Phylogenetic Networks Networks Phylogenetic Daniel H. Huson Daniel H. Huson www- -ab.informatik.uni ab.informatik.uni- -tuebingen.de tuebingen.de www 1 1
Phylogenetic Networks Networks Phylogenetic � As a data representation As a data representation � As a more complex As a more complex � � technique model of evolution technique model of evolution x 5 x 5 x 1 x x 2 x x 3 x x 6 x x 9 x x 4 x 10 x x x 8 x 1 2 3 6 9 4 10 8 � Splits graphs and others Splits graphs and others � Reticulation graphs: Reticulation graphs: � � such as hybridization such as hybridization graphs or ancestor graphs or ancestor recombination graphs recombination graphs 2 2
Phylogenetic Networks Networks Phylogenetic Either type of graph can be unrooted unrooted or rooted or rooted Either type of graph can be � Rooted splits graph Rooted splits graph � Unrooted Unrooted � � reticulation graph reticulation graph 3 3
What is a Splits Graph? What is a Splits Graph? � The The split encoding split encoding Σ (T) of a tree T: Σ (T) of a tree T: � G 6 G 6 G 4 G 4 G 1 G 1 G 8 G 8 G G 8 8 e e G 5 G 5 G 3 G G G 5 5 3 G 7 G G 2 G 2 G G 7 2 2 G 1 ,G 3 ,G 4 ,G 6 ,G 7 vs G G 2 ,G 5 ,G 8 G 1 ,G 3 ,G 4 ,G 6 ,G 7 vs 2 ,G 5 ,G 8 4 4
What is a Splits Graph? What is a Splits Graph? Cut- -set of parallel edges defines split { set of parallel edges defines split { A,B A,B } } vs vs rest rest Cut 5 5
Glossary Glossary � Splits system Splits system Σ : a set of splits Σ : a set of splits � (bipartitionings bipartitionings) of a given ) of a given taxon taxon set X set X ( � Splits graph G Splits graph G: graph representing : graph representing Σ Σ � (includes trees, not necessarily planar!) (includes trees, not necessarily planar!) � SplitsTree SplitsTree: a program providing various : a program providing various � algorithms for computing splits graphs algorithms for computing splits graphs � Split decomposition Split decomposition: an algorithm for : an algorithm for � computing splits from distances computing splits from distances (other: Neighbor Neighbor- -Net, consensus networks, Net, consensus networks, (other: or Z- -super networks) super networks) or Z 6 6
Example: Consensus Networks Example: Consensus Networks Six input trees: Six input trees: 1/6): 0): ( 1/6): ( 0): Σ( Σ( Σ Σ 1/2): ( 1/2): Σ( Σ 7 7
SplitsTree4 SplitsTree4 Provides many Provides many algorithms for algorithms for phylogenetic analysis analysis phylogenetic using trees and using trees and networks networks 8 8
The SplitsTree SplitsTree Program Program The 9 9
The SplitsTree SplitsTree Program Program The Taxa Unaligned Characters Distances Quartets Trees Splits Taxa Unaligned Characters Distances Quartets Trees Splits Main Window Main Window Method Window Method Window 10 10
Example: Z- -Super Network Super Network Example: Z � Five trees fungal trees from Five trees fungal trees from � (Pryor 2000) and (Pryor 2003) (Pryor 2000) and (Pryor 2003) � Trees: Trees: � � ITS (two trees) ITS (two trees) � � SSU (two trees) SSU (two trees) � � Gpd Gpd (one tree) (one tree) � � Numbers of Numbers of taxa taxa differ: “partial trees” differ: “partial trees” � � Trees from Trees from TreeBase TreeBase � � Unfortunately, no edge lengths Unfortunately, no edge lengths � 11 11
Individual Gene Trees Individual Gene Trees ITS00 ITS00 46 taxa taxa 46 12 12
Individual Gene Trees Individual Gene Trees ITS03 ITS03 40 taxa taxa 40 13 13
Individual Gene Trees Individual Gene Trees SSU00 SSU00 29 taxa taxa 29 14 14
Individual Gene Trees Individual Gene Trees SSU03 SSU03 40 taxa taxa 40 15 15
Individual Gene Trees Individual Gene Trees Gpd03 Gpd03 40 taxa taxa 40 16 16
Gene Trees as Super Network Gene Trees as Super Network Z- -closure: a fast super closure: a fast super- -network method (WABI 2004) network method (WABI 2004) Z 17 17
Gene Trees as Super Network Gene Trees as Super Network ITS00+ ITS00+ ITS03 ITS03 18 18
Gene Trees as Super Network Gene Trees as Super Network ITS03+ ITS03+ SSU00 SSU00 19 19
Gene Trees as Super Network Gene Trees as Super Network ITS00+ ITS00+ ITS00+ ITS00+ SSU03 SSU03 20 20
