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. 2020 Feb 4;10:1774. doi: 10.1038/s41598-020-58440-6

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© The Author(s) 2020

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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This figure shows the probability that an ecological network is stable as a function of the network dimension. Each point in the plot represents the percentage of stable networks with given dimension (n), over a sample of 500 mutualistic ecological networks⁴⁷ with randomly chosen small-world topology. As can be seen, the percentage of stable networks decreases to zero as the network cardinality increases. This suggests that ecological networks with increasing size are likely unstable or fragile, so that small parameter variations lead to unstable evolutions.