Expansion Dynamics Of Cooperatively Growing Populations On Networks

Species' range expansion to new areas may reduce local competition,give access to new resources, and cope with changing climates. As a result the pro-cess of range expansion is not only crucial to the survival of populations under constantly shifting environments, but also plays an important role in the mainte-nance of biodiversity, the stability of ecological communities, and the functioning of ecosystems. Range expansion is driven by the interactions among individual-and population-level processes and the spatial pattern of habitats. Existing re-searches primarily focus on one or two dimensional linear spaces, however the spatical structures of ecosystems in nature are usually very complex and the relating researches are still absent.To capture the effects of complex spatial structures, we study how cooper-atively growing populations spread on networks which represent the skeleton of complex landscapes in this work. By separating the slow and fast variables of the expansion process, we are able to give analytical predictions for the critical conditions that divide the dynamic behaviors into different phases (extinction,localized survival, and global expansion). We observe a resonance phenomenon in how the critical condition depends on the expansion rate, indicating the exis-tence of an optimal strategy for global expansion. To mimic the real ecological systems, we then apply theoretical analysis and numerical calculations and in-vestigate how the expanding processes can be altered by the system's different features including heterogeneity in degree distribution, local clusters, multiple seed nodes,system size and heterogeneity of local environments. Our results highlight the importance of both the underlying interaction pattern and migra-tion rate of the expanding populations for range expansion. We also discuss potential applications of the results to biological control and conservation.