A generalized adaptive harvesting model exhibits cusp bifurcation, noise, and rate-associated tipping pathways
Bibliographic record
Abstract
Abstract The sustainability of renewable resource harvesting may be threatened by environmental and socioeconomic changes that induce tipping points. Here, we propose a synthetic harvesting model with a comprehensive set of socioecological factors that have not been explored together, including market price and stock value, effort and processing costs, labour and natural capital elasticities, societal risk aversion, maximum sustainable yield ( MSY ), and population growth shape. We solve for harvest rate and stock biomass solutions by applying a timescale-separation between fast ecological dynamics and slow institutional adaptation that responds myopically to short-term net profit. The result is a cusp bifurcation with two composite bifurcation parameters: 1. consumptive scarcity λ c or the ratio of market price-to-processing cost divided by MSY (leading to a pitchfork), and 2. non-consumptive scarcity λ n or the stock value minus a scaled effort cost (leading to saddle-nodes or folds). Together, consumptive and non-consumptive scarcities create a cusp catastrophe. We further identify four tipping phenomena: 1. process (harvest rate) noise-induced tipping; 2. exogenous ( λ c ) rate+process noise-induced tipping; 3. exogenous noise-induced reduction in tipping; and 4. exogenous cycle-induced reduction in tipping. Case 2 represents the first mechanistically motivated example of rate-associated tipping in socioecological systems, while cases 3 and 4 resemble noise-induced stability. We discuss the empirical relevance of catastrophe and tipping in natural resource management. Our work shows that human institutional behaviour coupled with changing socioecological conditions can cause counterintuitive sustainability and resilience outcomes.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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".