Bibliographic record
Abstract
Convergence of discrete-time Markov chains with two timescales is a powerful tool to study stochastic evolutionary games in subdivided populations. Focusing on linear games within demes, convergence to a diffusion process for the strategy frequencies as the population size increases yields a strong-migration limit. The same limit is obtained for a linear game in a well-mixed population with effective payoffs that depend on reproductive values and identity measures between individuals. The first-order effect of selection on the fixation probability of a strategy introduced as a single mutant can be calculated by using the diffusion approximation, or alternatively by summing the successive expected changes in the mutant strategy frequency that involve expected coalescence times of ancestral lines under neutrality. These can be approached by resorting to the existence of two timescales in the genealogical process. Keeping the population size fixed but letting the intensity of migration go to zero, convergence to a continuous-time Markov chain after instantaneous initial transitions yields a low-migration limit that depends on fixation probabilities within demes in the absence of migration. In the limit of small uniform dispersal, the fixation probability of a mutant strategy in the whole population exceeds its initial frequency if it is risk-dominant over the other strategy with respect to the overall average payoffs in pairwise interactions. Finally, in the low-mutation limit in the presence of recurrent mutation, the average abundance of a strategy in the long run is determined by the fixation probabilities of both strategies when introduced as single mutants in a deme chosen at random.
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.004 |
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 teacher head, 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".