Optimum Forest Rotations of Alternative Tree Species
Bibliographic record
Abstract
We solve Faustmann's problem when two tree species are available for planting. The analysis also applies to optimal forest exploitation before an endogenous switch to some alternative land use such as agriculture, housing, or preservation, and vice versa. Each species has its own deterministic growth function and commands a timber price that grows exponentially at a constant rate. Therefore, it may be optimal to first exploit the species whose price is high but grows slowly, and then switch to the alternative species once its price has sufficiently increased relative to the price of the first one. When the land is bare, there exists a threshold of the relative price at which the investor is indifferent between planting either species. When the relative price lies below this switching threshold, it is optimal to plant and harvest the high-price low-rate species repeatedly until the value of the other species warrants its introduction; it is then repeatedly harvested and replanted indefinitely according to the standard Faustmann rule; the rotation does not depend on timber price. Before the switch, the optimal harvest age depends on the relative price; it defines a replanting boundary for relative prices below the switching threshold and a switching boundary for relative prices above the switching threshold. We show that the replanting boundary is a sequence of continuous segments giving the harvest age as function of the relative price; these segments differ depending on the number of harvests of the initial species that remain before the switch. Each segment is first decreasing, then increasing, and crosses Faustmann's rotation twice. On an optimal sequence of harvests, successive rotations are increasingly higher or decreasingly lower than Faustmann's rotation; they may also be constant and equal to Fausmann's rotation.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".