Self-similarity and vanishing diffusion in fluvial landscapes

Complex topographies exhibit universal properties when fluvial erosion dominates landscape evolution over other geomorphological processes. Similarly, we show that the solutions of a minimalist landscape evolution model display invariant behavior as the impact of soil diffusion diminishes compared to fluvial erosion at the landscape scale, yielding complete self-similarity with respect to a dimensionless channelization index. Approaching its zero limit, soil diffusion becomes confined to a region of vanishing area and large concavity or convexity, corresponding to the locus of the ridge and valley network. We demonstrate these results using one dimensional analytical solutions and two dimensional numerical simulations, supported by real-world topographic observations. Our findings on the landscape self-similarity and the localized diffusion resemble the self-similarity of turbulent flows and the role of viscous dissipation. Topographic singularities in the vanishing diffusion limit are suggestive of shock waves and singularities observed in nonlinear complex systems.

Density-Dependent and Species-Specific Effects on Self-Organization Modulate the Resistance of Mussel Bed Ecosystems to Hydrodynamic Stress

AbstractSelf-organized, regular spatial patterns emerging from local interactions among individuals enhance the ability of ecosystems to respond to environmental disturbances. Mussels self-organize to form large, regularly patterned biogenic structures that modify the biotic and abiotic environment and provide numerous ecosystem functions and services. We used two mussel species that form monospecific and mixed beds to investigate how species-specific behavior affects self-organization and resistance to wave stress. Perna perna has strong attachment but low motility, while Mytilus galloprovincialis shows the reverse. At low density, the less motile P. perna has limited spatial self-organization compared with M. galloprovincialis, while when coexisting, the two species formed random spatial patterns. At high density, the two species self-organized in similar ways, while when coexisting, patterns were less strong. Spatial pattern formations significantly shaped resistance to hydrodynamic stress. At low density, P. perna beds with strong attachment and M. galloprovincialis beds with strong spatial organization showed higher retention rates than mixed beds. At high density, the presence of strongly attached P. perna significantly increased retention in mixed and P. perna beds compared with M. galloprovincialis beds. Our study emphasizes the importance of the interplay of species-specific behaviors to spatial self-organization and stress tolerance in natural communities.