Forecasting Ecological Time Series Using Empirical Dynamic Modeling: A Tutorial for Simplex Projection and S-map

Abstract

Natural ecosystems are often complex, dynamic and state-dependent (i.e., nonlinear), and it is difficult to forecast their (near) future states if we rely only on linear statistical approaches. In the past few decades, tools of nonlinear time series analysis have been developed to analyze and forecast the state-dependent behavior of nonlinear systems. These methods do not assume any set of equations governing the system, and thus are suitable for analyzing systems which are complex and for which it is therefore often difficult to make reasonable assumptions about their underlying mechanisms. Instead of assuming equations, these methods recover the dynamics (and potentially, their underlying mechanism) directly from time series data, and are thus called Empirical Dynamic Modeling (EDM). In this chapter, we will introduce a basic concept in EDM (i.e., state space reconstruction) and explain practical and detailed algorithms of two core EDM tools (i.e., simplex projection and S-map) to forecast ecological time series. Then, we show applications of this algorithm to community ecology and its potential to answer ecological questions.KeywordsDelay embeddingEmpirical dynamic modelingForecastingNonlinear dynamicsSimplex projectionS-map