Beyond sensitivity: nonlinear perturbation analysis of transient dynamics

1. Perturbation analyses of population models are integral to population management: such analyses evaluate how changes in vital rates of members of the population translate to changes in population dynamics. Sensitivity and elasticity analyses of long?term (asymptotic) growth are popular, but limited: they ignore short?term (transient) dynamics and provide a linear approximation to nonlinear perturbation curves.2. Population inertia measures how much larger or smaller a non?stable population becomes compared with an equivalent stable population, as a result of transient dynamics. We present formulae for the transfer function of population inertia, which describes nonlinear perturbation curves of transient population dynamics. The method comfortably fits into wider frameworks for analytical study of transient dynamics, and for perturbation analyses that use the transfer function approach.3. We use case studies to illustrate how the transfer function of population inertia may be used in population management. These show that strategies based solely on asymptotic perturbation analyses can cause undesirable transient dynamics and/or fail to exploit desirable transient dynamics. This highlights the importance of considering both transient and asymptotic population dynamics in population management.4. Our case studies also show a tendency towards marked nonlinearity in transient perturbation curves. We extend our method to measure sensitivity of population inertia and show that it often fails to capture dynamics resulting from perturbations typical of management scenarios.