Testing models of biological scaling with mammalian population densities
Bibliographic record
Abstract
Two hypotheses have been suggested to explain the form of interspecific scaling of organismal characteristics to body size, such as the well-known increase in total metabolism with body mass. A hypothesis based on simple Euclidean geometry suggests that the scaling of many biological variables to body size should have a scaling exponent of 2/3, or [Formula: see text]0.667. On the other hand, according to a hypothesis based on fractal dimensions, the relationship between biological variables and body mass should have a scaling exponent of 0.750. We conducted a power analysis of the predicted exponents of scaling under the Euclidean and fractal hypotheses, using average adult body masses and population densities collected from the published literature on mammalian species. The collected data reflect 987 mammal populations from a broad variety of terrestrial habitats. Using statistical methods we determined the sample sizes required to decide between the values of the scaling exponent of the density-to-mass relationship based on the Euclidean (0.667) and fractal (0.750) hypotheses. Non-linearities in the dataset and insufficient power plagued our tests of the predictions. We found that mammalian species weighing less than 100 kg had a linear scaling pattern, sufficient power to reveal a difference between the scaling coefficients 0.667 and 0.750, and an actual scaling coefficient of 0.719 (barely significantly different from 0.667 but not from 0.750). Thus, our results support the fractal hypothesis, though the support was not particularly strong, which suggests that the relationship between body mass and population density should have a scaling exponent of 0.750.
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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 | 0.040 | 0.211 |
| 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 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".