Exploring Phylogenetic Data with SplitsGraphs

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Exploring Phylogenetic Data with Splits-Graphs
Phylogenetics Workhop, 16-18 August 2006
Barbara Holland
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Motivation
Table 1 North Island road distances

• 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.

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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

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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

mouse
dog
turtle
cat, dog, mouse, parrot turtle
parrot
cat
dog, cat mouse, turtle, parrot
cat, dog, mouse turtle, parrot
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Incompatible splits

• Some collections of splits cant 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

mouse
dog
turtle
cat
parrot
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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

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Circular Splits

• Can always be displayed on a planar graph

a
b
c
f
d
e
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The same split-system can be represented in
different ways
b
a
b
a
f
c
f
c
d
e
d
e
abcdef bcdefa cdefab
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Compatible splits are always circular
mouse
turtle
dog
parrot
cat
owl
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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
• abfcde
• acbdef
• adebcf
• Is not weakly compatible as it induces the
  quartets abcd, acbd, and adbc.

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Circular splits are always weakly compatible
a
v
abcd
bcad
v
X
acbd
b
d
c
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k-compatibility

• A split-system is said to be k-compatible if
  there is no subset of k1 splits that are all
  pairwise incompatible

k1 k2 k3 k4
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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.

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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

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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
• ReferencesHolland, 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.

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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.

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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.

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The problem with consensus trees

• EXAMPLE We have 10 trees
• 5 support the hypothesis ...(gorilla,(human,chim
  p))...
• 5 support ...(human,(chimp,gorilla))...
• None support ...(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
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Input trees
D
C
B
C
D
A
A
D
A
B
E
C
E
B
E
Weighted Splits A,B C,D,E 2 A,B,C D,E 2 A,C
B,D,E 1 A,B,D C,E 1
E
D
C
B
A
(100) Strict Consensus tree
(gt50) Majority-rule Consensus tree
( 33) Consensus network
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Controlling visual complexity

• By changing the threshold percentage we can
  control the worst case complexity of the
  network.

Threshold gt50 gt33.3 gt25
gt20
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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
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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.

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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 A b G c G d A
ad bc
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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 A b G c C d T
ab cd
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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.

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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?

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NeighborNet of uncorrected distances
S. kluyveri
S. bayanus
S. kudriavzevii
C. albicans
S. mikatae
S. paradoxus
S. cerevisiae
S. castellii
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Consensus Networks of gene trees
106 gene trees from Rokas et al. 2003
Parsimony trees
Maximum Likelihood trees
S_cerevisiae
S_cerevisiae
S_paradoxus
S_kudriavzevii
S_paradoxus
S_kudriavzevii
S_mikatae
S_bayanus
S_mikatae
S_bayanus
S_kluyveri
S_kluyveri
C_albicans
S_castellii
C_albicans
S_castellii
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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.

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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

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i.e. a long branch effect
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NeighborNet Uncorrected distances
Grasses
Outgroup (gymnosperms)
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Neighbornet ML dists (GTR I G)
Grasses
Outgroup (gymnosperms)
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Consensus network (parsimony trees) 61 1000
61,000 bootstrap trees combined Network displays
all splits gt 6000 trees
Support for grasses basal 14,371 / 61,000 Support
for Amb Nym basal 7,203 / 61,000
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Maximum Likelihood analysis Each gene fit to GTR
gamma 61 100 6,100 bootstrap trees
combined Network displays all splits gt 500 trees
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 574 /
6,100
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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.