  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.
