Classical models in theoretical ecology often neglect spatial structure and species displacement. Both components are essential to understand the propagation of bacterial communities in natural environments (e.g. the animal gut or the soils). In particular, we want to understand the effect of transport in these complex ecosystems. How is space modifying the resilience of ecosystems? If species can diffuse in the system, will there be ecological niches appearing at different places? How does space introduce correlations between species interactions (preys, predators, cooperation, competition)? For ecosystem advected by a fluid (e.g. phytoplanktons), what is the impact of the flow on the biodiversity? The candidate is expected to be eager to interact with ecologists and biophysicists. The study will combine theory of complex systems, dynamical system analysis, and numerical simulations to identify phase transitions between stable, oscillatory, or chaotic regimes, and to characterize their spatial signatures (fragmentation, patches, invasion fronts). The results will contribute to a deeper understanding of the collective mechanisms driving biodiversity and the robustness of complex ecosystems.