A modified growth function with interpretable parameters applied to the age–height relationship of individual trees
Bibliographic record
Abstract
Growth functions frequently used in forestry have in common that among the model parameters to be estimated, only the asymptote is expressed in the dimensions of the input data. By contrast, parameters determining rate and shape of the curve often exhibit indefinite scales. This might cause problems in specifying adequate starting values and in parameter interpretation. We present a mathematical derivation to obtain a modified growth function based on the four-parameter Richards function. Two of the rate and shape parameters were replaced by new parameters directly related to the growth process: time of maximum growth and maximum growth rate. Both the original model and its modified form were fitted to individual-tree height–age data from the National Forest Inventory in Germany. The modified function has several advantages: (i) easier interpretability of model parameters, (ii) easier specification of starting values, (iii) improved linear behavior allowing for more reliable asymptotic inferences and for better convergence, and (iv) reduced correlation between model parameters. As a further benefit, the presented model allows for deriving biologically interpretable forms of the Gompertz function, the von Bertalanffy function, and the logistic function. Based on the results, we suggest using the modified function provided for further applications in growth modeling.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| 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".