Phylogenetic inference

1. Bioinformatics Phylogenetic inference

2. Structure of phylogenetic trees A F H B C G I D Root E • Evolutionary relationships between objects of studies (organisms, organs, sequences) are represented by phylogenetic trees. • Trees are particular types of graphs made of nodes and branches • Nodes = taxonomic units • Leaves = Operational Taxonomic Units (OTU): extant species (ex: A, B, C, D, E) • Internal nodes = Hypothetical taxonomic units = HTU: ancestral species (F, G, H, I). • Branches = kin relationship (ancestry, descendence) between taxonomic units. • Internal branches • External branches • The set of branching of a tree is called topology • Source: Emese Meglézc

3. Rooted versus non-rooted trees A F H B C B C G D H G I F A I Racine D E E • The root defines a unique evolutionary path towards each leave. • It represents the last common ancestor (i.e. the most recent one) of all the OTU. • Non-rooted trees are not properly speaking phylogenetic, since they have no temporal direction -> do not indicate the type of relationship (ancestor, descendent, cousin, …) between nodes. Arbre enraciné Arbre non-enraciné

4. How to root a phylogenetic tree ? Loup F H Chien Souris Loup Souris G Rat H G I F Chien I Racine Rat Poulet Poulet • « Outgroup »: if the OTU of interest include an outgroup (a group very distant from all the other ones), one can enroot the tree on its branch. • Example: dog, wolf, mouse, rat and chicken • Based on our prior biological knowledge, we decide that the outgroup is chicken. • In absence of a prior knowledge on the outgroup: • Mean weight rooting: the tree is rooted on the branch which minimises the mean distance to the leaves. • This assumes a molecular clock: mutation rates are supposed to be constant during evolution, and similar along all the branches of the tree. • This hypothesis is generally not valid, it is only an approximation. • Adapté d’après Emese Meglézc

5. Isomorphisms of phylogenetic trees B C F G H H D A B C G F I I Racine Racine D A E E • One should avoid the trap consisting in evaluating distances between leaves on the basis of their vertical proximity on a tree drawing. • The two structures below are topologically absolutely identical. • However, leaves B and D seem close on the left graph, and distant on the right graph. • To evaluate the distance between two nodes of a tree, one must take into account the total length of the shortest path between them (sum of branch lengths). • Source: Emese Meglézc

6. Scale of a phylogenetic tree A F H B C G I Racine D E • Representation with scale • This tree represents the evolutionary distances between nodes. • Branch lengths are proportional to the number of evolutionary events (substitutions or substitutions/sites). • Scale-less representation • The tree only represents the branching order. • Branch lengths are not proportional to the number of evolutionary changes. A F B H C G I Racine D E 0,1 • Source: Emese Meglézc

7. Cladistics, cladograms and clades • Cladistics • (Greek: klados = branch) is a branch of biology that determines the evolutionary relationships between organisms based on derived similarities (source: Wilkipaedia). • Cladogram • tree-like drawing, usually with binary bifurcations, representing one evolutionary scenario about divergences between species or sequences. • Clade • Any sub-tree of a cladogram. • Note • Branch lengths to not reflect evolutionary time. • The cladogram only represents branching successions, not the time.

8. Cladistics, cladograms and clades • This is also a cladogram • Although branches are rectangular, the drawing only represents the succession of evolutionary events, without attempt to display any time scale.

9. Phylogram • Phylogram : branch lengths represent the number of evolutionary events (mutations, changes); • The phylogram shown here represents the inferred phylogeny of Mammalian opsins. The root should be placed between the groups SW (short-wave-sensitive) and LW+MW (Long-+medium-wave-sensitive). • Notes: • the relative scale is at the bottom. • this tree is unrooted, despite the fact that it is displayed in a left-to-right orientation; • the distance between two nodes is the sum of segment lengths to join them; • the vertical distance can thus be misleading: two successive leaves on the vertical axis (e.g. LW Tachyglossus and SW mouse) can nevertheless be very distant when following the branches; • lengths are only approximations of the inferred distances;

10. Molecular clock • Chronogram: branch lengths represent evolutionary time. • The "molecular clock" hypothesis (left tree) assumes that rates of evolution do not vary between branches. All leaf nodes are thus aligned vertically, since they represent contemporaneous species. • This hypothesis is not always valid: in some cases, two genes can diverge from a common ancestor, but one of them may have diverged faster than the other one. • This is a rather classical mechanism of evolution: a duplication creates some redundancy, and one copy of the gene will evolve whereas the other one retains the initial function (and mutations are counter-selected). Ultrametric tree (with clock) (e.g. UPGMA) Without clock (e.g. neighbour-joining)

11. Summary – tree-based representations • Didier Casane & Patrick Laurenti (2012). Penser la biologie dans un cadre phylogénétique: l’exemple de l’évolution des vertébrés. Médecine/Sciences.

