Substitution Models

Table of Contents

DNA models
- Base substitution rates
- Base frequencies
Protein models
- Amino-acid exchange rate matrices
- Amino-acid frequencies
Codon models
- Codon substitution rates
- Codon frequencies
Binary and morphological models
Ascertainment bias correction
Rate heterogeneity across sites

IQ-TREE supports a wide range of substitution models, including advanced partition and mixture models. This guide gives a detailed information of all available models.

TIP: If you do not know which model to use, simply run IQ-TREE with the standard model selection (-m TEST option) or the new model selection procedure (-m TESTNEW). It automatically determines best-fit model for your data.

DNA models

Base substitution rates

IQ-TREE includes all common DNA models (ordered by complexity):

Model	Explanation
JC or JC69	equal substitution rates and equal base frequencies (Jukes and Cantor, 1969).
F81	equal rates but unequal base freq. (Felsenstein, 1981).
K80 or K2P	unequal transition/transversion rates and equal base freq. (Kimura, 1980).
HKY or HKY85	unequal transition/transversion rates and unequal base freq. (Hasegawa, Kishino and Yano, 1985).
TN or TN93	Like `HKY` but unequal purine/pyrimidine rates (Tamura and Nei, 1993).
TNe	Like `TN` but equal base freq.
K81 or K3P	three substitution types model and equal base freq. (Kimura, 1981).
K81u	Like `K81` but unequal base freq.
TPM2	AC=AT, AG=CT, CG=GT and equal base freq.
TPM2u	Like `TPM2` but unequal base freq.
TPM3	AC=CG, AG=CT, AT=GT and equal base freq.
TPM3u	Like `TPM3` but unequal base freq.
TIM	transition model, AC=GT, AT=CG and unequal base freq.
TIMe	Like `TIM` but equal base freq.
TIM2	AC=AT, CG=GT and unequal base freq.
TIM2e	Like `TIM2` but equal base freq.
TIM3	AC=CG, AT=GT and unequal base freq.
TIM3e	Like `TIM3` but equal base freq.
TVM	transversion model, AG=CT and unequal base freq.
TVMe	Like `TVM` but equal base freq.
SYM	Symmetric model with unequal rates and equal base freq. (Zharkihk, 1994).
GTR	General time reversible model with unequal rates and unequal base freq. (Tavare, 1986).

Moreover, IQ-TREE supports arbitrarily restricted DNA model via a 6-digit code. The 6 digits define the equality for 6 nucleotide substitution rates: A-C, A-G, A-T, C-G, C-T and G-T. 010010 means that A-G rate is equal to C-T rate and the remaining four substitution rates are equal. Thus, 010010 is equivalent to K80 or HKY model (depending on whether base frequencies are equal or not). 123450 is equivalent to GTR or SYM model as there is no restriction defined by such 6-digit code.

If users want to fix model parameters, append the model name with a curly bracket {, followed by the comma-separated rate parameters, and a closing curly bracket }. For example, GTR{1.0,2.0,1.5,3.7,2.8,1.0} specifies 6 substitution rates A-C=1.0, A-G=2.0, A-T=1.5, C-G=3.7, C-T=2.8 and G-T=1.0.

Base frequencies

Users can specify three different kinds of base frequencies:

+F: empirical base frequencies. This is the default if model has unequal base freq.
+FQ: equal base frequencies.
+FO: optimized base frequencies by maximum-likelihood.

For example, GTR+FO optimizes base frequencies by ML whereas GTR+F (default) counts base frequencies from directly the alignment.

Finally, users can fix base frequencies with e.g. GTR+F{0.1,0.2,0.3,0.4} to fix the corresponding frequencies of A, C, G and T (must sum up to 1.0).

