Preston’s universal formula for avian egg shape
Bibliographic record
Abstract
Abstract Nearly 70 years ago, Preston published a pioneering study in which he provided formulae for the shapes of birds’ eggs. One of these formulae is universal in that it provides an almost perfect representation for all eggs, even pyriform ones, and is better than all other formulae published since. This essentially perfect representation of egg shape is obtained by estimating the parameters in Preston’s universal formula by least squares, using hundreds of measurements of the egg’s radii along its entire length. Preston’s universal formula can also be used to obtain an equation for avian egg shape that uses just 5 measurements (the length and 4 appropriately spaced diameters). The equation based solely on these 5 measurements provides an egg shape that is virtually indistinguishable from one based on hundreds of measurements. We demonstrate the usefulness of Preston’s formulations using digital photographs of eggs. Our perspective is that, despite a number of subsequent approaches, Preston’s original one has not been bettered and should be the standard for studying avian egg shape.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".