Transport on fractal river networks: Application to migration fronts

A quantitative model of the US colonization in the 19th century is presented. We explore the idea that landscape heterogeneities should have strongly affected this process, as the need for water made the colonizers follow the routes of main rivers and set up their towns near them. So, we study transport processes on fractal networks modeling river basins, a case which may have a great ecological relevance for the study of hydrochory, and in general for species which spread along corridors. The analytical reaction–diffusion model presented here allows to predict the propagation rate of fronts spreading through Peano-like basins, and comparison with the Optimal Channels Network model is also reported. Finally, the propagation rates observed are compared with the results from our model, concluding that migration through fractal media, in spite of being a mathematical idealization of the problem, mimics the dynamics of real systems reasonably well.