Complex Models

---

layout: userdoc title: "Complex Models" author: AUTHOR date: DATE docid: 11 icon: book doctype: manual tags:

• manual description: Complex models such as partition and mixture models. sections:
• name: Partition models url: partition-models
• name: Mixture models url: mixture-models
• name: Site-specific frequency models url: site-specific-frequency-models
• name: Heterotachy models url: heterotachy-models
• name: Branch-specific models (in AliSim only) url: branch-specific-models-in-alisim-only

---

Complex models

Complex models such as partition and mixture models.

This document gives detailed descriptions of complex maximum-likelihood models available in IQ-TREE. It is assumed that you know the basic substitution models already.

Partition models

Partition models are intended for phylogenomic (e.g., multi-gene) alignments, which allow each partition to have its own substitution models and evolutionary rates. IQ-TREE supports three types of partition models:

1. Edge-equal partition model with equal branch lengths: All partitions share the same set of branch lengths.
2. Edge-proportional partition model with proportional branch lengths: Like above but each partition has its own partition specific rate, that rescales all its branch lengths. This model accomodates different evolutionary rates between partitions (e.g. between 1st, 2nd, and 3rd codon positions).
3. Edge-unlinked partition model: Each partition has its own set of branch lengths. This is the most parameter-rich partition model, that accounts for e.g., heterotachy (Lopez et al., 2002).

TIP: The edge-equal partition model is typically unrealistic as it does not account for different evolutionary speeds between partitions, whereas the edge-unlinked partition model can be overfitting if there are many short partitions. Therefore, the edge-proportional partition model is recommended for a typical analysis. {: .tip}

Partition file format

To apply partition models users must first prepare a partition file in RAxML-style or NEXUS format. The RAxML-style is defined by the RAxML software and may look like:

DNA, part1 = 1-100
DNA, part2 = 101-384

This means two DNA partitions of an alignment, where one groups aligment sites 1-100 into part1 and 101-384 into part2.

The NEXUS format is more complex but more powerful. For example, the above partition scheme may look like:

#nexus
begin sets;
    charset part1 = 1-100;
    charset part2 = 101-384;
    charpartition mine = HKY+G:part1, GTR+I+G:part2;
end;

The first line contains the keyword #nexus to indicate a NEXUS file. It has a sets block, which contains two character sets (charset command) named part1 and part2. Furthermore, with the charpartition command we set the model HKY+G for part1 and GTR+I+G for part2. This is not possible with the RAxML-style format (i.e., one cannot specify +G rate model for one partition and +I+G rate model for the other partition).

TIP: IQ-TREE fully supports mixed rate heterogeneity types types between partitions (see above example). {: .tip}

One can also specify non-consecutive sites of a partition, e.g. under RAxML-style format:

DNA, part1 = 1-100, 250-384
DNA, part2 = 101-249\3, 102-249\3
DNA, part3 = 103-249\3

or under NEXUS format:

#nexus
begin sets;
    charset part1 = 1-100 250-384;
    charset part2 = 101-249\3 102-249\3;
    charset part3 = 103-249\3;
end;

This means, part2 contains sites 101, 102, 104, 105, 107, ..., 246, 248, 249; whereas part3 contains sites 103, 106, ..., 247. This is useful to specify partitions corresponding to 1st, 2nd and 3rd codon positions.

Moreover, the NEXUS file allows each partition to come from a separate alignment file (not possible under RAxML-style format) with e.g.:

#nexus
begin sets;
    charset part1 = aln1.phy: 1-100\3 201-300;
    charset part2 = aln1.phy: 101-200;
    charset part3 = aln2.phy: *;
    charpartition mine = HKY:part1, GTR+G:part2, WAG+I+G:part3;
end;

Here, part1 and part2 correspond to sub-alignments of aln1.phy file and part3 is the entire alignment file aln2.phy. Note that aln2.phy is a protein alignment in this example.

