Sensitivity analysis of reactive ecological dynamics
Citable URI
https://hdl.handle.net/1912/2347As published
https://doi.org/10.1007/s11538-008-9312-7Keyword
Ecological models; Transient dynamics; Reactivity; Sensitivity analysis; Consumer-resource interactions; Matrix population modelsAbstract
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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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/1912/2347Related items
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