A topological perspective on the spatiotemporal evolution of meta-communities – insights from Algerian charophytes

The study of the spatiotemporal evolution of ecological systems is steadily gaining prominence in conservation biology, especially for meta-populations and meta-communities, where entangled spatial and temporal dynamics jointly determine their persistence and evolution. In this context, topological approaches and the theory of homology group persistence can be effectively adopted to track temporal changes, at local to global scales, in the spatial structure of ecological systems and to derive references for their evolutionary trajectories. Here, we demonstrate how temporal changes in meta-community topology can shed light on the dynamics of endangered species. Specifically, our approach leverages over data-driven derivation of topological features through the unraveled voting algorithm and on zigzag persistence for the analysis of their temporal changes, using seasonal data of charophyte communities (one of the most threatened groups of macroalgae worldwide) from 21 Algerian ponds. Results reveal steady seasonal oscillations in connectivity and centrality, with regular annual cycles of formation and destruction of transient topological features and robust structures forming a backbone persisting throughout the time. On the one hand, findings provide crucial insights into the spatial evolution of the Algerian charophyte meta-community, defining references to evaluate the effects of local to global pressures and fostering informed prioritization of conservation efforts. On the other hand, the approach goes beyond the dynamics of topological structures embedded in metric spaces, allowing the understanding of the spatiotemporal evolution of every kind of ecological system.