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

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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.

LanguageEnglish
Pages1-11
Number of pages11
JournalMathematical Biosciences
Volume265
DOIs
StatusPublished - 1 Jul 2015

Fingerprint

Stage-structured
Invasion
Inertia
Population
Stage Structure
Transient Behavior
Deterministic Model
Lyapunov functions
Population Model
Model
dynamic models
Linear Function
Lyapunov Function
age structure
Dynamic models
Dynamic Model
population structure
Exponent
developmental stages
Scalar

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)

Cite this

The role of population inertia in predicting the outcome of stage-structured biological invasions. / Guiver, Chris; Dreiwi, Hanan; Filannino, Donna Maria; Hodgson, Dave; Lloyd, Stephanie; Townley, Stuart.

In: Mathematical Biosciences, Vol. 265, 01.07.2015, p. 1-11.

Research output: Contribution to journalArticle

Guiver C, Dreiwi H, Filannino DM, Hodgson D, Lloyd S, Townley S. The role of population inertia in predicting the outcome of stage-structured biological invasions. Mathematical Biosciences. 2015 Jul 1;265:1-11. Available from, DOI: 10.1016/j.mbs.2015.04.005
Guiver, Chris ; Dreiwi, Hanan ; Filannino, Donna Maria ; Hodgson, Dave ; Lloyd, Stephanie ; Townley, Stuart. / The role of population inertia in predicting the outcome of stage-structured biological invasions. In: Mathematical Biosciences. 2015 ; Vol. 265. pp. 1-11
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