Traveling waves in a free boundary problem for the spread of ecosystem engineers
Bibliographic record
Abstract
Reaction-diffusion equations are a trusted modeling framework for the dynamics of biological populations in space and time, and their traveling wave solutions are interpreted as the density of an invasive species that spreads at constant speed. Even though certain species can significantly alter their abiotic environment for their benefit, and even though some of these so-called "ecosystem engineers" are among the most destructive invasive species, most models neglect this feedback. Here, we extended earlier work that studied traveling waves of ecosystem engineers with a logistic growth function to study the existence of traveling waves in the presence of a strong Allee effect. Our model consisted of suitable and unsuitable habitat, each a semi-infinite interval, separated by a moving interface. The speed of this boundary depended on the engineering activity of the species. On each of the intervals, we had a reaction-diffusion equation for the population density, and at the interface, we had matching conditions for density and flux. We used phase-plane analysis to detect and classify several qualitatively different types of traveling waves, most of which have previously not been described. We gave conditions for their existence for different biological scenarios of how individuals alter their abiotic environment. As an intermediate step, we studied the existence of traveling waves in a so-called "moving habitat model", which can be interpreted as a model for the effects of climate change on the spatial dynamics of populations.
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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 | 0.002 | 0.002 |
| 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 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".