The change in a mean measurement that is invariant under reshuffling of genes
Bibliographic record
Abstract
Fisher's fundamental theorem of natural selection continues to be widely cited in the literature but there is still misunderstanding about its interpretation and significance. Even though it is now recognized that the additive genetic variance in its statement captures only a partial rate of change in mean fitness, the original terms and arguments used to present it remain unclear, not to mention its real meaning. Here, we revisit the interpretation of this partial rate of change. Applying the properties of the additive genetic values and residual addends of a quantitative trait to the relative growth rate of genotype frequency in a diploid population, and comparing two reproductive systems, clonal reproduction and sexual reproduction with either random union of gametes or random mating with additive fecundities of mating types, we argue that this additive genetic rate of change corresponds to the change that is invariant under reshuffling of genes. We show that this is actually the case for the partial rate of change in the mean of any measurement given by the additive genetic covariance with fitness. We focus on the one-locus multiallele setting in continuous time without age effects for simplicity, but the conclusion can be extended to multilocus settings with age effects in continuous time as well as discrete time.
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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 | 0.003 | 0.021 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".