Summarizing Multiple Gene Trees Using Cluster Networks Regula Rupp, - - PowerPoint PPT Presentation

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Summarizing Multiple Gene Trees Using Cluster Networks Regula Rupp, - - PowerPoint PPT Presentation

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Summarizing Multiple Gene Trees Using Cluster Networks Regula Rupp, Daniel H. Huson MIEP, June 2008 Overview Trees, Clusters and Cluster Networks Hardwired vs. Softwired Networks Lowest Single Ancestor (LSA) LSA Consensus vs.

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Summarizing Multiple Gene Trees Using Cluster Networks

Regula Rupp, Daniel H. Huson

MIEP, June 2008

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 2

Overview

 Trees, Clusters and Cluster Networks  Hardwired vs. Softwired Networks  Lowest Single Ancestor (LSA)  LSA Consensus vs. Adams Consensus

1

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 3

Clusters on Rooted Trees

 Every edge of a rooted tree defines a

cluster of the taxon set X:

E D C B A

2

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 4

Clusters on Rooted Trees

 Every edge of a rooted tree defines a

cluster of the taxon set X:

E D C B A

2

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 5

Clusters on Rooted Trees

 Every edge of a rooted tree defines a

cluster of the taxon set X:

E D C B A B A {A,B}

2

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 6

Compatible Clusters and Rooted Trees

A B C D E

3

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 7

Compatible Clusters and Rooted Trees

A B C D E

Rooted Tree -> Compatible Clusters

3

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 8

Compatible Clusters and Rooted Trees

A B C D E {E} {D} {C} {B} {A} {D,E} {A,B} {A,B,C}

Rooted Tree -> Compatible Clusters

3

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 9

Compatible Clusters and Rooted Trees

{E} {D} {C} {B} {A} {D,E} {A,B} {A,B,C}

Rooted Tree -> Compatible Clusters

3

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 10

Compatible Clusters and Rooted Trees

Compatible Clusters -> Rooted Trees

{E} {D} {C} {B} {A} {D,E} {A,B} {A,B,C}

Rooted Tree -> Compatible Clusters

3

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 11

Compatible Clusters and Rooted Trees

Compatible Clusters -> Rooted Trees

A B C D E {E} {D} {C} {B} {A} {D,E} {A,B} {A,B,C}

Rooted Tree -> Compatible Clusters

3

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 12

Incompatible Clusters

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 13

Incompatible Clusters

Incompatible Clusters: {A,B} {B,C} …

4

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 14

Incompatible Clusters

Incompatible Clusters: {A,B} {B,C} … Do not fit on one tree

4

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 15

Incompatible Clusters

Incompatible Clusters: {A,B} {B,C} … Question: How to represent incompatible clusters? Do not fit on one tree

4

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 16

Idea: Hasse Diagram (Cover Graph)

Idea: Use a “Hasse diagram” or “cover digraph”: {A} {B} {C} {D} {E} {F} {A,B} {B,C} {D,E} {B,C,D,E} {D,E,F} {A,B,C,D,E} Clusters:

5

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 17

{A} {B} {C} {D} {E} {F}

Idea: Hasse Diagram (Cover Graph)

Idea: Use a “Hasse diagram” or “cover digraph”: {A,B} {B,C} {D,E} {B,C,D,E} {D,E,F} {A,B,C,D,E} Clusters:

F A B C D E

5

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 18

F A B C D E

{A} {B} {C} {D} {E} {F}

AB BC DE

{A,B} {B,C} {D,E}

Idea: Hasse Diagram (Cover Graph)

Idea: Use a “Hasse diagram” or “cover digraph”: {B,C,D,E} {D,E,F} {A,B,C,D,E} Clusters:

5

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 19

F A B C D E

{A} {B} {C} {D} {E} {F}

AB BC DE

{A,B} {B,C} {D,E}

BCDE DEF

{B,C,D,E} {D,E,F}

Idea: Hasse Diagram (Cover Graph)

Idea: Use a “Hasse diagram” or “cover digraph”: {A,B,C,D,E} Clusters:

5

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 20

F A B C D E

{A} {B} {C} {D} {E} {F}

BCDE DEF

{B,C,D,E} {D,E,F}

AB BC DE

{A,B} {B,C} {D,E}

ABCDE

{A,B,C,D,E}

Idea: Hasse Diagram (Cover Graph)

Idea: Use a “Hasse diagram” or “cover digraph”: Clusters:

5

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 21

Problems:

F A B C D E AB BC DE BCDE DEF ABCDE

6

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 22

Problems:

 No single “root”

F A B C D E AB BC DE BCDE DEF ABCDE

5 6

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 23

Problems:

 No single “root”  Leaves with more than one in-edge

F A B C D E AB BC DE BCDE DEF ABCDE

5 6

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 24

Problems:

F A B C D E AB BC DE BCDE DEF ABCDE

5 6

 No single “root”  Leaves with more than one in-edge  Internal nodes with multiple in-edges and

multiple out-edges

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 25

Problems:

F A B C D E AB BC DE BCDE DEF ABCDE

5 6

 No single “root”  Leaves with more than one in-edge  Internal nodes with multiple in-edges and

multiple out-edges

 Clusters represented by nodes instead of edges

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 26

Solutions:

 No single “root” F A B C D E AB BC DE BCDE DEF ABCDE

7

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 27

Solutions:

F A B C D E AB BC DE BCDE DEF ABCDE

7

 No single “root”

  • > Add full set to the clusters
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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 28

Solutions:

ABCDEF F A B C D E AB BC DE BCDE DEF ABCDE

7

 No single “root”

  • > Add full set to the clusters
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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 29

Solutions:

 No single “root”

  • > Add full set to the clusters

 Leaves with more than one in-edge  Internal nodes with multiple in-edges and multiple out-

edges

7

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 30

Solutions:

 No single “root”

  • > Add full set to the clusters

 Leaves with more than one in-edge  Internal nodes with multiple in-edges and multiple out-

edges

  • > If in-degree >1, insert new edge:

7

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 31

Solutions:

 No single “root”

  • > Add full set to the clusters

C

7

 Leaves with more than one in-edge  Internal nodes with multiple in-edges and multiple out-

edges

  • > If in-degree >1, insert new edge:
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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 32

Solutions:

 No single “root”

  • > Add full set to the clusters
  • >

C C

7

 Leaves with more than one in-edge  Internal nodes with multiple in-edges and multiple out-

edges

  • > If in-degree >1, insert new edge:
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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 33

ABCDEF F A C AB BC BCDE DEF ABCDE B D E DE

8

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 34

B ABCDEF F A C AB BC BCDE DEF ABCDE D E DE

8

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 35

B D E DE ABCDEF F A C AB BC BCDE DEF ABCDE

7 8

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 36

Solutions:

 No single “root”

  • > Add full set to the clusters

 Leaves with more than one in-edge  Internal nodes with multiple in-edges and multiple out-edges

  • > If in-degree >1, insert new edge

 Clusters represented by nodes instead of edges

9

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 37

Solutions:

 No single “root”

  • > Add full set to the clusters

 Leaves with more than one in-edge  Internal nodes with multiple in-edges and multiple out-edges

  • > If in-degree >1, insert new edge

 Clusters represented by nodes instead of edges

  • > Represent every cluster by its in-edge

(which is unique now!)

9

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 38

B D E DE ABCDEF F A C AB BC BCDE DEF ABCDE

10

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 39

B D E F A C A B C D E DE DEF F AB BC BCDE ABCDE

10

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 40

B D E F A C

Reticulation edges

A B C D E DE DEF F AB BC BCDE ABCDE

10

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 41

Result: cluster network

11

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 42

Result: cluster network

A cluster network consists of a rooted directed acyclic graph together with a leaf-labeling and 3 additional properties:

11

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 43

Result: cluster network

11

A cluster network consists of a rooted directed acyclic graph together with a leaf-labeling and 3 additional properties:

  • Uniqueness
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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 44

