Bulletin of Mathematical Biology

, Volume 70, Issue 6, pp 1634–1659

Sensitivity Analysis of Reactive Ecological Dynamics

Original Article

DOI: 10.1007/s11538-008-9312-7

Cite this article as:
Verdy, A. & Caswell, H. Bull. Math. Biol. (2008) 70: 1634. doi:10.1007/s11538-008-9312-7


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.


Ecological models Transient dynamics Reactivity Sensitivity analysis Consumer-resource interactions Matrix population models 

Copyright information

© Society for Mathematical Biology 2008

Authors and Affiliations

  1. 1.Department of Earth, Atmospheric and Planetary SciencesMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Biology Department MS-34Woods Hole Oceanographic InstitutionWoods HoleUSA

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