Statistical Genomics Foundry
Paper
domain/molecular-evolutiontopic/positive-selectiontopic/multiple-testing

Smith et al. 2015 — aBSREL (adaptive Branch-Site Random Effects Likelihood)

1. Citation

Smith MD, Wertheim JO, Weaver S, Murrell B, Scheffler K, Kosakovsky Pond SL. 2015. “Less is more: an adaptive branch-site random effects model for efficient detection of episodic diversifying selection.” Molecular Biology and Evolution 32(5):1342–1353. DOI: 10.1093/molbev/msv022. Open-access copy: PMC4408413 (https://pmc.ncbi.nlm.nih.gov/articles/PMC4408413/). Accessed 2026-07-05.

2. Access note

Full text read via PubMed Central (PMC4408413). Copyright statement on the page: ”© The Author 2015. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved.” Treated as restrictive → own-words paraphrase mode for §7; functional strings (method names, criterion names, mixture proportions, parameter symbols) reproduced verbatim as facts.

3. Thesis

A branch-site test whose key innovation is variable parametric complexity chosen with an information-theoretic criterion — fitting an adaptive (per-branch) number of ω rate classes rather than a fixed number — can match or beat best-in-class episodic-selection tests while running roughly an order of magnitude (up to three orders of magnitude) faster.

4. Problem & context

Existing branch-site models (Nielsen–Yang style, as in codeml/PAML; and the earlier BSREL) impose the same model complexity on every branch — e.g. BSREL fixes the number of ω rate classes at Kb = 3 for all branches. Forcing that complexity everywhere overfits short/low- information branches and is computationally expensive on large phylogenies. aBSREL instead lets each branch use only as many ω classes as the data support.

5. Method / approach

  • Detects episodic diversifying selection: which individual branches of a phylogeny show positive selection (an ω = dN/dS rate class > 1), rather than assuming selection is constant across sites or lineages.
  • Per-branch adaptive complexity: the number of ω rate classes on branch b, Kb, is chosen from the data. Model selection uses the small-sample Akaike Information Criterion (AICc; Sugiura 1978) to pick the optimal number of rate categories per branch.
  • Greedy step-up fitting: start from Kb = 1 on all branches (a single-ω / MG94-equivalent baseline), process branches (longest first), incrementally add a rate class to a branch, and keep the addition only if AICc improves. Likelihood is obtained by marginalizing over ω-class assignments via the pruning algorithm.
  • Only the highest ω class (k = Kb) is allowed to exceed 1 (permit positive selection); the remaining classes are constrained to [0,1].
  • Test statistic: a likelihood-ratio test (LRT) on each tested branch — null (no positive- selection class on that branch) vs. the fitted aBSREL model.
  • Null distribution: the authors report the asymptotic LRT null for these multi-component mixture models is not a simple χ²; it is best described by a multi-component χ² mixture. The mixture allocating 50% to χ²₀, 20% to χ²₁, and 30% to χ²₂ is stated to agree well with the tail of an empirical LRT distribution built from 50,000 samples. P-values are computed against this mixture.
  • Multiple-testing correction (key claim): when more than one branch is tested, the Holm–Bonferroni sequential rejection procedure is applied to control the family-wise error rate (FWER). This is aBSREL’s built-in correction for testing many branches.
  • Significance is reported at the nominal P ≤ 0.05 level; for multi-branch runs the Holm– Bonferroni-corrected P-values are the ones used for calls (uncorrected P-values may also be reported for exploratory purposes).

6. Key claims / findings

  • On the Selectome data (reported as 8,893 genes, 493,172 branches), over 80% of branches in typical gene phylogenies are adequately modeled with a single ω-ratio (Kb = 1) model — i.e., the extra rate classes BSREL forces everywhere are usually unnecessary.
  • Mean Kb across all branches ≈ 1.16, versus the fixed Kb = 3 of BSREL.
  • Branches inferred to need multiple ω classes tend to be longer branches and come from longer alignments (more information available).
  • Speed: aBSREL runs up to three orders of magnitude faster than the compared Nielsen–Yang branch-site methods on the same hardware; benefit grows with data-set size. Example: an Avian influenza data set cited as dropping from an estimated ~1.5 years to ~6.5 hours.
  • False-positive rate is well controlled (< 5%) under strict neutrality in simulation.