Result: cluster network

11

A cluster network consists of a rooted directed acyclic graph together with a leaf-labeling and 3 additional properties:

  • Uniqueness
  • Nestedness
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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 45

Result: cluster network

A cluster network consists of a rooted directed acyclic graph together with a leaf-labeling and 3 additional properties:

  • Uniqueness
  • Nestedness
  • Reducedness

11

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 46

B D E F A C

Uniqueness

12

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 47

B D E F A C {B,C,D,E}

Uniqueness

12

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 48

B D E F A C {B,C,D,E}

Uniqueness

12

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 49

Nestedness

B D E F A C

13

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 50

Nestedness

B D E F A C {B,C} ⊂ {B,C,D,E}

13

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 51

Nestedness

B D E F A C {B,C} ⊂ {B,C,D,E}

13

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 52

B D E F A C

Reducedness

14

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 53

B D E F A C

Reducedness

14

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 54

B D E F A C

Reducedness

X

14

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 55

Displaying clusters in cluster networks

15

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 56

Displaying clusters in cluster networks

Every non-reticulation edge e in a cluster network defines a cluster, namely the set of labels of all nodes below e.

15

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 57

Displaying clusters in cluster networks

Every non-reticulation edge e in a cluster network defines a cluster, namely the set of labels of all nodes below e. We call this the „hardwired interpretation“.

15

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 58

Displaying clusters in cluster networks

Every non-reticulation edge e in a cluster network defines a cluster, namely the set of labels of all nodes below e. We call this the „hardwired interpretation“. In contrast we define the „softwired interpretation“ where we may switch reticulation edges on or off.

15

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 59

A B C D E F A B C D E F

Hardwired / Softwired

T1: T2:

16

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 60

A B C D E F A B C D E F

Hardwired / Softwired

A B C D E F

Hardwired: T1: T2:

16

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 61

A B C D E F A B C D E F

Hardwired / Softwired

A B C D E F A B C D E F

Hardwired: T1: T2:

16

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 62

A B C D E F A B C D E F

Hardwired / Softwired

A B C D E F A B C D E F

Hardwired: T1: T2:

16

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 63

A B C D E F A B C D E F

Hardwired / Softwired

A B C D E F A B C D E F

Hardwired: Softwired: T1: T2:

16

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 64

Hardwired / Softwired

 Cluster network, “Hardwired”: blue edges

always on

 Reticulate network, “Softwired”: For any

reticulation, any blue edge can be on or off

17

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 65

Hardwired / Softwired

 Cluster network, “Hardwired”: blue edges

always on

 Reticulate network, “Softwired”: For any

reticulation, any blue edge can be on or off

– More reticulations, “looks complicated”

17

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 66

Hardwired / Softwired

 Cluster network, “Hardwired”: blue edges

always on

 Reticulate network, “Softwired”: For any

reticulation, any blue edge can be on or off

– More reticulations, “looks complicated” – Number of reticulations can be minimized

17

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 67

Hardwired / Softwired

 Cluster network, “Hardwired”: blue edges

always on

 Reticulate network, “Softwired”: For any

reticulation, any blue edge can be on or off

– More reticulations, “looks complicated” – Number of reticulations can be minimized – Computationally hard

17

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 68

Hardwired / Softwired

 Cluster network, “Hardwired”: blue edges

always on

 Reticulate network, “Softwired”: For any

reticulation, any blue edge can be on or off

– More reticulations, “looks complicated” – Number of reticulations can be minimized – Canonical network, computationally easy – Computationally hard

17

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 69

Lowest Single Ancestor: LSA

B A C D E F

18

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 70

Lowest Single Ancestor: LSA

 In trees: LCA B A C D E F

18

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 71

Lowest Single Ancestor: LSA

 In trees: LCA  In cluster networks: LSA = Lowest Single Ancestor: B A C D E F

18

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 72

Lowest Single Ancestor: LSA

 In trees: LCA  In cluster networks: LSA = Lowest Single Ancestor:

LSA(S) = Lowest node that is on every path from the root to one of the nodes in S.

