  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.
