Reconciling the ecological and engineering definitions of resilience

Assessing and managing the human influence on the natural and anthropic ecosystems strongly demands for robust measures of their resilience, especially in a world facing global changes as it is the Earth now. Many definitions of resilience have been proposed in order to cover different contexts. However, they are mostly derived either from the ecological or the engineering definitions of resilience, which substantially differ between each other. Here, following the strategy for measuring the system perturbations by the return period of their impacts on production (or equivalently by the inverse frequency), I demonstrate the mathematical equivalence of the ecological and engineering definitions of resilience for a special class of production systems. These finding provides additional robustness to resilience assessments based on the recently proposed annual production resilience indicator.