A hybrid finite element method for moving-habitat models in two spatial dimensions
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Bibliographic record
Abstract
Moving-habitat models track the density of a population whose suitable habitat shifts as a consequence of climate change. Whereas most previous studies in this area consider 1-dimensional space, we derive and study a spatially 2-dimensional moving-habitat model via reaction-diffusion equations. The population inhabits the whole space. The suitable habitat is a bounded region where population growth is positive; the unbounded complement of its closure is unsuitable with negative growth. The interface between the two habitat types moves, depicting the movement of the suitable habitat poleward. Detailed modelling of individual movement behaviour induces a nonstandard discontinuity in the density across the interface. For the corresponding semi-discretised system we prove well-posedness for a constant shifting velocity before constructing an implicit-explicit hybrid finite element method. In this method, a Lagrange multiplier weakly imposes the jump discontinuity across the interface. For a stationary interface, we derive optimal a priori error estimates over a conformal mesh with nonconformal discretisation. We demonstrate with numerical convergence tests that these results hold for the moving interface. Finally, we demonstrate the strength of our hybrid finite element method with two biologically motivated cases, one for a domain with a curved boundary and the other for non-constant shifting velocity.
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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 | 0.001 |
| 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