Copyright (c) 2008 Daniel Huson. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation

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2 Copyright (c) 2008 Daniel Huson. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license can be found at

3 by George Richmond Darwin: "species have changed, and are still slowly changing by the preservation and accumulation of successive slight favorable variations."

4 Ernst Haeckel, Tree of Life 1866

5 Let X = {x 1,...,x n } denote a set of taxa. A phylogenetic tree T (or X-tree) ) is given by labeling the leaves of a tree by the set X: Taxa + tree phylogenetic tree

6 Unrooted tree tree inference methods usually produce unrooted trees Rooted tree, rooted using Chicken as outgroup biologically relevant, defines clades of related taxa

7 Each branch e of a phylogenetic tree T may be scaled to represent r t, the rate of evolution r time t along e: 0.01 Chicken Seal Blue Whale Mouse Fin Whale Seal Cow Rat Chimp Human Gorilla root

8 Sequences evolve along a pre-given tree T, called the evolutionary -, model - or the true tree Two types of events: mutations and speciation events

9 time Evolutionary tree Sequence of common ancestor Mutations along branches Speciation events at nodes

10 Tree? Evolutionary tree

11 (Doolittle, 2000)

12 Domain Bacteria Eukaryotes Archaea Kingdom Proteo obacteria Cyano obacteria Animals Fungi Plants Archezoa Euryar rchacota Crenar rchaeota Doolittle, 1999

13 What is a phylogenetic tree? The concept is very clearly defined Only ambiguity: unrooted or rooted?

14 The concept of a phylogenetic network is not so clear? 1. There are many different types, eg: trees, split networks, median networks, median joining networks, neighbor-net, net, consensus networks, reticulate networks, recombination networks, ARGs, hybridization networks, reticulgrams, haplotype networks, netting, etc

15 2. The general term phylogenetic network is often defined to mean some specific type of network, e.g.: Phylogenetic network = recombination network (Gusfield et al ) Phylogenetic network = hybridization network (Linder and Rieseberg 2004) Phylogenetic network = reticulate network with multi-edges (Huber and Moulton, 2005)

16 A phylogenetic network is any network that represents evolutionary relationships between taxa Usually: taxa are represented by nodes, and evolutionary relationships by edges

17 Split networks Phylogenetic trees Reticulate networks Other types of phylogenetic networks Median networks Consensus (super) networks Hybridization networks Special case: Galled trees Recombination networks Augmented trees, such as DLT trees Split decomposition, Neighbor-net Ancestor recombination graphs Any graph representing evolutionary data

18 3. source of confusion: there are two fundamentally different types of phylogenetic networks: ones that provide an explicit picture of evolution, and ones that provide an implicit picture of evolution

19 This distinction applies already to trees: implicit Visualization of signals explicit Evolutionary scenario

20 This distinction is even more important for networks: Unrooted vs. rooted distinction applies Additionally: some network methods aim at displaying (incompatible) phylogenetic signals, while others aim at explicitly modelling reticulate evolution

21 Split networks Phylogenetic trees Reticulate networks Other types of phylogenetic networks Median networks Consensus (super) networks Hybridization networks Special case: Galled trees Recombination networks Augmented trees, such as DLT trees Split decomposition, Neighbor-net Ancestor recombination graphs Any graph representing evolutionary data

22 Will look at split networks as a major class of implicit networks Other types of implicit networks exist, e.g. haplotype networks Splits and split networks from sequences from distances from trees

23 Every edge of a tree defines a split of the taxon set X: x 6 x 1 x 4 x 8 e x 5 x 2 x 7 x 3 x 1,x 3,x 4,x 6,x 7 vs x 2,x 5,x 8

24 Tree T: Split encoding Σ (T): 5 trivial splits: 2 non-trivial splits:

25 Two splits A 1 B 1 and A 2 B 2 of X are compatible,, if {A 1 A 2, A 1 B 2,B 1 A 2,B 1 A 2 } Two compatible splits: A 1 B 1 x 4 A 2 B 2 x 2 x 3 x 7 x 8 x 1 x 5 x 6 x 9 X

