Substitution Models

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.

DNA models

Base substitution rates

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

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).

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

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).

IQ-TREE also support combined empirical-mechanistic codon models, where the name of an empirical model (ECMK07, ECMrest or ECMS05) and a mechanistic model (remaining ones) are combined with 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.