Phylogenetic treesPhylogenetic trees

Level 3 Molecular Evolution and Level 3 Molecular Evolution and BioinformaticsBioinformatics

Jim ProvanJim Provan

Page and Holmes: Chapter 2Page and Holmes: Chapter 2

Tree terminologyTree terminology

A A phylogenetic treephylogenetic tree depicts depicts evolutionary relationshipsevolutionary relationships

A tree consists of A tree consists of nodesnodes connected by connected by branchesbranches

Nodes and branches of a Nodes and branches of a tree have different kinds of tree have different kinds of information associated with information associated with them:them:

Some phylogenetic methods Some phylogenetic methods reconstruct characters of reconstruct characters of hypothetical ancestorshypothetical ancestors

Most estimate amount of Most estimate amount of evolution (evolution (branch lengthbranch length))

Terminal node / terminal taxon / OTUTerminal node / terminal taxon / OTU

Internal node / hypothetical ancestorInternal node / hypothetical ancestor

RootRoot

BranchBranch

Trees are like mobilesTrees are like mobiles

A B C D ABCD

==

AB C D

==

PolytomiesPolytomies

Star treeStar tree Partially resolvedPartially resolved Fully resolvedFully resolved

““Hard” polytomyHard” polytomy

??

““Soft” polytomySoft” polytomy

A shorthand for treesA shorthand for trees

EEDDCCBBAA

(((A,B),C),(D,E))(((A,B),C),(D,E))

Information in treesInformation in trees

AA BB CC

CladogramCladogram

AA

BBCC

44

11

22 22

Additive treeAdditive tree

AA BB CC

Ultrametric treeUltrametric tree

Simply shows relativeSimply shows relativerecency of commonrecency of common

ancestryancestry

Contains extraContains extrainformation, namelyinformation, namely

branch lengthsbranch lengths(evolutionary change)(evolutionary change)

Depicts evolutionaryDepicts evolutionarytimetime

Rooted and unrooted treesRooted and unrooted trees

A A rooted treerooted tree has a has a node from which all node from which all other nodes descend:other nodes descend:

It has a “direction”: the It has a “direction”: the closer a node is to the closer a node is to the root, the older it is in timeroot, the older it is in time

It allows the definition of It allows the definition of ancestor-descendent ancestor-descendent relationshipsrelationships

Unrooted treesUnrooted trees do not do not specify evolutionary specify evolutionary relationships in the relationships in the same waysame way

H C G O B

H

CG

O

B

Numbers of rooted and unrooted Numbers of rooted and unrooted treestrees

The number of unrooted The number of unrooted trees trees UUnn for for nn sequences sequences is given byis given by UUnn = (2 = (2nn – 5)(2 – 5)(2nn – 7) ... (3)(1) – 7) ... (3)(1)

The number of rooted The number of rooted trees trees RRnn for for nn sequences sequences is given byis given by RRnn = (2 = (2nn – 3)(2 – 3)(2nn – 5) ... (3)(1) – 5) ... (3)(1)

= (2= (2nn – 3) – 3) UUnn

nn

2233445566778899

1010

UUnn

111133

1515105105949949

10 39510 395135 135135 135

2 027 0252 027 025

RRnn

1133

1515105105949949

10 39510 395135 135135 135

2 027 0252 027 02534 459 42534 459 425

20208 200 794 532 637 891 559 0008 200 794 532 637 891 559 000

Terminology of patterns of Terminology of patterns of ancestral and derived character ancestral and derived character

statesstates

ApomorphyApomorphyPlesiomorphyPlesiomorphy AutapamorphyAutapamorphy

SynapomorphySynapomorphy HomoplasyHomoplasy

AncestorsAncestors

Phylogenies presuppose ancestors:Phylogenies presuppose ancestors:Extinct organisms that left descendents which comprise Extinct organisms that left descendents which comprise modern speciesmodern speciesRepresented by internal nodes of a treeRepresented by internal nodes of a treeGenerally hypothetical and inferred from extant Generally hypothetical and inferred from extant sequencessequences