12. Molecular versus species tree

13. Species trees versus molecule tree • A species tree aims at representing the evolutionary relationships between species. • A molecule tree represents the evolutionary history of a family of related molecules (genes, proteins). • Species trees and molecule trees are generally related ... • Species tree can be inferred from various criteria, including the history of carefully chosen molecules. • ... but not identical. • A molecular family can contain several copies in the same species (in-paralogs), due to gene duplications. • Some molecules can be transferred horizontally between species. • Due to combinations of duplications/divergences/deletions, the tree of a given gene may be inconsistent with the species tree. • Illustration: Figure 7.3 from Zvelebil and Baum. Source: Zvelebil, M.J. and Baum, J.O. (2008) Understanding Bioinformatics. Garland Science, New York and London.

14. Reconciliation between molecular and species trees Source: Zvelebil, M.J. and Baum, J.O. (2008) Understanding Bioinformatics. Garland Science, New York and London.

15. Concept definitions from Fitch (2000) • Discussion about definitions of the paper • Fitch, W. M. (2000). Homology a personal view on some of the problems. Trends Genet 16, 227-31. • Homology • Owen (1843). « the same organ under every variety of form and function ». • Fitch (2000). Homology is the relationship of any two characters that have descendent, usually with divergence, from a common ancestral character. • Note: “character” can be a phenotypic trait, or a site at a given position of a protein, or a whole gene, ... • Molecular application: two genes are homologous if diverge from a common ancestral gene. • Analogy: relationship of two characters that have developed convergently from unrelated ancestors. • Cenancestor: the most recent common ancestor of the taxa under consideration • Orthology: relationship of any two homologous characters whose common ancestor lies in the cenancestor of the taxa from which the two sequences were obtained. • Paralogy: Relationship of two characters arising from a duplication of the gene for that character. • Xenology: relationship of any two characters whose history, since their common ancestor, involves interspecies (horizontal) transfer of the genetic material for at least one of those characters. • Analogy • Homology • Paralogy • Xenology or not (xeonologs from paralogs) • Orthology • Xenology or not • (xeonologs from orthologs)

16. Exercise • On the basis of Zvelebil & Baum’s definitions (below), qualify the relationships between each pair of genes in the illustrative schema. • P paralog • O ortholog • X xenolog • A analog • Orthologs can fomally be defined as a pair of genes whose last common ancestor occurred immediately before a speciation event (ex: a1 and a2). • Paralogs can fomally be defined as a pair of genes whose last common ancestor occurred immediately before a gene duplication event (ex: b2 and b2'). Source: Zvelebil & Baum, 2000

17. Exercise • Example: B1 versus C1 • The two sequences (B1 and C1) were obtained from taxa B and C, respectively. • The cenancestor (blue arrow) is the taxon that preceded the second speciation event (Sp2). • The common ancestor gene (green dot) coincides with the cenancestor • -> B1 and C1 are orthologs • Orthologs can fomally be defined as a pair of genes whose last common ancestor occurred immediately before a speciation event. • Paralogs can fomally be defined as a pair of genes whose last common ancestor occurred immediately before a gene duplication event. • Source: Zvelebil & Baum, 2000

18. Exercise • Example: B1 versus C2 • The two sequences (B1 and C2) were obtained from taxa B and C, respectively. • The common ancestor gene (green dot) is the gene that just preceded the duplication Dp1. • This common ancestor is much anterior to the coenancestor between the two species (blue arrow). • -> B1 and C2 are paralogs • Orthologs can fomally be defined as a pair of genes whose last common ancestor occurred immediately before a speciation event. • Paralogs can fomally be defined as a pair of genes whose last common ancestor occurred immediately before a gene duplication event. • Source: Zvelebil & Baum, 2000

19. Solution to the exercise • On the basis of Zvelebil & Baum’s definitions (below), qualify the relationships between each pair of genes in the illustrative schema. • P paralog • O ortholog • X xenolog • A analog • Orthologs can fomally be defined as a pair of genes whose last common ancestor occurred immediately before a speciation event (ex: a1 and a2). • Paralogs can fomally be defined as a pair of genes whose last common ancestor occurred immediately before a gene duplication event (ex: b2 and b2'). Source: Zvelebil & Baum, 2000

20. Reconciliation between species and molecular trees A1 AB1 B1 C1 B2 C2 C3 A, B, C represent species Speciation Duplication

21. Inferring a phylogenetic tree from a multple alignment

22. How many trees ? • The number of possible trees increases drastically with the number of terminal elements (leaves, which can represent molecules or species). • Only one of those trees corresponds to the real evolutionary history. • Since we do not dispose of this tree a priori, it must be inferred from the current elements (the operational taxonomic units, OTU).