26 Two splits A 1 B 1 and A 2 B 2 of X are compatible,, if {A 1 A 2,A 1 B 2,B 1 A 2,B 1 A 2 } Two splits: A 1 B 1 x 4 x 5 A 2 B 2 x 6 x 2 x 1 x 7 x 3 X

27 Cut-set of parallel edges defines split { {A,B}} vs rest

28 Consider the following two trees T 1 and T 2, for which the splits are incompatible: p T 1 + T 2 SN(Σ ) A split network SN(Σ ) represents an incompatible set of splits Σ :=Σ (T 1 ) Σ (T 2 ), using bands of parallel edges for incompatible splits. q p q

29 Six gene trees: Σ(1/2): majority consensus: splits contained in more than 50% of trees Σ(1/6): splits contained in more than one tree Σ(0): splits contained in at least one tree

30 Any given system Σ of splits can be represented by a split network N. N Note that: N is a tree iff Σ is compatible (e.g. Neighbor-Joining) N is outer- labeled- planar iff Σ is circular (e.g. Neighbor-Net, Net, Bryant & Moulton 2002) N is usually planar or only mildy non-planar iff Σ is weakly compatible (e.g. Split Decomposition) N is always subgraph of n-dim. hypercube (e.g. recoding of sequences, spectral analysis, median networks, consensus networks, Z-super networks) (Theory of splits introduced by Bandelt and Dress 1992)

31 Data: 60 variable sites of DNA for 35 haplotypes of Dusky Dolphins (Cassens et al, 2003) One type of split network, essentially a median network (Bandelt 1995)

32 Split Decomposition (Bandelt, Dress 1992) or Neighbor-NetNet (Bryant, Moulton 2002) produces network from distances

33 Aligned sequences ACGACCTACGACTGCATCAGCATCGCATCAGCTACGCTCGCTC AGACTATCGGATTAAAAGCATCAGCATCGACATCAGCATCAGC GGCGCCATCGATCGCAATCAAGGGGGGGCCCTACCGCATTCAG CATCACGCTCGCCCAATCGCATCACGCATCGCATCGCATCGCA TCGCATCGACTCGCAT ACGACCTACGACTGCATCAGCATCGCATCAGCTACGCTCGCTC AGACTATCGGATTAAAAGCATCAGCATCGACATCAGCATCAGC GGCGCCATCGATCGCAATCAAGGGGGGGCCCTACCGCATTCAG CATCACGCTCGCCCAATCGCATCACGCATCGCATCGCATCGCA TCGCATCGACTCGCAT ACGACCTACGACTGCATCAGCATCGCATCAGCTACGCTCGCTC AGACTATCGGATTAAAAGCATCAGCATCGACATCAGCATCAGC GGCGCCATCGATCGCAATCAAGGGGGGGCCCTACCGCATTCAG CATCACGCTCGCCCAATCGCATCACGCATCGCATCGCATCGCA TCGCATCGACTCGCAT Distance transformation Tree-building method, e.g. Neighbor-Joining Tree Network method, e.g. Split Decomposition Distance matrix Network

34 Split Decomposition is useful for visualizing imcompatible signals in a data set. Distances in network approximate input matrix Sensitive to noise and only has good resolution for small or very clean data sets. The Neighbor-NetNet method is a hybrid of Neighbor-Joining and Split Decomposition. Applicable to data sets with hundreds of taxa. Restricted to planar graphs and tends to produce spider-webs. (Bryant and Moulton, 2002)

