Summary1. 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. 2. 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. 3. We apply the Kreiss bound to a discrete-time model of an endangered species and a continuous-time rainforest model. 4. We promote the analysis of transient amplification relative to both initial conditions and asymptotic dynamics. 5. Transient amplification of ecological systems, following exogenous disturbances, has been implicated in the success of invasive species, persistence of extinction debts and species coexistence. 6. 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.

Global CO 2 emissions are understood to be the largest contributor to anthropogenic climate change, and have, to date, been highly correlated with economic output. However, there is likely to be a negative feedback between climate change and human wealth: economic growth is typically associated with an increase in CO 2 emissions and global warming, but the resulting climate change may lead to damages that suppress economic growth. This climate-economy feedback is assumed to be weak in standard climate change assessments. When the feedback is incorporated in a transparently simple model it reveals possible emergent behaviour in the coupled climate-economy system. Formulae are derived for the critical rates of growth of global CO 2 emissions that cause damped or long-term boom-bust oscillations in human wealth, thereby preventing a soft landing of the climate-economy system. On the basis of this model, historical rates of economic growth and decarbonization appear to put the climate-economy system in a potentially damaging oscillatory regime.