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Extinctions in a Metapopulation with Nonlinear Dispersal Coupling

Author

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  • Alexander Korotkov

    (Faculty of Science, Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., Moscow 117198, Russia)

  • Sergei Petrovskii

    (Faculty of Science, Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., Moscow 117198, Russia
    School of Computing and Mathematical Sciences, University of Leicester, Leicester LE1 7RH, UK)

Abstract

Major threats to biodiversity are climate change, habitat fragmentation (in particular, habitat loss), pollution, invasive species, over-exploitation, and epidemics. Over the last decades habitat fragmentation has been given special attention. Many factors are causing biological systems to extinct; therefore, many issues remain poorly understood. In particular, we would like to know more about the effect of the strength of inter-site coupling (e.g., it can represent the speed with which species migrate) on species extinction or persistence in a fragmented habitat consisting of sites with randomly varying properties. To address this problem we use theoretical methods from mathematical analysis, functional analysis, and numerical methods to study a conceptual single-species spatially-discrete system. We state some simple necessary conditions for persistence, prove that this dynamical system is monotone and we prove convergence to a steady-state. For a multi-patch system, we show that the increase of inter-site coupling leads to the formation of clusters—groups of populations whose sizes tend to align as coupling increases. We also introduce a simple one-parameter sufficient condition for a metapopulation to persist.

Suggested Citation

  • Alexander Korotkov & Sergei Petrovskii, 2023. "Extinctions in a Metapopulation with Nonlinear Dispersal Coupling," Mathematics, MDPI, vol. 11(20), pages 1-22, October.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4337-:d:1262556
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

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