A system of nonlinear simultaneous equations for crown length and crown radius for the forest dynamics model SORTIE-ND
Bibliographic record
Abstract
A system of equations was developed to predict crown length (CL) and crown radius (CRAD) for trees in structurally complex stands. The equations address two problems that often arise in crown allometry. First, relationships between the main stem and the crown are likely to change with intertree competition. Therefore, explicit measures of density were used along with main stem measurements as explanatory variables. Second, the physiological relationship between CL and CRAD is often overlooked when modeling crowns. This relationship is incorporated through the use of a simultaneous system of equations. Parameters were estimated using nonlinear three-stage least squares (N3SLS) in which first-stage equation estimates of CRAD are used to estimate CL and vice versa in the second and third stages of N3SLS. The equations were fitted and validated for four species: lodgepole pine (Pinus contorta Douglas ex Louden var. latifolia Engelm. ex S. Watson), hybrid spruce (Picea engelmannii Parry ex Engelm. × P. glauca (Moench) Voss), Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco var. glauca (Beissn.) Franco), and trembling aspen (Populus tremuloides Michx.). The intent is to use the equations as alternatives to the crown equations in the spatially explicit forest growth model SORTIE-ND that use only main stem variables in estimating crowns over time.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".