A Bayesian Analysis of Biological Uncertainty for a Whole-Lake Fertilization Experiment for Sockeye Salmon in Chilko Lake, British Columbia, and Implications for the Benefit–Cost Ratio
Bibliographic record
Abstract
Abstract Chilko Lake in British Columbia, Canada, was fertilized with nitrogen and phosphorus in the late 1980s and early 1990s to increase abundance and harvests of adult sockeye salmon Oncorhynchus nerka. Because of the short, 5-year duration of this program and the large inherent natural variation in adult recruits produced per spawner both before and during lake fertilization, there is considerable uncertainty about the efficacy of that fertilization. Recent analyses suggest a high probability that more adult sockeye salmon were produced per spawner from fertilization than would have been produced without fertilization, but the confidence interval on that increase is large. Furthermore, no economic analysis has been done to determine the effect of the large biological uncertainties on the benefit–cost (BC) ratio of the project. We filled this need by using Bayesian statistical analysis to estimate uncertainty in the parameters of four models that reflected different hypotheses about the biological effects of fertilization on sockeye salmon. We then used those estimated posterior probability distributions for (1) additional sockeye salmon recruits that were attributable to fertilization and (2) the resulting economic BC ratio. This ratio took into account costs of fertilization as well as costs and benefits of harvesting additional fish. We found evidence of biological and net economic benefits for the Chilko Lake fertilization project. Depending on the model, the posterior probability was at least 81% that the abundance of adult sockeye salmon increased owing to fertilization and at least 84% that the BC ratio was greater than 1.0 (mean BC ratio = 27). Nevertheless, considerable uncertainty remains because the 95% probability interval was large for the BC ratio. The breadth of the distribution for the BC ratio was probably underestimated because of uncertainties (omitted here) concerning various economic components of our analysis as well as the costs and benefits of the indirect effects of fertilization.
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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 | 0.025 | 0.051 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".