Tricks for trees: Having reconstructed phylogenies what can we do with them?

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Tricks for trees Having reconstructed
phylogenies what can we do with them?
Mike Steel Allan Wilson Centre for Molecular
Ecology and Evolution Biomathematics Research
Centre University of Canterbury, Christchurch,
New Zealand
DIMACS, June 2006
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Where are phylogenetic trees used?

• Evolutionary biology species relationships,
  dating divergences, speciation processes,
  molecular evolution.
• Ecology classifying new species biodiversity,
  co-phylogeny, migration of populations.
• Epidemiology systematics, processes, dynamics
• Extras - linguistics, stematology, psychology.

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Phylogenetic trees

• Definition A phylogenetic X-tree is a tree
  T(V,E) with a set X of labelled leaves, and all
  other vertices unlabelled and of degree gt3.
• If all non-leaf vertices have degree 3 then T is
  binary

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Trees and splits
3
1
2
4
5
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Partial order
Bunemans Theorem
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Quartet trees

• A quartet tree is a binary phylogenetic tree on
  4 leaves (say, x,y,w,z) written xywz.

x
w
y
z

• A phylogenetic X-tree displays xywz if there is
  an edge in T whose deletion separates x,y from
  w,z

x
y
w
r
z
u
s
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Corresponding notions for rooted trees

• Clusters (in place of splits)
• Triples in place of quartets

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How are trees useful in epidemiology?

• Systematics and reconstruction
• How are different types/strains of a virus
  related?
• When, where, and how did they arise?
• What is their likely future evolution?
• What was the ancestral sequence?

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How are trees useful in epidemiology?

• Processes and dynamics (Phylodynamics)
• How do viruses change with time in a population?
  Population size etc
• What is their rate of mutation, recombination,
  selection?
• Within-host dynamcs
• How do viruses evolve in a single patient?
• How is this related to the progression of the
  disease?
• How much compartmental variation exists?

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What do the shapes of these trees tell us about
the processes governing their evolution?Eg.
Population dynamics, selection
Coalescent prediction
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Tree shapes (non-metric)
George Yule
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Why do trees on the same taxa disagree?

• Model violation
• true model differs from assumed model
• true model assumed model but estimation
  method not
  appropriate to model
• model true but too parameter rich
  (non-identifyability)
• Sampling error (and factors that make it worse!)
• Alignment error
• Evolutionary processes
• Lineage sorting
• Recombination
• Horizontal gene transfer hybrid taxa
• Gene duplication and loss

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Sampling error thats hard to deal with
Sequences
Sequences
Sequences
Sequences
T2
T1
T3
T4
Time
?
e
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Example Deep divergence in the Metazoan
phylogeny
From Huson and Bryant, 2006
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Models
2
1
1
3
vs
3
4
2
4
Finite state Markov process
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Models
3
1
3
1
vs
2
2
4
4

• site saturation
• subdividing long edges only offers a partial
  remedy (trade-off).

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Why do trees on the same taxa disagree?

• Model violation
• true model differs from assumed model
• true model assumed model but estimation
  method not
  appropriate to model
• model true but too parameter rich
  (non-identifyability)
• Sampling error (and factors that make it worse!)
• Alignment
• Evolutionary processes
• Lineage sorting
• Recombination
• Horizontal gene transfer hybrid taxa
• Gene duplication and loss

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Gene trees vs species trees
a b c
a b c

• Theorem J. H. Degnan and N.A. Rosenberg, 2006.
• For ngt5, for any tree, there are branch lengths
  and population sizes for which the most likely
  gene tree is different from the species tree.
• Discordance of species trees with their most
  likely gene trees.
• PLoS Genetics, 2(5), e68 May, 2006

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Example
?
Orangutan
Human
Gorilla
Chimpanzee
Adapted From the Tree of the Life
Website,University of Arizona
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Distinguishing between signals

• Lineage sorting vs sampling error vs HGT

A B C
A B C
A C B
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Why do trees on the same taxa disagree?

