Consensus Trees

1
Consensus Trees

• Anders Gorm Pedersen
• Molecular Evolution Group
• Center for Biological Sequence Analysis
• Technical University of Denmark
• gorm_at_cbs.dtu.dk

2
Strict Consensus Tree
Hu
Ch
Go
Or
Gi
Hu
Ch
Go
Or
Gi
Hu
Ch
Go
Or
Gi
Tree 1
Tree 3
Tree 2
Hu
Ch
Go
Or
Gi
Strict consensus
3
Majority Rule Consensus Tree
Hu
Ch
Go
Or
Gi
Hu
Ch
Go
Or
Gi
Hu
Ch
Go
Or
Gi
Tree 3
Tree 1
Tree 2
Hu
Ch
Go
Or
Gi
Majority rule consensus
4
Majority Rule Consensus Tree
C
A
B
E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
5
Majority Rule Consensus Tree
C
A
B
A B C D E F Count








E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
6
Majority Rule Consensus Tree
C
A
B
A B C D E F Count








E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
7
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - -







E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
8
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - I







E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
9
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - I







E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
10
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - I
- - -






E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
11
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - I
- - - I






E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
12
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - I
- - - I






E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
13
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - I
- - - I
- - I





E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
14
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - I
- - - I
- - I





E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
15
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - I
- - - I
- - I





E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
16
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - I
- - - I
- - I
- - - - I




E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
17
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - I
- - - I
- - I
- - - - I




E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
18
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - I
- - - I
- - I
- - - - I




E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
19
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - I
- - - I
- - I
- - - - I




E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
20
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - I
- - - II
- - I
- - - - I




E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
21
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - I
- - - II
- - I
- - - - I




E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
22
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - I
- - - II
- - I
- - - - I




E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
23
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - I
- - - II
- - I
- - - - I
- - I



E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
24
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - I
- - - II
- - I
- - - - I
- - I



E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
25
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - II
- - - II
- - I
- - - - I
- - I



E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
26
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - II
- - - II
- - I
- - - - I
- - I



E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
27
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - II
- - - II
- - I
- - - - I
- - I
- - - I


E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
28
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - II
- - - II
- - I
- - - - I
- - I
- - - I


E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
29
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - II
- - - II
- - I
- - - - I
- - I
- - - I
- - I

E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
30
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - II
- - - II
- - I
- - - - I
- - I
- - - I
- - I

