Predicting the structure and mode of vegetation dynamics: An application of graph theory to state-and-transition models

The recent literature suggests that the network structure of ecological states within a system can determine whether the system's response to environmental changes is reinforced by positive feedback mechanisms (amplification); rapidly propagated throughout the entire network of states (synchronization); or structurally constrained. The purpose of this research was to predict these various modes of system dynamics in the context of vegetation change represented as state-and-transition models (STMs) at a salt marsh of the Danish Wadden Sea. In the STM framework, several different plant communities identified by a classification approach were regarded as multiple alternative “states,” with “transitions” defined by observed transformations among the communities over time. Treating these STMs as mathematical graphs, three metrics from algebraic graph theory—spectral radius, algebraic connectivity, and S-metric—were calculated to characterize the degree of amplification, synchronization, and structural constraint, respectively. Results demonstrated that observed vegetation dynamics underwent stronger amplification and synchronization, and weaker constraint than hypothesized benchmark patterns such as linear sequential, cyclic, convergent, and divergent dynamics. These findings indicate that, as marsh development proceeds through vegetation processes, the connectivity among plant communities becomes enhanced, which corresponds to a higher possibility for abrupt and complex system reorganization in response to environmental changes (e.g., gradual sea-level variations and storm surges). In this way, the coupled graph theory and STM approach contributes to identifying holistic properties of an ecological system that are otherwise not evident from the conventional theories (e.g., the continuum concept) and methodologies (e.g., gradient analysis).