Recent developments in empirical dynamic modelling

Ecosystems are complex and sparsely observed making inference and prediction challenging. Empirical dynamic modelling (EDM) circumvents the need for a parametric model and complete observations of all system variables. Classical univariate approaches, which require time-series observations of only a single focal variable, can produce verifiable out-of-sample forecasts; however, they can sometimes require long time series that may be difficult to obtain. More importantly, classical approaches limit the depth of mechanistic understanding that can be gained and the generalizability of forecasts to non-analogue futures. We review the main ideas of EDM and more recent extensions that expand their capabilities for improving forecasts and understanding mechanism. Algorithms are now available that allow for missing data, unequal sampling intervals and combining short time series, which increase the number of datasets that can be used. Recent extensions of EDM to multivariate time series substantially expand the range of applications and mechanistic questions that can be addressed, including detecting causal coupling, tracking changing interactions in real time, leveraging short time series from information shared in coupled variables, modelling dynamically changing stability, scenario exploration, and management applications involving optimal control.