OPTIMAL PHOSPHORUS LOADING FOR A POTENTIALLY EUTROPHIC LAKE
Bibliographic record
Abstract
We are concerned with the management of ecological and economic systems with threshold responses and with several time scales. Although optimal control of such systems is seldom attainable, the form of such optimal controls provides important insights for more practical schemes. Here we optimize the expected discounted net benefits of phosphorus (P) loadings for a potentially eutrophic lake. The benefits accrue to agricultural interests from activities that result in loading, and costs accrue to other interests from the resulting deterioration of water quality. We extend the 1999 results of S. R. Carpenter, D. Ludwig, and W. A. Brock to account for dependence of P recycling upon the concentration of P in sediments. We obtain optimal policies using methods of dynamic programming with two state variables. We find a strong interaction between economic and ecological parameters in determining the optimal policy: the economic discount rate determines whether the time horizon is long or short, and this in turn strongly influences the magnitude of the optimal loadings. Simple policies that neglect dynamics of P in the sediments are inadequate unless the time horizon is short and the dynamics are slow. A stochastic model is essential if there are substantial random fluctuations in loadings. Uncertainty in the determination of the critical P density that triggers recycling cannot be neglected. Our results may be interpreted as a quantitative precautionary principle that takes account of both economic and ecological aspects of the management of the lake. Our results may also be used to illustrate economic ideas such as sustainable development, natural capital, option values, and income.
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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 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".