The role of population inertia in predicting the outcome of stage-structured biological invasions

Chris Guiver, Hanan Dreiwi, Donna Maria Filannino, Dave Hodgson, Stephanie Lloyd, Stuart Townley

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3 Citations (SciVal)
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Deterministic dynamic models for coupled resident and invader populations are considered with the purpose of finding quantities that are effective at predicting when the invasive population will become established asymptotically. A key feature of the models considered is the stage-structure, meaning that the populations are described by vectors of discrete developmental stage- or age-classes. The vector structure permits exotic transient behaviour-phenomena not encountered in scalar models. Analysis using a linear Lyapunov function demonstrates that for the class of population models considered, a large so-called population inertia is indicative of successful invasion. Population inertia is an indicator of transient growth or decline. Furthermore, for the class of models considered, we find that the so-called invasion exponent, an existing index used in models for invasion, is not always a reliable comparative indicator of successful invasion. We highlight these findings through numerical examples and a biological interpretation of why this might be the case is discussed.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalMathematical Biosciences
Publication statusPublished - 1 Jul 2015


  • Biological invasion
  • Lyapunov functions
  • Non-linear system
  • Population inertia
  • Positive system

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability
  • Modelling and Simulation
  • Agricultural and Biological Sciences(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Medicine(all)


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