Demographic analysis of gummy shark (<i>Mustelus antarcticus</i>) and school shark (<i>Galeorhinus galeus</i>) off southern Australia by applying a generalized Lotka equation and its dual equation
Bibliographic record
Abstract
Although Lotka's equation is commonly used for calculating the intrinsic rate of increase with time of a fish population in demographic analysis, its dual equation has never been derived. In this paper, we establish an explicit relationship between the intrinsic rate of increase with time of a fish population and its instantaneous rate of natural mortality from an age-dependent population dynamics model, derive a generalized Lotka equation for calculating the intrinsic rate of increase with time, and derive its dual equation for calculating the intrinsic rate of decrease with age. The virginal intrinsic rate of increase with time of the gummy shark (Mustelus antarcticus) population was calculated as 0.115957·year-1 and its intrinsic rate of decrease with age as -0.312957·year-1. The virginal intrinsic rate of increase with time of the school shark (Galeorhinus galeus) population was calculated as 0.109480·year-1 and its intrinsic rate of decrease with age as -0.216980·year-1. The generalized Lotka equation and its dual equation thus derived imply that both reproductive schedules of a population of animals and its instantaneous rate of total mortality determine its intrinsic rate of increase with time, whereas its reproductive schedules alone determine its intrinsic rate of decrease with age.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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".