The influence of the migration network topology on the stability of a small food web

The stability of ecosystems as well as the relation between topology and dynamics on multilayer networks are important questions that are usually discussed in separate communities. Here, we combine these two topics by investigating the influence of the topology of the migration network on the stability of a four-species foodweb module on six patches. The parameters are chosen such that the dynamics on an isolated patch have a periodic attractor with all four species present as well as an attractor where the prey that is preferred by the top predator dies out. The stability measure used here is robustness, which is the average proportion of surviving species in the system, and which shows a complex dependence on the migration rate. We use principal component analysis to quantify the migration network structure in terms of the most relevant network measures, and we evaluate correlations between these measures and characteristics of the robustness curves. Our most important findings are that higher connectivity of the migration network leads to a larger maximum robustness, that a broad distribution of connectivities favors extinction of the preferred prey at intermediate migration rates, and that migration topologies with a larger betweenness centrality are more prone to extinction of the preferred prey at the onset of synchronization. Our study thus demonstrates a strong correlation between dynamical robustness and spatial topology and can serve as an example for similar studies in other types of multilayer networks.