Evaluating Empirical Dynamic Modeling for forecasting: The role of variation among time series replicates

Accurate forecasting of ecological systems is essential for effective environmental management but remains challenging. One tool for this purpose is Empirical Dynamic Modeling (EDM). EDM typically requires long time series as input. To overcome data limitations, time series from similar sources (replicates) are often combined. Although EDM with replicates has been evaluated using simulated data, the impact of adding time series remains not fully understood. In this study, we use simulated data from the Lorenz-63 system, a three-species food chain, and a four-species Lotka–Volterra model of competition to evaluate the performance of EDM’s S-Map algorithm across various scenarios, employing three different approaches to generate time series replicates, each with a different type of variation between the replicates: varying initial conditions (Scenario A), sampling distinct sections of the attractor (Scenario B), and varying the system’s parameter controlling chaotic behavior (Scenario C). Our findings demonstrate that EDM performs better with longer time series, but that combining replicates can often compensate for short time series length, in line with expectations from previous results. However, both the type and level of variation among the combined replicates affect forecasting accuracy. Adding replicates in Scenario B consistently improves outcomes. However, in Scenarios A and C (involving different long-term behaviors or transient phases), combining replicates may negate these benefits, particularly for periodic and chaotic systems and large inter-replicate variations. Our results show that not all time series replicates are equally suitable for improving EDM forecasts, highlighting the importance of careful selection and combination of replicates.