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Finding analytical approximations for discrete, stochastic, individual-based models of ecology
Department of Mathematics, Uppsala University, Uppsala, Sweden.
Department of Information Technology, Uppsala University, Uppsala, Sweden.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Complexity Science and Evolution Unit, Okinawa Institute of Science and Technology Graduate University, Kunigami, Japan.
2023 (English)In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 365, article id 109084Article in journal (Refereed) Published
Abstract [en]

Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how ’bottom up’, individual-based models can be approximated by ’top down’ models of dynamics. Here, we study a class of spatially explicit individual-based models with contest competition: where species compete for space in local cells and then disperse to nearby cells. We start by describing simulations of the model, which exhibit large-scale discrete oscillations and characterize these oscillations by measuring spatial correlations. We then develop two new approximate descriptions of the resulting spatial population dynamics. The first is based on local interactions of the individuals and allows us to give a difference equation approximation of the system over small dispersal distances. The second approximates the long-range interactions of the individual-based model. These approximations capture demographic stochasticity from the individual-based model and show that dispersal stabilizes population dynamics. We calculate extinction probability for the individual-based model and show convergence between the local approximation and the non-spatial global approximation of the individual-based model as dispersal distance and population size simultaneously tend to infinity. Our results provide new approximate analytical descriptions of a complex bottom-up model and deepen understanding of spatial population dynamics.

Place, publisher, year, edition, pages
Elsevier, 2023. Vol. 365, article id 109084
Keywords [en]
Approximation, Difference equations, Individual-based model, Site-based model, Spatial correlations, Spatial ecology
National Category
Ecology
Identifiers
URN: urn:nbn:se:umu:diva-215955DOI: 10.1016/j.mbs.2023.109084PubMedID: 37778619Scopus ID: 2-s2.0-85174520418OAI: oai:DiVA.org:umu-215955DiVA, id: diva2:1808182
Available from: 2023-10-30 Created: 2023-10-30 Last updated: 2023-10-30Bibliographically approved

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Brännström, Åke
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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • Other style
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Language
  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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