Exploring Phylogenetic Data with Splits-Graphs

Phylogenetics Workhop, 16-18 August 2006

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

cat

dog mouseturtle

parrot

dog, cat | mouse, turtle, parrot cat, dog, mouse | turtle, parrot

cat, dog, mouse, parrot | turtle

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

cat

mouse

turtle

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

a

b

c

d

e

f

•Can always be displayed on a planar graph

a b

c

de

f

The same split-system can be represented in different ways

a b

c

de

f

a b

c

de

f

abc|defbcd|efacde|fab

Compatible splits are always circular

cat

dog

mouse

turtle

parrot

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-systemabf|cdeac|bdefade|bcf

Is not weakly compatible as it induces the quartets ab|cd, ac|bd, and ad|bc.

Circular splits are always weakly compatible

a

b

c

d

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.

Pick a pair of clusters to minimise the standard NJ formula

where

• Choose which node from each cluster are to be made neighbours

Minimise

SELECTION

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 treesEXAMPLE: We have 10 trees

5 support the hypothesis ...(gorilla,(human,chimp))...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

(>50%) Majority-rule

Consensus tree

Weighted Splits:A,B | C,D,E 2A,B,C | D,E 2A,C | B,D,E 1A,B,D | C,E 1

(≥ 33%)Consensus network

A

B

C D

E

A

C

B D

E

A

B

D C

E

Input trees:

(100%) Strict Consensus tree

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

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 have3 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 …A…b …G…c …G…d …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 …A…b …G…c …C…d …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 AGGATTCAGb TGGATCTGGc TAGGTTTAA d TAAGCTCGA

ab|cd 3ac|bd 1ad|bc 1a|bcd 1b|cda 1c|dab 0d|abc 2

a

b

d

c

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?

C. albicans

S. kluyveri

S. castellii

S. bayanus

S. kudriavzevii

S. cerevisiae

S. paradoxus

S. mikatae

NeighborNet of uncorrected distances

Maximum Likelihood trees Parsimony trees

106 gene trees from Rokas et al. 2003

C_albicans

S_kluyveri

S_kudriavzevii

S_bayanus

S_cerevisiae

S_paradoxus

S_mikatae

S_castelliiC_albicans

S_kudriavzevii

S_bayanus

S_cerevisiae

S_paradoxus

S_mikatae

S_kluyveri

S_castellii

Consensus Networks of gene trees

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

NeighborNetUncorrected distances

Grasses

Outgroup (gymnosperms)

NeighbornetML dists (GTR + I + G) Grasses

Outgroup (gymnosperms)

Amborella

Lotus

Arabidopsi

Oenothera

Nicotiana

Spinacia

OryzaZeaTriticum

Marchantia

Psilotum

Pinus

NymphaeaCalycanthu

Consensus network (parsimony trees)61 * 1000 = 61,000bootstrap trees combined

Network displays all splits > 6000 trees

Support for grasses basal 14,371 / 61,000Support for Amb +Nym basal 7,203 / 61,000

Maximum Likelihood analysisEach gene fit to GTR + gamma

61 * 100 = 6,100bootstrap trees combinedNetwork displays all splits > 500 trees

Support for Amb +Nym basal 1,277 / 6,100Support for Nym basal684 / 6,100Support for grasses basal 599 / 6,100Support for Amb basal574 / 6,100

Amborella

Arabidopsi

Spinacia

Lotus

Oenothera

Zea

TriticumOryza

Calycanthu

Nymphaea

Nicotiana

Marchantia

Psilotum

Pinus

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.