Protein models

Amino-acid exchange rate matrices

IQ-TREE supports all common empirical amino-acid exchange rate matrices:

BLOSUM62: BLOcks SUbstitution Matrix (Henikoff and Henikoff, 1992). Note that BLOSUM62 is not recommended as it was designed mainly for sequence alignment.
cpREV: chloroplast matrix (Adachi et al., 2000).
Dayhoff: general matrix (Dayhoff et al., 1978).
DCMut: revised Dayhoff matrix (Kosiol and Goldman, 2005).
FLU: influenza virus (Dang et al., 2010).
HIVb: HIV matrix (Dang et al., 2010).
HIVw: HIV matrix (Dang et al., 2010).
JTT: general matrix (Jones et al., 1992).
JTTDCMut: revised JTT matrix (Kosiol and Goldman, 2005).
LG: general matrix (Le and Gascuel, 2008).
mtART: mitochondrial Arthropoda (Abascal et al., 2007).
mtMAM: mitochondrial Mammalia (Yang et al., 1998).
mtREV: mitochondrial Verterbrate (Adachi and Hasegawa, 1996).
mtZOA: mitochondrial Metazoa (Animals) (Rota-Stabelli et al., 2009).
Poisson: equal amino-acid exchange rates and frequencies.
PMB: Probability Matrix from Blocks, revised BLOSUM matrix (Veerassamy et al., 2004).
rtREV: Retrovirus (Dimmic et al., 2002).
VT: general matrix (Mueller and Vingron, 2000).
WAG: general matrix (Whelan and Goldman, 2001).

Moreover, IQ-TREE also supports a series of protein mixture models:

C10, C20, C30, C40, C50, C60: 10- to 60-profile mixture models under Gamma rate heterogeneity (Le et al., 2008a).
EX2: two-matrix model for exposed/buried AA sites (Le et al., 2008b).
EX3: three-matrix model for highly exposed/intermediate/buried AA sites (Le et al., 2008b).
EHO: three-matrix model for extended/helix/other sites (Le et al., 2008b).
UL2, UL3: unsupervised-learning variants of EX2 and EX3, respectively.
EX_EHO: six-matrix model combining EX2 and EHO (Le and Gascuel, 2010).
LG4M: four-matrix model fused with Gamma rate heterogeneity (Le et al., 2012).
LG4X: four-matrix model fused with FreeRate heterogeneity (Le et al., 2012).
CF4: five-profile mixture model (Wang et al., 2008).

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

LG+C20: applying LG matrix for all 20 mixture classes.
JTT+CF4+G: applying JTT matrix for all 5 mixture classes and Gamma rate heteorogeneity.
JTTCF4G: alias for JTT+CF4+G.

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

LG+C20+R4: Like LG+C20 but replace Gamma by FreeRate heterogeneity.

If the matrix name does not match the above listed models, IQ-TREE assumes that it is a file containing AA exchange rates and frequencies in PAML format. It contains the lower diagonal part of the matrix and 20 AA frequencies, e.g.:

0.425093 
0.276818 0.751878 
0.395144 0.123954 5.076149 
2.489084 0.534551 0.528768 0.062556 
0.969894 2.807908 1.695752 0.523386 0.084808 
1.038545 0.363970 0.541712 5.243870 0.003499 4.128591 
2.066040 0.390192 1.437645 0.844926 0.569265 0.267959 0.348847 
0.358858 2.426601 4.509238 0.927114 0.640543 4.813505 0.423881 0.311484 
0.149830 0.126991 0.191503 0.010690 0.320627 0.072854 0.044265 0.008705 0.108882 
0.395337 0.301848 0.068427 0.015076 0.594007 0.582457 0.069673 0.044261 0.366317 4.145067 
0.536518 6.326067 2.145078 0.282959 0.013266 3.234294 1.807177 0.296636 0.697264 0.159069 0.137500 
1.124035 0.484133 0.371004 0.025548 0.893680 1.672569 0.173735 0.139538 0.442472 4.273607 6.312358 0.656604 
0.253701 0.052722 0.089525 0.017416 1.105251 0.035855 0.018811 0.089586 0.682139 1.112727 2.592692 0.023918 1.798853 
1.177651 0.332533 0.161787 0.394456 0.075382 0.624294 0.419409 0.196961 0.508851 0.078281 0.249060 0.390322 0.099849 0.094464 
4.727182 0.858151 4.008358 1.240275 2.784478 1.223828 0.611973 1.739990 0.990012 0.064105 0.182287 0.748683 0.346960 0.361819 1.338132 
2.139501 0.578987 2.000679 0.425860 1.143480 1.080136 0.604545 0.129836 0.584262 1.033739 0.302936 1.136863 2.020366 0.165001 0.571468 6.472279 
0.180717 0.593607 0.045376 0.029890 0.670128 0.236199 0.077852 0.268491 0.597054 0.111660 0.619632 0.049906 0.696175 2.457121 0.095131 0.248862 0.140825 
0.218959 0.314440 0.612025 0.135107 1.165532 0.257336 0.120037 0.054679 5.306834 0.232523 0.299648 0.131932 0.481306 7.803902 0.089613 0.400547 0.245841 3.151815 
2.547870 0.170887 0.083688 0.037967 1.959291 0.210332 0.245034 0.076701 0.119013 10.649107 1.702745 0.185202 1.898718 0.654683 0.296501 0.098369 2.188158 0.189510 0.249313 

