Scaling of connectivity metrics in river networks

Abstract

Rivers exhibit fractal-like properties that are associated with scaling laws linking geometry and size. The optimal channel network (OCN) model, which is a mathematically tractable representation of river networks often used in theoretical studies, is based on the fractal properties of rivers and consequently reproduces geometric scaling laws. However, purely geometric relationships may not fully capture the interaction between river structure and species' movement strategies that is most relevant to many large-scale ecological processes. In contrast, connectivity, which is a concept that blends habitat geometry and individual movement, has been shown both theoretically and empirically to influence relevant large-scale ecological outcomes across a broad array of ecosystems. Here, we analyze networks from more than 1000 major rivers around the world, including the Amazon, Mississippi, and Nile, to investigate how river network connectivity metrics scale with system size. Specifically, we found clear power-law scaling of both the harmonic centrality and betweenness centrality network connectivity metrics. To assess the extent to which OCNs can capture these empirical connectivity patterns, we generated synthetic river networks by fitting an OCN model to each real river. We found excellent agreement between empirical and OCN-based scaling laws, supporting the notion that OCNs can accurately represent rivers in network-based models and analyses. Finally, we examined the robustness of the connectivity scaling laws to species movement strategies ranging from ideal shortest-path navigation to suboptimal random-path navigation. Surprisingly, we found that random navigation breaks the power-law scaling relationship for harmonic centrality, but not for betweenness centrality.