Network analysis reveals phase transitions in agro-food nitrogen systems with contrasting feeding capacity and land requirement

Abstract

Agro-food transitions are commonly assessed using optimization models or scenario approaches that return a single feasible configuration. These approaches provide estimates of system performance but limited information on feasible nitrogen cycling configurations. In this study, we develop a network-based modelling framework to characterize alternative steady-state configurations of agro-food nitrogen systems and identify phase transitions between these configurations. We formulate a continuous-time compartmental network model in which production, allocation, recycling, and losses are represented as mass-conserving flows. The system is analyzed under steady-state conditions. A coarse-graining procedure identifies dominant recycling cycles and derives aggregate indicators describing system configuration. The model is parameterized using French reference data and applied to case studies covering fertilization, livestock, and dietary patterns. The analysis identifies distinct steady-state configurations of the nitrogen network, separated by phase transitions in dominant recycling structures. These transitions correspond to changes in system performance indicators. For the French reference system, cropland-based feeding capacity is about 8.7 people per hectare of cropland (depending on constraints), while strict dietary autonomy requires about 19.7 million hectares of agricultural land. Reducing synthetic fertilization without changes in diet or nitrogen sourcing leads to higher land requirements or greater dependence on external inputs. The framework provides a method for mapping feasible nitrogen system configurations and analyzing phase transitions in agro-food nitrogen networks under alternative parameters and constraints.