A mathematical model of national-level food system sustainability

TL;DR

This paper introduces a mathematical model to assess national food system sustainability, focusing on supply, trade, demand, and prices, and applies it to the UK pork industry to identify vulnerability thresholds.

Contribution

It presents a stylised mathematical framework for analyzing food system sustainability and demonstrates its application to real-world data, highlighting critical dependence on imports.

Findings

UK pork industry is currently sustainable.

Dependence on imports exceeds 50%, risking collapse.

Model identifies critical self-sufficiency threshold.

Abstract

The global food system faces various endogeneous and exogeneous, biotic and abiotic risk factors, including a rising human population, higher population densities, price volatility and climate change. Quantitative models play an important role in understanding food systems' expected responses to shocks and stresses. Here, we present a stylised mathematical model of a national-level food system that incorporates domestic supply of a food commodity, international trade, consumer demand, and food commodity price. We derive a critical compound parameter signalling when domestic supply will become unsustainable and the food system entirely dependent on imports, which results in higher commodity prices, lower consumer demand and lower inventory levels. Using Bayesian estimation, we apply the dynamic food systems model to infer the sustainability of the UK pork industry. We find that the UK pork industry is currently sustainable but because the industry is dependent on imports to meet demand, a decrease in self-sufficiency below 50% (current levels are 60-65%) would lead it close to the critical boundary signalling its collapse. Our model provides a theoretical foundation for future work to determine more complex causal drivers of food system vulnerability.