Destabilizing factors in slow–fast systems

The problem of (de)stabilization of ecosystems is discussed in this paper by focusing on two basic questions: (i) Is it possible to derive from a mathematical model exact measures of the (de)stabilizing power of a parameter?; (ii) Are these measures robust with respect to perturbations of the environmental and demographic parameters? After recalling that (de)stabilization can refer to various characteristics of ecosystems, like stability (in the strict sense), resilience, complexity, and risk of extinction, we show that the first question has a positive answer in the special context of slow–fast population assemblies. Then, through the comparative analysis of a few significant cases, we show that there is a convincing evidence that these measures are very strongly influenced by details of the models (or of the real ecosystem). This poses serious doubts on the validity of sharp conclusions on (de)stabilizing factors obtained through simulation and data analysis.