Topological rethinking: structure, dynamics and stability of ecological systems
The structural architecture of ecological systems evolves across space and time, with profound implications for biodiversity conservation. Through the combined use of spectral graph theory and topological zigzag persistence, we previously unveiled the spatio-temporal evolution of an Algerian charophyte metacommunity, laying the foundations for a multi-purpose prioritization of conservation actions based on the relative role of nodes in preserving topological structures. In this study, we shifted focus from structural evolution to the evolution of dynamical responses to perturbation as shaped by the changing topology. To this end, we extended spectral graph theory to higher-order interactions, investigating how disturbance diffuses among communities, how it circulates along cyclic pathways, and how node- and edge-level perturbations couple to produce a unified picture of propagation across the whole system. Through targeted node removal, we further simulated how topological changes induced by the loss of specific communities translate into functional changes in system-wide responses to disturbance. Our results reveal stable seasonal oscillations, with the metacommunity cyclically moving across stages of high and low susceptibility to disturbance, alongside dramatic shifts induced by node removal - even with modest topological alterations - that either dampen or amplify metacommunity vulnerability. Overall, this framework moves beyond a purely structural description of ecological networks toward a dynamic understanding of how they absorb, transmit or attenuate perturbations.