Smaller population size at the MRCA time for stationary branching processes
Bibliographic record
Abstract
We consider an elementary model of random size varying population governed by a stationary continuous-state branching process. We compute the distributions of various variables related to the most recent common ancestor (MRCA): the time to the MRCA, the size of the current population and the size of the population just before the MRCA. In particular we observe a natural mild bottleneck effect as the size of the population just before the MRCA is stochastically smaller than the size of the current population. We also compute the number of individuals involved in the last coalescent event of the genealogical tree, that is, the number of individuals at the time of the MRCA who have descendants in the current population. By studying more precisely the genealogical structure of the population, we get asymptotics for the number of ancestors just before the current time. We give explicit computations in the case of the quadratic branching mechanism. In this case, the size of the population at the MRCA is, in mean, $2/3$ of the size of the current population. We also provide in this case the fluctuations for the renormalized number of ancestors.
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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 | 0.013 |
| 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 | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".