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    Sensitivity analysis of reactive ecological dynamics

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    verdy_caswell_whoas.pdf (442.0Kb)
    Date
    2008-02
    Author
    Verdy, Ariane  Concept link
    Caswell, Hal  Concept link
    Metadata
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    Citable URI
    https://hdl.handle.net/1912/2347
    As published
    https://doi.org/10.1007/s11538-008-9312-7
    Keyword
     Ecological models; Transient dynamics; Reactivity; Sensitivity analysis; Consumer-resource interactions; Matrix population models 
    Abstract
    Ecological systems with asymptotically stable equilibria may exhibit significant transient dynamics following perturbations. In some cases, these transient dynamics include the possibility of excursions away from the equilibrium before the eventual return; systems that exhibit such amplification of perturbations are called reactive. Reactivity is a common property of ecological systems, and the amplification can be large and long-lasting. The transient response of a reactive ecosystem depends on the parameters of the underlying model. To investigate this dependence, we develop sensitivity analyses for indices of transient dynamics (reactivity, the amplification envelope, and the optimal perturbation) in both continuous- and discrete-time models written in matrix form. The sensitivity calculations require expressions, some of them new, for the derivatives of equilibria, eigenvalues, singular values, and singular vectors, obtained using matrix calculus. Sensitivity analysis provides a quantitative framework for investigating the mechanisms leading to transient growth. We apply the methodology to a predator-prey model and a size-structured food web model. The results suggest predator-driven and prey-driven mechanisms for transient amplification resulting from multispecies interactions.
    Description
    Author Posting. © Springer, 2008. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Bulletin of Mathematical Biology 70 (2008): 1634-1659, doi:10.1007/s11538-008-9312-7.
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    • Biology
    Suggested Citation
    Preprint: Verdy, Ariane, Caswell, Hal, "Sensitivity analysis of reactive ecological dynamics", 2008-02, https://doi.org/10.1007/s11538-008-9312-7, https://hdl.handle.net/1912/2347
     

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