Statistical Genomics Foundry
Paper
domain/phylogenetics

Compositionally Constrained Sites Drive Long-Branch Attraction

1. Citation

  • Authors (exact, as printed): Lénárd L Szánthó, Nicolas Lartillot, Gergely J Szöllősi, Dominik Schrempf.
    • Byline note (verbatim): “Gergely J. Szöllősi and Dominik Schrempf contributed equally to this article.”
    • Citation-error correction: the downstream bioSkills skill mis-attributes this locus (Syst Biol 72:767) to “Sun M et al. 2023.” That is wrong. The four authors above are the correct list, verified from the source byline. There is no “Sun” author.
  • Year: 2023 (received/published 2022–2023; issue July 2023).
  • Title: “Compositionally Constrained Sites Drive Long-Branch Attraction.”
  • Venue: Systematic Biology, Volume 72, Issue 4, Pages 767–780.
  • DOI: 10.1093/sysbio/syad013.
  • Open-access URL: https://pmc.ncbi.nlm.nih.gov/articles/PMC10405358/ (full text). Journal: https://academic.oup.com/sysbio/article/72/4/767/7083631 . Preprint: bioRxiv 2022.03.03.482715.
  • Access date: 2026-07-03.

2. Access note

Read the full text via PubMed Central (PMC10405358). The OUP journal page itself is subscription-gated, but the article is Open Access under CC-BY 4.0, and PMC carries the complete text — no paywall boundary on the content summarized here. (Guidance assumed OUP “all-rights-reserved”; the actual license is CC-BY 4.0, so verbatim quoting is permitted — see §7. This is a correction to the guidance’s stated posture.)

3. Thesis (1 sentence)

Models that ignore across-site compositional heterogeneity are prone to long-branch attraction (LBA) because they underestimate the probability of convergent substitutions at compositionally constrained sites, and CAT-PMSF — a pipeline that estimates site-specific amino-acid preferences with the CAT model and applies them via posterior mean site frequencies — diagnoses and resolves this bias.

4. Problem & context

Phylogenies at deep timescales (long branches) are controversial because models of differing complexity give conflicting, strongly supported topologies. Empirically, alignments including Microsporidia, Nematoda, or Platyhelminthes show that inadequate modeling of across-site compositional heterogeneity — the result of biochemical constraints that make different sites accept different sets of amino acids — produces erroneous but well-supported topologies. Models that adequately capture across-site compositional heterogeneity (notably the Bayesian nonparametric CAT model) are computationally challenging or intractable for large modern datasets, and their MCMC convergence often cannot be assured. The paper targets both the diagnosis of this bias and a tractable resolution.

5. Method / approach

Two contributions: a diagnostic (“compositional constraint analysis”) and an inference pipeline (CAT-PMSF).

Per-site constraint measure — Keff (effective number of amino acids). For a site with stationary distribution π, the probability of homoplasy is G(π)=∑ᵢ πᵢ² (sum over the 20 amino acids), and the effective number of amino acids is its inverse: Keff(π)=G(π)⁻¹. Low Keff = strongly constrained site (few accepted amino acids); high Keff = less constrained.

Compositional constraint analysis (the diagnostic). For two competing topologies A and B, compute per-site log-likelihood difference ΔlogLᵢ = log Lᵢᴮ − log Lᵢᴬ (positive ⇒ site i supports topology B). Order and bin sites by their Keff value and sum ΔlogL within each bin. Under an adequate model, phylogenetic signal is consistent across Keff bins; conflicting signal across bins (e.g., low-Keff bins favoring one topology, high-Keff bins the other) indicates model misspecification driving LBA. Correlation between Keff and ΔlogL is assessed with rank correlation coefficients.

CAT-PMSF pipeline (three steps).

  1. Guide tree (IQ-TREE 2): infer an ML tree under a site-homogeneous model — LG exchangeabilities, empirical amino-acid frequencies, 4-category discrete gamma rates, i.e. LG + F + G4 in IQ-TREE 2 terminology.
  2. Site frequencies (PhyloBayes): fix that guide topology; run the CAT model to obtain the posterior mean site-specific stationary distributions of amino acids. CAT is run with Poisson, LG, or GTR exchangeabilities.
  3. Final inference (IQ-TREE 2 / PMSF): feed the custom site-specific stationary distributions into the second step of the PMSF (posterior mean site frequencies) method and re-estimate under the fixed frequencies to produce the final tree.

Fixing the topology before the expensive CAT step, and pushing the site frequencies into fast ML via PMSF, is what makes the approach tractable relative to a full CAT MCMC tree search.

Model strings evaluated (see §7 for the verbatim reference): LG + F + G4 (site-homogeneous baseline), Poisson + CAT-PMSF, LG + CAT-PMSF, GTR + CAT-PMSF, and empirical-mixture PMSF baselines LG + C10 + PMSF and LG + C60 + PMSF. [Note: C10/C60 mixture strings reported by extraction; treat the exact mixture set as [re-check] against the source if load-bearing.]

