The transient behavior of an ecosystem perturbed away from equilibrium can be described in terms of the "reactivity" and "amplification envelope" associated with the equilibrium. These properties describe the transient amplification of perturbations. They depend on the parameters of the underlying model, and sensitivity analysis predicts the effect of parameter changes on the transient response of reactive ecosystems. By doing so, it provides a quantitative framework for investigating the ecological mechanisms and processes leading to reactive dynamics.
We have developed new mathematical approaches to investigate the dependence of transient dynamics on the parameters, and will present analytical formulations for the sensitivity and elasticity of the reactivity and the amplification envelope. We will show the results of applying the methodology to a predator-prey model and a size-structured food web model. We find that perturbations can be amplified in two different ways. The predation rate may be slow but the energy transfer very efficient, in which case the consumer can take advantage of transient increases of resources (prey-driven mechanism). Alternatively, resources may be removed quickly but poorly assimilated by the consumer, in which case the resources can grow opportunistically when the consumer biomass is below equilibrium (predator-driven mechanism). Reactivity in the food web model is highly elastic to assimilation efficiency, suggesting that the amplification of perturbations is related to the efficiency of energy transfer between trophic levels.