TIP: IQ-TREE fully supports mixed data types between partitions. {: .tip}

If you want to specify codon model for a partition, use the CODON keyword (otherwise, the partition may be detected as DNA):

#nexus
begin sets;
    charset part1 = aln1.phy:CODON, 1-300;
    charset part2 = aln1.phy: 301-400;
    charset part3 = aln2.phy: *;
    charpartition mine = GY:part1, GTR+G:part2, WAG+I+G:part3;
end;

Note that this assumes part1 has standard genetic code. If not, append CODON with the right genetic code ID.

Partitioned analysis

Having prepared a partition file, one is ready to start a partitioned analysis with -q (edge-equal), -spp (edge-proportional) or -sp (edge-unlinked) option. See this tutorial for more details.

Partitioned Simulation (with AliSim)

Example 1: Simulating mixed data with an Edge-equal partition model

AliSim allows users to simulate mixed data (e.g., DNA, Protein, and MORPH) in a single simulation, in which each kind of data is exported into a different alignment file. Here is an example for mixing DNA, protein, and morphological data:

#nexus
begin sets;
    charset part1 = DNA, 1-200\2;
    charset part2 = DNA, 2-200\2;
    charset part3 = MORPH, 1-300;
    charset part4 = AA, 1-200;
    charset part5 = MORPH{30}, 1-200\2;
    charset part6 = MORPH{30}, 2-200\2;
    charset part7 = DNA, 201-400;
    charpartition mine = HKY:part1, GTR+G:part2, MK:part3, Dayhoff:part4, MK:part5, ORDERED:part6, GTR+G:part7;
end;

Here, part1, part2, and part7 contain three DNA sub-alignments, whereas part3, part5, and part6 contain sub-alignments for morphological data. Besides, part4 contains an amino-acid alignment with 200 sites. Note that users could specify the parameters for each model of each partition (see Substitution Models). In this example, for simplicity, we ignore that feature, thus, using randomly generated parameters.

Assuming that the above partition file is named example_mix.nex and one would like to simulate alignments from a single tree in tree.nwk, one could start the simulation with the following command:

iqtree2 --alisim partition_mix -q example_mix.nex -t tree.nwk

At the end of the run, AliSim writes out the simulated alignments into four output files. The first file named partition_mix_part1_part2_part7.phy stores the merged 400-site DNA alignment from part1, part2, and part7. Although part3, part5, and part6 contain morphological data, part3 simulates a morphological alignment with 32 states while part5 and part6 have 30 states. Thus, AliSim outputs the alignment of part3 into partition_mix_part3.phy, whereas partition_mix_part5_part6.phy stores the alignment merging part5 and part6. Lastly, partition_mix_part4.phy stores the simulated amino-acid alignment of part4.

Example 2: Simulating mixed data with an Edge-proportional partition model

Unlike Edge-equal, the Edge-proportional partition requires each partition to have its own partition specific rate, which rescales all its branch lengths. One could specify the partition-specific rates by specifying the tree length for each partition in the NEXUS file via partX{<tree_length>} as in the following example. Note that <tree_length> of a partition is equal to the length of the common tree times the partition_rate of that partition. For example, assuming the length of the common tree is 2.61045, the partition-specific rate of partition 1 is 0.3, then the <tree_length> of part1 should be 0.783135 (=2.61045 * 0.3):

#nexus
begin sets;
    charset part1 = DNA, 1-200\2;
    charset part2 = DNA, 2-200\2;
    charset part3 = MORPH, 1-300;
    charset part4 = AA, 1-200;
    charset part5 = MORPH{30}, 1-200\2;
    charset part6 = MORPH{30}, 2-200\2;
    charset part7 = DNA, 201-400;
    charpartition mine = HKY:part1{0.783135}, GTR+G:part2{1.51542}, MK:part3{1.03066}, Dayhoff:part4{0.489315}, MK:part5{0.680204}, ORDERED:part6{1.346}, GTR+G:part7{1.78177};
end;

After preparing the example_mix_edge_proportion.nex file, one could start the simulation by:

iqtree2 --alisim partition_mix_edge_proportition -p example_mix_edge_proportion.nex -t tree.nwk

Example 3: Simulating mixed data with Edge-unlinked partition model

AliSim supports tree-mixture models, which allow each partition has its own tree topology with even different sets of taxa as long as the supertree contains all of the taxa in all partitions.

