Last update: Mar 15, 2021, Contributors: Minh Bui

Assessing phylogenetic assumptions

It is important to know that phylogenetic models rely on various simplifying assumptions to ease computations. If your data severely violate these assumptions, it might cause bias in phylogenetic estimates of tree topologies and other model parameters. Some common assumptions include treelikeness (all sites in the alignment have evolved under the same tree), stationarity (nucleotide/amino-acid frequencies remain constant over time), reversibility (substitutions are equally likely in both directions), and homogeneity (substitution rates remain constant over time).

This document shows several ways to check some of these assumptions that you should perform before doing phylogenetic analysis.

Tests of symmetry

IQ-TREE provides three matched-pairs tests of symmetry (Naser-Khdour et al., 2019) to test the two assumptions of stationarity and homogeneity. A simple analysis:

iqtree2 -s example.phy -p example.nex --symtest-only

will perform the three tests of symmetry on every partition of the alignment and print the result into a .symtest.csv file. --symtest-only option tells IQ-TREE to only perform the tests of symmetry and then exit. In this example the content of example.nex.symtest.csv looks like this:

# Matched-pair tests of symmetry
# This file can be read in MS Excel or in R with command:
#    dat=read.csv('example.nex.symtest.csv',comment.char='#')
# Columns are comma-separated with following meanings:
#    Name:    Partition name
#    SymSig:  Number of significant sequence pairs by test of symmetry
#    SymNon:  Number of non-significant sequence pairs by test of symmetry
#    SymPval: P-value for maximum test of symmetry
#    MarSig:  Number of significant sequence pairs by test of marginal symmetry
#    MarNon:  Number of non-significant sequence pairs by test of marginal symmetry
#    MarPval: P-value for maximum test of marginal symmetry
#    IntSig:  Number of significant sequence pairs by test of internal symmetry
#    IntNon:  Number of non-significant sequence pairs by test of internal symmetry
#    IntPval: P-value for maximum test of internal symmetry
Name,SymSig,SymNon,SymPval,MarSig,MarNon,MarPval,IntSig,IntNon,IntPval
part1,44,92,0.475639,50,86,0.722371,4,132,0.23869
part2,43,93,0.142052,49,87,0.205232,5,131,0.169618
part3,53,83,0.00499855,58,78,0.00164132,6,130,0.343127

The three important columns are:

• SymPval: a small p-value (say < 0.05) indicates that the assumptions of stationarity or homogeneity or both is rejected. In this case, partition part3 does not comply with these two assumptions (p-value = 0.00499855), whereas the other two partitions are “good”.
• MarPval: a small p-value means that the assumption of stationarity is rejected. In this case, only partition part3 does not comply with the stationary condition (p-value = 0.00164132).
• IntPval: a small p-value means that the homogeneity assumption is reject. In this case, no partitions are “bad” according to this test, i.e., they all comply with the homogeneity assumption.

This little example shows that only part3 is problematic by not complying with the stationary assumption.

Now you may want to perform the phylogenetic analysis excluding all “bad” partitions by:

iqtree2 -s example.phy -p example.nex --symtest-remove-bad

that will remove all “bad” partitions where SymPval < 0.05 and continue the analysis with the remaining “good” partitions. You may then compare the trees from “all” partitions and from “good” only partitions to see if there is significant difference between them with tree topology tests.

Other options can be seen when running iqtree2 -h:

TEST OF SYMMETRY:
  --symtest               Perform three tests of symmetry
  --symtest-only          Do --symtest then exist
  --symtest-remove-bad    Do --symtest and remove bad partitions
  --symtest-remove-good   Do --symtest and remove good partitions
  --symtest-type MAR|INT  Use MARginal/INTernal test when removing partitions
  --symtest-pval NUMER    P-value cutoff (default: 0.05)
  --symtest-keep-zero     Keep NAs in the tests

Likelihood mapping

Likelihood mapping (Strimmer and von Haeseler, 1997) is a visualisation method to display the phylogenetic information of an alignment. It visualises the treelikeness of all quartets in a single triangular graph and therefore renders a quick interpretation of the phylogenetic content.

A simple likelihood mapping analysis can be conducted with:

iqtree -s example.phy -lmap 2000 -n 0

where -lmap option specify the number of quartets of taxa that will be drawn randomly from the alignment. -n 0 tells IQ-TREE to stop the analysis right after running the likelihood mapping. IQ-TREE will print the result in the .iqtree report file as well as the likelihood mapping plot .lmap.svg (in SVG format) and .lmap.eps file (in EPS figure format).

You can now view the likelihood mapping plot file example.phy.lmap.svg, which looks like this:

It shows phylogenetic information of the alignment example.phy.

• Top sub-figure: distribution of quartets depicted by dots on the likelihood mapping plot.
• Left sub-figure: percentages of quartets falling in each of the three areas. The three areas show support for one of the different groupings like (a,b)-(c,d).
• Right sub-figure: percentages of quartets falling in each of the seven areas. Quartets falling into the three corners are informative and called fully-resolved quartets. Those in three rectangles are partly informative (partly resolved quartets) and those in the center are uninformative (unresolved quartets). A good data set should have high number of fully resolved quartets and low number of unresolved quartets.

The meanings can also be found in the LIKELIHOOD MAPPING STATISTICS section of the report file example.phy.iqtree:

LIKELIHOOD MAPPING STATISTICS
-----------------------------

           (a,b)-(c,d)                              (a,b)-(c,d)      
                /\                                      /\           
               /  \                                    /  \          
              /    \                                  /  1 \         
             /  a1  \                                / \  / \        
            /\      /\                              /   \/   \       
           /  \    /  \                            /    /\    \      
          /    \  /    \                          / 6  /  \  4 \     
         /      \/      \                        /\   /  7 \   /\    
        /        |       \                      /  \ /______\ /  \   
       /   a3    |    a2  \                    / 3  |    5   |  2 \  
      /__________|_________\                  /_____|________|_____\ 
(a,d)-(b,c)            (a,c)-(b,d)      (a,d)-(b,c)            (a,c)-(b,d) 

Division of the likelihood mapping plots into 3 or 7 areas.
On the left the areas show support for one of the different groupings
like (a,b|c,d).
On the right the right quartets falling into the areas 1, 2 and 3 are
informative. Those in the rectangles 4, 5 and 6 are partly informative
and those in the center (7) are not informative.
.....

The command reference will provide more options and how to perform 2-, 3-, or 4-cluster likelihood mapping analysis.