The impacts of dispersal on the competition outcome of multi-patch competition models
Bibliographic record
Abstract
In this paper, we study a two-species competition model over patchy environments. One species is assumed to disperse randomly between patches with a constant dispersal delay. We show that the dispersal does not affect the stability and instability of the homogeneous coexistence equilibrium in two configurations (fully connected configuration and ring-structured configuration) of an arbitrary number of patches. For the weak competition case, we show that the homogeneous coexistence equilibrium is the unique coexistence equilibrium and both species can coexist. However, for the strong competition case, we show that the homogeneous coexistence equilibrium is unstable, in addition, small dispersal rate can induce multiple coexistence equilibria and the dispersal (including the dispersal rate and the dispersal delay) does have impacts on determining the competition outcome and can induce multi-stability. As a result, transient coexistence of both species can be observed in all patches, and long-term coexistence of both species in some patches, though not in all patches, becomes possible.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".