Ecological network analysis for a virtual water network.

The notions of virtual water flows provide important indicators to manifest the water consumption and allocation between different sectors via product transactions. However, the configuration of virtual water network (VWN) still needs further investigation to identify the water interdependency among different sectors as well as the network efficiency and stability in a socio-economic system. Ecological network analysis is chosen as a useful tool to examine the structure and function of VWN and the interactions among its sectors. A balance analysis of efficiency and redundancy is also conducted to describe the robustness (RVWN) of VWN. Then, network control analysis and network utility analysis are performed to investigate the dominant sectors and pathways for virtual water circulation and the mutual relationships between pairwise sectors. A case study of the Heihe River Basin in China shows that the balance between efficiency and redundancy is situated on the left side of the robustness curve with less efficiency and higher redundancy. The forestation, herding and fishing sectors and industrial sectors are found to be the main controllers. The network tends to be more mutualistic and synergic, though some competitive relationships that weaken the virtual water circulation still exist.