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