Throughflow centrality is a global indicator of the functional   importance of species in ecosystems
  To better understand and manage complex systems like ecosystems it is critical to know the relative contribution of system components to system functioning. Ecologists and social scientists have described many ways that individuals can be important; This paper makes two key contributions to this research area. First, it shows that throughflow, the total energy-matter entering or exiting a system component, is a global indicator of the relative contribution of the component to the whole system activity. It is global because it includes the direct and indirect exchanges among community members. Further, throughflow is a special case of Hubbell status as defined in social science. This recognition effectively joins the concepts, enabling ecologists to use and build on the broader centrality research in network science. Second, I characterize the distribution of throughflow in 45 empirically-based trophic ecosystem models. Consistent with expectations, this analysis shows that a small fraction of the system components are responsible for the majority of the system activity. In 73% of the ecosystem models, 20% or less of the nodes generate 80% or more of the total system throughflow. Four or fewer dominant nodes are required to account for 50% of the total system activity. 121 of the 130 dominant nodes in the 45 ecosystem models could be classified as primary producers, dead organic matter, or bacteria. Thus, throughflow centrality indicates the rank power of the ecosystems components and shows the power concentration in the primary production and decomposition cycle. Although these results are specific to ecosystems, these techniques build on flow analysis based on economic input-output analysis. Therefore these results should be useful for ecosystem ecology, industrial ecology, the study of urban metabolism, as well as other domains using input-output analysis. 
Stuart R. Borrett
q-bio.QM physics.soc-ph q-bio.PE