35 Split network computed via Neighbor-net from distances between human mtdna sequences.

36 Split network representing all maximum parsimony trees (trees computed by dnapars)

37 A collection of trees can be represented by a consensus network or super network

38 Z-closure method [Huson [Huson et al,, 2004] Partial trees for five plant genes Super network

39 Idea: Extend partial splits. Z-rule: A 1 A 2 A 1 A 1 A 2, B 1 B 2 B 1 B 2 B 2 Repeatedly apply to completion. A 2 B 1 Return all full splits. A 1 [Huson, Dezulian, Kloepper and Steel, 2004] B 2

40 Computed by SplitsTree4 Computed by SplitsTree4 Computed by SplitsTree4 Computed by SplitsTree4 Computed by SplitsTree4 1.0 Alternaria_solani_GB2 Alternaria_solani_GB1 Alternaria_porri_GB1 Alternaria_porri 1.0 Stemphylium_sarcinaeforme Stemphylium_vesicarium Stemphylium_botryosum Pleospora_herbarum Alternaria_japonica Alternaria_carotiincultae 1.0 Ulocladium_consortiale Alternaria_cheiranthi Ulocladium_atrum Embellisia_indefessa Ulocladium_botrytis Alternaria_selini Alternaria_petroselini Alternaria_solani Alternaria_solani_GB3 Alternaria_dauci Alternaria_brassicicola Alternaria_macrospora Alternaria_japonica Alternaria_brassicicola_GB2 Ulocladium_alternariae Alternaria_crassa Alternaria_brassicicola_GB1 Pleospora_infectoria Alternaria_infectoria Alternaria_alternata_GB2 Alternaria_alternata_GB1 Alternaria_infectoria_GB1 Alternaria_tenuissima Bipolaris_tetramera Alternaria_alternata Exserohilum_pedicellatum Alternaria_brassicae_GB1 Stemphylium_sarcinaeforme Alternaria_brassicae Stemphylium_callistephi Alternaria_cheiranthi Ulocladium_chartarum Stemphylium_botryosum_GB1 Pleospora_herbrum_GB5 Ulocladium_atrum Alternaria_smyrnii Pleospora_herbarum Ulocladium_botrytis Pleospora_herbarum_GB1 Alternaria_radicina Stemphylium_botryosum Pleospora_herbarum_GB4 Alternaria_carotiincultae Alternaria_petroselini Pleospora_herbarum_GB2 Alternaria_selini Pleospora_herbrum_GB3 Stemphylium_vesicarium Stemphylium_herbarum_GB1 ITS Stemphylium_callistephi Ulocladium_alternariae Alternaria_radicina Bipolaris_tetramera Exserohilum_pedicellatum Alternaria_brassicicola Alternaria_petroselini Alternaria_smyrnii Alternaria_selini Alternaria_brassicae Alternaria_alternata Ulocladium_atrum Alternaria_tenuissima Ulocladium_chartarum Alternaria_infectoria Pleospora_infectoria Alternaria_cheiranthi Alternaria_macrspora Ulocladium_botrytis Alternaria_crassa Alternaria_dauci Alternaria_porri Alternaria_solani SSU Nimbya_caricis Nimbya_scirpicola Alternaria_triticina Embellisia_hyacinthi Alternaria_ethzedia Alternaria_infectoria Embellisia_novae-zelandiae Embellisia_proteae Lewia_infectoria Embellisia_allii Stemphylium_botryosum Ulocladium_chartarum Ulocladium_alternariae Embellisia_leptinellae Exserohilum_pedicillatum Stemphylium_vesicarium Stemphylium_callistephi Pleospora_herbarum Alternaria_japonica Alternaria_brassicicola gpd Alternaria_smyrnii Alternaria_carotiincultae Alternaria_radicina Alternaria_destruens Alternaria_tenuissima Alternaria_arborescens Alternaria_alternata Alternaria_longipes Alternaria_crassa Alternaria_macrospora Alternaria_dauci Alternaria_solani Alternaria_porri 1.0 Stemphylium_botryosum Stemphylium_callistephi 1.0 Ulocladium_atrum Ulocladium_consortiale Ulocladium_botrytis Ulocladium_chartarum Alternaria_cheiranthi Pleospora_herbarum Stemphylium_vesicarium Exserohilum_pedicillatum Lewia_infectoria Alternaria_infectoria Alternaria_ethzedia Alternaria_triticina Nimbya_caricis Nimbya_scirpicola Embellisia_allii Embellisia_novae-zelandiae Embellisia_hyacinthi Embellisia_proteae Embellisia_leptinellae Ulocladium_alternariae Alternaria_japonica Alternaria_porri Alternaria_solani Alternaria_dauci Alternaria_brassicicola Alternaria_radicina ITS Alternaria_macrospora Alternaria_crassa Alternaria_tenuissima Alternaria_arborescens Alternaria_alternata Alternaria_destruens Alternaria_longipes Ulocladium_chartarum Alternaria_smyrnii Alternaria_selini Alternaria_petroselini Alternaria_carotiincultae Embellisia_indefessa Alternaria_cheiranthi Ulocladium_botrytis Ulocladium_atrum Ulocladium_consortiale Alternaria_longipes Alternaria_destruens Alternaria_alternata Alternaria_arborescens Embellisia_indefessa Alternaria_smyrnii Alternaria_selini Alternaria_petroselini Alternaria_radicina Alternaria_tenuissima Alternaria_carotiincultae Alternaria_brassicicola Alternaria_dauci Ulocladium_alternariae Alternaria_japonica Alternaria_solani Alternaria_crassa Alternaria_macrospora Alternaria_porri SSU Stemphylium_callistephi Embellisia_hyacinthi Pleospora_herbarum Stemphylium_vesicarium Stemphylium_botryosum Exserohilum_pedicillatum Embellisia_allii Lewia_infectoria Alternaria_infectoria Alternaria_ethzedia Alternaria_triticina Nimbya_caricis Nimbya_scirpicola Embellisia_novae-zelandiae Embellisia_proteae Embellisia_leptinellae Fungal trees from (Pryor & Bigelow 2000) and (Pryor & Gilbertson 2003)

