Modeling and Analyzing Xylem Vulnerability to Embolism as an Epidemic Process

Abstract

Xylem vulnerability to embolism can be quantified by "vulnerability curves" (VC) that are obtained by subjecting wood samples to increasingly negative water potential and monitoring the progressive loss of hydraulic conductivity. VC are typically sigmoidal, and various approaches are used to fit the experimentally obtained VC data for extracting benchmark data of vulnerability to embolism. In addition to such empirical methods, mechanistic approaches to calculate embolism propagation are epidemic modeling and network theory. Both describe the transmission of "objects" (in this case, the transmission of gas) between interconnected elements. In network theory, a population of interconnected elements is described by graphs in which objects are represented by vertices or nodes and connections between these objections as edges linking the vertices. A graph showing a population of interconnected xylem conduits represents an "individual" wood sample that allows spatial tracking of embolism propagation. In contrast, in epidemic modeling, the transmission dynamics for a population that is subdivided into infection-relevant groups is calculated by an equation system. For this, embolized conduits are considered to be "infected," and the "infection" is the transmission of gas from embolized conduits to their still water-filled neighbors. Both approaches allow for a mechanistic simulation of embolism propagation.

Keywords: Embolism; Epidemic model; Model; Network theory; SIR model; Vulnerability curves; Xylem.