Sensitivity analysis of Markov models for communities of competing sessile organisms
Bibliographic record
Abstract
1. Communities of competing sessile organisms are often modelled using Markov chains. Sensitivity analysis of the stationary distribution of these models tells us how we expect the abundance of each organism to respond to changes in interactions between species. This is important for conservation and management. 2. Markov models for such communities have usually been formulated in discrete time. Each column of the discrete-time transition matrix must sum to 1 (column stochasticity). Sensitivity analysis therefore involves defining a pattern of compensation that maintains column stochasticity as a single transition probability changes. There is little biological theory about the appropriate compensation pattern, but the usual choices involve changing only the elements of a single column of the transition matrix. 3. I argue that if the underlying dynamics occur in continuous time, each transition probability is the net outcome of direct and many indirect interactions. 4. Determining the consequences of changing a single direct interaction will often be of interest. I show how this can be achieved using a continuous-time model. The resulting discrete-time compensation pattern is quite different from those that have been considered elsewhere, with changes occurring in many columns. 5. I also show how to determine which direct interactions are being changed under any discrete-time compensation pattern.
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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 | 0.013 | 0.043 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
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".