Bulletin of Mathematical Biology

, Volume 78, Issue 11, pp 2186–2211 | Cite as

Stability of Ecosystems Under Invasions

  • Vladimir Kozlov
  • Sergey VakulenkoEmail author
  • Uno Wennergren
Original Article


This paper considers a model of foodwebs taking into account species extinction and invasion. We show that system stability depends not only on usual parameters (mortality rates, self-limitation coefficients, and resource abundances), but also on an additional parameter (“biodiversity potential”). The main result is as follows. For foodwebs with random parameters, we obtain an estimate of probability that the foodweb exposed to invasion survives. This estimate involves different system parameters, size and its topological properties.


Ecosystem stability Invasions Species extinctions 

Mathematics Subject Classification

14T05 92C42 



We are grateful to referees for interesting comments and remarks. The second author was financially supported by Linkoping University, in part by Government of Russian Federation, Grant 074-U01 and by Grant 16-01-00648 of Russian Fund of Basic Research.


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Copyright information

© Society for Mathematical Biology 2016

Authors and Affiliations

  • Vladimir Kozlov
    • 1
  • Sergey Vakulenko
    • 2
    • 3
  • Uno Wennergren
    • 4
  1. 1.Department of MathematicsUniversity of LinkopingLinkopingSweden
  2. 2.Institute for Mechanical Engineering ProblemsRussian Academy of SciencesSaint PetersburgRussia
  3. 3.ITMO UniversitySaint PetersburgRussia
  4. 4.Department of EcologyUniversity of LinkopingLinkopingSweden

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