Takeover, fixation and identifiability in finite neutral genealogy models
Why this work is in the frame
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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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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.002 |
| 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 | 0.001 |
| 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 it