41 Five fungal trees from (Pryor 2000) and (Pryor 2003) Trees: ITS (two trees) SSU (two trees) Gpd (one tree) Numbers of taxa differ: partial trees

42 ITS00 46 taxa

43 ITS03 40 taxa

44 SSU00 29 taxa

45 SSU03 40 taxa

46 Gpd03 40 taxa

47 Z-closure: a fast super-network method

48 ITS00+ ITS03

49 ITS03+ SSU00

50 ITS00+ ITS00+ SSU03

51 ITS00+ ITS03+ SSU03+ Gpd03

52 ITS00+ ITS03+ SSU00+ SSU03+ Gpd03

53 We will look at hybridization networks as a major type of explicit networks A simple model of reticulate evolution Implicit-explicit approach

54 Occurs when two organisms from different species interbreed and combine their chromosomes Copyright 2003 University of Illinois Copyright 2003 University of Illinois Copyright 2003 University of Illinois Water hemp Hybrid Pigs weed

55 Bacteria can become resistant to an antibiotic by having contact with other types of bacteria that are already resistant to the drug. This is due to the fact that bacteria commonly swap genes

56 Ask two different genes what the phylogeny of a set of species is and you will get two different answers T 1 T 2 T 3 T 1 T 2 T 3 Gene Tree1 Gene Tree2

57 Even given only vertical descent of genes, gene trees can differ from species trees: T 1 T 2 T 3 A A B x x x A A B T 1 T 2 T 3 Gene duplication A B G Gene Tree Species Tree

58 Perhaps the evolution of life is best described as a web: Bacteria Eukaryotes Archaea Proteobac cteria Cyanobac cteria An nimals Fungi Plants Archezoa Euryarcha acota Crenarcha aeota Doolittle, 1999

