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. 2020 Feb 11;8:e8533.
doi: 10.7717/peerj.8533. eCollection 2020.

Ecosystem Antifragility: Beyond Integrity and Resilience

Free PMC article

Ecosystem Antifragility: Beyond Integrity and Resilience

Miguel Equihua et al. PeerJ. .
Free PMC article


We review the concept of ecosystem resilience in its relation to ecosystem integrity from an information theory approach. We summarize the literature on the subject identifying three main narratives: ecosystem properties that enable them to be more resilient; ecosystem response to perturbations; and complexity. We also include original ideas with theoretical and quantitative developments with application examples. The main contribution is a new way to rethink resilience, that is mathematically formal and easy to evaluate heuristically in real-world applications: ecosystem antifragility. An ecosystem is antifragile if it benefits from environmental variability. Antifragility therefore goes beyond robustness or resilience because while resilient/robust systems are merely perturbation-resistant, antifragile structures not only withstand stress but also benefit from it.

Keywords: Antifragility; Complexity; Ecosystem integrity; Resilience.

Conflict of interest statement

The authors declare that they have no competing interests.


Figure 1
Figure 1. Ecosystem integrity three-tier model.
Ecological integrity is understood to be an underlying attribute in the constitution of ecosystems that produce specific manifestations in their structural characteristics, development processes and acquired composition. In short, ecosystem integrity arises from processes of self-organization derived from thermodynamic mechanisms that operate through the locally existing biota, as well as the energy and materials at their disposition, until attaining “optimal” operational points which are not fixed, but rather vary according to variations in the physical conditions or changes produced in the biota or the environment. we show the three-tier model of ecosystem integrity (3TEI), the inner tier is hidden to the observer, but its status can be inferred by the information available at the instrumental or observational tier where measurements on structure (including composition or other biodiversity features) and function are obtained, of course considering the context where the ecosystem is developing. Arrow tips indicate the direction of assumed mechanistic influence, although information can go either way.
Figure 2
Figure 2. Summary of concepts and narratives in selected papers.
Figure 3
Figure 3. In red the normalized NDVI time series for the 1 km2 pixel corresponding to the coordinates of the US-Me1 site of Ameriflux with a monthly sampling.
In blue, the corresponding values of Fisher’s information using the Cabezas and collaborators algorithm (
Figure 4
Figure 4. Basic characteristics of systems in terms of antifragility, which is the property of a system to respond in a convex way to perturbations or variability.
(A–C) are examples of fragile, robust/resilient and antifragile systems respectively; (D–F) are examples of profile responses to perturbations; (J–L) are examples of typical probability distributions; and (M–O) are the characteristic values obtained with the metric based on complexity change.

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    1. Abe S, Sarlis N, Skordas E, Tanaka H, Varotsos P. Origin of the usefulness of the natural-time representation of complex time series. Physical Review Letters. 2005;94(17):170601. doi: 10.1103/PhysRevLett.94.170601. - DOI - PubMed
    1. Ahmad N, Derrible S, Eason T, Cabezas H. Using fisher information to track stability in multivariate systems. Royal Society Open Science. 2016;3(11):160582. doi: 10.1098/rsos.160582. - DOI - PMC - PubMed
    1. Aronson J, Floret C, Le Floc’h E, Ovalle C, Pontanier R. Restoration and rehabilitation of degraded ecosystems in arid and semi-arid lands. ii. case studies in southern Tunisia, central Chile and northern Cameroon. Restoration Ecology. 1993;1(3):168–187. doi: 10.1111/j.1526-100X.1993.tb00023.x. - DOI
    1. Aronson J, Le Floc’h E. Vital landscape attributes: missing tools for restoration ecology. Restoration Ecology. 1996;4(4):377–387. doi: 10.1111/j.1526-100X.1996.tb00190.x. - DOI
    1. Bak P, Tang C, Wiesenfeld K. Self-organized criticality. Physical Review A. 1988;38(1):364–374. doi: 10.1103/PhysRevA.38.364. - DOI - PubMed

Grant support

This work was supported by CONACyT fund M0037-2018-07, Number 296842, Cátedras CONACyT fellowship program (Project Number 30), and Sistema Nacional de Investigadores SNI, Numbers 62929. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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