There are many reasons for this non-stationarity in ecological dynamics. For instance, recent studies have shown switch between different dynamics at multi-decadal scales, triggered by small environmental changes in different regions for different species. Long-term changes in climate and/or human activities have also considerable effects on the dynamics of numerous ecological systems explaining they transient behaviors. Wavelet analysis has been suggested as a way to overcome this complexities. Wavelet analysis performs a time-scale decomposition of the signal, which means the estimation of its spectral characteristics as a function of time. This approach provides no information about the underlying ecological mechanisms, yet can provide useful clues about the non-stationary nature of the underlying ecological processes , which then can be incorporated in mathematical models. In this context, I will also demonstrate the efficiency of stochastic models with time varying parameters coupled with Bayesian approaches and discuss their advantages.
Institut de Biologie de l’École Normale Supérieure UMR8197, Eco- Evolutionary Mathematics, École Normale Supérieure, Paris, France and Unité Mixte Internationale 209, Mathematical and Computational Modeling of Complex Systems, Sorbonne Université, Paris, France.