Together with colleagues from China and the UK we just published work on a paleo limnological record in a big chinese lake that shows a transition to eutrophication during the last 30 years. Interestingly, the data offer the possibility to show that the system exhibits bimodality and that approaching to the permanent shift ‘flickering’ between the oligotrophic and eutrophic state may be observed. We compared these results to model simulations and we conclude that flickering may be more possible to detect in the most common ecological records at hand.
In a recent work with Tony Ives, we showed how modified linear models with time-varying parameters can be used to extract an indicator of instability for a time series that may be drifting towards a regime shift. The paper is available online in Ecosphere. The idea is simply that instead of fitting an autoregressive model and finding a fixed value for its parameters, to fit an autoregressive model with parameters that change based on the point one is along the time series. This is possible due to a Kalman filter fitting proceedure and seems to not require a too much long time series. We also show that fitting threshold autoregressive models can distinguish alternative attractors in a flickering time series. The code to execute all this is currently in Matlab, but we aim in converting it to an easy to use routine in the R environment.