specific model predictions. We thus followed a ‘pool last’ approach that applies Rubin’s rules to the final estimate of interest, as doing so maintains between-imputation variability and accounts for non-linearities in their proper place104,105.

Modelled response functions and predicted fit estimates do not necessarily go through the origin (meaning a non-zero intercept exists), yet theory requires zero yield change with zero temperature change59,88. We performed post-hoc adjustments by estimating projected yields twice; once as described above (i.e., original) and once on adjusted prediction data where temperature, precipitation and \(\hbox {CO}_2\) changes are set equal to zero. We then subtracted the original predictions from yield changes predicted on zero change in climate variables.

Evaluating uncertainty

We quantified four different sources of uncertainty arising from model choice, sampling, missing data and CMIP6 multi-model variation across GCMs, following the approach in Ref.2. We fit and predicted on 100 block bootstrap samples per combination of model choice, crop, GCM and imputation-augmented dataset, yielding 230,000 predicted estimates of global production-weighted yield change in 2081–2100 (i.e. estimates calculated as global mean yield changes in percentage terms, weighted by gridded crop production volumes c. 200092). Bootstraps were blocked by study, meaning that a random set of studies and estimates therein are drawn in each bootstrap sample. We then estimated the crop production-weighted global mean yield change, yielding 575 estimates representing unique combinations of block bootstrap sample, imputation-augmented dataset, model choice and GCMs from the CMIP6 ensemble.

We characterised uncertainty from model choice by holding constant the imputation-augmented dataset, bootstrap sample and GCM output data used, varying the model specification and calculating the average standard deviation in global weighted yield change across model specifications. We characterised the other sources of uncertainty in the same way.

Food calorie gap

We estimated calorie supply and calorie demand using FAO data on country-scale production, import and export quantities and the share of crops allocated to food, average daily energy requirements, calories of energy supplied to the food system by crop and country, and detailed trade patterns (see “Methods” section)14,29. We also used crop calorie conversion factors from the literature30, gridded yield data and hectares harvested c. 2015 from a new high resolution global spatial dataset31 and population projections for SSP1–2.6, SSP2–4.5 and SSP5–8.5 developed by the International Institute for Applied Systems Analysis (IIASA)32.

To estimate baseline production in the year 2015 of maize, rice, soy and wheat in tons by country, we multiplied gridded hectares harvested (ha) by gridded yields (t/ha) in a spatial dataset with 5-min resolution31. We estimated the share of each country’s domestic supply of each crop allocated to the food system and the share of each country’s production of each crop that is exported, averaged across 2014–2016 using data from the FAO Food Balance Sheets14. We estimated the share of each country’s exports of each crop that are exported to each trade partner, averaged across 2014–2016 using data from the FAO Detailed Trade Matrix29. From this calculation we recovered each country’s imports of each crop by summing exports across importing partners. We used the FAO’s concordance between food products in the Detailed Trade Matrix and Food Balance Sheets (Supplementary Table 2). To estimate the domestic supply of maize, rice, soy and wheat in calories we applied calorie conversion factors for each crop from the literature to our estimate of domestic supply from production and imports in tons30. To estimate the total domestic supply of calories from all crops for each country, we scaled the four staple crop calories by their share of total calories supplied by all crops per country14. To estimate future production, we applied the gridded projected yield percentage changes from the GLMM random slopes model to baseline gridded yields and hectares harvested as described above. We repeated each of the steps to estimate total domestic supply of calories from all crops in each future time period.

These steps assume that the export share of country production and export partner share remain fixed in the future. We use data on harvested area data c. 201531, which assumes that harvest frequency and total standing cropland area remain fixed. These make our results conservative, as historical trends show that harvested land has increased in the last few decades35. Our results are also conservative due to the narrower selection of staple crop products represented in the gridded yields and hectares harvested dataset31 and thus in our estimates (Supplementary Table 2).

To estimate baseline calorie demand in the year 2015 by country, we multiplied annual per capita average daily energy requirements (ADER) averaged over 2014–2016 by population figures from FAOSTAT14. To estimate future calorie demand taking into account population growth but keeping dietary patterns fixed, we multiplied annual per capita ADER by SSP projections of country-level population counts from IIASA averaged across each of the 20-year future periods32. We calculated the calorie gap for each country as the supply of total calories subtracted from total calories demanded. A positive calorie gap indicates that a country is unable to meet national calorie demand from calories supplied by domestic production and imports. As we did this for the baseline year of 2015 and for each of the four 20-year periods from 2021 to 2100, we were able to determine the change in calorie gap from 2015 to future time periods.