Takeover, fixation and identifiability in finite neutral genealogy models
Bibliographic record
Abstract
For neutral genealogy models in a finite, possibly non-constant population, there is a convenient ordered rearrangement of the particles, known as the lookdown representation [6], that greatly simplifies the analysis of the family trees. By introducing the dual notions of forward and backward neutrality, we give a more intuitive implementation of this rearrangement. We also show that the lookdown arranges subtrees in size-biased order of the number of their descendants, a property that is familiar in other settings [2] but appears not to have been previously established in this context. In addition, we use the lookdown to study three properties of finite neutral models, as a function of the sequence of unlabelled litter sizes of the model: uniqueness of the infinite path (fixation), existence of a single lineage to which almost all individuals can trace their ancestry (takeover) and whether or not we can infer the lookdown rearrangement by examining the unlabelled genealogy model (identifiability). Identifiability of the spine path in size-biased Galton-Watson trees was studied in [1], so we also discuss connections to those results, by relating the spinal decomposition to the lookdown.
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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 | 0.006 | 0.047 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.007 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.003 | 0.004 |
| 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".