This project was aimed to develop empirical dynamic modeling (EDM) as a practical framework for studying and managing ecosystems. A key challenge was to address the complex reality of ecosystems that are nonlinear, nonstationary and not in equilibrium – properties of real ecosystems that are not addressed by classical models (and that may explain their poor predictive ability). The goal was to develop capacity to build mechanistic models that can be used to confidently forecast environmental futures in a dynamically changing world. Though many of the tactical objectives of the project are technically framed, together they provide tools that have practical utility to support the Department of Defense's (DoD) environmental interests and SERDP’s deployment of best-available science at the cutting edge.

Empirical dynamic modelling is an inductive data-driven approach for studying complex systems from time series observations. While classical approaches involve hypothesized models, EDM attempts to minimize these assumptions by allowing the data to speak for itself. Thus, instead of assuming a particular model, EDM allows the data to tell us what the underlying model should look like. EDM is based on reconstructing an attractor from time series data (https://youtu.be/fevurdpiRYg). This allows the identification and ability to study causal variables and interactions that are nonlinear and state-dependent and make skillful out-of-sample predictions. The abilities developed here to forecast and to explore alternative scenarios (e.g. different future environmental constraints), and to evaluate state dependent risk in terms of uncertainty (e.g., local sensitivity to dramatic change driven by dynamic instability), are essential for ecosystem management – the stated goals of this project.

Central among the new high-level insights brought to the fore is the fact that causal drivers can be completely uncorrelated with their effects. The project team found that uncorrelated variables (that are therefore invisible to normal data exploration) are ubiquitous in nature and can be key elements for understanding mechanisms and for predicting and managing environmental futures — an inconvenient fact that profoundly impacts the normal study protocols and model-building efforts. To this end, the project demonstrated real solutions for understanding environmental futures in two tactical case studies. In the first case, EDM allowed the project team to untangle causal drivers of red tides (potentially harmful algal blooms) in the Southern California bight ­and demonstrate short-term prediction capability where none had seemed possible. By allowing for non-equilibrium and nonlinear dynamics, EDM analysis confirmed hypothesized drivers like nitrate and ocean temperature had predictable effects even though traditional methods had previously found them to be uncorrelated with the algal blooms. Combined with regional ocean simulations (ROMS) of future ocean conditions, the hybrid ROMS-EDM model predicts an increase in red tides over the next three decades. The second case study develops a predictive framework for conservation management of reef areas that continue to be long-term DoD responsibilities in the U.S. Pacific Islands. This required developing new EDM methods for cases where historical time series are short. These methods uncovered the major environmental drivers operating at the reef sites, which in turn can identify specific areas in the U.S. Pacific Island region where conservation investments are most likely to succeed.

Both case studies are useful SERDP targets on their own, but together they have grown the methodology and serve as road maps for new practitioners and applications. Critically, the project developed a standardized set of computational tools in R, Python, and C++ with documentation to communicate the essential foundations for new users wishing to apply EDM to their research. The benefits of this work can be quantified by how highly subscribed the resources are. The rEDM package has more than 19,000 downloads from CRAN; and pyEDM has more than 76,729 downloads through the central PyPI server in the first year of its launch. Together the code and documentation are already having a transformative effect on multiple scientific domains with well over 100 new publications citing EDM in just the first few months of 2020. It seems likely that beyond the conservation benefits of the two specific case studies, EDM should be useful to future SERDP projects ranging from hydrology to fire ecology. It is a natural tool set for environmental science.