Food production significantly impacts the environment, driving deforestation and freshwater withdrawals. Human pressures may have exceeded the Earth's safe operating space, increasing the risk of irreversible environmental change. Existing studies provide initial quantitative estimates of interactions among Earth system processes, suggesting that cascades and feedbacks amplify human impacts. However, many interactions relevant to food production remain unquantified, particularly concerning marine processes. Achieving sustainable food futures likely necessitates greater food system reforms than previously considered. Analyzing these interactions is challenging due to unknown interaction strengths, context specificity, and limitations of spatial models. This research focuses on four key Earth system processes (biogeochemical flows, biosphere integrity (BI), freshwater use, and land system change), divided into seven control variables (BI land, BI freshwater, BI ocean, land system change, biogeochemical flows, blue water (high and low flow), and green water). These processes are bottom-up in nature, unlike top-down processes like climate change. The study aims to understand the richness and strength of interactions among these processes.

The literature review highlights the significant environmental impacts of food production, particularly biodiversity loss, eutrophication, and overexploitation of marine resources. It emphasizes that human pressures may have pushed the Earth system beyond its safe operating space, as defined by planetary boundaries. Existing studies have provided some quantitative estimates of interactions among Earth system processes, but many interactions relevant to food production remain unquantified. These gaps are particularly pronounced for marine processes. The existing literature emphasizes the need for more comprehensive quantitative understanding of Earth system interactions to inform sustainable food production strategies.

This study employed a two-round expert knowledge elicitation following the IDEA (investigate, discuss, estimate, aggregate) protocol. The elicitation focused on a hypothetical 100 km² area with control variables within safe ranges, allowing assessment of state-dependent interactions. Experts evaluated interactions between the seven control variables, providing lower and upper plausible values, best estimates, and confidence intervals. A scenario-based technique guided experts' inferences relative to a fixed baseline, facilitating exploration of a wider range of interactions compared to model-based approaches. The data were aggregated using quantile aggregation after fitting individual expert responses with a PERT distribution. Interaction strengths were calculated by normalizing control variables relative to their theoretical natural states and estimating the ratio of normalized changes between variables. The study also analyzed mediating mechanisms and created a prioritization scheme for future research based on interaction strength and uncertainty.

Experts identified 37 direct biophysical interactions (out of a possible 54), indicating considerable local interconnections among Earth system processes. Strong impacts on aquatic biodiversity (BI freshwater and BI ocean) were observed, particularly from changes in blue water, biogeochemical flows, and BI land. Green water and land system change were involved in many strong interactions, such as the impact of decreased soil moisture on blue water and land system change. Few interactions were attenuating; land system change to blue water was the only strongly attenuating interaction identified (locally). Many interactions were extremely weak, possibly due to context-specific occurrences or complexity beyond simplified linearity assumptions. Seven interactions were quantified at a global scale in prior literature, and this study's findings agree on interaction direction, with some differences in strength. The three Earth system processes with the most connections were BI land, land system change, and green water. Three main categories emerged: processes mainly receiving impacts, processes mainly originating impacts, and processes acting as mediators. The study mapped a network of mediating mechanisms, highlighting the complex and interconnected nature of interactions and the potential for synergistic actions. A prioritization scheme was created for future research, focusing on strong interactions with high uncertainty and/or limited current knowledge.

The findings address the research question by quantifying the strength and direction of interactions among Earth system processes relevant to food production. The results highlight the complex interplay between these processes, suggesting a need for holistic approaches to sustainable food production. The identification of mostly amplifying interactions indicates that the safe operating space may be more constrained than previously thought. However, the study also identifies potential synergies, suggesting that alleviating pressure on one process can simultaneously benefit others. The study’s prioritization scheme can guide future research efforts, focusing on high-impact interactions with high uncertainty and potential for unexpected consequences. The integration of expert knowledge contributes valuable insights into complex interactions where data are scarce, particularly considering the challenge of modeling the entirety of the Earth system.

This study provides a systems view of Earth system interactions relevant to food production, quantifying interaction strengths and mapping mediating mechanisms. The findings highlight the crucial roles of BI components, green water, land system change, and biogeochemical flows, and reveal the complex interconnectedness of these processes. The prioritization scheme guides future research towards high-impact interactions needing further investigation. This work contributes to a more comprehensive understanding of Earth system limits, supporting improved Earth system modeling and informing sustainable food production strategies.

The study's reliance on expert elicitation introduces inherent uncertainties associated with subjective judgements. The hypothetical scenario used may not fully capture the complexity and diversity of real-world situations. The limited number of responses for some interactions increased uncertainty in the results. Regional variations in interaction strengths and mechanisms were not fully captured due to insufficient region-specific responses.