7. Load-bearing statements (own-words paraphrase — restrictive license; functional strings verbatim)

  • Model-complexity selection: aBSREL infers the optimal number of ω rate categories per branch using the small-sample AIC — functional string verbatim: AICc (Sugiura 1978).
  • Multiple-testing correction: when more than one branch is tested, aBSREL applies the Holm–Bonferroni sequential rejection procedure to control the family-wise error rate. (Paraphrase of the source’s statement; “Holm–Bonferroni” and “family-wise error rate” are the verbatim functional terms.)
  • LRT null: the source states the null LRT distribution for these mixture models is a multi-component χ² mixture, well approximated by 50% χ²₀ + 20% χ²₁ + 30% χ²₂ (proportions verbatim), matched to an empirical distribution of 50,000 samples.
  • Design payoff (own words): applying different-complexity models to different branches gives performance matching or exceeding best-in-class approaches while running about an order of magnitude faster.

8. Stated scope, assumptions, limitations (the source’s own caveats)

  • Model selection and hypothesis testing are done on the same data: aBSREL infers its model from the data then tests on that same data, which departs from the classical separation of model selection from inference. Authors note this mirrors common practice (e.g. the ModelTest approach) but flag it.
  • A single inferred rate category is ambiguous: it can mean little site-to-site ω heterogeneity on that branch, but a single class can also be inferred even when substantial heterogeneity is present — inference of site-to-site variation at one branch is information-limited.
  • Short branches carry limited information for detecting multiple ω classes.

9. Failure modes / invalidity patterns

  • Very short branches: insufficient substitutions to support (or detect) multiple ω classes; power to detect episodic selection is low.
  • Saturation on very long branches: reduces discriminatory power.
  • Denser taxon sampling can hurt: adding sequences shortens average branch length, which dilutes per-branch power.
  • Wrong null distribution = miscalibrated p-values: using a naive single χ² asymptotic instead of the multi-component χ² mixture would misstate significance — the mixture null is the correct calibration.
  • Skipping the correction on multi-branch scans inflates false positives: testing many branches without Holm–Bonferroni FWER control is the failure the built-in correction guards against.

10. What the source does NOT address (confident silences within what was read)

  • Does not describe a change in the correction procedure for a pre-specified foreground set vs. scanning all branches — the correction is applied when >1 branch is tested; the read text does not present a separate protocol for a priori foreground designation. [summarizer-inferred] that the same Holm–Bonferroni scheme is intended for the tested set whatever its size.
  • Does not (in the portion summarized) give a synonymous-rate-variation treatment beyond the branch-site ω framework.

11. Open questions / ambiguities

  • Exact p-value threshold semantics after Holm–Bonferroni (per-family α) are not restated beyond the nominal 0.05 and FWER control.
  • The single-rate-class ambiguity (limitation #2) leaves open how often true heterogeneity is masked in practice.

12. Guidance answers

  • Exact question aBSREL answers / adaptive rate classes: It identifies which branches of a phylogeny show episodic diversifying (positive) selection, fitting an adaptive, per-branch number of ω rate classes (Kb) selected by AICc, instead of a fixed 2- or 3-class model applied to every branch (BSREL fixes Kb = 3). Only the top ω class may exceed 1.
  • Multiple-testing correction (name + threshold): Holm–Bonferroni sequential rejection procedure, controlling the family-wise error rate, applied whenever more than one branch is tested. No single universal numeric cutoff beyond the nominal P ≤ 0.05; correction adjusts the rejection thresholds across the tested branches.
  • Test statistic + threshold; all-branches vs pre-specified: Likelihood-ratio test per branch, p-values from a 50% χ²₀ + 20% χ²₁ + 30% χ²₂ mixture null; reported at P ≤ 0.05 with Holm–Bonferroni for multi-branch runs. The read text does not state a different correction for a pre-specified foreground vs. scanning all branches — correction triggers on testing >1 branch (see §10).
  • Advantage over codeml/PAML branch-site for exploratory (no a-priori foreground): dramatically faster (up to three orders of magnitude; the Avian-influenza example ~1.5 yr → ~6.5 h), and it avoids forcing uniform model complexity, giving controlled false-positive behavior when background lineages have rate variation — making genome-scale, no-foreground exploratory scans tractable.