Simulated diffusion dynamics in river networks

Abstract River networks and the associated riparian zones are important landscape elements. The movement of organisms within river or riparian networks can be regarded as a diffusion process. The dynamics of diffusion in such networks will depend upon an interplay of (1) the geometry of the network, (2) the movement behavior of individual organisms, and (3) the spatiotemporal scale of observation. We examine the interplay of these factors by simulating unbiased and biased random walks on two types of artificial river networks. The resulting diffusion dynamics often depart strongly, both quantitatively and qualitatively, from classical (Fickian) dynamics. Measures of diffusive behavior, such as mean squared displacement and mean number of sites visited, can typically be described as power-law functions of time. However, the exponents of power laws often have non-classical values, and crossovers between different power-law behaviors at different temporal scales are common. Many qualitative features of the simulated diffusion dynamics are explicable in terms of network geometry; the potential role of tributaries in impeding diffusion is particularly apparent. An understanding of diffusion dynamics is likely to be a key factor in predicting rates of gene flow, spread of diseases or invading species, predator-prey interactions, and other ecological processes in river networks.