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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 studies^{1,2,3,4,5,6,7}. Predictions from such models are highly relevant to climate policyclimate 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 production^4,8. 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 studiesthe technique of meta-analysisis 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 dataset^10,11. 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 dataset^4,12. 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.