Allele Age Under Non-Classical Assumptions is Clarified by an Exact Computational Markov Chain Approach
Bibliographic record
Abstract
Abstract Determination of the age of an allele based on its population frequency is a well-studied problem in population genetics, for which a variety of approximations have been proposed. We present a new result that, surprisingly, allows the expectation and variance of allele age to be computed exactly (within machine precision) for any finite absorbing Markov chain model in a matter of seconds. This approach makes none of the classical assumptions (e.g., weak selection, reversibility, infinite sites), exploits modern sparse linear algebra techniques, integrates over all sample paths, and is rapidly computable for Wright-Fisher populations up toNe = 100,000. With this approach, we study the joint effect of recurrent mutation, dominance, and selection, and demonstrate new examples of “selective strolls” where the classical symmetry of allele age with respect to selection is violated by weakly selected alleles that are older than neutral alleles at the same frequency. We also show evidence for a strong age imbalance, where rare deleterious alleles are expected to be substantially older than advantageous alleles observed at the same frequency when population-scaled mutation rates are large. These results highlight the under-appreciated utility of computational methods for the direct analysis of Markov chain models in population genetics.
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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 | 0.002 | 0.011 |
| 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 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".