Walk partitions of flow in Ecological Network Analysis: Review and synthesis of methods and indicators

Abstract

Abstract Ecological Network Analysis (ENA) has provided insights into the structure, function, and transformation of ecosystems for more than forty years. Key insights from ENA focus on how the patterns of directed weighted transactions among system components (e.g., species, functional groups, economic sectors) create emergent and often unexpected relationships in ecosystems that affect system function and sustainability. Flow analysis, also called throughflow analysis, is one of several core techniques in ENA. Generally, it traces the flux of energy or matter through the network from inputs to outputs. During the forty-years of development, flow analysis has accreted multiple extensions and modifications. In this concept and synthesis paper, we review four flow analyses and show how they are conceptually linked by partitioning flows across subsets of pathways within networks. These flow analyses include: (1) the definition of throughflow, a measure of the total processing power of a network; (2) Leontief’s decomposition based on walk length, indicating the direction and distance of energy or matter flow; (3) Finn’s measure of recycling of matter in networks; and (4) five mode analysis, characterizing flows according to their origin and destination. Presenting these techniques side-by-side with a common conceptual framework reveals overlaps and distinctive elements among the analytic products. This synthesis clarifies the flow analyses tools and their applications to ecological and socio-economic networks and provides example applications. Further, new insights are presented by combining existing flow analyses to calculate novel indices that further characterize the flow structure of networks. For example, both indirect flows in networks and cycling are highly important features in networks. In order to determine the proportion of indirect flows generated through cycling, we can use the ratio of Cycled Flow identified from Finn’s analysis and the indirect flows identified in the Leontief analysis. As ENA matures through additional analysis development and applications, it will continue to provide insights into ecosystems and contribute to the broader area of network science.