Some ecosystems, like many other complex systems, can occasionally shift between alternative stable states. For management purposes it is crucial to quantify the resilience of ecosystem states. However, that is challenging as ecosystems are stochastic systems. To address this challenge we borrow the techniques from mathematics of stochastic systems and apply them to simulated and real data, from both ecology and environmental sciences.
Results/Conclusions
Stochastic dynamical systems found their place in many branches of science in the century starting by the pioneering work of Albert Einstein, Max Planck, Werner Heisenberg, etc., and were rigorously developed mainly by the great mathematician Andrey Kolmogorov. Kolmogorov developed Fokker-Planck equations which can be used to find the average transition times between alternative stable states. While the notion of “exit time” has been widely used in physics it still has not found its place in ecological sciences. We argue that it can suitably and appropriately be used to address a central topic in ecosystem studies: resilience. We applied exit time as a measure of resilience of tropical tree cover states: tree less, savannah, and forest. Furthermore, we have applied it to model and study the average transition times between climate states during the last glacial period.