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


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Guiver, C., Dreiwi, H., Filannino, D. M., Hodgson, D., Lloyd, S. and Townley, S., 2015. The role of population inertia in predicting the outcome of stage-structured biological invasions. Mathematical Biosciences, 265, pp. 1-11.

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    Official URL:

    http://dx.doi.org/10.1016/j.mbs.2015.04.005

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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.

    Details

    Item Type Articles
    CreatorsGuiver, C., Dreiwi, H., Filannino, D. M., Hodgson, D., Lloyd, S. and Townley, S.
    DOI10.1016/j.mbs.2015.04.005
    Related URLs
    URLURL Type
    http://www.scopus.com/inward/record.url?scp=84930066114&partnerID=8YFLogxKUNSPECIFIED
    http://dx.doi.org/10.1016/j.mbs.2015.04.005Free Full-text
    Uncontrolled Keywordsbiological invasion,lyapunov functions,non-linear system,population inertia,positive system,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)
    DepartmentsFaculty of Science > Mathematical Sciences
    Research CentresCentre for Mathematical Biology
    EPSRC Centre for Doctoral Training in Statistical Mathematics (SAMBa)
    RefereedYes
    StatusPublished
    ID Code50920

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