Five-leaf generalizations of the <i>D</i> -statistic reveal the directionality of admixture
Bibliographic record
Abstract
Abstract Over the past 15 years, the D -statistic, a four-taxon test for organismal admixture (hybridization, or introgression) which incorporates single nucleotide polymorphism data with allelic patterns ABBA and BABA, has seen considerable use. This statistic seeks to discern significant deviation from either a given species tree assumption, or from the balanced incomplete lineage sorting that could otherwise defy this species tree. However, while the D -statistic can successfully discriminate admixture from incomplete lineage sorting, it is not a simple matter to determine the directionality of admixture using only four-leaf tree models. As such, methods have been developed that use 5 leaves to evaluate admixture. Among these, the D FOIL method, which tests allelic patterns on the “symmetric” tree S = (((1, 2), (3, 4)), 5), succeeds in finding admixture direction for many five-taxon examples. However, D FOIL does not make full use of all symmetry, nor can D FOIL function properly when ancient samples are included because of the reliance on singleton patterns (such as BAAAA and ABAAA). Here, we take inspiration from D FOIL to develop a new and completely general family of five-leaf admixture tests, dubbed Δ-statistics, that can either incorporate or exclude the singleton allelic patterns depending on individual taxon and age sampling choices. We describe two new shapes that are also fully testable, namely the “asymmetric” tree A = ((((1, 2), 3), 4), 5) and the “quasisymmetric” tree Q = (((1, 2), 3), (4, 5)), which can considerably supplement the “symmetric” S = (((1, 2), (3, 4)), 5) model used by D FOIL . We demonstrate the consistency of Δ-statistics under various simulated scenarios, and provide empirical examples using data from black, brown and polar bears, the latter also including two ancient polar bear samples from previous studies. Recently D FOIL and one of these ancient samples was used to argue for a dominant polar bear → brown bear introgression direction. However, we find, using both this ancient polar bear and our own, that by far the strongest signal using both D FOIL and Δ-statistics on tree S is actually bidirectional gene flow of indistinguishable direction. Further experiments on trees A and Q instead highlight what were likely two phases of admixture: one with stronger brown bear → polar bear introgression in ancient times, and a more recent phase with predominant polar bear → brown bear directionality. Code and documentation available at https://github.com/KalleLeppala/Delta-statistics .
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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 | 0.009 | 0.032 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 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".