Repairing gaps in ecological time series

Abstract

Missing values are ubiquitous in ecological time series. Methods like linear interpolation, k-nearest neighbour (kNN) imputation or regression-based imputation are commonly used to repair these gaps, but may be unsuitable when the data are infrequently sampled or have nonlinear dynamics. We introduce multiview cross-mapping (MVCM), a novel method based in empirical dynamic modelling (EDM) that exploits shared information between dynamically coupled time series. Rather than using points nearby in time, MVCM uses similar system states on an attractor to estimate the value of a missing data point. MVCM works best where other dynamically coupled variables have been observed, but it can also predict into short gaps where all variables are missing (data void). Using model data from a coupled five-species system, and observational data from a long-term plankton survey in Lake Zurich, Switzerland, we show that MVCM is robust and performs significantly better than linear methods (linear interpolation, linear regression-based imputation) and kNN imputation. Crucially, this approach differs from methods based on a purely statistical paradigm because it assumes that the time series are generated by underlying deterministic rules. This dynamical framework allows us to exploit information shared between time series from a mechanistically coupled system, making complexity an asset for the analysis of imperfect observational data.