In this example, we re-use the example_mix.nex file to define seven partitions with DNA, amino-acid, and morphological data.

Then, we need to prepare a multiple-tree file. In an Edge-unlinked partition, AliSim requires a multiple-tree file that specifies a supertree (combining all taxa in all partitions) in the first line. Following that, each tree for each partition should be specified in a single line one by one in the input multiple-tree file as the following example_mix_unlinked_partitions.parttrees file:

(T0:0.0181521877,(((T5:0.1771956842,(T6:0.0614336000,T7:0.2002480501)23:0.1532476871)18:0.0332679438,(T8:0.0677273831,T9:0.0305167387)19:0.1180907531)16:0.0365283318,(T3:0.0681218610,T4:0.0527632742)17:0.1350927217)8:0.0393042588,(T1:0.1523260216,T2:0.0214431611)9:0.0733969175);
(((T4:0.0843970070,T5:0.0286349627)4:0.1220779923,T2:0.0146182510)1:0.2353878387,(T1:0.0238257189,((T6:0.0106472245,T7:0.2282782466)12:0.0946749939,(T8:0.1456716825,T9:0.2407945609)13:0.3296837366)9:0.0160168752)2:0.0450985623,T0:0.0596020470);
(T0:0.0671385689,T1:0.5298317367,((T4:0.0064005330,(T5:0.2918771232,T6:0.0059750004)11:0.1537117251)4:0.1158362293,(T2:0.0349557476,(T3:0.1152013065,(T7:0.2847312268,T8:0.0349557476)9:0.0062939800)7:0.0725670372)5:0.0689155159)3:0.0318828801);
(((T1:0.1313043899,T2:0.0011060947)4:0.2128631786,((T6:0.1987774353,T7:0.1127011763)8:0.0673344553,T3:0.0980829253)5:0.0470003629)1:0.1532476871,((T4:0.0994252273,T5:0.1532476871)10:0.2162823151,(T8:0.0139262067,T9:0.1241328591)11:0.0110931561)2:0.0362405619,T0:0.0297059234);
(T0:0.0277071893,((T2:0.1845160246,T3:0.1448169765)12:0.0055512710,((T8:0.0401971219,T9:0.0016129382)14:0.0176737179,(T6:0.1461017907,T7:0.0972861083)15:0.1624551550)13:0.0079043207)4:0.0484508315,(T1:0.0908818717,(T4:0.0382725621,T5:0.0047091608)11:0.1870802677)5:0.1645065090);
(T0:0.0574475651,T1:0.0081210055,(((T4:0.0832409248,((T8:0.1614450454,T9:0.3540459449)22:0.0964955904,T5:0.0291690094)21:0.0949330586)16:0.0034591445,(T6:0.0339677368,T7:0.0038740828)17:0.0388607991)14:0.0303811454,(T3:0.0703197516,T2:0.0345311185)11:0.1061316504)3:0.0872273846);
(T0:0.0205794913,(((T2:0.1093624747,((T8:0.2017406151,T9:0.0650087691)14:0.0695149183,T7:0.4135166557)9:0.2234926445)6:0.1924148657,T1:0.0614336000)4:0.0287682072,(T5:0.1010601411,T6:0.3194183212)5:0.0385662481)2:0.1671313316,(T3:0.1546463113,T4:0.1139434283)3:0.0321583624);
((((T8:0.0306525160,T9:0.0125563223)16:0.1546463113,T7:0.0102032726)1:0.2501036032,(T1:0.0616186139,(T2:0.1565421027,(T5:0.0018470000,T6:0.0594207233)11:0.0505838082)9:0.0027371197)6:0.1443923474)0:0.4710530702,(T3:0.0372514008,T4:0.0322963887)4:0.0491022996,T0:0.0669430654); 

The above tree file contains 8 lines, in which the first line specifies the supertree (consisting of 10 taxa of all partitions), and the 7 remaining lines are the trees corresponding to 7 partitions. Note that taxon 3 (T3) is missing in the tree of part1, taxon 9 (T9) is missing in the tree of part2.

