Mesoscale symmetries explain dynamical equivalence of food webs

TL;DR

This paper reveals that mesoscale symmetries in ecological food webs underpin their dynamical equivalence, with eigenvectors localizing on symmetric motifs, explaining observed similarities in system responses.

Contribution

It demonstrates how mesoscale symmetries in food webs determine dynamical modes, providing a new understanding of structure-function relationships in ecological networks.

Findings

Eigenvectors localize on symmetric motifs

Removing symmetry alters specific dynamical modes

Symmetric structures have distinct dynamical implications

Abstract

A present challenge in complex systems is to identify mesoscale structures that have distinct dynamical implications. In this paper we present a detailed investigation of a previously observed dynamical equivalence of certian ecological food webs. We show that this equivalence is rooted in mesoscale symmetries that exist in these webs. Certain eigenvectors of the Jacobian describing dynamical modes of the system, such as specific instabilities or responses to perturbations, localize on these symmetric motifs. On the one hand this means that by removing a symmetry from the network one obtains a system which has identical dynamics except for the removal of the localized mode. This explains the previously observed equivalence. On the other hand it means that we can identify dynamical modes that only depend on the symmetric motif. Symmetric structures thus provide an example for mesoscale network motifs having distinct and exact implications for the dynamics.