Total equilibrium biomass of a two-patch logistic equation with density-dependent dispersal
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Bibliographic record
Abstract
Recent research has extensively examined the impacts of dispersal intensity and dispersal asymmetry on the total equilibrium biomass in the context of the multi-patch logistic equation with density-independent dispersal. In this study, we introduce an alternative model for the two-patch logistic equation featuring density-dependent dispersal. Specifically, we propose that the dispersal rate from one patch to another is inversely proportional to the fitness of individuals within that patch. Through rigorous analysis, we establish the existence and uniqueness of a globally asymptotically stable equilibrium and elucidate the conditions under which dispersal enhances or diminishes the total equilibrium biomass. Furthermore, we establish the minimum and maximum bounds for the total equilibrium biomass and conduct a comparative analysis with the standard two-patch logistic model.
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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 | 0.000 | 0.000 |
| 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 | 0.000 |
| 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 it