Sensitivity analysis of reactive ecological dynamics
MetadataShow full item record
KeywordEcological models; Transient dynamics; Reactivity; Sensitivity analysis; Consumer-resource interactions; Matrix population models
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.
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.
Showing items related by title, author, creator and subject.
Flow and nutrient dynamics in a subterranean estuary (Waquoit Bay, MA, USA) : field data and reactive transport modeling Spiteri, Claudette; Slomp, Caroline P.; Charette, Matthew A.; Tuncay, Kagan; Meile, Christof (2008-04-25)A two-dimensional (2D) reactive transport model is used to investigate the controls on nutrient (NO3-, NH4+, PO4) dynamics in a coastal aquifer. The model couples density dependent flow to a reaction network which includes ...
Matrix models and sensitivity analysis of populations classified by age and stage : a vec-permutation matrix approach Caswell, Hal (Springer, 2011-06-14)Matrix population models in which individuals are classified by both age and stage can be constructed using the vec-permutation matrix. The resulting age-stage models can be used to derive the age-specific consequences of ...
Caswell, Hal; Shyu, Esther (2012-04)Periodic matrix models are frequently used to describe cyclic temporal variation (seasonal or interannual) and to account for the operation of multiple processes (e.g., demography and dispersal) within a single projection ...