Sensitivity analysis of continuous-time models for ecological and evolutionary theories

Abstract

National audienceSensitivity analyses are of paramount importance in ecological and evolutionary theories, but their application to continuous time models has been virtually ignored from these fields. We present a simple and general method that makes this analysis possible for any model specified by a system of ordinary differential equations, using the direct method from mathematical theory. The resulting analysis may be used to study the effect of parameter perturbation on the whole trajectories of the state variables as well as for deriving the sensitivity of composite metrics such as the population growth rate. We also present methods for analyzing the sensitivity of discrete events within a continuous-time framework, such as the age at maturation, where timing may be affected by the perturbation. These methods are applied to a model for the energetics of individual growth, reproduction, and mortality. The method is versatile and can be applied to study transient as well as asymptotic dynamics, and its application may benefit many fields of ecology and evolution

Transient Population Dynamics

“…10 briefly considers the sensitivity analysis of equilibria to continuous-time systems. Richard et al (2015) have developed a very general sensitivity analysis of transient dynamics in continuous systems (both linear and nonlinear). They point out and nicely demonstrate the parallels between continuoustime models and the discrete-time models considered here, the link being the creation of a dynamic model for the sensitivities that is solved along with the dynamics of the system itself.…”

Detecting Tipping points in Ecological Models with Sensitivity Analysis

“…(2.1) for odes can be estimated using the direct differential method [9,23]. This method expresses each sensitivity index as an additional differential equation to be solved alongside the original ode model.…”

Characterizing Species Interactions to Understand Press Perturbations: What Is the Community Matrix?

“…A few methods for gaining insight into the temporal and species-to-species propagation of perturbations through the community (Burns et al 2014;Takimoto et al 2009;Yodzis 1988aYodzis , 1989Yodzis , 1995 and for considering systems exhibiting transient and bounded oscillatory dynamics (Levins & Schultz 1996, Puccia & Levins 1991, Richard et al 2015 have also been developed but are not discussed further here. Previous work has also emphasized how sensitive predictions are to interaction strength uncertainty (Novak et al 2011, Roberts & Stone 2004, Yodzis 1988b).…”