Individual-level evolutions manifest population-level scaling in complex supply networks

Scaling in complex supply networks is a population-level optimization phenomenon thought to arise from the evolutions of the underlying individual networks, but the evolution-scaling connection has not been empirically demonstrated. Here, using individually resolved, temporally serial, and population-scope datasets from public water supply networks, we empirically demonstrate this connection. On the log-log plot, structural properties of individual supply networks trace out evolutionary paths describable as linear projectiles, each characterized by a slope reflecting optimized physical economies of scale and an intercept reflecting morphological adaptation to settlement contexts. The universality in scaling slope coexists with the variability in scaling intercept, so that networks of diverse morphologies advance in time along a “common evolutionary track.” This cross-level observation establishes that individual-level dynamic evolutions cumulatively manifest population-level optimal scaling in complex water supply networks.