59 Differing gene trees give rise to mosaic sequences Gene 1 Gene 2 Gene 3 Gene 4

60 P Hybridization: Recombination: Mixture Order of matters genomes Q Ancestral genome

61 P Q Tree for gene g 1 g 1

62 P Q g 1 -tree is P -variant g 1

63 g 1 -tree is P -variant

64 c P Q Tree for gene g 2 g 2

65 P Q g2-tree is Q -variant g 2

66 g2-tree is Q -variant

67 The evolutionary history associated with any given gene is a tree A network N with k reticulations gives rise to 2 k different gene trees b 1 a h c b 3 b 1 a h c b 3 P Q b 1 a h c b 3 P-tree N Q-tree

68 Given a set of trees, determine a reticulate network N such that T(N) and N contains a minimum number of reticulation nodes. In fully generality, this is known to be a computationally hard problem [Wang et al 2001].

69 Reticulation nodes r i, r j N are independent, if they are not contained in a common cycle: r 1 r 2 r 3 Galled trees, Gusfield Gusfield et al. ( ) 2005)

70 A new splits-based approach [Huson [Huson et al. RECOMB2005, ECCB2005]: gene tree1 gene tree2 split network of all splits reticulate network

71 Two reticulations four different gene trees all splits Reticulate network that explains all input trees

72 Method goes far beyond galled trees and gt-networks Input trees all splits Reticulate network that explains all input trees

73 Each incompatibility component can be considered independently: (Gusfield et al. 2005) (Huson et al. 2005) 2005)

74 A reticulation corresponds to a subtree that attaches at two places: A X B 1 B 2 B 3 B 4 X C (Maddison 1997, Wang et al,, 2001, Gusfield et al , 2005, Nakhleh et al. 2004)

75 A reticulation corresponds to a subtree that attaches at two places: A X B 1 B 2 B 3 B 4 X C (Maddison 1997, Wang et al,, 2001, Gusfield et al , 2005, Nakhleh et al. 2004)

76 u 1 u 2 u 3 u 4 A X B 1 B 2 B 3 B 4 C d 1 d 2 d 3 d 4 A B 1 B 2 B 3 B 4 X C

77 The associated split network B 1 B 2 B 3 B 4 A u 1 d 1 u 2 d 2 u 3 d 3 u 4 d 4 C d 1 u 4 d 2 u 3 d 3 u 2 d 4 u 1 lattice X

78 The associated split network B 1 B 2 B 3 B 4 A C Delete all internal edges lattice X

79 The associated split network & the reticulate network B 1 B 2 B 3 B 4 A C Delete all internal edges lattice X

80 Multiple reticulations can overlap along a path: B 1 B 2 B 3 B 4 A X Y C

81 Pair of reticulations can overlap along a path: B 1 B 2 B 3 B 4 A X Y Y X C More general than galled trees

82 New Zealand Ranunculus (buttercup) species JSA region in chloroplast ITS region in nuclear genome

83 JSA ITS Split network representing both trees simultaneously

84 Split network for ITS & JSA trees Filter splits Hybridization network Two cases of hybridization

85 Data (Zink et al. 1991): 19 restriction endonucleases applied to mtdna of Zonotrichia (sparrows), obtaining 122 sites:

86 Split network showing all 122 sites

87 Split network showing all splits supported by more than one character, rooted using outgroup

88 Zink et al. discuss two trees that differ by swapping two taxa Recombination network with two reticulation events (Recombinations? mtdna is not believed to recombine)

89 Fungus Fusarium, 37 strains reported in [52] Locus TRI101 known to undergone intragenic recombination

90 Implicit network

91 Explicit network

92 Our program SplitsTree4 provides many methods for implicit and explicit phylogenetic networks and trees Java, runs on Linux, MacOS and Windows Freely available from: D.H. & Dave Bryant: Application of Phylogenetic Networks in Evolutionary Studies, MBE, 2006

93