# Functional motifs in food webs and networks

## TL;DR

The paper explains how small network structures, called motifs, can predict violent responses to disturbances in complex systems like food webs or power grids.

## Contribution

The paper introduces motif reactivity as a novel property to identify parts of a network likely to respond violently to disturbances.

## Key findings

- Reactivity in complex systems is often caused by small network motifs.
- Motif reactivity can reveal parts of a network prone to violent responses.
- This approach applies to food webs, epidemics, and power grids.

## Abstract

Understanding how complex systems respond to disturbances and which parts of a system could respond violently when perturbed is a major challenge across disciplines. Using food webs as an example, we show that a system’s immediate response to disturbance, reactivity, is often caused by small motifs within the network. In ecology, where network data are scarce, this enables identification of subgroups of interacting species that pose the greatest risk. This approach also applies to other complex networks, from detecting risky friend groups in epidemics to tracing local origins of cascading failures in power grids.

When studying a complex system, it is often useful to think of the system as a network of interacting units. One can then ask if some properties of the entire network are already explained by a small part of the network, a network motif. A famous example of an ecological motif is exploitative competition in food webs, where the presence of two species competing for a shared resource precludes the existence of a stable equilibrium for the whole system. However, other examples of motifs with such direct impacts on stability are not known. Here, we show why small motifs that allow conclusions on systemic stability are rare. More importantly, we show that another dynamical property, reactivity, is typically rooted in motifs. Computing the reactivity of motifs can reveal which parts of a network are prone to respond violently to perturbations. This highlights motif reactivity as a useful property to measure in real-world systems to understand likely modes of systemic failure in food webs or other networks in epidemics, supply chains, or power grids.