It's contagious: calculation and analysis of xylem vulnerability to embolism by a mechanistic approach based on epidemic modeling

Vulnerability of xylem to embolism is expressed by vulnerability curves (VC) depicting accumulating loss of hydraulic conductivity against mounting pressure stress. VCs are obtained experimentally by curve fitting, providing important benchmark data on vulnerability of a species, organ, or other specific xylem categories. Since embolism spread by air seeding represents principally an epidemic process, a method based on epidemic modeling is introduced in this contribution which allows rapid and efficient calculation of continuous VC directly from mechanistic equations. The approach is based on the classic SIR model which considers the population to be divided into susceptibles S (functional), infectives I (embolized), and "removed" R individuals (embolized conduits which have exhausted their capacity to pass gas to their neighbors). It is also possible to consider xylem which is composed of different conduit groups (differing in interconnectivity and/or conduit vulnerability). The approach is able to reconstruct all sorts of VC shapes on the basis of two key parameters of embolism, conduit vulnerability and interconnectivity, and the amount of native embolism (initial proportion of I and R conduits). The effect of I and R conduits on VC is different. High initial I leads to non-sigmoidal VC, whereas high initial R promotes sigmoidal VC. Heterogeneous conduit populations being composed of conduit groups of different sizes, interconnectivities, and conduit vulnerabilities can also lead to non-sigmoidal VC with complex shapes.