Sensitivity analysis of reactive ecological dynamics

Bulletin of Mathematical Biology
Ariane Verdy, Hal Caswell

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...Continue Reading

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Citations

Nov 6, 2009·Ecology·Michael G NeubertAndrew R Solow
Jan 15, 2013·Theoretical Population Biology·Hal Caswell, Esther Shyu
Mar 30, 2010·Theoretical Population Biology·Robin E Snyder
Oct 3, 2015·Science·Peter D Roopnarine, Kenneth D Angielczyk
Sep 25, 2014·Ecology Letters·György BarabásAnnette Ostling
Jan 28, 2017·Journal of Theoretical Biology·Riccardo Vesipa, Luca Ridolfi
Jun 22, 2016·PloS One·Francesco Caravelli, Phillip P A Staniczenko
Aug 25, 2019·Bulletin of Mathematical Biology·Xiaoying WangFrithjof Lutscher
Sep 17, 2020·Journal of the Royal Society, Interface·Suzanne M O'ReganJohn M Drake
Dec 18, 2018·Ecological Monographs·Hal CaswellSilke F van Daalen
Dec 17, 2009·SIAM Journal on Applied Dynamical Systems·Judy DayCarson C Chow
Mar 29, 2018·Journal of Theoretical Biology·Lorenzo MariMarino Gatto

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