Predicting Long Pendant Edges in Model Phylogenies, with Applications to Biodiversity and Tree Inference
Bibliographic record
Abstract
In the simplest phylogenetic diversification model (the pure-birth Yule process), lineages split independently at a constant rate $\lambda$ for time $t$. The length of a randomly chosen edge (either interior or pendant) in the resulting tree has an expected value that rapidly converges to $\frac{1}{2\lambda}$ as $t$ grows and thus is essentially independent of $t$. However, the behavior of the length $L$ of the longest pendant edge reveals remarkably different behavior: $L$ converges to $t/2$ as the expected number of leaves grows. Extending this model to allow an extinction rate $\mu$ (where $\mu<\lambda$), we also establish a similar result for birth-death trees, except that $t/2$ is replaced by $t/2 \cdot (1-\mu/\lambda)$. This "complete" tree may contain subtrees that have died out before time $t$; for the "reduced tree" that just involves the leaves present at time $t$ and their direct ancestors, the longest pendant edge length $L$ again converges to $t/2$. Thus, there is likely to be at least one extant species whose associated pendant branch attaches to the tree approximately half-way back in time to the origin of the entire clade. We also briefly consider the length of the shortest edges. Our results are relevant to phylogenetic diversity indices in biodiversity conservation, and to quantifying the length of aligned sequences required to correctly infer a tree. We compare our theoretical results with simulations and with the branch lengths from a recent phylogenetic tree of all mammals. [Birth-death process; phylogenetic diversification models; phylogenetic diversity.].
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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 | 0.000 | 0.000 |
| 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 | 0.000 |
| 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 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".