Cycling and reciprocity in weighted food webs and economic networks

Mateusz Iskrzyński,Francesco Picciolo,Brian Fath,Franco Ruzzenenti,Freek Janssen

doi:10.1111/jiec.13217

Abstract

AbstractNetworks 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.

Highlights

Goods and services move between companies and consumers in an economy
Mass cycling in aquatic food webs has a very broad and skewed distribution that reflects the diversity of these networks
The generality of cycling and reciprocity patterns observed in food webs and economic networks relies on the availability and the reliability of empirical data

Summary

Introduction

Goods and services move between companies and consumers in an economy. Biomass flows between groups of organisms in ecosystems (Hannon, 1973) arise mostly from feeding relationships, and are known in ecology as food webs. The flows of mass in both systems define their fundamental, physical structure (Leontief, 1991). The mass flows are encoded as weights of links between vertices (nodes) that represent aggregated industries in economic input–output tables or groups of species in ecological food webs (Nebbia, 2000)

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