B A C D E F

18

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 73

Lowest Single Ancestor: LSA

 In trees: LCA  In cluster networks: LSA = Lowest Single Ancestor:

LSA(S) = Lowest node that is on every path from the root to one of the nodes in S.

B A C D E F B

18

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 74

Lowest Single Ancestor: LSA

 In trees: LCA B A C D E F B N

18

 In cluster networks: LSA = Lowest Single Ancestor:

LSA(S) = Lowest node that is on every path from the root to one of the nodes in S.

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 75

Lowest Single Ancestor: LSA

 In trees: LCA  In cluster networks: LSA = Lowest Single Ancestor:

LSA(S) = Lowest node that is on every path from the root to one of the nodes in S.

B A C D E F B R N

18

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 76

Lowest Single Ancestor: LSA

 In trees: LCA  In cluster networks: LSA = Lowest Single Ancestor:

LSA(S) = Lowest node that is on every path from the root to one of the nodes in S.

B A C D E F B R N

18

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 77

Lowest Single Ancestor: LSA

 In trees: LCA  In cluster networks: LSA = Lowest Single Ancestor:

LSA(S) = Lowest node that is on every path from the root to one of the nodes in S.

B A C D E F B ? LSA{B,N,R} -> R N

18

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 78

Lowest Single Ancestor: LSA

 In trees: LCA  In cluster networks: LSA = Lowest Single Ancestor:

LSA(S) = Lowest node that is on every path from the root to one of the nodes in S.

B A C D E F B ? LSA{B,N,R} ->

  • > no!

R N

18

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 79

Lowest Single Ancestor: LSA

 In trees: LCA  In cluster networks: LSA = Lowest Single Ancestor:

LSA(S) = Lowest node that is on every path from the root to one of the nodes in S.

B A C D E F B LSA{B,N,R} -> R N

18

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 80

LSA consensus tree

LSA of a reticulation

A B D E F C

19

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  • Regula Rupp 81

LSA consensus tree

LSA of a reticulation

A B D E F C R

19

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  • Regula Rupp 82

LSA consensus tree

LSA of a reticulation

A B D E F C R

19

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  • Regula Rupp 83

LSA consensus tree

LSA of a reticulation

A B D E F C R LSA(R)

19

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 84

LSA consensus tree

LSA of a reticulation

A B D E F C

19

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 85

LSA consensus tree

LSA of a reticulation

A B D E F C

19

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 86

LSA consensus tree

LSA of a reticulation

A B D E F C

19

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  • Regula Rupp 87

LSA consensus tree

LSA of a reticulation

A B D E F C

19

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 88

LSA consensus tree

LSA of a reticulation

A B D E F C

  • > new consensus method!

19

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 89

LSA consensus tree

LSA of a reticulation

A B D E F C

  • > new consensus method!

19

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 90

LSA Consensus

20

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 91

LSA Consensus

 New consensus method

20

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 92

LSA Consensus

 New consensus method  LSA is lowest node for which all input

trees agree that it is an ancestor

20

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 93

LSA Consensus

 New consensus method  LSA is lowest node for which all input

trees agree that it is an ancestor

 Easy to compute

20

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 94

LSA Consensus

 New consensus method  LSA is lowest node for which all input

trees agree that it is an ancestor

 Easy to compute  Different from all other consensus

methods (?)

20

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MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 95

LSA Consensus

 New consensus method  LSA is lowest node for which all input

trees agree that it is an ancestor

 Easy to compute  Different from all other consensus

methods (?)

 Philippe Gambette: LSA consensus =

Adams consensus?

20

slide-96
SLIDE 96

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 96

Adams Consensus

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slide-97
SLIDE 97

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 97

Adams Consensus

 Sets of trees T1,T2,...,Tn

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slide-98
SLIDE 98

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 98

Adams Consensus

 Sets of trees T1,T2,...,Tn  Maximal clusters in Adams Consensus:

non-empty intersections of maximal clusters in T1,T2,...,Tn

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slide-99
SLIDE 99

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 99

Adams Consensus

 Sets of trees T1,T2,...,Tn  Maximal clusters in Adams Consensus:

non-empty intersections of maximal clusters in T1,T2,...,Tn

 Restrict trees to maximal clusters of

Adams consensus and repeat procedure recursively.

