Some guidance on using mathematical notation in ecology
Bibliographic record
Abstract
Abstract Mathematical modelling is playing an increasing role in studies of ecological systems. This requires the communication of the details of a mathematical model, including the use of mathematical notation to represent ecological variables, parameters and processes. In our experience, the clarity of mathematical notation varies between papers and can often be inconsistent with general conventions. Poor notation can impede communication and understanding of ideas, and make models appear more complicated than necessary. Here, we present some guidelines, including: (a) define every term in an equation, (b) use fonts appropriately (italicise mathematical symbols, use bold lower case for vectors and bold upper case for matrices), (c) use subscripts appropriately (to index quantities, for example, by year), (d) use superscripts appropriately (to indicate a power, the transpose of a matrix or the steady‐state value of a quantity), (e) avoid multiletter variable names, and (f) revisit notation early on in a project to see if it should be refined. Although we focus mainly on ecology, our guidelines should be of interest to researchers applying models in evolutionary biology and broader areas of biology.
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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 | 0.047 | 0.125 |
| Meta-epidemiology (narrow) | 0.005 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.004 |
| Bibliometrics | 0.007 | 0.008 |
| Science and technology studies | 0.004 | 0.014 |
| Scholarly communication | 0.009 | 0.028 |
| Open science | 0.010 | 0.006 |
| Research integrity | 0.008 | 0.019 |
| Insufficient payload (model declined to judge) | 0.031 | 0.040 |
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".