Feedback spectra of soil food webs across a complexity gradient, and the importance of three-species loops to stability

It has been shown that in real food webs, the strongest omnivorous feedback, a three-link positive feedback, is a good indicator of system stability, suggesting that the strongest positive feedback in a food web could be the Achilles heel of stability. However, the complete spectrum of feedbacks in observed food webs has never been analyzed. Here, we have quantified all the feedbacks in 32 soil food webs along a complexity gradient, including trophic feedbacks and feedbacks resulting from recycling of organic matter. We found that, although the maximum omnivorous feedback was rarely the strongest positive feedback in a system, it stood out over longer and stronger feedbacks as the indicator of stability. The results emphasize the importance of small substructures in complex networks.