A practical guide to characterising ecological coexistence
Bibliographic record
Abstract
Coexistence is simultaneously one of the most fundamental concepts of ecology, and one of the most difficult to define. A particular challenge is that, despite a well-developed body of research, several different schools of thought have developed over the past century, leading to multiple independent, and largely isolated, branches of literature with distinct methodologies. Here, we provide a broad overview of the most common concepts and metrics currently used to detect and characterise ecological coexistence. We first introduce four classes of behaviour, which jointly describe the ways in which community dynamics can unfold: (i) the existence of a feasible steady state (or invariant set), i.e. where all coexisting species retain positive abundances in the long-term in the absence of interference by external forces; (ii) the existence of a local attractor that draws the community towards a feasible steady state from within a restricted set of starting conditions; (iii) the existence of a global attractor that draws the community towards feasible steady states from any non-zero starting condition; and (o) a null transient state, where species abundances vary over time irrespective of steady states and attractors. Next, we explain how these classes of behaviour relate to commonly used metrics for identifying and characterising coexistence, including analyses of parameter sensitivity, asymptotic return rates, invasion growth rates, and time to extinction. We then discuss the scope and limitations of each of these behavioural classes and corresponding metrics, with a particular focus on applications in empirical systems. Finally, we provide a potential workflow for matching empirical questions to theoretical tools, and present a brief prospectus looking forward to opportunities for advancing and integrating research on coexistence.
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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 | 0.004 | 0.020 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.005 | 0.005 |
| Insufficient payload (model declined to judge) | 0.125 | 0.082 |
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".