Now, one could simulate alignments using the following command:

iqtree2 --alisim partition_mix_unlinked  -Q example_mix.nex -t example_mix_unlinked_partitions.parttrees

At the end of the run, AliSim writes out the simulated alignments into four output files, as seen in the previous example with the Edge-equal partition model. However, when you check the merged alignment in partition_mix_unlinked_part1_part2_part7.phy, you should see several gaps - in the sequences of taxon 3 (T3) and taxon 9 (T9) as these taxa are missing in the input trees of part1 and part2.

10 400
T0         TACGCTTCAATTGCTGCTCTATTTCTATGTAGCCAGTTTTAGTCCTATCGTGG...
T5         TACAGTCTCTTCGAAGCACTATTGCGCTAAATCCTGTTTTAGTACTGTTATAT...
T6         TACTCTTGATTTGATGCCCTATTTCGATGTAGCCAGTTTTAGTCCTATCGTGG...
T7         TATTCTTCAGTTGATGCTCTATTTCAAGGTAGCCAGTTTTTGCGTTATCTCCG...
T8         GAATTTTCATTTAAGGACCTATATACATGTCGACCGTTATTGCCGTATCCTGG...
T9         G-C-C-T-C-T-C-C-C-T-A-A-T-A-G-C-C-G-T-A-T-T-G-A-G-T-G...
T3         -A-T-T-C-T-T-A-G-C-T-T-T-C-T-G-G-C-G-T-T-G-C-T-T-A-A-...
T4         TACTGTGCCTTTGAAGCCCTTTTTAGCTATAGCCTGTTTTAGTCCTGTTGTGT...
T1         TACTCCTGATTTGCTGCTCTAGTACCAGGTAGCTAGTTTTAGTCCTATCGTTG...
T2         TACTGTTCCTTTGCTGCCCTACTTCCCCATAGCCAGTTTTAGTCCTGTTGTGT...

Example 4: Simulating multi-gene alignments

To simulate an alignment consisting of multiple genes, where each gene evolves under a different substitution model, one should first define those genes (each gene as a partition) and specify the corresponding model for each gene. Assuming we have multi_genes.nex file as following

#nexus
begin sets;
    charset gene_1 = DNA, 1-846;
    charset gene_2 = DNA, 847-1368;
    charset gene_3 = DNA, 1369-2040;
    charset gene_4 = DNA, 2041-2772;
    charset gene_5 = DNA, 2773-3738;
    charpartition mine = HKY{2}+F{0.2/0.3/0.1/0.4}:gene_1, GTR{1.2/0.8/0.5/1.7/1.5}+F{0.1/0.2/0.3/0.4}+G{0.5}:gene_2, JC:gene_3, HKY{1.5}+I{0.2}:gene_4, K80{2.5}:gene_5;
end;

The above file defines five genes, each of them has a different length, which sums to 3738 sites. These genes evolved independently under HKY, GTR (with discrete Gamma rate variance), JC, HKY (with a proportion of invariant sites), and K80 model, respectively.

Then, you can simulate an alignment consisting of these five genes by

iqtree2 --alisim partition_multi_genes  -q multi_genes.nex -t tree.nwk

That simulation outputs the new alignment into a single file named partition_multi_genes.phy.

Example 5: Simulating multi-gene alignments from multiple gene trees

Similar to example 4 but each gene can evolve from a different gene tree. Assuming we have multi_genes.nex file as in example 4, we then need to specify a multiple gene trees (in multi_trees.nwk as following.

(A:0.1,(B:0.2,C:0.15):0.1,D:0.05);
(A:0.1,(B:0.2,C:0.15):0.1,D:0.05);
(A:0.1,B:0.2,(C:0.15,D:0.05):0.1);
((A:0.1,B:0.2):0.1,C:0.15,D:0.05);
((A:0.1,C:0.15):0.1,B:0.2,D:0.05);
(A:0.1,C:0.15,(B:0.2,D:0.05):0.1);

The first line specify the supertree, containing all taxa in all other tree. The remaining line specify the corresponding tree for 6 gene trees.

Then, you can simulate an alignment consisting of these five genes from multiple gene trees by

iqtree2 --alisim partition_multi_genes_trees  -Q multi_genes.nex -t multi_trees.nwk

That simulation outputs the new alignment into a single file named partition_multi_genes_trees.phy.

