ArticleProceedings of the National Academy of Sciences of the United States of America2022
Delay effects on the stability of large ecosystems.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
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6 citing papers in PubMed, 18 citations in OpenAlex.
- Catalysts and inhibitors of critical transitions in ecological systems.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
- Article
- Stability of Ecological Systems: A Theoretical Review.Physics reports · 2024Article
- Reactivity of complex communities can be more important than stability.Nature communications · 2023Article
- Intrinsic neural diversity quenches the dynamic volatility of neural networks.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
- Delay effects on the stability of large ecosystems.Proceedings of the National Academy of Sciences of the United States of America · 2022Article
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Authors and funding
5 authors at 2 institutions in 2 countries.
Funding
No grant is acknowledged in the PubMed record.
Abstract
The common intuition among the ecologists of the midtwentieth century was that large ecosystems should be more stable than those with a smaller number of species. This view was challenged by Robert May, who found a stability bound for randomly assembled ecosystems; they become unstable for a sufficiently large number of species. In the present work, we show that May's bound greatly changes when the past population densities of a species affect its own current density. This is a common feature in real systems, where the effects of species' interactions may appear after a time lag rather than instantaneously. The local stability of these models with self-interaction is described by bounds, which we characterize in the parameter space. We find a critical delay curve that separates the region of stability from that of instability, and correspondingly, we identify a critical frequency curve that provides the characteristic frequencies of a system at the instability threshold. Finally, we calculate analytically the distributions of eigenvalues that generalize Wigner's as well as Girko's laws. Interestingly, we find that, for sufficiently large delays, the eigenvalues of a randomly coupled system are complex even when the interactions are symmetric.
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