WK 20

A Hands-on Tutorial in Empirical Dynamic Modeling and Convergent Cross-Mapping

Empirical dynamic modeling (EDM) is an emerging non-parametric framework for modeling nonlinear dynamic systems. In an ecological context, EDM has numerous applications, including forecasting population abundances, unraveling species interactions, and identifying causal drivers. In contrast to the conventional approach of fitting assumed model equations to data, EDM relies on the fact that ecosystems have dynamics that allows us to reconstruct attractors directly from time series. This approach (with minimal assumptions) makes EDM particularly suitable for studying ecosystems, which exhibit non-equilibrium dynamics (problematic for models that typically assume stable equilibria) and state-dependent behavior (interactions that change with system state). The basic principles of EDM are clearly illustrated in a brief (3-minute) video animation (http://simplex.ucsd.edu/EDM_101_RMM.mov).

In the first half of this workshop, the organizers will review the basic concepts of EDM and demonstrate the application of EDM methods for identifying optimal embedding dimension, testing for nonlinearity, and forecasting. In addition, we will discuss the usage of convergent cross mapping (CCM), a powerful new tool for detecting causation among time series variables. Since CCM is based on the EDM framework, it relies solely on time series data without any assumptions about how variables may be interacting. Thus, it can succeed in identifying causal drivers where other methods may fail because of incorrect assumptions about linearity or the separability of effects (e.g., linear correlation, Granger causality, structural equation modeling).

In the second half of the workshop, participants will receive hands-on experience in using rEDM, a collection of EDM tools compiled as a freely available software package for the R programming language. As such, familiarity with data analysis software (R or Matlab) is required (though experience with R preferred). In addition, participants are invited to bring their own time series data (in a suitable digital format, such as .xls, .csv, .dat, .mat, or .Rdata) to investigate using EDM.