Mixture models

What is the difference between partition and mixture models?

Mixture models, like partition models, allow more than one substitution model along the sequences. However, while a partition model assigns each alignment site a given specific model, mixture models do not need this information. A mixture model will compute for each site its probability (or weight) of belonging to each of the mixture classes (also called categories or components). Since the site-to-class assignment is unknown, the site likelihood under mixture models is the weighted sum of site likelihoods per mixture class.

For example, the discrete Gamma rate heterogeneity is a simple mixture model type. It has several rate categories with equal weight. IQ-TREE also supports a number of predefined protein mixture models such as the profile mixture models C10 to C60 (The ML variants of Bayesian CAT models).

Here, we discuss several possibilities to define new mixture models in IQ-TREE.

Defining mixture models

To start with, the following command:

iqtree -s example.phy -m "MIX{JC,HKY}"

specifies a mixture model (via the MIX keyword in the model string) with two components. The components (1) JC model, and (2) HKY model, are given in curly brackets and separated with a comma. IQ-TREE will then estimate the parameters of both mixture components as well as their weights: the proportion of sites belonging to each component.

NOTE: Do not forget the double-quotes around model string! They prevent interpretation of the curly brackets by the command line shell, i.e., MIX{JC,HKY} would otherwise be interpreted as MIXJC MIXHKY.

Mixture models can be combined with rate heterogeneity, e.g.:

iqtree -s example.phy -m "MIX{JC,HKY}+G4"

Here, we specify two mixture components and four Gamma rate categories. Effectively, this means that there are eight mixture components. Each site has a probability belonging to either JC or HKY and to one of the four rate categories.

Profile mixture models

Sometimes one only wants to model the changes in nucleotide or amino-acid frequencies along the sequences while keeping the substitution rate matrix the same. This can be specified in IQ-TREE via FMIX{...} model syntax. For convenience the mixture components can be defined in a NEXUS file like this (example corresponds to the CF4 model of (Wang et al., 2008)):

#nexus
begin models;
    frequency Fclass1 = 0.02549352 0.01296012 0.005545202 0.006005566 0.01002193 0.01112289 0.008811948 0.001796161 0.004312188 0.2108274 0.2730413 0.01335451 0.07862202 0.03859909 0.005058205 0.008209453 0.03210019 0.002668138 0.01379098 0.2376598;
    frequency Fclass2 = 0.09596966 0.008786096 0.02805857 0.01880183 0.005026264 0.006454635 0.01582725 0.7215719 0.003379354 0.002257725 0.003013483 0.01343441 0.001511657 0.002107865 0.006751404 0.04798539 0.01141559 0.000523736 0.002188483 0.004934972;
    frequency Fclass3 = 0.01726065 0.005467988 0.01092937 0.3627871 0.001046402 0.01984758 0.5149206 0.004145081 0.002563289 0.002955213 0.005286931 0.01558693 0.002693098 0.002075771 0.003006167 0.01263069 0.01082144 0.000253451 0.001144787 0.004573568;
    frequency Fclass4 = 0.1263139 0.09564027 0.07050061 0.03316681 0.02095119 0.05473468 0.02790523 0.009007538 0.03441334 0.005855319 0.008061884 0.1078084 0.009019514 0.05018693 0.07948 0.09447839 0.09258897 0.01390669 0.05367769 0.01230413;

    frequency CF4model = FMIX{empirical,Fclass1,Fclass2,Fclass3,Fclass4};
end;

NOTE: 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.

Here, the NEXUS file contains a models block to define new models. More explicitly, we define four AA profiles Fclass1 to Fclass4, each containing 20 AA frequencies. Then, the frequency mixture is defined with

FMIX{empirical,Fclass1,Fclass2,Fclass3,Fclass4}

This means, we have five components: the first corresponds to empirical AA frequencies to be inferred from the data and the remaining four components are specified in this NEXUS file. Please save this to a file, say, mymodels.nex. One can now start the analysis with:

iqtree -s some_protein.aln -mdef mymodels.nex -m JTT+CF4model+G

The -mdef option specifies the NEXUS file containing user-defined models. Here, the JTT matrix is applied for all alignment sites and one varies the AA profiles along the alignment. One can use the NEXUS syntax to define all other profile mixture models such as C10 to C60.

