Self‐shading affects allometric scaling in trees
Bibliographic record
Abstract
Summary 1. Westet al.[Science,284(1999) 1677] derived an optimal body‐size scaling exponent under the assumption that resources are evenly distributed among exchange surfaces, leading to the well‐known ¾ scaling rule. In trees, this implies a volume‐filling branching network (a fractal dimension of 3 for foliage). However, there is evidence that the fractal dimension is less than 3 in trees. 2. Here, we include self‐shading in the derivation of optimal fractal dimensions. With self‐shading, resources are not evenly distributed among leaves because light enters the crown at the surface and is gradually attenuated within the crown. We find that the optimal fractal dimension can take values between 2 and 3, depending on light interception properties and crown size. 3. For a large data set on foliage and woody biomass in gymnosperm trees, we confirm that the fractal dimension of foliage is less than 3, and that it shows a weak dependence on crown size. However, foliage biomass scaled with crown woody biomass with an exponent of 0·78, very close to the theoretical expectation of ¾ scaling. This can be explained by a deviation from the theoretical prediction in the scaling of crown woody biomass and crown length. 4. Overall, these results confirm a deviation from volume filling in gymnosperm trees, and we provide an explanation for this deviation in terms of optimal metabolic scaling. Because ¾ scaling of foliage biomass is still approximately valid, this implies that metabolic scaling exponents may not be as tightly linked to the fractal dimension of foliage as previously assumed.
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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 | 0.001 | 0.003 |
| 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 | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".