Simulation design (Felsenstein/Farris zone). Four-leaf quartet trees; alignments of 10,000 amino acids; branch-length parameter q fixed to 0.1 while p varied between 0.1 and 2.0 (p = the long/terminal branch parameter placing two long branches).

Empirical datasets analyzed:

  • Microsporidia — 40 species, 24,294 amino acids.
  • Nematoda — 37 species, 35,371 amino acids. [re-check: same site count as Platyhelminthes below]
  • Platyhelminthes — 32 species, 35,371 amino acids. [re-check duplicate value]
  • Simion et al. 2017 (Metazoa) — 97 species, 401,632 amino acids.
  • Ryan et al. 2013 (Metazoa) — 61 species, 88,384 amino acids.

6. Key claims / findings (atomic)

  • Models ignoring across-site compositional heterogeneity underestimate the probability of convergent substitutions at compositionally constrained (low-Keff) sites, and this is the stated cause of their LBA susceptibility.
  • More constrained (low-Keff) sites bias toward the incorrect LBA topology; less constrained (high-Keff) sites carry the correct signal — the two classes give “ostensibly conflicting signal” under site-homogeneous models.
  • In simulation, site-homogeneous models fail (recover the wrong topology) once p ≥ 0.8. “The true topology was not recovered with site-homogeneous models when p ≥ 0.8.”
  • CAT-PMSF is robust against LBA in all alignments examined, and shows no bias even for large p (extraction: “even for large values of p ≥ 1.2”). [The exact upper p at which CAT-PMSF was tested/robust — reported variously as ~1.2 up to ~2.0 — treat the precise ceiling as [re-check]; the robustness claim itself is verbatim in the abstract.]
  • More complex models accounting for across-site compositional heterogeneity ameliorate (do not always fully eliminate) the bias.
  • Empirical result: compositionally constrained sites drive LBA in two metazoan datasets; CAT-PMSF recovers Porifera (sponges) as the sister group to all other animals — evidence against Ctenophora-sister.
  • The authors recommend using CAT-PMSF specifically when CAT-model MCMC convergence cannot be assured (its practical niche).

7. Load-bearing statements — VERBATIM (license: CC-BY 4.0, reproduction permitted)

Quoting mode: verbatim permitted (CC-BY 4.0). Short load-bearing quotes below; locations from PMC full text.

  1. (Abstract — mechanism / thesis) “We show that more constrained sites with lower diversity and less constrained sites with higher diversity exhibit ostensibly conflicting signal under models ignoring across-site compositional heterogeneity that lead to long-branch attraction artifacts and demonstrate that more complex models accounting for across-site compositional heterogeneity can ameliorate this bias.”
  2. (Motivation — the causal mechanism) “Our primary motivation is that models ignoring across-site compositional heterogeneity are prone to LBA because they underestimate the probability of convergent substitutions at compositionally constrained sites.”
  3. (Robustness — must-quote) “CAT-PMSF is robust against long-branch attraction in all alignments we have examined.”
  4. (When to use it) “We suggest using CAT-PMSF when convergence of the CAT model cannot be assured.”
  5. (Empirical conclusion) “We find evidence that compositionally constrained sites are driving long-branch attraction in two metazoan datasets and recover evidence for Porifera as the sister group to all other animals.”

Functional strings (verbatim, facts): Keff(π)=G(π)⁻¹ ; G(π)=∑ πᵢ² ; ΔlogLᵢ = log Lᵢᴮ − log Lᵢᴬ ; model strings LG + F + G4, Poisson + CAT-PMSF, LG + CAT-PMSF, GTR + CAT-PMSF, LG + C10 + PMSF, LG + C60 + PMSF; simulation p ≥ 0.8 threshold; q = 0.1, p ∈ [0.1, 2.0].

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

  • CAT-PMSF assumes across-branch homogeneity (stationarity of the process across branches of the tree); it addresses across-site heterogeneity, not across-branch compositional heterogeneity.
  • Results are described as conservative because the site-specific stationary distributions are estimated on a guide topology that is itself prone to LBA artifacts (Step-1 site-homogeneous tree).
  • Guide-topology dependency: the initial site-homogeneous tree could bias the site-frequency estimates; empirically the authors argue this is mitigated in practice.
  • Computational cost: estimating the site-specific stationary distributions (the CAT/PhyloBayes step) remains by far the most time-consuming part.
  • Outgroup sensitivity: adding distant outgroups lengthens the basal branch and raises LBA risk even with CAT-PMSF; closest outgroups give the most robust signal.
  • Tests for across-branch compositional heterogeneity were less conclusive for the empirical datasets than for the simulations.

