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    A general theory of coexistence and extinction for stochastic ecological communities

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    Author
    Hening, Alexandru
    Nguyen, Dang H.
    Chesson, Peter
    Affiliation
    Department of Ecology and Evolutionary Biology, The University of Arizona
    Issue Date
    2021-05-07
    Keywords
    Auxiliary variables
    Coexistence
    Environmental fluctuations
    Extinction
    Population dynamics
    Stochastic differential equations
    
    Metadata
    Show full item record
    Publisher
    Springer Science and Business Media LLC
    Citation
    Hening, A., Nguyen, D.H. & Chesson, P. A general theory of coexistence and extinction for stochastic ecological communities. J. Math. Biol. 82, 56 (2021).
    Journal
    Journal of Mathematical Biology
    Rights
    © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021.
    Collection Information
    This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
    Abstract
    We analyze a general theory for coexistence and extinction of ecological communities that are influenced by stochastic temporal environmental fluctuations. The results apply to discrete time (stochastic difference equations), continuous time (stochastic differential equations), compact and non-compact state spaces and degenerate or non-degenerate noise. In addition, we can also include in the dynamics auxiliary variables that model environmental fluctuations, population structure, eco-environmental feedbacks or other internal or external factors. We are able to significantly generalize the recent discrete time results by Benaim and Schreiber (J Math Biol 79:393–431, 2019) to non-compact state spaces, and we provide stronger persistence and extinction results. The continuous time results by Hening and Nguyen (Ann Appl Probab 28(3):1893–1942, 2018a) are strengthened to include degenerate noise and auxiliary variables. Using the general theory, we work out several examples. In discrete time, we classify the dynamics when there are one or two species, and look at the Ricker model, Log-normally distributed offspring models, lottery models, discrete Lotka–Volterra models as well as models of perennial and annual organisms. For the continuous time setting we explore models with a resource variable, stochastic replicator models, and three dimensional Lotka–Volterra models. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
    Note
    12 month embargo; published: 07 May 2021
    ISSN
    0303-6812
    EISSN
    1432-1416
    PubMed ID
    33963448
    DOI
    10.1007/s00285-021-01606-1
    Version
    Final accepted manuscript
    Sponsors
    Division of Mathematical Sciences
    ae974a485f413a2113503eed53cd6c53
    10.1007/s00285-021-01606-1
    Scopus Count
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    UA Faculty Publications

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