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11 changes: 8 additions & 3 deletions doc/Substitution-Models.md
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---
layout: userdoc
title: "Substitution Models"
author: Hector Banos, Cuong Cao Dang, Heiko Schmidt, Jana Trifinopoulos, Minh Bui, Nhan Ly-Trong, Hiroaki Sato
date: 2025-06-10
author: Hector Banos, Cuong Cao Dang, Heiko Schmidt, Jana Trifinopoulos, Minh Bui, Nhan Ly-Trong, Hiroaki Sato, Ryo Harada
date: 2026-05-19
docid: 10
icon: book
doctype: manual
Expand Down Expand Up @@ -170,6 +170,7 @@ IQ-TREE supports all common empirical amino-acid exchange rate matrices (alphabe
| FLAVI | viral | Flavivirus ([Le and Vinh, 2020]). |
| FLU | viral | Influenza virus ([Dang et al., 2010]). |
| GTR20 | general | General time reversible models with 190 rate parameters. *WARNING: Be careful when using this parameter-rich model as parameter estimates might not be stable, especially when not having enough phylogenetic information (e.g. not long enough alignments).* |
| G.pfam | nuclear | General GTRpmix exchangeability matrix estimated from Pfam version 31 database ([El-Gebali et al., 2018]). To be used with profile mixture models (for eg. G.pfam+C60)<!-- ([Harada et al., 2026])-->. |
| HIVb | viral | HIV between-patient matrix HIV-B<sub>m</sub> ([Nickle et al., 2007]). |
| HIVw | viral | HIV within-patient matrix HIV-W<sub>m</sub> ([Nickle et al., 2007]). |
| JTT | nuclear | General matrix ([Jones et al., 1992]). |
Expand Down Expand Up @@ -215,12 +216,16 @@ IQ-TREE also supports a series of protein mixture models:
| LG4M | Four-matrix model fused with [Gamma rate heterogeneity](#rate-heterogeneity-across-sites) ([Le et al., 2012]).
| LG4X | Four-matrix model fused with [FreeRate heterogeneity](#rate-heterogeneity-across-sites) ([Le et al., 2012]).
| CF4 | Five-profile mixture model ([Wang et al., 2008]).
| S10pfamC60, S28pfamC59, S28pfamC60 | General GTRspmix models estimated from Pfam version 31 database ([El-Gebali et al., 2018]). Profiles from the C60 set are grouped into 10 or 28 clusters using Site Posterior Probability Co-occurrence (SPPC), with each profile cluster linked to a unique exchangeability matrix. `S28pfamC59` and `S28pfamC60` are variants optimized by adjusting a low-weight profile<!-- ([Harada et al., 2026])-->.
| S10pfamC10, S20pfamC20, S30pfamC30 | Computationally efficient general GTRspmix models estimated from the Pfam version 31 database ([El-Gebali et al., 2018]). Each profile in the C10, C20, or C30 sets is directly linked to its own unique exchangeability matrix, designed to minimize computational cost for massive datasets<!-- ([Harada et al., 2026])-->.


One can even combine a protein matrix with a profile mixture model like:

* `LG+C20`: Applying `LG` matrix instead of `Poisson` for all 20 classes of AA profiles and a Gamma rate heterogeneity.
* `LG+C20+F`: Applying `LG` matrix for 20 classes plus the 21th class of empirical AA profile (counted from the current data) and Gamma rate heterogeneity.
* `JTT+CF4+G`: Applying `JTT` matrix for all 5 classes of AA profiles and Gamma rate heteorogeneity.
* `S28pfamC60+G`: Applying `S28pfamC60` mixture model with Gamma rate heterogeneity.

Moreover, one can override the Gamma rate by FreeRate heterogeneity:

Expand Down Expand Up @@ -495,4 +500,4 @@ Users can fix the parameters of the model. For example, `+I{0.2}` will fix the p
[ej91016/MorphoParse]: https://github.com/ej91016/MorphoParse
[davidcerny/GEOS26100-Fall2022]: https://github.com/davidcerny/GEOS26100-Fall2022
[Černý & Simonoff (2023)]: https://doi.org/10.1038/s41598-023-35784-3

<!--[Harada et al., 2026]: https://doi.org/XXXXX-->