NEXUS model file

In fact, IQ-TREE uses this NEXUS model file internally to define all protein mixture models. In addition to defining state frequencies, one can specify the entire model with rate matrix and state frequencies together. For example, the LG4M model (Le et al., 2012) can be defined by:

#nexus
begin models;
    model LG4M1 =
        0.269343
        0.254612 0.150988
        0.236821 0.031863 0.659648
        ....;
    ....
    model LG4M4 = ....;
    
    model LG4M = MIX{LG4M1,LG4M2,LG4M3,LG4M4}*G4;
end;

Here, we first define the four matrices LG4M1, LG4M2, LG4M3 and LG4M4 in PAML format (see protein models). Then LG4M is defined as mixture model with these four components fused with Gamma rate heterogeneity (via *G4 syntax instead of +G4). This means that, in total, we have 4 mixture components instead of 16. The first component LG4M1 is rescaled by the rate of the lowest Gamma rate category. The fourth component LG4M4 corresponds to the highest rate.

Note that both frequency and model commands can be embedded into a single model file.

In AliSim, users could easily simulate alignments with mixture models as described above by the following commands.

iqtree2 --alisim MIX_JC_HKY_G -m "MIX{JC,HKY}+G4" -t tree.nwk
iqtree2 --alisim JTT_CF4_G -mdef mymodels.nex -m "JTT+CF4model+G" -t tree.nwk

Site-specific frequency models

Starting with version 1.5.0, IQ-TREE provides a new posterior mean site frequency (PMSF) model as a rapid approximation to the time and memory consuming profile mixture models C10 to C60 (Le et al., 2008a; a variant of PhyloBayes' CAT model). The PMSF are the amino-acid profiles for each alignment site computed from an input mixture model and a guide tree. The PMSF model is much faster and requires much less RAM than C10 to C60 (see table below), regardless of the number of mixture classes. Our extensive simulations and empirical phylogenomic data analyses demonstrate that the PMSF models can effectively ameliorate long branch attraction artefacts.

If you use this model in a publication please cite:

H.C. Wang, B.Q. Minh, S. Susko and A.J. Roger (2018) Modeling site heterogeneity with posterior mean site frequency profiles accelerates accurate phylogenomic estimation. Syst. Biol., 67:216-235. https://doi.org/10.1093/sysbio/syx068

Here is an example of computation time and RAM usage for an Obazoa data set (68 sequences, 43615 amino-acid sites) from Brown et al. (2013) using 16 CPU cores:

Models	CPU time	Wall-clock time	RAM usage
LG+F+G	43h:38m:23s	3h:37m:23s	1.8 GB
LG+C20+F+G	584h:25m:29s	46h:39m:06s	38.8 GB
LG+C60+F+G	1502h:25m:31s	125h:15m:29s	112.8 GB
LG+PMSF+G	73h:30m:37s	5h:7m:27s	2.2 GB

Example usages

To use the PMSF model you have to provide a guide tree, which, for example, can be obtained by a quicker analysis under the simpler LG+F+G model. The guide tree can then be specified via -ft option, for example:

iqtree -s <alignment> -m LG+C20+F+G -ft <guide_tree>

Here, IQ-TREE will perform two phases. In the first phase, IQ-TREE estimates mixture model parameters given the guide tree and then infers the site-specific frequency profile (printed to .sitefreq file). In the second phase, IQ-TREE will conduct typical analysis using the inferred frequency model instead of the mixture model to save RAM and running time. Note that without -ft option, IQ-TREE will conduct the analysis under the specified mixture model.

