Phylogenetic trees Level 3 Molecular Evolution and Bioinformatics Jim Provan Page and Holmes: Chapter 2

Tree terminology A phylogenetic tree depicts evolutionary relationships A tree consists of nodes connected by branches Nodes and branches of a tree have different kinds of information associated with them: Some phylogenetic methods reconstruct characters of hypothetical ancestors Most estimate amount of evolution (branch length) Terminal node / terminal taxon / OTU Internal node / hypothetical ancestor Root Branch

Trees are like mobiles ABCDABCD = ABCD =

Polytomies Star tree Partially resolved Fully resolved “Hard” polytomy ? “Soft” polytomy

A shorthand for trees EDCBA (((A,B),C),(D,E))

Information in trees ABCCladogramA B C Additive tree ABC Ultrametric tree Simply shows relative recency of common ancestry Contains extra information, namely branch lengths (evolutionary change) Depicts evolutionary time

Rooted and unrooted trees A rooted tree has a node from which all other nodes descend: It has a “direction”: the closer a node is to the root, the older it is in time It allows the definition of ancestor-descendent relationships Unrooted trees do not specify evolutionary relationships in the same way HCGOB H C G O B

Numbers of rooted and unrooted trees The number of unrooted trees U n for n sequences is given by U n = (2n – 5)(2n – 7)... (3)(1) U n = (2n – 5)(2n – 7)... (3)(1) The number of rooted trees R n for n sequences is given by R n = (2n – 3)(2n – 5)... (3)(1) R n = (2n – 3)(2n – 5)... (3)(1) = (2n – 3) U n = (2n – 3) U nn U n R n

Terminology of patterns of ancestral and derived character states ApomorphyPlesiomorphyAutapamorphy SynapomorphyHomoplasy

Ancestors Phylogenies presuppose ancestors: Extinct organisms that left descendents which comprise modern species Represented by internal nodes of a tree Generally hypothetical and inferred from extant sequences Two recent developments have provided new problems in dealing with ancestors: Recovery of DNA from extinct taxa Viral sequences which evolve quickly enough to be tracked in “real time” Cladists have adopted the convention that extinct taxa lacking autapomorphies are ancestral

Metric distances In order for a distance measure to be used for building phylogenies, it must be a metric and it must be additive A distance d between two sequences, a and b, is a metric if it satisfies these properties: d(a,b)  0(non-negativity) d(a,b) = d(b,a) (symmetry) d(a,c)  d(a,b) + d(b,c)(triangle inequality) d(a,b) = 0 if and only if a = b(distinctness) In general, conditions 1, 2 and 4 are true for all measures of dissimilarity calculated directly from sequences

Ultrametric and additive distances A metric is an ultrametric if it satisfies the additional criterion that: d(a,b)  maximum [d(a,c), d(b,c)] Ultrametric distances have the very useful evolutionary property of implying a constant rate of evolution: Idea of a molecular clock Relative rate test is a measure of how far pairwise differences between three sequences depart from ultrametricity To be additive, a measure must also satisfy the four- point condition: d(a,b) + d(c,d)  maximum [d(a,c) + d(b,d), d(a,d) + d(b,c)] Of the three sums, the two largest must be equal

An ultrametric distance matrix ABCD2610A610B10CD A B C D

An additive distance matrix ABCD6714A310B9CD A B C D

Monophyletic Non-monophyletic Clades and classification

Non-monophyletic groups BirdsCrocodilesLizardsTurtles New World vulturesStorks Birds of prey Old World vultures Reptiles VulturesParaphyleticPolyphyletic

Consensus trees HCGOBHCGOB HCGOB

ABCDEABCDEABCDE ABCDEStrictABCDEMajority-rule