Predicting transient amplification in perturbed ecological systems

Ecological systems are prone to disturbances and perturbations. For stage-structured populations, communities and ecosystems, measurements of system magnitude in the short term will depend on how biased the stage structure is following a disturbance. We promote the use of the Kreiss bound, a lower bound predictor of transient system magnitude that links transient amplification to system perturbations. The Kreiss bound is a simple and powerful alternative to other indices of transient dynamics, in particular reactivity and the amplification envelope. We apply the Kreiss bound to a discrete-time model of an endangered species and a continuous-time rainforest model. We promote the analysis of transient amplification relative to both initial conditions and asymptotic dynamics. Transient amplification of ecological systems, following exogenous disturbances, has been implicated in the success of invasive species, persistence of extinction debts and species coexistence. Synthesis and applications. The Kreiss bound allows simple assessment of transient amplification in ecological systems and the response of potential amplification to changes in system parameters. Hence it is an important tool for comparative analyses of ecological systems and should provide powerful predictions of optimal population management strategies.