Gene Trees as Super Network Gene Trees as Super Network ITS00+ ITS00+ ITS03+ ITS03+ SSU03+ SSU03+ Gpd03 Gpd03 21 21
Gene Trees as Super Network Gene Trees as Super Network ITS00+ ITS00+ ITS03+ ITS03+ SSU00+ SSU00+ SSU03+ SSU03+ Gpd03 Gpd03 22 22
Z- -Super Network Super Network Z � Idea: Idea: Extend Extend partial splits. partial splits. � A 1 A 1 A 2 � Z Z- -rule: rule: A A ∪ A A 1 A 2 A A ∩ ∩ � 1 ∪ 1 2 1 2 , , B 1 B 2 B 2 B ∪ B B B 1 B 2 B B 1 ∪ 2 2 1 2 B 1 B � Repeatedly apply to completion. Repeatedly apply to completion. 1 � A 2 A 2 � Return all full splits. Return all full splits. � A 1 A B 2 B 1 2 23 23
Reticulation Networks Reticulation Networks Ancestral genome Ancestral genome g 1 g 1 Build gene trees Build gene trees Q Q P P b 2 b 2 h h b 1 b a a c c b 3 b 1 3 24 24
Reticulation Networks Reticulation Networks g 1 g 1 P- -tree tree P Q Q P P h h b 1 a c b 3 b a c b 1 3 25 25
Reticulation Networks Reticulation Networks g 2 g 2 Q Q P P h h b 1 a c b 3 b a c b 1 3 26 26
Reticulation Networks Reticulation Networks g 2 g 2 Q- -tree tree Q Q Q P P h h b 1 a c b 3 b a c b 1 3 27 27
From Gene Trees to Reticulation Graphs From Gene Trees to Reticulation Graphs gene tree1 gene tree2 gene tree1 gene tree2 combined combined reticulation reticulation splits graph splits graph 28 28
Multiple Independent Reticulations Multiple Independent Reticulations reconstructed reconstructed Two hybridizations ⇒ Two hybridizations all splits all splits ⇒ reticulations reticulations four different gene trees four different gene trees 29 29
Non- -Independent Reticulation Events Independent Reticulation Events Non base tree base tree 30 30
Splits Graph Splits Graph 31 31
Reticulation Graph Reticulation Graph 32 32
Reticulation Graph Reticulation Graph Ambiguous, Ambiguous, unless root in unless root in {t 5 ,t 6 } or {b 1 ,…,b 4 } {t 5 ,t 6 } or {b 1 ,…,b 4 } 33 33
Application to Real Data: Buttercups Application to Real Data: Buttercups ITS (nuclear genome) ITS (nuclear genome) JSA (chloroplast genome) JSA (chloroplast genome) 34 34 jointly with Pete Lockhart jointly with Pete Lockhart
Application to Real Data: Buttercups Application to Real Data: Buttercups 35 35
Application to Real Data: Buttercups Application to Real Data: Buttercups 36 36
Algorithm to Detect Reticulation Algorithm to Detect Reticulation • Input: set of splits Input: set of splits Σ • Σ • Process each component of the Process each component of the • incompatibility graph IG( Σ ) separately incompatibility graph IG( Σ ) separately • Generate all possible “linear” Generate all possible “linear” • reticulation scenarios reticulation scenarios • Check necessary conditions on splits Check necessary conditions on splits • • Check sufficient conditions on splits Check sufficient conditions on splits • • Modify splits graph to display Modify splits graph to display • detected reticulations detected reticulations 37 37
Splits Graphs and Reticulations Splits Graphs and Reticulations B 3 B B 4 B 2 B B 1 B B 3 4 2 1 A C A C X X X X 38 38
Recognizing an Isolated Reticulation Recognizing an Isolated Reticulation u 1 u 2 u 3 u 4 u u u u 1 3 2 4 B 3 B B 4 B B 2 B B 1 B 3 4 2 1 A C A C X X d 2 d 1 d d d 3 d d 4 d 1 2 3 4 B 3 B B 4 B 2 B B 1 B B 3 4 2 1 A C A C X X 39 39
Recognizing an Isolated Reticulation Recognizing an Isolated Reticulation The associated splits graph… The associated splits graph… B 1 B 2 B 3 B 4 B B B B 1 2 3 4 u 1 d 1 u 2 d 2 u 3 d 3 u 4 d 4 u d u d u d u d 1 1 2 2 3 3 4 4 A A C C d 1 d u 4 u 1 4 u 3 u d 2 d 3 2 u 2 u d 3 d 2 3 u 1 d 4 u d 1 4 X X 40 40
Splits Graph to Reticulation Graph Splits Graph to Reticulation Graph The associated splits graph… The associated splits graph… B 1 B 2 B 3 B 4 B B B B 1 2 3 4 A A C C Delete all Delete all internal edges internal edges X X 41 41
Splits Graph to Reticulation Graph Splits Graph to Reticulation Graph The associated splits graph… & the reticulation graph & the reticulation graph The associated splits graph… B 1 B 2 B 3 B 4 B B B B 1 2 3 4 A A C C Delete all Delete all internal edges internal edges X X 42 42
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