Dynamics of coral reef models in the presence of parrotfish
Bibliographic record
Abstract
Abstract The decline of coral reefs characterized by macroalgae increase has been a global threat. We consider a slightly modified version of an ordinary differential equation (ODE) model proposed in Blackwood, Hastings, and Mumby [Theor. Ecol. 5 (2012), pp. 105–114] that explicitly considers the role of parrotfish grazing on coral reef dynamics. We perform complete stability, bifurcation, and persistence analysis for this model. If the fishing effort (f) is in between two critical values and , then the system has a unique interior equilibrium, which is stable if and unstable if . If is less (more) than these critical values, then the system has up to two (zero) interior equilibria. Also, we develop a more realistic delay differential equation (DDE) model to incorporate the time delay and treating it as the bifurcation parameter, and we prove that Hopf bifurcation about the interior equilibria could occur at critical time delays, which illustrate the potential importance of the inherent time delay in a coral reef ecosystem. Recommendations for Resource Managers One serious threat to coral reefs is overfishing of grazing species, including high level of algal abundance. Fishing alters the entire dynamics of a reef (Hughes, Baird, & Bellwood, 2003), for which the coral cover was predicted to decline rapidly (Mumby, 2006). One major issue is to reverse and develop appropriate management to increase or maintain coral resilience. We have provided a detailed local and global analysis of model (Blackwood, Hastings, & Mumby, 2012) and obtained an ecologically meaningful attracting region, for which there is a chance of stable coexistence of coral–algal–fish state. The healthy reefs switch to unhealthy state, and the macroalgae–parrotfish state becomes stable as the fishing effort increases through some critical values. Also, for some critical time delays, a switch between healthy and unhealthy reef states occurs through a Hopf bifurcation, which can only appear in the delay differential equation (DDE) model. Eventually, for large enough time delay, oscillations appear and an unhealthy state occurs.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".