Explaining empirical dynamic modelling using verbal, graphical and mathematical approaches
Bibliographic record
Abstract
Empirical dynamic modelling (EDM) is becoming an increasingly popular method for understanding the dynamics of ecosystems. It has been applied to laboratory, terrestrial, freshwater and marine systems, used to forecast natural populations and has addressed fundamental ecological questions. Despite its increasing use, we have not found full explanations of EDM in the ecological literature, limiting understanding and reproducibility. Here we expand upon existing work by providing a detailed introduction to EDM. We use three progressively more complex approaches. A short verbal explanation of EDM is then explicitly demonstrated by graphically working through a simple example. We then introduce a full mathematical description of the steps involved. Conceptually, EDM translates a time series of data into a path through a multi-dimensional space, whose axes are lagged values of the time series. A time step is chosen from which to make a prediction. The state of the system at that time step corresponds to a 'focal point' in the multi-dimensional space. The set (called the library) of candidate nearest neighbours to the focal point is constructed, to determine the nearest neighbours that are then used to make the prediction. Our mathematical explanation explicitly documents which points in the multi-dimensional space should not be considered as focal points. We suggest a new option for excluding points from the library that may be useful for short-term time series that are often found in ecology. We focus on the core simplex and S-map algorithms of EDM. Our new R package, pbsEDM, enhances understanding (by outputting intermediate calculations), reproduces our results and can be applied to new data. Our work improves the clarity of the inner workings of EDM, a prerequisite for EDM to reach its full potential in ecology and have wide uptake in the provision of advice to managers of natural resources.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.057 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.005 | 0.004 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.007 | 0.009 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.017 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".