A unifying theory for two-dimensional spatial redistribution kernels with applications in population spread modelling
Bibliographic record
Abstract
When building models to explain the dispersal patterns of organisms, ecologists often use an isotropic redistribution kernel to represent the distribution of movement distances based on phenomenological observations or biological considerations of the underlying physical movement mechanism. The Gaussian, two-dimensional (2D) Laplace and Bessel kernels are common choices for 2D space. All three are special (or limiting) cases of a kernel family, the Whittle-Matérn-Yasuda (WMY), first derived by Yasuda from an assumption of 2D Fickian diffusion with gamma-distributed settling times. We provide a novel derivation of this kernel family, using the simpler assumption of constant settling hazard, by means of a non-Fickian 2D diffusion equation representing movements through heterogeneous 2D media having a fractal structure. Our derivation reveals connections among a number of established redistribution kernels, unifying them under a single, flexible modelling framework. We demonstrate improvements in predictive performance in an established model for the spread of the mountain pine beetle upon replacing the Gaussian kernel by the Whittle-Matérn-Yasuda, and report similar results for a novel approximation, the product-Whittle-Matérn-Yasuda, that substantially speeds computations in applications to large datasets.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".