Phloem Catastrophe: Using Bifurcation Analysis to Predict Plant Tipping Points

A mathematical framework is developed to analyze phloem failure in plants using bifurcation analysis and catastrophe theory. The framework balances sucrose production from leaf photosynthesis modeled using stomatal optimality theory with sucrose transport through the much studied pressure-driven Münch mechanism. The model also integrated xylem water potential, osmotic gradients, and sucrose sink strength along the phloem. Systematic variation of key control variables, including xylem water potential and sucrose removal rate, reveals the emergence of multiple equilibria and identifies thresholds beyond which phloem transport becomes dynamically unstable to small perturbations. Phloem failure is shown to arise through an imperfect super-critical pitchfork bifurcation, characterized by two stable sucrose loading concentration states separated by an unstable intermediate one. The lower concentration stable state was within the range of sucrose loading values reported in the literature. Such phloem catastrophe was mathematically analogous to critical transitions in other eco-hydrological systems including xylem cavitation in plants. The analysis provides a mechanistic basis for quantifying phloem vulnerability and indicates that vascular stability requires coordination and balance between photosynthetic demand and phloem hydraulic capacity.