23. Characters and character states • Character: feature (quantitative or qualitative) that can be observed in an organism. • State of a character: particular form of a character in a particular OTU (continuous or discrete variable). • Examples • Character: size of left posterior leg. Character state: 1.68cm. • Character: aminoacid at position 68 of the protein encoded by the gene CYTB. Character state: alanine.

24. Example: opsins • To infer a phylogenetic tree for a family of sequences, we start from a multiple alignment. • The figure below shows the first half of a multiple alignment between 50 Mammalian opsins. • By simple visual inspection, we already distinguish 2 obvious groups: • Top : long- (LW) and medium-wave-sensitive (MW) opsins • Bottom: short-wave-sensitive (SW) opsins

25. Methods for inferring a phylogenetic tree • Cladistic methods • Based on the study of characters (nucleotides, aminoacids, presence/absence of a deletion/insertion, …) • Maximum of parsimony. • Distance-based methods • Based on distance measurements (ex: number of substitutions per site). • UPGMA, Neighbour-Joining (NJ), evolutionary minimum, least squares, … • Statistical methods • Based on a study of the states of characters + on distances • Maximum likelihood • Bayesian methods

26. Phylogenetic inference from sequence comparison • Alternative approaches • Maximum parsimony • Distance • Maximum likelihood Unaligned sequences Sequence alignment Aligned sequences strong similarity ? many (> 20) sequences ? Maximum parsinomy yes no Source: Mount (2000)

27. Parsimony method • Principle: • Identify the topoloy (T) involving the smallest umber of evolutionary changes, which is sufficient to account for observed differences between studied OTUs. • Based on discrete characters => the most parcimonious tree correspond to the shortest path (in terms of changes) leading to the observed character states. • Algorithm • Build all possible trees • For each site (position in the alignment), count the minimal number of substitutions explaining this tree • Retain the tree requiring the smallest total number of substitutions (taking all sites into account). • Features of the trees • Multiple solutions can be found : several trees with the same minimal number of changes • Branch lengths do not indicate the evolutionary distance (scale-less tree) • Unrooted trees.

28. Matrice de caractères Sites Séquences

29. Maximum de parcimonie - Méthode Déterminer toutes les topologies possibles 4 UTO => 3 arbres non racinés

30. A A A C B B D D C B C D Maximum de parcimonie - Méthode Déterminer toutes les topologies possibles 4 UTO => 3 arbres non racinés

31. A A A C B B A A A A A A A A A A A A C D D D C B Maximum de parcimonie - Méthode Étude du caractère n°1 Caractère constant (même état de caractère à tous les sites) Caractère ne favorisant aucune topologie par rapport à une autre Nb CE= 0 Nb CE= 0 Nb CE= 0

32. A A A C B B A A A G G G G G G G G G C D D D C B Maximum de parcimonie - Méthode Étude du caractère n°2 Caractère variable mais non informatif Caractère ne favorisant aucune topologie par rapport à une autre Nb CE= 1 Nb CE= 1 Nb CE= 1

33. A A A C B B G G G C C A C A A A A A D D C D C B Maximum de parcimonie - Méthode Étude du caractère n°3

34. A A A A A C B C C B G G G A C C C A A A A A D D C D D C B B D B Maximum de parcimonie - Méthode Étude du caractère n°3 G A C A Arbre 1 G A C A Nb CE= 2

35. A A A C B B G G G C A C C A A A A A C D D D C B Maximum de parcimonie - Méthode Étude du caractère n°3 Caractère variable mais non informatif Caractère ne favorisant aucune topologie par rapport à une autre Nb CE= 2 Nb CE= 2 Nb CE= 2

36. A A A C B B A A A C T C C T G G G T C D D D C B Maximum de parcimonie - Méthode Étude du caractère n°4 Caractère variable mais non informatif Caractère ne favorisant aucune topologie par rapport à une autre Nb CE= 3 Nb CE= 3 Nb CE= 3

37. A A A C B B D D C B C D Maximum de parcimonie - Méthode Étude du caractère n°5 Nb CE= ? Nb CE= ? Nb CE= ?

38. A A A C B B G G G G A G G A A A A A C D D D C B Maximum de parcimonie - Méthode Étude du caractère n°5 Caractère variable et informatif (au moins 2 états de caractère sont partagés par au moins 2 OTU) Caractère favorisant la première topologie par rapport aux deux autres Nb CE= 1 Nb CE= 2 Nb CE= 2

39. Maximum parsimony Column 5 mutation seq1 G A seq3 G A seq2 G A seq4 seq 1G G seq 2 A A seq 3 A A seq 4 seq 1G G seq 2 A A seq 4 A A seq 3 • For each column of the alignment, all possible trees are evaluated and the tree with the smallest number of mutations is retained • The trees which fit with the highest number of columns are retained • The program can return several trees Adapted from Mount (2000)