• Model violation
• true model differs from assumed model
• true model assumed model but estimation
  method not
  appropriate to model
• model true but too parameter rich
  (non-identifyability)
• Sampling error (and factors that make it worse!)
• Alignment
• Evolutionary processes
• Lineage sorting
• Recombination
• Horizontal gene transfer hybrid taxa
• Gene duplication and loss

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Given a tree what questions might we want to
answer?

• How reliable is a split?
• Where is the root of the tree? Relative ranking
  of vertices? Dating?
• How well supported is some deep divergence
  resolved?
• What model best describes the evolution of the
  sequences
• (molecular clock? dS/dN ratio constant? etc)
• Statistical approaches
• Non-parametric bootstrap
• Parametric bootstrap
• Likelihood ratio tests
• Bayesian posterior probabilities
• Tests (KH, SH, SOWH)
• Goldman, N., J. P. Anderson, and A. G. Rodrigo.
  2000.
• Likelihood-based tests of topologies in
  phylogenetics. Systematic Biology 49 652-670.

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From Steve Thompson, Florida State Uni
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Example
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Non-parametric bootstrap
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Dealing with incompatibility Consensus trees

• Strict
• Majority rule
• Semistrict consensus

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Consensus networks

• Take the splits that are in at least x of the
  trees and represent them by a graph
• Splits Graph (G(S)) Dress and Huson
• Each split is represented by a class of
  parallel edges
• Simplest example (n4).

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(NS)
(NS)
(SS)
(A)
(A)
(SS)
(NS)
(NS)
(SS)
(SS)
(SS)
(SS)
(SS)
(NS)
(NS)
(N,NS)
(N)
chloroplast JSA tree
(C,S)
(NS, N)
(SS)
(NS)
(SS)
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(SS)
(A)
(SS)
(SS)
(SS)
(SS)
(NS)
(SS)
(SS)
(N)
(SS)
(NS,N)
(A)
(NS)
(NS)
(NS)
(SS,NS)
(NS)
(NS)
(NS,N)
nuclear ITS tree
(SS)
(NS)
(SS)
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consensus network (ITStreeJSAtree)
I
III
II
R.nivicola
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Maximum agreement subtrees

• Concept
• Computational complexity

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Comparing trees

• Splits metric (Robinson-Foulds)
• Statistical aspects.
• Tree rearrangement operations the graph of
• trees (rSPR).
• Cophylogeny

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Co-phylogeny (m. charleston)
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Supertrees

• Compatibility concept
• Compatibility of rooted trees (BUILD)
• Why do we want to do this?
• Extension higher order taxa, dates
• Methods for handling incompatible trees
• (MRP mincut variants minflip)

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Compatibility
A set Q of quartets is compatible if there is a
phylogenetic X-tree T that displays each quartet
of Q

• Example Q1234, 1345, 1426

Complexity?
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Supertrees

• Compatibility concept
• Compatibility of rooted trees (BUILD)
• Why do we want to do this?
• Extension higher order taxa, dates
• Methods for handling incompatible trees
• (MRP mincut variants minflip)

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Phylogenetic networks

• Consensus setting consensus networks
• Minimizing hybrid/reticulate vertices
• Supernetworks Z closure, filtering

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d
a
b
a
d
a
b
c
c
d
c
b

• Networks can represent
• Reticulate evolution (eg. hybrid species)
• Phylogenetic uncertainty (i.e. possible
  alternative trees)
• Z-closure Given T1,, Tk on overlapping sets of
  species,
• let
• construct spcl2(S) and construct the
• splits graph of the resulting splits that are
  full.

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Split closure operation (Meacham 1986)
,
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Reconstructing ancestral sequences

• Methods (MP, Likelihood, Bayesian)
• Quiz. MP for a balanced tree majority state?
• Information-theoretic considerations

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Statistics of parsimony (clustering on a tree)