Emergence of efficient channel networks in fluvial landscapes

Abstract

It is believed that channel networks across fluvial landscapes are self-organized into fractal patterns in order to minimize energy expenditure, as evidenced by the similarities between computer-generated optimal channel networks (OCNs) and real networks. However, the specific mechanisms driving such energy minimization remain largely elusive. Here, we propose that the energy minimization tendency of channel networks results from the ‘hierarchical’ role of randomness in their evolution – flow direction is more likely to change at lower flow-accumulation areas, and vice versa. The proposed probabilistic growth model then employs a power function to simulate channel-network evolution, where exponent (η) quantifies the role of randomness such that greater η would ensure less randomness and more network stability. Any positive η leads to an asymptotic decrease in energy expenditure implying that energy minimization is merely a consequence of adaptive evolutionary processes rather than an intended goal. Interestingly, the most efficient networks are consistently observed to emerge at η = 0.5, implying a delicate balance between randomness and the forces resisting change as a necessary condition for the emergence of the most efficient networks. Thus, the proposed framework holds promise for explaining the evolution of other tree-like networks in nature and for developing more efficient optimization methods for practical applications.