The PMSF model allows one, for the first time, to conduct nonparametric bootstrap under such complex models, for example (with 100 bootstrap replicates):

iqtree -s <alignment> -m LG+C20+F+G -ft <guide_tree> -b 100

Please note that the first phase still consumes as much RAM as the mixture model. To overcome this, you can perform the first phase in a high-memory server and the second phase in a normal PC as follows:

iqtree -s <alignment> -m LG+C20+F+G -ft <guide_tree> -n 0

This will stop the analysis after the first phase and also write a .sitefreq file. You can now copy this .sitefreq file to another low-memory machine and run with the same alignment:

iqtree -s <alignment> -m LG+C20+F+G -fs <file.sitefreq> -b 100

This will omit the first phase and thus need much less RAM.

Finally, note that for long (phylogenomic) alignments you can utilize the multicore IQ-TREE version to further save the computing times with, say, 24 cores by:

# For IQ-TREE version <= 1.5.X
iqtree-omp -nt 24 -s <alignment> -m LG+C20+F+G -fs <file.sitefreq>

# For IQ-TREE version >= 1.6.0
iqtree -nt 24 -s <alignment> -m LG+C20+F+G -fs <file.sitefreq>

See also the list of relevant command line options.

Heterotachy models

Sequence data that have evolved under heterotachy, i.e., rate variation across sites and lineages (Lopez, Casane, and Philippe, 2002), are known to mislead phylogenetic inference (Kolaczkowski and Thornton, 2004). To address this issue we introduce the General Heterogeneous evolution On a Single Topology (GHOST) model. More specifically, GHOST is an edge-unlinked mixture model consisting of several site classes, each having a separate set of model parameters and edge lengths on the same tree topology. Thus, GHOST naturally accounts for heterotachous evolution. In contrast to an edge-unlinked partition model, the GHOST model does not require the a priori data partitioning, a possible source of model misspecification.

Extensive simulations show that the GHOST model can accurately recover the tree topology, branch lengths, substitution rate and base frequency parameters from heterotachously-evolved sequences. Moreover, we compare the GHOST model to the partition model and show that, owing to the minimization of model constraints, the GHOST model is able to offer unique biological insights when applied to empirical data.

If you use this model in a publication please cite:

S.M. Crotty, B.Q. Minh, N.G. Bean, B.R. Holland, J. Tuke, L.S. Jermiin and A. von Haeseler (2019) GHOST: Recovering historical signal from heterotachously-evolved sequence alignments. Syst. Biol., in press. https://doi.org/10.1093/sysbio/syz051

Quick usages (for phylogenetic Inference with IQ-Tree)

Make sure that you have IQ-TREE version 1.6.0 or later. The GHOST model with k mixture classes is executed by adding +Hk to the model option (-m). For example if one wants to fit a GHOST model with 4 classes in conjunction with the GTR model of DNA evolution to sequences contained in data.fst, one would use the following command:

iqtree -s data.fst -m GTR+H4

By default the above command will link GTR parameters across all classes. If you want to unlink GTR parameters, so that IQ-TREE estimates them separately for each class, replace +H4 by *H4:

iqtree -s data.fst -m GTR*H4

Note that this infers one set of empirical base frequencies and apply those to all classes. If one wishes to infer separate base frequencies for each class then the +FO option is required:

iqtree -s data.fst -m GTR+FO*H4

The -wspm option will generate a .siteprob output file. This contains the probability of each site belonging to each class:

iqtree -s data.fst -m GTR+FO*H4 -wspm

Quick usages (for phylogenetic Simulation with AliSim)

If one wants to simulate sequences based on a GHOST model with 4 classes in conjunction with the GTR model of DNA evolution, one should use the following command:

iqtree2 --alisim GTR_plus_H4 -m GTR+H4 -t tree.nwk

Assuming that we have an input alignment example.phy evolving under the GHOST model with 4 classes in conjunction with the GTR model. If one wants to simulate an alignment that mimics that input alignment, one should use the following command:

iqtree2 --alisim GTR_plus_H4_inference -m GTR+H4 -s example.phy

If you want to unlink GTR parameters so that AliSim could use them separately for each class, replace +H4 by *H4:

iqtree2 --alisim GTR_time_H4_inference -m GTR*H4 -s example.phy

If one wishes to use separate base frequencies for each class, then the +FO option is required:

iqtree2 --alisim GTR_FO_time_H4_inference -m GTR+FO*H4 -s example.phy