Impossible ecologies: Interaction networks and stability of coexistence in ecological communities

Yu Meng; Szabolcs Horvát; Carl D Modes; Pierre A Haas

doi:10.1016/j.cels.2025.101297

Impossible ecologies: Interaction networks and stability of coexistence in ecological communities

Cell Syst. 2025 Jun 16:101297. doi: 10.1016/j.cels.2025.101297. Online ahead of print.

Authors

Yu Meng¹, Szabolcs Horvát², Carl D Modes³, Pierre A Haas⁴

Affiliations

¹ Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany; Center for Systems Biology Dresden, Pfotenhauerstraße 108, 01307 Dresden, Germany.
² Center for Systems Biology Dresden, Pfotenhauerstraße 108, 01307 Dresden, Germany; Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstraße 108, 01307 Dresden, Germany.
³ Center for Systems Biology Dresden, Pfotenhauerstraße 108, 01307 Dresden, Germany; Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstraße 108, 01307 Dresden, Germany; Cluster of Excellence Physics of Life, TU Dresden, Arnoldstraße 18, 01069 Dresden, Germany. Electronic address: modes@mpi-cbg.de.
⁴ Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany; Center for Systems Biology Dresden, Pfotenhauerstraße 108, 01307 Dresden, Germany; Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstraße 108, 01307 Dresden, Germany. Electronic address: haas@pks.mpg.de.

PMID: 40527317
DOI: 10.1016/j.cels.2025.101297

Abstract

Does an ecological community allow stable species coexistence? Identifying the general effects of competitive, mutualistic, and predator-prey interactions on stability remains a central problem of systems ecology because established approaches cannot account for the full network arrangement of these interactions. Here, we therefore analyze all interaction networks of N≤5 species with Lotka-Volterra dynamics by combining exact results and numerical exploration. We find that a very small subset of these networks is "impossible ecologies," in which stable coexistence is non-trivially impossible. We prove that the possibility of stable coexistence is determined by similarly rare "irreducible ecologies." Statistical sampling shows that this probability varies over orders of magnitude even in ecologies that differ only in the network arrangement of identical interactions. Thus, our approach reveals that the full network structure of interactions can influence stability of coexistence more than the established effect of interaction-type proportions. A record of this paper's transparent peer review process is included in the supplemental information.

Keywords: Lotka–Volterra equations; ecological stability; theoretical ecology.