Download Exploratory Data Analysis Tools for Phylogenetics: Visualizing

Phylogenetics Workhop,
16-18 August 2006
Exploring Phylogenetic
Data with Splits-Graphs
Barbara Holland
Motivation

When analysing phylogenetic data we usually expect the
historical signal to match a tree.

So we often use software that specifically outputs a tree.

However, there are many processes that can lead to
conflicting signal:



some historical (e.g. hybridisation, recombination);
and some misleading (e.g. long branch attraction, compositional
bias, changing patterns of variable sites).
To see if any of these effects are present in our data it is
no use using software that can only produce a tree.
Tools

Fortunately, there are a number of tools (some old and
some quite recent) that allow conflicting phylogenetic
signals to be displayed in a network.

In this talk I will discuss some splits-based methods:
 Neighbour Nets,
 Consensus Networks and
 Spectral Graphs
Splits-based approaches




A split is a bipartition of the taxa (labels) into two sets
A bipartition of one taxa vs. the rest is known as a trivial split
A split corresponds to a branch in a tree
Trees correspond to compatible split systems
dog
mouse
turtle
cat, dog, mouse, parrot | turtle
cat
dog, cat | mouse, turtle, parrot
parrot
cat, dog, mouse | turtle, parrot
Incompatible splits


Some collections of splits can’t fit on a tree
e.g. dog, cat | mouse, turtle, parrot
dog, mouse | cat, turtle, parrot
turtle, parrot | cat, dog, mouse
But they can fit on a splits-graph
dog
mouse
turtle
cat
parrot
Split-systems

Different methods produce different
varieties of split-systems, e.g.
 Tree
estimation → Compatible splits
 NeighborNet → Circular splits
 Split decomposition → Weakly compatible splits
 Consensus Networks → k-compatible splits
Circular Splits
•Can always be displayed on a planar graph
a
a
b
b
f
c
f
c
e
d
e
d
The same split-system can be
represented in different ways
a
b
f
a
c
e
abc|def
bcd|efa
cde|fab
d
b
f
c
e
d
Compatible splits are always circular
mouse
turtle
dog
parrot
cat
owl
Weakly compatible

A split-system is said to be weakly compatible if does not
induce on any subset of four taxa all three possible
splits.

E.g., the split-system
abf|cde
ac|bdef
ade|bcf
Is not weakly compatible as it induces the quartets ab|cd,
ac|bd, and ad|bc.
Circular splits are always
weakly compatible
a
d
b
c
ab|cd
√
bc|ad
√
ac|bd
X
k-compatibility

A split-system is said to be k-compatible if there is no
subset of k+1 splits that are all pairwise incompatible
k=1
k=2
k=3
k=4
Neighbor Net




INPUT: Distance matrix
OUTPUT: A circular split-system, i.e. a split-system that
can be displayed as a planar graph.
Runtime: O(n3)
Reference: Bryant, D. and V. Moulton, Neighbor-net: an
agglomerative method for the construction of
phylogenetic networks. Mol Biol Evol, 2004. 21(2): p.
255-265.
SELECTION
 Pick a pair of clusters to minimise the standard NJ formula
where
•
Choose which node from each cluster are to be made neighbours
Minimise
AGGLOMERATION
• If a node y has two neighbors x and z, we replace x,y,z with u,v
Consensus Networks




INPUT: (a) a set of leaf-labelled trees, all on the same
set of taxa. (b) A threshold t.
OUTPUT: a splits-graph
Runtime: in practice very fast
References:Holland, B., F. Delsuc, and V. Moulton,
Visualizing conflicting evolutionary hypotheses in large
collections of trees: using consensus networks to study
the origins of placentals and hexapods. Syst Biol, 2005.
54(1): p. 66-76.
We have too many trees!

Many phylogenetic methods produce a collection of
trees rather than a single best tree.



Monte Carlo Markov Chain (MCMC)
Bootstrapping.
Sometimes trees for different genes produce a collection
of trees.
How can we summarize this
information?

Large collections of trees can be difficult to interpret.

Consensus tree methods attempt to summarize the
information contained within a collection of trees by a
single tree.