9. Failure modes / invalidity patterns (referee-relevant)

  • Symptom of compositional inadequacy (the diagnostic to run): in a compositional constraint analysis, ΔlogL signal that conflicts across Keff bins — low-Keff bins supporting one topology while high-Keff bins support another — signals that a site-homogeneous model is being driven to an LBA artifact. Consistent signal across bins is the “healthy” pattern. Significant Keff–ΔlogL rank correlation is corroborating evidence.
  • When site-homogeneous models (LG/WAG/JTT-style, constant equilibrium frequencies) become invalid: deep nodes / long terminal branches. Concrete simulation trigger: p ≥ 0.8. Direction of the error: strongly constrained (low-Keff) sites pull toward the incorrect (LBA / Farris-type) topology, wrongly grouping distantly related fast-evolving lineages.
  • CAT-PMSF’s own failure surface: across-branch compositional heterogeneity (its stationarity assumption is violated); pathological guide topologies; distant outgroups inflating basal branch length.
  • No named error-message/threshold from software output; the diagnostic is the Keff-binned ΔlogL plot plus rank correlations, and topology rejection is assessed with Approximately Unbiased (AU) tests.

10. What the source does NOT address

  • Does NOT use or recommend posterior-predictive checks for compositional adequacy (searched; NOT FOUND in full text). Its diagnostic is the Keff-vs-ΔlogL “compositional constraint analysis,” not a posterior-predictive compositional statistic. (This distinguishes it from Foster 2004-style posterior-predictive compositional tests, which the skill may pair separately — this paper does not provide that.)
  • Does not address nucleotide/codon compositional heterogeneity (amino-acid focus).
  • Does not resolve across-branch (lineage-specific) compositional heterogeneity — explicitly out of scope.

11. Open questions / ambiguities left unresolved

  • The exact upper bound of p at which CAT-PMSF remains unbiased (extraction gave both ~1.2 and up-to-2.0 phrasings) — precise ceiling is [re-check] against the figures.
  • Whether the reported empirical dataset site counts for Nematoda and Platyhelminthes are genuinely identical (both 35,371 aa) or an extraction artifact — [re-check].
  • Exact AU-test P-values for rejecting Ctenophora-sister in the Simion dataset (a secondary extraction gave values on the order of 10⁻⁴; treat as [re-check], not verified verbatim here).
  • The precise empirical-mixture PMSF baselines used (C10/C20/C60) — [re-check] the exact set.

12. Guidance answers

  • Mechanism (across-site compositional heterogeneity → LBA): answered. Biochemical constraints make each site accept a different set of amino acids (captured by Keff = 1/∑πᵢ²). The probability of independent (convergent) substitutions to the same state depends on how few amino acids a site accepts; site-homogeneous models pool all sites and underestimate convergent substitutions at low-Keff sites, so those sites’ shared states are misread as homology and drive LBA. Paper’s own statement: “models ignoring across-site compositional heterogeneity are prone to LBA because they underestimate the probability of convergent substitutions at compositionally constrained sites” (verbatim, §7).
  • What site-homogeneous models get wrong, and where it bites: they impose a single equilibrium frequency vector across sites; low-Keff sites then produce conflicting signal and bias toward the incorrect LBA topology. It bites at deep nodes / long branches — simulation threshold p ≥ 0.8. Ancestor/attraction bias direction: distantly related fast-evolving long-branch lineages (e.g., Microsporidia, Ctenophora) are wrongly drawn together.
  • CAT-PMSF — what it is / corrects / robustness: a 3-step pipeline (IQ-TREE 2 LG+F+G4 guide tree → PhyloBayes CAT posterior mean site-specific stationary distributions → IQ-TREE 2 PMSF with those frequencies). It corrects inadequate modeling of across-site compositional heterogeneity by supplying site-specific amino-acid preferences to a fast fixed-frequency ML step. Robustness (verbatim must-quote): “CAT-PMSF is robust against long-branch attraction in all alignments we have examined.” IQ-TREE 2 + PhyloBayes workflow captured in §5.
  • Diagnostic for compositional inadequacy: This paper states its own diagnostic — “compositional constraint analysis” (Keff-binned ΔlogL signal + Keff–ΔlogL rank correlation), NOT posterior-predictive compositional checks. So: it recommends a diagnostic, but a different one than Foster-2004 posterior predictive; it describes the phenomenon AND supplies its own detector. Posterior-predictive checks: NOT FOUND.
  • Functional strings (model specs) verbatim: LG + F + G4, Poisson + CAT-PMSF, LG + CAT-PMSF, GTR + CAT-PMSF, LG + C10 + PMSF, LG + C60 + PMSF; PMSF = posterior mean site frequencies. (C-series mixture set [re-check].)
  • Must-quote items: both delivered verbatim (CC-BY permits) in §7 — the constrained-sites-drive-LBA statement (#1/#2) and the CAT-PMSF robustness statement (#3).