# Network structure, predator–prey modules, and stability in large food webs

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## Abstract

Large, complex networks of ecological interactions with random structure tend invariably to instability. This mathematical relationship between complexity and local stability ignited a debate that has populated ecological literature for more than three decades. Here we show that, when species interact as predators and prey, systems as complex as the ones observed in nature can still be stable. Moreover, stability is highly robust to perturbations of interaction strength, and is largely a property of structure driven by predator–prey loops with the stability of these small modules cascading into that of the whole network. These results apply to empirical food webs and models that mimic the structure of natural systems as well. These findings are also robust to the inclusion of other types of ecological links, such as mutualism and interference competition, as long as consumer–resource interactions predominate. These considerations underscore the influence of food web structure on ecological dynamics and challenge the current view of interaction strength and long cycles as main drivers of stability in natural communities.

## Keywords

Predator–prey Complexity/stability Food webs Sign-stability Weak interactions## Notes

### Acknowledgements

We thank D. Alonso, A. Bodini, J.M. Dambacher and A. P. Dobson for stimulating discussions. This work was supported by a Centennial Fellowship by the J. S. McDonnell Foundation to M.P.

## Supplementary material

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