替换模型速查（IQ-TREE）

前言：IQ-TREE里的替换模型介绍。
转载来源：http://www.iqtree.org/doc/Substitution-Models
IQ-TREE version 1.6.8Tutorials and ManualPhylogenomic software by maximum likelihood.pdf

Substitution models
All common substitution models and usages.
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 ModelFinder (-m MFP). It automatically determines best-fit model for your data.

1. DNA models

(1)Base substitution rates

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

The last column Code is a 6-digit code defining the equality constraints for 6 relative 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 (corresponding to 1 in the code) and the remaining four substitution rates are equal (corresponding to 0 in the code). Thus, 010010 is equivalent to K80 or HKY model (depending on whether base frequencies are equal or not). 012345 is equivalent to GTR or SYM model as there is no restriction defined by such 6-digit code.
Moreover, IQ-TREE supports arbitrarily restricted DNA model via a 6-digit code, e.g. with option -m 012012+G.

NOTE: The digits in the codes do not necessarily have to have the same order as above. That means ‘101101’ describes the same matrix as ‘010010’. The last rate, which corresponds to G-T, (and all rates with the same digit) is always set equal to 1.0 for convenience because the rates are relative.

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} 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.
Another example is for model TIM2 that has the 6-digit code 010232. Thus, TIM2{4.39,5.30,12.1} means that A-C=A-T=4.39 (coded 1), A-G=5.30 (coded 2), C-T=12.1 (coded 3) and C-G=G-T=1.0 (coded 0). This is, in turn, equivalent to specifying GTR{4.39,5.30,4.39,1.0,12.1}.

(2)Base frequencies

Users can specify three different kinds of base frequencies:

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

(3)Lie Markov models

Starting with version 1.6, IQ-TREE supports a series of Lie Markov models (Woodhams et al., 2015), many of which are non-reversible models. Lie Markov models have a consistent property, which is lacking in other common models such as GTR. The following table shows the list of all Lie Markov models (the number before . in the name shows the number of parameters of the model):

Column Rev? shows whether the model is reversible or not. Column Freq shows the number of free base frequencies. 0 means equal base frequency; 1 means f(A)=f(G) and f(C)=f(T); 2 means f(A)+f(G)=0.5=f(C)+f(T); 3 means unconstrained frequencies.
All Lie Markov models can have one of the following prefices:

2. Protein models

(1)Amino-acid exchange rate matrices

IQ-TREE supports all common empirical amino-acid exchange rate matrices (alphabetical order):

(2)Protein mixture models

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

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.

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

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

(3)User-defined empirical protein models

If the matrix name does not match any of 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 an 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

(4)Amino-acid frequencies

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

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 the AA frequencies of the LG matrix).

3. Codon models

To apply a codon model one should use the 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 an other genetic code by appending the appropriate ID to the CODON keyword:

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

(1)Codon substitution rates

IQ-TREE supports several codon models:

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.
Starting with version 1.5.6: If the model name does not match any of the above listed models, IQ-TREE assumes that it is a file containing lower diagonal part of non-stop codon exchange rate matrix, non-stop codon frequencies and a list of non-stop codons. The rest of the file will be ignored. Example files (ECMrest.dat and ECMunrest.dat) can be downloaded from the supplementary material (Kosiol et al., 2007).

NOTE: 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.

(2)Codon frequencies

IQ-TREE supports the following codon frequencies:

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.

4. 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.

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

TIP: 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.

5. 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.

6. Rate heterogeneity across sites

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

TIP: The new ModelFinder (-m MFP 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 the number of categories). Here, w1, ..., wk are the weights and r1, ..., rk the rates for each category.

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