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

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.

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 (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.

Assessing Phylogenetic Assumptions

Simulating sequence alignments