A general theory of coexistence and extinction for stochastic ecological communities
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Affiliation
Department of Ecology and Evolutionary Biology, The University of ArizonaIssue Date
2021-05-07Keywords
Auxiliary variablesCoexistence
Environmental fluctuations
Extinction
Population dynamics
Stochastic differential equations
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Springer Science and Business Media LLCCitation
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 BiologyRights
© 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 2021ISSN
0303-6812EISSN
1432-1416PubMed ID
33963448Version
Final accepted manuscriptSponsors
Division of Mathematical Sciencesae974a485f413a2113503eed53cd6c53
10.1007/s00285-021-01606-1
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