0.079066 0.055941 0.041977 0.053052 0.012937 0.040767 0.071586 0.057337 0.022355 0.062157 0.099081 0.064600 0.022951 0.042302 0.044040 0.061197 0.053287 0.012066 0.034155 0.069147

(this is an example of LG matrix taken from PAML package). Note that the amino-acid order in this file is:

 A   R   N   D   C   Q   E   G   H   I   L   K   M   F   P   S   T   W   Y   V
Ala Arg Asn Asp Cys Gln Glu Gly His Ile Leu Lys Met Phe Pro Ser Thr Trp Tyr Val

Amino-acid frequencies

By default, AA frequencies are given by the model. Users can change this with:

+F: empirical AA frequencies from the data.
+FO: ML optimized AA frequencies from the data.
+FQ: Equal AA frequencies.

Users can also specify AA frequencies with, e.g.:

+F{0.079066,0.055941,0.041977,0.053052,0.012937,0.040767,0.071586,0.057337,0.022355,0.062157,0.099081,0.064600,0.022951,0.042302,0.044040,0.061197,0.053287,0.012066,0.034155,0.069147}

(example corresponds to AA frequencies of LG matrix).

Codon models

To apply codon model one should use option -st CODON to tell IQ-TREE that the alignment contains protein coding sequences (otherwise, IQ-TREE thinks that it contains DNA sequences and will apply DNA models). This implicitly applies the standard genetic code. You can change to other genetic code by appending appropriate ID:

Option	Genetic code
`-st CODON1`	The Standard Code (same as `-st CODON`)
`-st CODON2`	The Vertebrate Mitochondrial Code
`-st CODON3`	The Yeast Mitochondrial Code
`-st CODON4`	The Mold, Protozoan, and Coelenterate Mitochondrial Code and the Mycoplasma/Spiroplasma Code
`-st CODON5`	The Invertebrate Mitochondrial Code
`-st CODON6`	The Ciliate, Dasycladacean and Hexamita Nuclear Code
`-st CODON9`	The Echinoderm and Flatworm Mitochondrial Code
`-st CODON10`	The Euplotid Nuclear Code
`-st CODON11`	The Bacterial, Archaeal and Plant Plastid Code
`-st CODON12`	The Alternative Yeast Nuclear Code
`-st CODON13`	The Ascidian Mitochondrial Code
`-st CODON14`	The Alternative Flatworm Mitochondrial Code
`-st CODON16`	Chlorophycean Mitochondrial Code
`-st CODON21`	Trematode Mitochondrial Code
`-st CODON22`	Scenedesmus obliquus Mitochondrial Code
`-st CODON23`	Thraustochytrium Mitochondrial Code
`-st CODON24`	Pterobranchia Mitochondrial Code
`-st CODON25`	Candidate Division SR1 and Gracilibacteria Code

(the IDs follow the specification at http://www.ncbi.nlm.nih.gov/Taxonomy/Utils/wprintgc.cgi).

Codon substitution rates

IQ-TREE supports several codon models:

MG: nonsynonymous/synonymous (dn/ds) rate ratio (Muse and Gaut, 1994).
MGK: Like MG with additional transition/transversion (ts/tv) rate ratio.
MG1KTS or MGKAP2: Like MG with a transition rate (Kosiol et al., 2007).
MG1KTV or MGKAP3: Like MG with a transversion rate (Kosiol et al., 2007).
MG2K or MGKAP4: Like MG with a transition rate and a transversion rate (Kosiol et al., 2007).
GY: nonsynonymous/synonymous and transition/transversion rate ratios (Goldman and Yang, 1994).
GY1KTS or GYKAP2: Like GY with a transition rate (Kosiol et al., 2007).
GY1KTV or GYKAP3: Like GY with a transversion rate (Kosiol et al., 2007).
GY2K or GYKAP4: Like GY with a transition rate and a transversion rate (Kosiol et al., 2007).
ECMK07 or KOSI07: empirical codon model (Kosiol et al., 2007).
ECMrest: restricted version of ECMK07 that allows only one nucleotide exchange.
ECMS05 or SCHN05: empirical codon model (Schneider et al., 2005).