Information about conflicting hypotheses is necessarily
lost.
The problem with consensus trees
EXAMPLE: We have 10 trees
5 support the hypothesis
5 support
None support
...(gorilla,(human,chimp))...
...(human,(chimp,gorilla))...
...(chimp,(human,gorilla))...
In a majority rule consensus tree this would be represented as a
polytomy ...(gorilla, human, chimp)...
We would lose the information that only 2 of the 3 possible hypothesis
have any support in the data.
human
chimp
gorilla
human
chimp
gorilla
Input trees:
A
C
B
D
A
E
C
B
D
A
E
B
Weighted Splits:
A,B | C,D,E
A,B,C | D,E
A,C | B,D,E
A,B,D | C,E
D
C
E
2
2
1
1
E
A
C
D
A
D
B
C
D
E
E
B
B
C
A
(100%) Strict
Consensus tree
(>50%) Majority-rule
Consensus tree
(≥ 33%)
Consensus network
Controlling visual complexity

By changing the threshold percentage we can control the
worst case complexity of the network.
Threshold
>50%
>33.3%
>25%
>20%
Why is this so?
Example: Given 10 trees and a threshold of 40% the split system will
never have 3 mutually incompatible splits.
Any split in the split system must be in at least 4 trees.
Consider three incompatible splits:
By the pigeonhole principle we can see that it is impossible to have
3 mutually incompatible splits
Spectral Graphs

Spectral Graphs exploit the relationship between
site patterns in alignments and splits to give a
very direct visual representation of a sequence
alignment.

Typically an alignment contains many different
splits that are not compatible so the resulting
splits-graphs tend to be rather complex.
Recoding sites as splits

If a site in an alignment has only 2 states it
is easy to see how to recode it as a split.
E.g.
a
b
c
d
…A…
…G…
…G…
…A…
ad | bc
Recoding sites as splits

.
If a site in an alignment has more than 2
states then we need to group states in
some way, e.g. purines {A,G} and
pyrimidines {C,T}.
a
b
c
d
…A…
…G…
…C…
…T…
ab | cd
Creating the graph
Each split is given a weight proportional to
the number of sites that support that split.
 Can display all splits or just those splits
with weight greater than some threshold.

a
b
c
d
AGGATTCAG
TGGATCTGG
TAGGTTTAA
TAAGCTCGA
ab|cd
ac|bd
ad|bc
a|bcd
b|cda
c|dab
d|abc
3
1
1
1
1
0
2
a
b
c
d
Example – Rokas et al 2003

Species phylogeny of 8 yeast based on a concatenation
106 nuclear genes, ~126,000 bps

Found 100% bootstrap support for every edge on the
tree

Are all problems in phylogeny solvable with enough
data?
NeighborNet of uncorrected distances
S. kluyveri
S. bayanus
S. kudriavzevii
C. albicans
S. mikatae
S. paradoxus
S. cerevisiae
S. castellii
Consensus Networks of gene trees
106 gene trees from Rokas et al. 2003
Parsimony trees
Maximum Likelihood trees
S_cerevisiae
S_paradoxus
S_cerevisiae
S_paradoxus
S_kudriavzevii
S_kudriavzevii
S_mikatae
S_mikatae
S_bayanus
S_bayanus
S_kluyveri
S_kluyveri
S_castellii
C_albicans
S_castellii
C_albicans
What have we learned?

Bootstrap support of 100% indicates that sampling error
is not a problem, i.e. the result is robust to slight changes
in the data.

However, sampling error is not the only source of
phylogenetic error and there may still be some strong
conflicting signals in the data.
Example 2 – Angiosperm
phylogeny

Data taken from Goremykin et al. (MBE, 2004) includes
11 angiosperms

Three gymnosperms for an outgroup

All alignable parts of the chloroplast genome

~80,000 aligned nucleotide sites for 14 taxa.

Similar to the Rokas example many methods of analysis
give high bootstrap support – however, changing the
method/model can change the position of the root
i.e. a long branch effect
NeighborNet
Uncorrected distances
Grasses
Outgroup (gymnosperms)
Neighbornet
ML dists (GTR + I + G)
Outgroup (gymnosperms)
Grasses
Consensus network (parsimony trees)
61 * 1000 = 61,000
bootstrap trees combined
Amborella
Network displays
all splits > 6000 trees Calycanthu
Nymphaea
Spinacia
Pinus
Nicotiana
Oenothera
Arabidopsi
Psilotum
Lotus
Marchantia
Support for grasses basal 14,371 / 61,000
Support for Amb +Nym basal 7,203 / 61,000
Oryza
Triticum
Zea
Amborella
Maximum Likelihood analysis
Each gene fit to GTR + gamma
Calycanthu
Oenothera
61 * 100 = 6,100
bootstrap trees combined
Network displays
all splits > 500 trees
Lotus
Nymphaea
Arabidopsi
Support for Amb +Nym basal
1,277 / 6,100
Support for Nym basal
684 / 6,100
Support for grasses basal
599 / 6,100
Support for Amb basal Pinus
574 / 6,100
Spinacia
Nicotiana
Zea
Triticum
Psilotum
Marchantia
Oryza
What have we learned

Long branch attraction is likely to be causing problems for
parsimony

Similar to the Rokas data it is probably dangerous to
interpret bootstrap scores as measures of accuracy

On the basis of this data there are 4 hypotheses that are still
in contention regarding the root of the angiosperm tree.