[DSRP Evidence](https://dsrpevidence.org/)

# Functional motifs in food webs and networks

## Details

**Authors** Melanie Habermann, Ashkaan K. Fahimipour, Justin D. Yeakel, Thilo Gross

**Year** 2026

**Publisher** Proceedings of the National Academy of Sciences

**Kind of work** article

**Discipline** Ecology

**Secondary disciplines** Network Science

**Applied** false

[Read it at the publisher](https://doi.org/10.1073/pnas.2521927123) 
10.1073/pnas.2521927123

## In authors' words

### Abstract

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.

### What they set out to do (purpose)

To determine whether small network motifs can explain system-level dynamical properties, focusing on reactivity (how strongly a whole network responds immediately after a perturbation) rather than only long-term stability.

### Who or what was studied (sample)

Theoretical and computational analysis of network motifs (units of two or three interacting nodes) in food-web and generic network models.

### How they did it (methods)

Mathematical and computational analysis computing the reactivity of small network motifs and testing how much of a whole network's reactivity is explained by its motifs, contrasted with motifs' limited power to predict long-term stability.

### What they found (results)

Small motifs of just two or three interacting units account for a substantial share of a network's reactivity, its immediate response to a perturbation, even though such motifs rarely determine a network's long-term stability.

## Commentary

### In short

A whole system's immediate behavior under stress is largely explained by small interacting parts nested within it, and shocks propagate outward from those parts through the network's connections.

**Patterns it shows** S, R

**Added** 2026-09-26

**How to cite this** Melanie Habermann, Ashkaan K. Fahimipour, Justin D. Yeakel, Thilo Gross (2026). Functional motifs in food webs and networks. Proceedings of the National Academy of Sciences.