Safe Operating Regimes for Phloem Carbon Transport: A Bifurcation Framework

A mathematical framework is developed to quantify the stability of phloem transport and delineate “safe operating” regimes using bifurcation analysis. Sucrose production is linked to leaf photosynthesis using stomatal optimality, while sucrose translocation follows pressure-driven flow based on the Munch mechanism. The model couples xylem water potential, osmotic driving force, hydraulic resistance (using a sucrose-dependent viscosity), and distributed sink removal along the transport pathway. Systematic variation of key carbon transport controls, such as xylem water potential and sink strength, reveals multiple equilibria and stability boundaries beyond which phloem transport becomes unstable to small carbon loading fluctuations. Phloem failure emerges through a saddle-node bifurcation, yielding two stable sucrose loading states separated by an unstable branch where the lower equilibrium falls within reported sucrose loading ranges. The resulting stability maps provide a mechanistic basis for phloem vulnerability and suggest that vascular safety requires coordination between photosynthetic supply (e.g., $V_{c,max}$), pathway length, and transport capacity as water potential declines. This stability map provides a mechanistic constraint that can inform trait-based ecosystem modeling and provide hypotheses about acclimation and vulnerability across environments.