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

Research output: Contribution to journalArticle

2 Citations (Scopus)
121 Downloads (Pure)

Abstract

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
Volume265
DOIs
Publication statusPublished - 1 Jul 2015

Keywords

  • 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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