E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
31
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - II
- - - II
- - I
- - - - I
- - I
- - - I
- - I
- - - - I
E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
32
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - II
- - - II
- - I
- - - - I
- - I
- - - I
- - I
- - - - I
E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
33
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - II
- - - III
- - I
- - - - I
- - I
- - - I
- - I
- - - - I
E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
34
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - II
- - - III
- - I
- - - - I
- - I
- - - I
- - I
- - - - I
E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
35
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - II
- - - III
- - I
- - - - I
- - II
- - - I
- - I
- - - - I
E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
36
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - II
- - - III
- - I
- - - - I
- - II
- - - I
- - I
- - - - I
E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
37
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - III
- - - III
- - I
- - - - I
- - II
- - - I
- - I
- - - - I
E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
38
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - III
- - - III
- - I
- - - - I
- - II
- - - I
- - I
- - - - I
E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
39
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - III
- - - III
- - I
- - - - I
- - III
- - - I
- - I
- - - - I
E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
40
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - III
- - - III
- - I
- - - - I
- - III
- - - I
- - I
- - - - I
E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
41
Majority Rule Consensus Tree
C
A
B
A B C D E F Count
- - - - III
- - - III
- - I
- - - - I
- - III
- - - I
- - II
- - - - I
E
E
D
A
D
F
F
F
C
B
A
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
42
Majority Rule Consensus Tree
A B C D E F Count
- - - - III
- - - III
- - I
- - - - I
- - III
- - - I
- - II
- - - - I
43
Majority Rule Consensus Tree
A B C D E F Freq
- - - - 60
- - - 60
- - 20
- - - - 20
- - 60
- - - 20
- - 40
- - - - 20
44
Majority Rule Consensus Tree
A B C D E F Freq
- - - 60
- - - - 60
- - 60
- - 40
- - 20
- - - - 20
- - - 20
- - - - 20
45
Majority Rule Consensus Tree
A B C D E F Freq
- - - 60
- - - - 60
- - 60
- - 40
- - 20
- - - - 20
- - - 20
- - - - 20
C
A
D
E
F
B
46
Majority Rule Consensus Tree
A B C D E F Freq
- - - 60
- - - - 60
- - 60
- - 40
- - 20
- - - - 20
- - - 20
- - - - 20
C
A
D
E
F
B
47
Majority Rule Consensus Tree
A B C D E F Freq
- - - 60
- - - - 60
- - 60
- - 40
- - 20
- - - - 20
- - - 20
- - - - 20
C
A
D
60
E
F
B
48
Majority Rule Consensus Tree
A B C D E F Freq
- - - 60
- - - - 60
- - 60
- - 40
- - 20
- - - - 20
- - - 20
- - - - 20
C
A
D
60
E
F
B
49
Majority Rule Consensus Tree
A B C D E F Freq
- - - 60
- - - - 60
- - 60
- - 40
- - 20
- - - - 20
- - - 20
- - - - 20
C
A
D
60
60
E
F
B
50
Majority Rule Consensus Tree
A B C D E F Freq
- - - 60
- - - - 60
- - 60
- - 40
- - 20
- - - - 20
- - - 20
- - - - 20
C
A
D
60
60
E
F
B
51
Majority Rule Consensus Tree
A B C D E F Freq
- - - 60
- - - - 60
- - 60
- - 40
- - 20
- - - - 20
- - - 20
- - - - 20
C
A
D
60
60
60
E
F
B
52
Majority Rule Consensus Tree
A B C D E F Freq
- - - 60
- - - - 60
- - 60
- - 40
- - 20
- - - - 20
- - - 20
- - - - 20
C
A
D
?
60
60
60
E
F
B
53
Majority Rule Consensus Tree
A B C D E F Freq
- - - 60
- - - - 60
- - 60
- - 40
- - 20
- - - - 20
- - - 20
- - - - 20
C
A
D
60
60
60
?
E
F
B
54
Majority Rule Consensus Tree
A B C D E F Freq
- - - 60
- - - - 60
- - 60
- - 40
- - 20
- - - - 20
- - - 20
- - - - 20
C
A
D
60
60
60
E
F
?
B
55
Majority Rule Consensus Tree
A B C D E F Freq
- - - 60
- - - - 60
- - 60
- - 40
- - 20
- - - - 20
- - - 20
- - - - 20
C
A
D
60
60
60
E
F
B
?
56
Majority Rule Consensus Tree
A B C D E F Freq
- - - 60
- - - - 60
- - 60
- - 40
- - 20
- - - - 20
- - - 20
- - - - 20
C
A
D
60
60
60
E
F
B
?
57
Majority Rule Consensus Tree
C
A
B
E
E
D
A
D
F
C
A
D
F
F
C
B
A
B
60
60
60
E
F
B
E
C
A
D
D
C
B
A
E
F
B
E
C
F
D
58
Ancestral Reconstruction

• Anders Gorm Pedersen
• Molecular Evolution Group
• Center for Biological Sequence Analysis
• Technical University of Denmark
• gorm_at_cbs.dtu.dk

59
Sankoff length of 4 possible subtrees starting
at internal node?
C
A
C
A
G

A C G T


60
Sankoff length of subtree having nucleotide A
at internal node
C
A
1
0
1
T
G
C
A
61
Sankoff length of subtree having nucleotide C
at internal node
C
A
1
0
1 1
T
G
C
A
62
Sankoff length of subtree having nucleotide G
at internal node
C
A
1
1
1 1 2
T
G
C
A
63
Sankoff length of subtree having nucleotide T
at internal node
C
A
1
1
1 1 2 2
T
G
C
A
64
Sankoff length of 4 possible subtrees starting
at internal node?
A
C
C
A
G

1 1 2 2


65
Sankoff length of 4 possible subtrees starting
at internal node?
G
A
A
C
C
1 2 1 2
1 1 2 2


66
Sankoff length of shortest possible subtree
having A at internal node?
G
C
A
A
C
1 2 1 2
1 1 2 2
A

67
Sankoff length of shortest possible subtree
having A at internal node?
G
C
A
A
C
1
1 2 1 2
1 1 2 2
0
A
length of subtree 101 2

68
Sankoff length of shortest possible subtree
having A at internal node?
G
C
A
A
C
1
1 2 1 2
1 1 2 2
1
A
length of subtree 112 4

69
Sankoff length of shortest possible subtree
having A at internal node?
G
C
A
A
C
1
1 2 1 2
1 1 2 2
1
A
length of subtree 111 3

70
Sankoff length of shortest possible subtree
having A at internal node?
G
C
A
A
C
1
1 2 1 2
1 1 2 2
1
A
length of subtree 112 4

71
Sankoff length of shortest possible subtree
having A at internal node?
G
C
A
A
C
1
1 2 1 2
1 1 2 2
0
A
length of subtree 101 2

