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Stability-instability transition in tripartite merged ecological networks

Lookup NU author(s): Dr Clive Emary



This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


Although ecological networks are typically constructed based on a single type of interaction, e.g. trophic interactions in a food web, a more complete picture of ecosystem composition and functioning arises from merging networks of multiple interaction types. In this work, we consider tripartite networks constructed by merging two bipartite networks, one mutualistic and one antagonistic. Taking the interactions within each sub-network to be distributed randomly, we consider the stability of the dynamics of the network based on the spectrum of its community matrix. In the asymptotic limit of a large number of species, we show that the spectrum undergoes an eigenvalue phase transition, which leads to an abrupt destabilisation of the network as the ratio of mutualists to antagonists is increased. We also derive results that show how this transition is manifest in networks of finite size, as well as when disorder is introduced in the segregation of the two interaction types. Our random-matrix results will serve as a baseline for understanding the behaviour of merged networks with more realistic structures and/or more detailed dynamics.

Publication metadata

Author(s): Emary C, Malchow A-K

Publication type: Article

Publication status: Published

Journal: Journal of Mathematical Biology

Year: 2022

Volume: 85

Print publication date: 12/08/2022

Online publication date: 12/08/2022

Acceptance date: 05/07/2022

Date deposited: 23/08/2022

ISSN (print): 0303-6812

ISSN (electronic): 1432-1416

Publisher: Springer

URL: .

DOI: 10.1007/s00285-022-01783-7


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