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Cited by 1,232Mathematical and Theoretical Epidemiology and Ecology ModelsEcosystem dynamics and resilienceEcology and Vegetation Dynamics Studies

Stability criteria for complex ecosystems

Open access
Allesina, Stefano, Tang, Si·2012·Nature
DOI 10.1038/nature10832
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Abstract

Forty years ago, May proved that sufficiently large or complex ecological networks have a probability of persisting that is close to zero, contrary to previous expectations. May analysed large networks in which species interact at random. However, in natural systems pairs of species have well-defined interactions (for example predator-prey, mutualistic or competitive). Here we extend May's results to these relationships and find remarkable differences between predator-prey interactions, which are stabilizing, and mutualistic and competitive interactions, which are destabilizing. We provide analytic stability criteria for all cases. We use the criteria to prove that, counterintuitively, the probability of stability for predator-prey networks decreases when a realistic food web structure is imposed or if there is a large preponderance of weak interactions. Similarly, stability is negatively affected by nestedness in bipartite mutualistic networks. These results are found by separating the contribution of network structure and interaction strengths to stability. Stable predator-prey networks can be arbitrarily large and complex, provided that predator-prey pairs are tightly coupled. The stability criteria are widely applicable, because they hold for any system of differential equations.

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  • Most previous work on food web dynamics has relied on hypothetically parameterised networks.

    “Although the effects of species interactions on foodweb dynamics have been widely studied, most previous work has relied on hypothetically parameterised networks (Allesina and Tang 2012;May 2019;Yodzis 1988)”

    From A Food Web Model of the Serengeti: Stability, Dynamics and Indirect Effects (2026) · cites this paper as Allesina and Tang 2012

    The Abstract describes May’s influential analysis of networks with random interactions, and the main text says simulated cascade and niche models are widely used for food webs. These passages support the use of hypothetical networks in prior work, but do not establish that *most* previous work relied on them. (LLM, conf=0.79)

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Cites

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Authors
Allesina, S., & Tang, S.
Affiliations
University of Chicago (US)
ORCID
Tang, Si
Venue
Nature
Publisher
Springer Science and Business Media LLC
Published
2012-02-19
Volume
483
Issue
7388
Pages
205-208
ISSN
  • 0028-0836 (ISSN-L)
  • 1476-4687
DOI
10.1038/nature10832
OpenAlex
W2069994241
Cited by
1,232
References
1
Citations by year
2026: 102 · 2025: 112 · 2024: 129 · 2023: 100 · 2022: 117 · 2021: 81 · 2020: 99 · 2019: 64 · 2018: 84 · 2017: 70 · 2016: 76 · 2015: 81 · 2014: 53 · 2013: 44 · 2012: 20
FWCI
61.20
Type
journal article
Language
en
Open access
Licence
www.springer.com/tdm (tdm)
Locations
  • Nature (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Health Sciences › Medicine › Public Health, Environmental and Occupational Health › Mathematical and Theoretical Epidemiology and Ecology Models
  • Physical Sciences › Environmental Science › Global and Planetary Change › Ecosystem dynamics and resilience
  • Physical Sciences › Environmental Science › Nature and Landscape Conservation › Ecology and Vegetation Dynamics Studies
Keywords
complex ecosystems, predator-prey interactions, mutualism, competitive interactions, food web structure, nestedness, interaction strength, network structure, stability criteria, bipartite graphs
MeSH terms
Animals, Competitive Behavior, Models, Biological, Predatory Behavior, Symbiosis, Ecosystem, Plant Physiological Phenomena, Food Chain

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