The SI compartment model describes embolism spreading in networks of vessels and bordered pits in angiosperm xylem

Abstract

Plant xylem consists of a network of interconnected vessels, through which water is transported under negative pressure. Filling of vessels with air, or embolism, disturbs this transport process and, in extreme cases, leads to tree mortality. Despite this significance, embolism propagation dynamics are still poorly understood, primarily because xylem is opaque to direct observation. Furthermore, existing models of embolism spreading build excessively on physiological and anatomical parameters, and many misrepresent the inter-vessel pit membrane as a 2D surface. Here, we first extend these physiological models by implementing the pit membrane as a 3D object. Then, we introduce a susceptible-infected (SI) model, a simple stochastic model for tracking spreading through a population, for embolism propagation. After correctly fitting the spreading probability, our SI model reproduces vulnerability curves produced by both the physiological model and empirical data, highlighting that the SI model can address embolism spreading dynamics in plant species, for which detailed physiological data are not available. Furthermore, relating the SI model to the physiological one allows interpreting embolism spreading as a directed percolation process. Elucidating the exact mapping between directed percolation and embolism spreading will likely yield new fundamental insights into the relationships between xylem network architecture and embolism dynamics.