Revealing unseen dynamical regimes of ecosystems from population time-series data.

Many dynamical systems can exist in alternative regimes for which small changes in an environmental driver can cause sudden jumps between regimes. In ecology, predicting the regime of population fluctuations under unobserved levels of an environmental driver has remained an unsolved challenge with important implications for conservation and management. Here, we show that integrating time-series data and information on a putative driver into a Gaussian Process regression model for the system's dynamics allows us to predict dynamical regimes without the need to specify the equations of motion of the system. As a proof of concept, we demonstrate that we can accurately predict fixed-point, cyclic, or chaotic dynamics under unseen levels of a control parameter for a range of simulated population dynamics models. For a model with an abrupt population collapse, we show that our approach goes beyond an early warning signal by characterizing the regime that follows the tipping point. We then apply our approach to data from an experimental microbial food web and from a lake planktonic food web. We find that we can reconstruct transitions away from chaos in the microbial food web and anticipate the dynamics of the oligotrophic regime in the planktonic food web. These results lay the groundwork for making rational decisions about preventing, or preparing for, regime shifts in natural ecosystems and other dynamical systems.