Age-independent difference equations for modelling tree and stand growth
Bibliographic record
Abstract
Modelling growth of trees or stands when age is not available is often necessary. This is the case in national forest inventories or when age is not a main determinant of growth (e.g., trees growing in uneven-aged stands). Even if age is not known, functions used to model growth should follow the required pattern, with a maximum and a slow decline after the maximum is attained. There are some empirical functions with these properties; however, direct modelling with difference equations derived from the so-called theoretical growth functions has not been used for this purpose, as they are age dependent. This paper presents a methodology to formulate growth functions as age-independent difference equations. These can be used when age is not available or is not relevant. The proposed equations have the advantage of allowing the direct modelling of yield instead of growth. If the parameters are expressed as a function of site variables, the equations are invariant for projection length and therefore can be used when data is not equally spaced in time, as is the case of most data sets. The methodology is applied to the Lundqvist and Richards growth functions, the most commonly used in growth and yield modelling. The use of the age-independent growth functions is illustrated by using two case studies in Portugal: dominant height growth of eucalyptus (Eucalyptus globulus Labill.) plantations and individual tree growth in diameter at breast height in sparse cork oak (Quercus suber L.) stands.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| 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 | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".