Leveraging spatial information to forecast nonlinear ecological dynamics

There has been a recent demand for forecasting in ecology, particularly in the field of ecosystem management. Empirical dynamic modelling (EDM), an equation‐free nonlinear forecasting method, is receiving growing attention, but it requires long time series to produce accurate predictions. Though most ecological time series are short, spatial replicates are often available. Here we explore how utilizing available spatial data can improve our ability to forecast ecological dynamics. There are several ways to incorporate spatial information into EDM and not all have been applied in ecology. We compare spatial EDM approaches used in ecology and physics and introduce a flexible Bayesian model that makes use of prior movement information. We test these methods on simulated data generated with three population dynamics models with varying levels of complexity, time series length, spatial symmetry and heterogeneity. Adding spatial data generally improves accuracy, though the best method depends on the spatial process. We applied the methods to empirical fisheries data, highlighting the complexity of real population dynamics. Leveraging spatial data is an effective way to overcome the problem of short ecological time series. Since the best forecasting method depends on the underlying dynamics, we suggest that users apply several in concert and that this may be useful in identifying spatial heterogeneity in dynamics.