Fitting Nonstationary General-Time-Reversible Models to Obtain Edge-Lengths and Frequencies for the Barry–Hartigan Model
Bibliographic record
Abstract
Among models of nucleotide evolution, the Barry and Hartigan (BH) model (also known as the General Markov Model) is very flexible as it allows separate arbitrary substitution matrices along edges. For a given tree, the estimates of the BH model are a set of joint probability matrices, each giving the pairwise frequencies of nucleotides at the ends of the edge. We have previously shown that, due to an identifiability problem, these cannot be expected to consistently estimate the actual pairwise frequencies. A further consequence is that internal node frequency estimates are likely to be incorrect. Here we define a nonstationary GTR model for each edge that we refer to as the NSGTR model. We fit the NSGTR model by minimizing the sums of squares between the estimates of transition probabilities under the NSGTR model and the estimates provided by a fitted BH model. This NSGTR model provides estimates that avoid the identifiability difficulties of the BH model while closely fitting it. With the best-fitting NSGTR estimates, we are able to get interpretable frequency vectors at internal nodes as well as edge length estimates that are otherwise not yielded by the BH model. These edge lengths are interpretable as the expected number of substitutions along an edge for the model. We also show that for a nonstationary continuous-time model these are not the same as the edge length parameters for conventional substitution matrices that are output by nonstationary model phylogenetic estimation programs such as nhPhyML.
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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 | 0.004 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".