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

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. The current network models of embolism spreading from embolised vessels to their sap-filled neighbours use an excessive number of parameters related to xylem physiology and anatomy. Further, most of these models interpret the intervessel pit membrane as a 2D surface. Here, we first extend the existing physiological network models of embolism spreading by implementing a 3D pit membrane model. Then, we introduce a susceptible-infected (SI) spreading model for embolism propagation. After correct fitting of the spreading probability, our SI model produces vulnerability curves matching those produced by the physiological model or extracted from empirical data. This demonstrates that the SI model can address embolism spreading dynamics also in plant species, for which detailed physiological data are not available. The combination of the SI model and intervessel network structure allows interpreting embolism spreading as an instance of directed percolation, suggesting that xylem hydraulics fail merely due to break-down of the intervessel network than loss of sap in plant tissue.