Two recent developments have provided new Two recent developments have provided new problems in dealing with ancestors:problems in dealing with ancestors:

Recovery of DNA from extinct taxaRecovery of DNA from extinct taxaViral sequences which evolve quickly enough to be Viral sequences which evolve quickly enough to be tracked in “real time”tracked in “real time”

Cladists have adopted the convention that extinct Cladists have adopted the convention that extinct taxa lacking autapomorphies are ancestraltaxa lacking autapomorphies are ancestral

Metric distancesMetric distances

In order for a distance measure to be used for In order for a distance measure to be used for building phylogenies, it must be a metric and it building phylogenies, it must be a metric and it must be additivemust be additiveA distance A distance dd between two sequences, a and b, between two sequences, a and b, is a is a metricmetric if it satisfies these properties: if it satisfies these properties:

dd(a,b) (a,b) 0 0 (non-negativity)(non-negativity)dd(a,b) = (a,b) = dd(b,a) (b,a) (symmetry)(symmetry)dd(a,c) (a,c) dd(a,b) + (a,b) + dd(b,c)(b,c) (triangle (triangle inequality)inequality)dd(a,b) = 0 if and only if a = b(a,b) = 0 if and only if a = b (distinctness)(distinctness)

In general, conditions 1, 2 and 4 are true for all In general, conditions 1, 2 and 4 are true for all measures of dissimilarity calculated directly measures of dissimilarity calculated directly from sequencesfrom sequences

Ultrametric and additive Ultrametric and additive distancesdistances

A metric is an A metric is an ultrametricultrametric if it satisfies the additional if it satisfies the additional criterion that:criterion that:

dd(a,b) (a,b) maximum [ maximum [dd(a,c), (a,c), dd(b,c)](b,c)]

Ultrametric distances have the very useful Ultrametric distances have the very useful evolutionary property of implying a constant rate of evolutionary property of implying a constant rate of evolution:evolution:

Idea of a molecular clockIdea of a molecular clockRelative rate test is a measure of how far pairwise Relative rate test is a measure of how far pairwise differences between three sequences depart from differences between three sequences depart from ultrametricityultrametricity

To be To be additiveadditive, a measure must also satisfy the , a measure must also satisfy the four-four-point conditionpoint condition::

dd(a,b) + (a,b) + dd(c,d) (c,d) maximum [ maximum [dd(a,c) + (a,c) + dd(b,d), (b,d), dd(a,d) + (a,d) + dd(b,c)](b,c)]

Of the three sums, the two largest must be equalOf the three sums, the two largest must be equal

2

6

6 10

10

10

An ultrametric distance matrixAn ultrametric distance matrix

AABBCCDD

2266

1010AA

661010BB

1010CC DD

AA

BB

CC

DD

11

11

22

33

55

22

6

7

3 14

10

9

An additive distance matrixAn additive distance matrix

AABBCCDD

6677

1414AA

331010BB

99CC DD

AA

BB

CC

DD

55

11

11

11

66

22

MonophyleticMonophyletic Non-monophyleticNon-monophyletic

Clades and classificationClades and classification

Non-monophyletic groupsNon-monophyletic groups

BirdsBirds CrocodilesCrocodiles LizardsLizards TurtlesTurtlesNew WorldNew World

vulturesvultures StorksStorksBirds ofBirds of

preypreyOld WorldOld Worldvulturesvultures

ReptilesReptiles

VulturesVultures

ParaphyleticParaphyletic PolyphyleticPolyphyletic

Consensus treesConsensus trees

HH CC GG OO BB HH CC GG OO BB

HH CC GG OO BB

Consensus treesConsensus trees

AA BB CC DD EE AA BB CC DD EE AA BB CC DD EE

AA BB CC DD EE

StrictStrict

AA BB CC DD EE

Majority-ruleMajority-rule

6767

100100

6767