Accounting for non-stationarity when analyzing ecological time series

Increasingly studies highlight the non-stationary features of population dynamics. For instance, recent studies have shown that population dynamics can switch between different dynamics at multi-decadal scales, triggered by small environmental changes. These regime shifts were observed in different regions for different species. Transient behaviors in population dynamics have also been documented in epidemiology. Long-term changes in climate, human demography and/or social features of human populations have considerable effects on the dynamics of numerous epidemics.
To overcome the problems of analyzing non-stationary time series, applying wavelet analysis has recently been suggested. Wavelet analysis performs a time-scale decomposition of the signal, which means the estimation of its spectral characteristics as a function of time. After a short introduction on wavelet decomposition, the interest of wavelet analysis will be illustrated with examples on the estimation of the relationships between ecological time series and environmental signals. In these examples, wavelet analysis will help us to interpret multi-scale, non-stationary time-series data and will reveal features one could not see otherwise. New developments around wavelets for multiple time series analysis (wavelet clustering, global and partial coherency) will also be introduced.
Wavelet analysis thus appears very attractive as a first step for exploring the complexity of both the population dynamics and their links with environmental signals before the modeling stage. This modeling stage must also take into account the non-stationary features of the observed system. In this context, Bayesian approaches such as Kalman filtering or particle filters seem very promising. I will also evoke the advantages of these approaches.