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SLIDE 100

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 100

Adams vs. LSA

Question: LSA consensus = Adams consensus?

22

slide-101
SLIDE 101

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 101

Adams vs. LSA

Question: LSA consensus = Adams consensus?

D A B C

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slide-102
SLIDE 102

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 102

Adams vs. LSA

Question: LSA consensus = Adams consensus?

A B C D D A B C

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slide-103
SLIDE 103

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 103

Adams vs. LSA

Question: LSA consensus = Adams consensus?

A B C D

Adams consensus:

A B C D D A B C

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slide-104
SLIDE 104

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 104

Adams vs. LSA

Question: LSA consensus = Adams consensus?

A B C D

Adams consensus:

A B C D

Cluster network:

D A B C

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slide-105
SLIDE 105

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 105

Adams vs. LSA

Question: LSA consensus = Adams consensus?

A B C D

Adams consensus:

A B C D

Cluster network:

D A B C D A B C

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slide-106
SLIDE 106

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 106

Adams vs. LSA

Question: LSA consensus = Adams consensus?

A B C D

Adams consensus:

A B C D

Cluster network:

D A B C D A B C

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slide-107
SLIDE 107

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 107

Adams vs. LSA

Question: LSA consensus = Adams consensus?

A B C D

Adams consensus:

A B C D D A B C

LSA consensus:

D A B C

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slide-108
SLIDE 108

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 108

Adams vs. LSA

Question: LSA consensus = Adams consensus?

  • > LSA consensus ≠ Adams consensus

A B C D

Adams consensus:

A B C D D A B C

LSA consensus:

D A B C

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slide-109
SLIDE 109

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 109

Adams vs. LSA

Question: LSA cons. refinement of Adams cons.?

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slide-110
SLIDE 110

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 110

Adams vs. LSA

Question: LSA cons. refinement of Adams cons.?

D A B C

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slide-111
SLIDE 111

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 111

Adams vs. LSA

Question: LSA cons. refinement of Adams cons.?

A D B C D A B C

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slide-112
SLIDE 112

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 112

Adams vs. LSA

Question: LSA cons. refinement of Adams cons.?

A D B C

Adams consensus:

A C B D D A B C

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slide-113
SLIDE 113

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 113

Adams vs. LSA

Question: LSA cons. refinement of Adams cons.?

A D B C

Adams consensus:

A C B D A B C D

LSA consensus:

D A B C

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slide-114
SLIDE 114

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 114

Adams vs. LSA

Question: LSA cons. refinement of Adams cons.?

  • > LSA not a refinement

A D B C

Adams consensus:

A C B D A B C D

LSA consensus:

D A B C

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slide-115
SLIDE 115

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 115

Adams vs. LSA

Combination of two examples:

A B D E C A E D B C

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slide-116
SLIDE 116

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 116

Adams vs. LSA

Combination of two examples:

A B D E C A E D B C

Adams consensus:

A C E B D

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slide-117
SLIDE 117

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 117

Adams vs. LSA

Combination of two examples:

A B D E C A E D B C

Adams consensus: LSA consensus:

A C E B D A E B C D

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slide-118
SLIDE 118

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 118

Adams vs. LSA

  • > consensus trees are compatible

Combination of two examples:

A B D E C A E D B C

Adams consensus: LSA consensus:

A C E B D A E B C D

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slide-119
SLIDE 119

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 119

Adams vs. LSA

  • > consensus trees are compatible

Is this always true? -> Open Question Combination of two examples:

A B D E C A E D B C

Adams consensus: LSA consensus:

A C E B D A E B C D

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SLIDE 120

MIEP 08 - Summarizing Multiple Gene Trees Using Cluster Networks

  • Regula Rupp 120

Coming soon: Dendroscope 2.0

 Trees and networks  Cluster networks  LSA consensus

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