Algorithms for Visualizing Phylogenetic Networks Ioannis G. Tollis - - PowerPoint PPT Presentation

Algorithms for Visualizing Phylogenetic Networks

Ioannis G. Tollis

Department of Computer Science, University of Crete, Greece

and Konstantinos G. Kakoulis

Department of Mechanical and Industrial Design Engineering,

T.E.I. of West Macedonia, Greece.

PHYLOGENETIC TREE: A model to represent evolution (of some species, or genes).

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PHYLOGENETIC TREE: A model to represent evolution (of some species, or genes).

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Darwin's first sketch of an evolutionary tree (1837)

PHYLOGENETIC TREE: A model to represent evolution (of some species, or genes).

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Darwin's first sketch of an evolutionary tree (1837) Five Kingdom Classification (by R.H Whittaker,1969)

Evolution cannot be properly represented as a tree.

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Evolution cannot be properly represented as a tree.

• horizontal gene transfer,
• Hybridization,
• genetic recombination

WHY?

Evolution cannot be properly represented as a tree.

• horizontal gene transfer,
• Hybridization,
• genetic recombination

WHY?

A

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H G F E D C B

Evolution cannot be properly represented as a tree.

• horizontal gene transfer,
• Hybridization,
• genetic recombination

WHY? Phylogenetic Networks

A

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Phylogenetic Networks

H G F E D C B

Phylogenetic Networks

Phylogenetic Networks

Reticulation node Has more than one ancestors.

Phylogenetic Networks

Reticulation cycle Every reticulation node

Reticulation node

Has more than one ancestors.

Every reticulation node belongs to a cycle.

Phylogenetic Networks

Reticulation cycle

Every reticulation node belongs to a cycle.

Reticulation node

Has more than one ancestors.

GALL A single (isolated) reticulation cycle

Phylogenetic Networks

Gall Reticulation cycle

Every reticulation node belongs to a cycle.

Reticulation node

Has more than one ancestors.

Galled tree A network in which the galls do not share edges or nodes

Gall

A single (isolated) reticulation cycle

Phylogenetic Networks

Galled network A network in which the galls can share edges but not reticulation nodes

Phylogenetic Networks

Galled network A network in which the galls can share edges but not reticulation nodes

Visualization of Phylogenetic Trees and Networks

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Visualization of Phylogenetic Trees and Networks

node-link representation Huge graphs. Visual clutter.

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Tree of life for 3,000 of the 1.8 million known species based on RNA sequences.

Visualization of Phylogenetic Trees and Networks

node-link representation Huge graphs. Visual clutter.

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Tree of life for 3,000 of the 1.8 million known species based on RNA sequences.

alternative visualization ???

Visualization of Phylogenetic Trees and Networks

node-link representation Huge graphs. Visual clutter.

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Tree of life for 3,000 of the 1.8 million known species based on RNA sequences.

alternative visualization ???

• Space filling techniques

Treemaps DAGmaps

Visualization of Phylogenetic Trees and Networks

node-link Treemap

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C-type opsins

TREEMAP DRAWINGS (Johnson and Shneiderman, 1990)

A space filling technique for visualizing large hierarchical data sets Display trees as a set of nested rectangles

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rectangles

TREEMAP DRAWINGS

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TREEMAP DRAWINGS

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TREEMAP DRAWINGS

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DAGMAP DRAWINGS (Tsiaras, Triantafilou, and Tollis, 2007)

An extension of treemaps for visualizing Directed Acyclic Graphs (DAGs). It is not always possible to visualize a DAG with a DAGmap without having node duplications.

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DAGMAP DRAWINGS

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DAGMAP DRAWINGS

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Treemaps have been used in bioinformatics to visualize:

• 1. Phylogenetic trees
• 2. Gene expression data

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• 3. Gene ontologies
• 4. Encyclopedia of Life

Main Results

Linear time algorithms for:

• 1. Drawing Galled Trees as DAGmaps
• 2. Drawing Planar Galled Networks as DAGmaps

Drawing Galled Networks as DAGmaps, without node duplications, is NP-Complete.

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• 2. Drawing Planar Galled Networks as DAGmaps

Main Results

Linear time algorithms for:

• 1. Drawing Galled Trees as DAGmaps
• 2. Drawing planar galled networks as DAGmaps

Drawing Galled Networks as DAGmaps, without node duplications, is NP-Complete.

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• 2. Drawing planar galled networks as DAGmaps

NOTE

Galled trees and galled networks have received much attention in recent years. They are important types of phylogenetic networks. A galled tree or network may suffice to accurately describe an evolutionary process when the number of recombination events is limited and most of them have occurred recently (Guseld, Eddhu, and Langley, 2004).

DRAWINGS GALLED TREES AS DAGMAPS Algorithm Input: A galled tree G. Output: A DAGmap drawing of G.

• 1. Transform the galled tree G into a tree T, by

unifying the two chains of each gall.

• 2. Draw the treemap of T.
• 3. Split the rectangles, corresponding to the nodes
• f the unified chains of the galls, to obtain the

initial parallel chains.

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DRAWINGS GALLED TREES AS DAGMAPS

STEP 1: Transform the galled tree G into a tree T, by unifying the two chains of each gall.

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DRAWINGS GALLED TREES AS DAGMAPS

STEP 2: Draw the treemap of T.

