A general theory of coexistence and extinction for stochastic ecological communities
AffiliationDepartment of Ecology and Evolutionary Biology, The University of Arizona
Stochastic differential equations
MetadataShow full item record
PublisherSpringer Science and Business Media LLC
CitationHening, A., Nguyen, D.H. & Chesson, P. A general theory of coexistence and extinction for stochastic ecological communities. J. Math. Biol. 82, 56 (2021).
JournalJournal of Mathematical Biology
Rights© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021.
Collection InformationThis 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 firstname.lastname@example.org.
AbstractWe 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.
Note12 month embargo; published: 07 May 2021
VersionFinal accepted manuscript
SponsorsDivision of Mathematical Sciences
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