Resilience assessment in complex natural systems

Ecological resilience is the capability of an ecosystem to maintain the same structure and function and to avoid crossing catastrophic tipping points (i.e. 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 of marine ecosystems in the North Sea and the Mediterranean Sea. We show that CUSPRA is a powerful method to empirically estimate resilience in support of a sustainable management of our adapting ecosystems under global climate change.

Methods
The data were collected three different publications. The first dataset used to test the method was the stock assessment of North-East Arctic cod collected from Sguotti et al., 2019. These data can be found in the ICES Stock Assessment data. The second dataset was the North Sea community. These data were collected from Sguotti et al., 2022. Finally, the last dataset was a trait dataset and was collected from Tsimara et al., 2021.