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DRAWINGS GALLED TREES AS DAGMAPS

STEP 2: Split the rectangles, corresponding to the nodes

• f the unified chains of the galls, to obtain the

initial parallel chains.

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DRAWINGS GALLED TREES AS DAGMAPS

Example 2

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DRAWINGS PLANAR GALLED NETWORKS AS DAGMAPS

Algorithm Input: A planar galled network G. Output: A DAGmap drawing of G.

• 1. Transform the galled network G into a galled tree GT.
• 2. Construct a planar embedding of GT.
• 3. Draw the DAGmaps of the galls of GT.
• 4. Unify the split nodes and remove unused space.

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DRAWINGS PLANAR GALLED NETWORKS AS DAGMAPS

STEP1: Transform the galled network G into a galled tree GT.

Split the nodes that belong to

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more than one galls.

DRAWINGS PLANAR GALLED NETWORKS AS DAGMAPS

STEP 2: Construct a planar embedding of GT.

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Each planar galled network is a single source upward planar DAG. Bertolazzi et al. (1998) have shown that a drawing of a single source upward planar DAG can be constructed in O(n) time. Thus, we can construct an upward planar drawing of a planar galled network in linear time.

DRAWINGS PLANAR GALLED NETWORKS AS DAGMAPS

STEP 3: Draw the DAGmaps of the galls of GT.

7 1 1 1 1 2 2 5 4 6 3 3 4 4 5

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DRAW AS TREEMAP

DRAWINGS PLANAR GALLED NETWORKS AS DAGMAPS

STEP 3: Draw the DAGmaps of the galls of GT.

9 7 1 1 1 1 2 2 5 4 6 3 3 4 4 5 7 1 1 1 1 2 2 5 4 6 3 3 4 4 5

11 10

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Nested galls are drawn recursively.

DRAWINGS PLANAR GALLED NETWORKS AS DAGMAPS

STEP 3: Draw the DAGmaps of the galls of GT.

9 7 1 1 1 1 2 2 5 4 6 3 3 4 4 5 7 1 1 1 1 2 2 5 4 6 3 3 4 4 5 11

10

8

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Nested galls are drawn recursively.

DRAWINGS PLANAR GALLED NETWORKS AS DAGMAPS

STEP 3: Draw the DAGmaps of the galls of GT.

9 7 1 1 1 1 2 2 5 4 6 3 3 4 4 5 7 1 1 1 1 2 2 5 4 6 3 3 4 4 5 11

10

8

14

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Nested galls are drawn recursively.

DRAWINGS PLANAR GALLED NETWORKS AS DAGMAPS

STEP 3: Draw the DAGmaps of the galls of GT.

9 7 1 1 1 1 2 2 5 4 3 3 4 4 5 7 1 1 1 1 2 2 5 4 6 3 3 4 4 5 11

10

8 12 4

14 15 16 17 13

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Nested galls are drawn recursively.

DRAWINGS PLANAR GALLED NETWORKS AS DAGMAPS

STEP 3: Draw the DAGmaps of the galls of GT.

7 1 1 1 1 2 2 5 4 3 3 4 4 5 7 1 1 1 1 2 2 5 4 6 3 3 4 4 5 4 14 15 16 17 13 9 11 10 8 12 14 15 16 17 13

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ADJUST THE SIZE OF THE RECTANGLES CORRESPONDING TO RETICULATION NODES.

DRAWINGS PLANAR GALLED NETWORKS AS DAGMAPS

STEP 3: Draw the DAGmaps of the galls of GT.

7 1 1 1 1 2 2 5 4 3 3 4 4 5 7 1 1 1 1 2 2 5 4 6 3 3 4 4 5 4 14 15 16 17 13 9 11 10 8 12 14 15 16 17 13

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7 1 2 6 3 15 4 16 17 7 5

r

3 4 13 14 2 DRAWINGS PLANAR GALLED NETWORKS AS DAGMAPS

STEP 4: Unify the split nodes and remove unused space.

11 12 8 8 9

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Future Work and Open Problems

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Future Work and Open Problems

We have presented linear time algorithms for the visualization of two categories of phylogenetic networks (galled trees and planar galled networks) as DAGmap drawings.

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Future Work and Open Problems

We have presented linear time algorithms for the visualization of two categories of phylogenetic networks (galled trees and planar galled networks) as DAGmap drawings.

Future Work

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1.Development of a visualization tool for processing phylogenetic networks and displaying them as DAGmaps.

Future Work and Open Problems

We have presented linear time algorithms for the visualization of two categories of phylogenetic networks (galled trees and planar galled networks) as DAGmap drawings.

Future Work

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• 1. Development of a visualization tool for processing phylogenetic

networks and displaying them as DAGmaps.

• 2. Devise DAGmap drawing algorithms for more categories of

phylogenetic networks.

Future Work and Open Problems

We have presented linear time algorithms for the visualization of two categories of phylogenetic networks (galled trees and planar galled networks) as DAGmap drawings.

Future Work

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Open Problems

• Heuristics for reducing the number of node duplications for

drawing non planar galled networks as DAGmaps.

• 1. Development of a visualization tool for processing phylogenetic

networks and displaying them as DAGmaps.

• 2. Devise DAGmap drawing algorithms for more categories of

phylogenetic networks.

Thank you for your Thank you for your

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for your attention attention