Resilience assessment in complex natural systems

Ecological resilience is the capability of an ecosystem to maintain the same structure and function and avoid crossing catastrophic tipping points (i.e. undergoing irreversible regime shifts). While fundamental for management, concrete ways to estimate and interpret resilience in real ecosystems are still lacking. Here, we develop an empirical approach to estimate resilience based on the stochastic cusp model derived from catastrophe theory. The cusp model models tipping points derived from a cusp bifurcation. We extend cusp in order to identify the presence of stable and unstable states in complex natural systems. Our Cusp Resilience Assessment (CUSPRA) has three characteristics: (i) it provides estimates on how likely a system is to cross a tipping point (in the form of a cusp bifurcation) characterized by hysteresis, (ii) it assesses resilience in relation to multiple external drivers and (iii) it produces straightforward results for ecosystem-based management. We validate our approach using simulated data and demonstrate its application using empirical time series of an Atlantic cod population and marine ecosystems in the North Sea and the Mediterranean Sea. We show that Cusp Resilience Assessment is a powerful method to empirically estimate resilience in support of a sustainable management of our constantly adapting ecosystems under global climate change.