The effect of landscape fragmentation on Turing-pattern formation
Bibliographic record
Abstract
Diffusion-driven instability and Turing pattern formation are a well-known mechanism by which the local interaction of species, combined with random spatial movement, can generate stable patterns of population densities in the absence of spatial heterogeneity of the underlying medium. Some examples of such patterns exist in ecological interactions between predator and prey, but the conditions required for these patterns are not easily satisfied in ecological systems. At the same time, most ecological systems exist in heterogeneous landscapes, and landscape heterogeneity can affect species interactions and individual movement behavior. In this work, we explore whether and how landscape heterogeneity might facilitate Turing pattern formation in predator-prey interactions. We formulate reaction-diffusion equations for two interacting species on an infinite patchy landscape, consisting of two types of periodically alternating patches. Population dynamics and movement behavior differ between patch types, and individuals may have a preference for one of the two habitat types. We apply homogenization theory to derive an appropriately averaged model, to which we apply stability analysis for Turing patterns. We then study three scenarios in detail and find mechanisms by which diffusion-driven instabilities may arise even if the local interaction and movement rates do not indicate it.
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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 | 0.000 |
| 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".