40. A A A C B B T T T T T T T T T T T T C D D D C B Maximum de parcimonie - Méthode Étude du caractère n°6 Caractère constant (même état de caractère chez tous les OTUs) Caractère ne favorisant aucune topologie par rapport à une autre Nb CE= 0 Nb CE= 0 Nb CE= 0

41. A A A C B B T T T T C T T C C C C C C D D D C B Maximum de parcimonie - Méthode Étude du caractère n°7 Caractère variable et informatif Caractère favorisant la première topologie par rapport aux deux autres Nb CE= 1 Nb CE= 2 Nb CE= 2

42. A A A C B B C C C C C C C C C C C C C D D D C B Maximum de parcimonie - Méthode Étude du caractère n°8 Caractère constant (même état de caractère à tous les OTUs) Caractère ne favorisant aucune topologie par rapport à une autre Nb CE= 0 Nb CE= 0 Nb CE= 0

43. A A A C B B D D C B C D Maximum de parcimonie - Méthode Étude du caractère n°9 Nb CE= ? Nb CE= ? Nb CE= ?

44. A A A C B B A A A T A T T A T T T A C D D D C B Maximum de parcimonie - Méthode Étude du caractère n°9 Caractère variable et informatif Caractère favorisant la deuxième topologie par rapport aux deux autres Nb CE= 2 Nb CE= 1 Nb CE= 2

45. A A A C B B D D C B C D Maximum de parcimonie - Méthode Bilan: T1 = 0+1+2+3+1+0+1+0+2=10 T2 = 0+1+2+3+2+0+2+0+1=11 T3 = 0+1+2+3+2+0+2+0+2=12 L’arbre le plus parcimonieux = arbre 1 Nb CE= 10 Nb CE= 11 Nb CE= 12

46. Maximum de parcimonie – classification des sites • Caractères invariants si toutes les OTU possèdent le même état de caractères pour un site donné • Caractères variables • Non informatif si les états de caractères à ce site ne favorisent aucune topologie parmi l’ensemble des topologies possibles • Informatif si les états de caractères à ce site favorise une (ou plusieurs) topologie(s) parmi l’ensemble des topologies possibles

47. Maximum parsimony example • Parsimony tree calculated from a multiple alignment of the E.coli proteins containing a lacI-type HTH domain • Scale-less unrooted tree • Left: text representation (protpars output) • Bottom right: visualized with njplot (in the ClustalX distribution) +-----------CYTR_ECOLI +--------------------------6 ! ! +--------EBGR_ECOLI ! +-13 ! ! +-----CSCR_ECOLI ! +-12 ! ! +--IDNR_ECOLI ! +--5 ! +--GNTR_ECOLI +--4 ! ! +-----MALI_ECOLI ! ! +-10 ! ! ! ! +--TRER_ECOLI ! ! +--------------9 +-14 ! ! ! ! +--YCJW_ECOLI ! ! ! ! ! ! ! +--------LACI_ECOLI ! +--------------8 +--2 ! +--FRUR_ECOLI ! ! ! +-------15 ! ! ! ! +--RAFR_ECOLI ! ! +----------11 ! ! ! +-----ASCG_ECOLI ! ! +-----7 --1 ! ! +--GALS_ECOLI ! ! +--3 ! ! +--GALR_ECOLI ! ! ! +-----------------------------------------RBSR_ECOLI ! +--------------------------------------------PURR_ECOLI remember: this is an unrooted tree! requires a total of 4095.000

48. Maximum of parsimony – drawbacks of the method • The number of possible trees increases rapidly with the number of UTOs (sequences). • In the preceding example we analyzed 4 sequences only. • For 20 sequences, we would need to treat an astronomical number of possibilities. • Parsimony intrinsically relies on an assumption of molecular clock -> assumes that all the branches evolved at the same speed. • This method only works with highly conserved sequences.

49. Phylogenetic inference from sequence comparison • Alternative approaches • Maximum parsimony • Distance • Maximum likelihood • Source: Mount (2000) Unaligned sequences Sequence alignment Aligned sequences strong similarity ? many (> 20) sequences ? Maximum parsinomy yes no no yes clear similarity ? Distance yes

50. Distance method • Starting from a multiple alignment, calculate the distance between each pair of sequences • Calculate a tree which fits as well as possible with the distance matrix • branch lengths should correspond to distances • rooted or unrooted • Several methods can be used for calculating a tree from the distance matrix. • Fitch-Margoliah • Neighbour-Joining • UPGMA Aligned sequences Distance calculation Distance matrix Tree calculation Tree