Functional Integration of Ecological Networks through Pathway   Proliferation
  Large-scale structural patterns commonly occur in network models of complex systems including a skewed node degree distribution and small-world topology. These patterns suggest common organizational constraints and similar functional consequences. Here, we investigate a structural pattern termed pathway proliferation. Previous research enumerating pathways that link species determined that as pathway length increases, the number of pathways tends to increase without bound. We hypothesize that this pathway proliferation influences the flow of energy, matter, and information in ecosystems. In this paper, we clarify the pathway proliferation concept, introduce a measure of the node--node proliferation rate, describe factors influencing the rate, and characterize it in 17 large empirical food-webs. During this investigation, we uncovered a modular organization within these systems. Over half of the food-webs were composed of one or more subgroups that were strongly connected internally, but weakly connected to the rest of the system. Further, these modules had distinct proliferation rates. We conclude that pathway proliferation in ecological networks reveals subgroups of species that will be functionally integrated through cyclic indirect effects. 
Stuart R. Borrett, Brian D. Fath, Bernard C. Patten