72
Ancestral Reconstruction Step IKeep Track of
Shortest Subtrees
G
C
A
A
C
1 2 1 2
1 1 2 2
2

73
Ancestral Reconstruction Step IKeep Track of
Shortest Subtrees
G
C
A
A
C
1 2 1 2
1 1 2 2
2 2

74
Ancestral Reconstruction Step IKeep Track of
Shortest Subtrees
G
C
A
A
C
1 2 1 2
1 1 2 2
2 2 2 3

75
Ancestral Reconstruction Step IKeep Track of
Shortest Subtrees
G
C
A
A
C
1 2 1 2
1 1 2 2
2 2 2 3
3 3 4 5
76
Ancestral Reconstruction Step IKeep Track of
Shortest Subtrees
G
C
A
A
C
1 2 1 2
1 1 2 2
2 2 2 3
3 3 4 5
77
Ancestral Reconstruction Step II Backtracking
G
C
A
A
C



A
78
Ancestral Reconstruction Step II Backtracking
G
C
A
A
C

A
A
A
79
Ancestral Reconstruction Step II Backtracking
G
C
A
A
C

A
A
A
80
Ancestral Reconstruction Step II Backtracking
G
C
A
A
C
A
A
A
A
81
Ancestral Reconstruction Step II Backtracking
G
C
A
A
C
A
A
A
A
82
Ancestral Reconstruction Step III Placement of
Changes
G
C
A
A
C
A
A
A
A
83
Ancestral Reconstruction Step II Backtracking
G
C
A
A
C
A
A
A
A C
84
Ancestral Reconstruction Step II Backtracking
G
C
A
A
C
A
A C
A C
A C
85
Ancestral Reconstruction Step II Backtracking
G
C
A
A
C
A
A C
A C
A C
86
Ancestral Reconstruction Step II Backtracking
G
C
A
A
C
A C G
A C
A C
A C
87
Ancestral Reconstruction Step II Backtracking
G
C
A
A
C
A C G
A C
A C
A C
88
Ancestral Reconstruction Step III Placement of
Changes
G
C
A
A
C
A C G
A C
A C
A C
89
Ancestral Reconstruction Step III Placement of
Changes
G
C
A
A
C
A C G
A C
A C
A C
90
Ancestral Reconstruction Step III Placement of
Changes
G
C
A
A
C
A C G
A C
A C
A C
91
Ancestral Reconstruction State Sets
G
C
A
A
C
A C G
A C
A C
A C
92
Ancestral reconstruction experimental analysis
of extinct molecules
93
Ancestral reconstruction
94
Ancestral reconstruction dinosaur night vision
95
Ancestral reconstruction thermostability of
ancestral proteins
96
Ancestral reconstruction thermostability of
ancestral proteins
97
Phylogeny and ancestral reconstruction for
manuscripts
98
Branch Lengths
0.25
0.75
0.75
0.5
0.25
0.5
0
0
99
Problems With Parsimony

• Anders Gorm Pedersen
• Molecular Evolution Group
• Center for Biological Sequence Analysis
• Technical University of Denmark
• gorm_at_cbs.dtu.dk

100
Phylogenetically Informative Sites
1
3
4
2
1 A C G G G G G A A 2 A C G G G G C A A 3 A
C G C C G T A A 4 A C G C T C A A A
1
2
4
3
1
2
3
4
101
Phylogenetically Informative Sites
G
C
G
C
C
G
1 A C G G G G G A A 2 A C G G G G C A A 3 A
C G C C G T A A 4 A C G C T C A A A
G
G
C
C
C
C
G
G
C
C
C
C
102
Not Informative
G
C
G
G
T
G
1 A C G G G G G A A 2 A C G G G G C A A 3 A
C G C C G T A A 4 A C G C T C A A A
G
G
G
G
T
C
G
G
G
G
C
T
103
Not Informative
G
G
G
G
C
G
1 A C G G G G G A A 2 A C G G G G C A A 3 A
C G C C G T A A 4 A C G C T C A A A
G
G
G
G
C
G
G
G
G
G
G
C
104
Not Informative
G
T
T
T
A
C
1 A C G G G G G A A 2 A C G G G G C A A 3 A
C G C C G T A A 4 A C G C T C A A A
G
C
C
C
A
T
G
C
C
C
T
A
105
Long Branch Attraction
1
4
3
2
106
Long Branch Attraction
A
A
A
A
A
107
Uninformative
A
A
A
A
A
A
A
108
Uninformative
C
A
A
A
A
A
A
109
Uninformative
C
G
A
A
A
A
A
110
Misinformative
G
G
A
A
A
A
A
111
Informative
A
G
G
A
G
A
A