Cycling and reciprocity in weighted food webs and economic networks

Networks of mass flows describe the basic structure of ecosystems as food webs, and of economy as input–output tables. Matter leaving a node in these networks can return to it immediately as part of a reciprocal flow, or completing a longer, multi‐node cycle. Previous research comparing cycling of matter in ecosystems and economy was limited by relying on unweighted or few networks. Overcoming this limitation, we study mass cycling in large datasets of weighted real‐world networks: 169 mostly aquatic food webs and 155 economic networks. We quantify cycling as the portion of all flows that is due to cycles, known as the Finn Cycling Index (FCI). We find no correlation between FCI and the largest eigenvalues of unweighted adjacency matrices used as a cycling proxy in the past. Unweighted networks ignore the actual flow values that in reality can differ by even 10 orders of magnitude. FCI can be decomposed into a sum of contributions of individual nodes. This enables us to quantify how organisms recycling dead organic matter dominate mass cycling in weighted food webs. FCI of food webs has a geometric mean of 5%. We observe lower average mass cycling in the economic networks. The global production network had an FCI of 3.7% in 2011. Cycling in economic networks (input–output tables and trade relationships) and food webs strongly correlates with reciprocity. Encouraging reciprocity could enhance cycling in the economy by acting locally, without the need to perfectly know its global structure.