The last three models (ECMK07, ECMrest or ECMS05) are called empirical codon models, whereas the others are called mechanistic codon models.

Moreover, IQ-TREE supports combined empirical-mechanistic codon models using an underscore separator (_). For example:

ECMK07_GY2K: The combined ECMK07 and GY2K model, with the rate entries being multiplication of the two corresponding rate matrices.

Thus, there can be many such combinations.

If the model name does not match the above listed models, IQ-TREE assumes that it is a file containing codon exchange rates and frequencies in PAML format. It contains the lower diagonal part of the matrix and codon frequencies. For an example, see http://www.ebi.ac.uk/goldman/ECM/.

NOTICE: Branch lengths under codon models are interpreted as number of nucleotide substitutions per codon site. Thus, they are typically 3 times longer than under DNA models.

Codon frequencies

IQ-TREE supports the following codon frequencies:

+F: empirical codon frequencies counted from the data.
+FQ: equal codon frequencies.
+F1X4: unequal nucleotide frequencies but equal nt frequencies over three codon positions.
+F3X4: unequal nucleotide frequencies and unequal nt frequencies over three codon positions.

If not specified, the default codon frequency will be +F3X4 for MG-type models, +F for GY-type models and given by the model for empirical codon models.

Binary and morphological models

The binary alignments should contain state 0 and 1. Whereas for morphological data, the valid states are 0 to 9 and A to Z.

JC2: Jukes-Cantor type model for binary data.
GTR2: general time reversible model for binary data.
MK: Jukes-Cantor type model for morphological data.
ORDERED: allowing exchange of neighboring states only.

Except for GTR2 that has unequal state frequencies, all other models have equal state frequencies.

NOTICE: If morphological alignments do not contain constant sites (typically the case), then an ascertainment bias correction model (+ASC) should be applied to correct the branch lengths for the absence of constant sites.

Ascertainment bias correction

An ascertainment bias correction (+ASC) model (Lewis, 2001) should be applied if the alignment does not contain constant sites (such as morphological or SNPs data). For example:

MK+ASC: for morphological data.
GTR+ASC: for SNPs data.

+ASC will correct the likelihood conditioned on variable sites. Without +ASC, the branch lengths might be overestimated.

Rate heterogeneity across sites

IQ-TREE supports all common rate heterogeneity across sites model:

+I: allowing for a proportion of invariable sites.
+G: discrete Gamma model (Yang, 1994) with default 4 rate categories. The number of categories can be changed with e.g. +G8.
+I+G: invariable site plus discrete Gamma model (Gu et al., 1995).
+R: FreeRate model (Yang, 1995; Soubrier et al., 2012) that generalizes +G model by relaxing the assumption of Gamma-distributed rates. The number of categories can be specified with e.g. +R6 (default 4 categories if not specified). The FreeRate model typically fits data better than +G model and is recommended for analysis of large data sets.

TIP: the new model selection procedure (-m TESTNEW option) tests the FreeRate model, whereas the standard procedure (-m TEST) does not.

Users can fix the parameters of the model. For example, +I{0.2} will fix the proportion of invariable sites (pinvar) to 0.2; +G{0.9} will fix the Gamma shape parameter (alpha) to 0.9; +I{0.2}+G{0.9} will fix both pinvar and alpha. To fix the FreeRate model parameters, use the syntax +Rk{w1,r1,...,wk,rk} (replacing k with number of categories). Here, w1, ..., wk are the weights and r1, ..., rk the rates for each category.

NOTICE: For +G model IQ-TREE implements the mean approximation approach (Yang, 1994). The same is done in RAxML and PhyML. However, some software like TREE-PUZZLE implements the median approximation approach, which makes the resulting log-likelihood not comparable. IQ-TREE can change to this approach via -gmedian option.