Sensitivity Analysis of Reactive Ecological Dynamics

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 longlasting. 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.

Hot temperatures can force delayed mosquito outbreaks via sequential changes in Aedes aegypti demographic parameters in autocorrelated environments

“…In fact, the additional environmental noise can be amplified by the reactive nature of the model (Verdy & Caswell 2008). The nature of the additional environmental noise could be related to other environmental factors.…”

Detecting reactivity

“…Theoretical studies have shown that reactivity is a common property of models of populations, communities, and ecosystems (Neubert and Caswell 2000, Chen and Cohen 2001, Caswell and Neubert 2005, Verdy and Caswell 2008. In this note we have described what is, to our knowledge, the first formal statistical test for reactivity.…”

“…Reactivity has been studied in both discrete-time and continuous-time models of predator-prey and food-web dynamics (Chen and Cohen 2001, Caswell and Neubert 2005, Verdy and Caswell 2008, spatial pattern formation (Neubert et al 2002), aquatic ecology (Ives et al 2003, Anderson et al 2008, invasive species (Marvier et al 2004), density-dependent matrix population models (Caswell and Neubert 2005), and epidemiology (Hosack et al 2008). Caswell and Neubert (2005) and Verdy and Caswell (2008) studied the sensitivity of reactivity to changes in model parameters.…”

Reproductive value, the stable stage distribution, and the sensitivity of the population growth rate to changes in vital rates

“…Thus sensitivity analysis of growth rate is only the beginning of its applications in demography. Recently it has been applied to measures of longevity, net reproductive rate, and generation time (Caswell 2006;2009b), to nonlinear demographic models (Caswell 2008;2009a;Verdy and Caswell 2008;Jenouvrier et al 2010), to stage-structured epidemic models (Klepac and Caswell 2010), and to transient dynamics (Caswell 2007).…”