CONSENSUSCONSENSUS“general or widespread “general or widespread

agreement”agreement”• Consensus treeConsensus tree – a tree depicting – a tree depicting

agreement among a set of treesagreement among a set of treesa representation of a set of treesa representation of a set of treesa phylogenetic inference from a set of treesa phylogenetic inference from a set of trees

• Consensus methodsConsensus methods can be characterised can be characterised in terms of:in terms of:

Procedures - algorithms Procedures - algorithms Axioms - desirable properties they satisfyAxioms - desirable properties they satisfyObjective functions - as trees that optimise some Objective functions - as trees that optimise some measure of fit between it and the input trees.measure of fit between it and the input trees.

Conservative/Liberal CMsConservative/Liberal CMs• CMs characterised by CMs characterised by

• Type of information/relationships (e.g. full Type of information/relationships (e.g. full splits)splits)

• Condition for inclusion in consensusCondition for inclusion in consensus

• Conservative Conservative • StrictStrict• Semi-strictSemi-strict

• Liberal Liberal • Majority ruleMajority rule

Types of RelationshipsTypes of Relationships

A C B D

R

A C B D

R

A C B D

R

C B A D

R

A D B C

R

A D B C

R

A D B

R

A B C

R

A D C

R

D B C

R

A B

D C

A C B

R

A B D

R

A C D

R

B C D

R

A B

C D

Wilkinson et al. Fig. 2

Greatest Agreement Greatest Agreement SubtreesSubtrees

A B C D E F G

TWO INPUT TREES

GAS/LCP TREE

Taxon G is excluded

A G B C D E F

A B C D E FA B C D E F G

Strict component consensuscompletely unresolved

Reduced CMsReduced CMs

• Focus is upon any relationships (splits) Focus is upon any relationships (splits) rather than only full splitsrather than only full splits

• Occur in strict, majority-rule and semi-Occur in strict, majority-rule and semi-strict varietiesstrict varieties

• Uses polytomies (branch contractions) Uses polytomies (branch contractions) and pruning leaves or both to remove and pruning leaves or both to remove conflictconflict

• May be more sensitive than May be more sensitive than conventional methods focusing only on conventional methods focusing only on full splitsfull splits

Strict Reduced CMStrict Reduced CM

A B C D E F G

TWO INPUT TREES

STRICT REDUCED CONSENSUS TREE

Taxon G is excluded

A G B C D E F

A B C D E F

A B C D E F G

Strict component consensus

B C D E F A C D E F

A B D E F

Agreement Subtrees

Parsimony analysis of poorly Parsimony analysis of poorly known fossils - known fossils - an extreme an extreme

casecase• Phylogenetic palaeontologists Phylogenetic palaeontologists

often have data sets that include often have data sets that include very poorly known fossil taxavery poorly known fossil taxa

• Inclusion of such taxa is sometimes Inclusion of such taxa is sometimes associated with a proliferation of associated with a proliferation of most parsimonious tree and poorly most parsimonious tree and poorly resolved consensus treesresolved consensus trees

• ‘‘Rogue’ taxa obfuscate consistent Rogue’ taxa obfuscate consistent relationships among other taxarelationships among other taxa

RhynchosaursH. gordoniH. huxleyiS. fischeriS. sanjaunensisSupradapedonNova ScotiaTexasIsalorhnchusAcrodentusR. spenceriR. brodeiR. articepsMesodapedonStenaulorhynchusHowesiaMesosuchus

1

H. gordoniH. huxleyiS. fischeriS. sanjaunensisSupradapedonNova ScotiaIsalorhnchusR. spenceriR. brodeiR. articepsMesodapedonStenaulorhynchusHowesiaMesosuchus

2

H. gordoniH. huxleyiS. fischeriS. sanjaunensisSupradapedonNova ScotiaIsalorhnchusR. spenceriR. brodeiR. articepsStenaulorhynchusHowesiaMesosuchus

3

H. gordoniH. huxleyiS. fischeriS. sanjaunensisNova ScotiaR. spenceriR. brodeiR. articeps

StenaulorhynchusHowesiaMesosuchus

4

Mesodapedon

H. gordoniH. huxleyiS. fischeri

R. spenceriR. brodeiR. articeps

StenaulorhynchusHowesiaMesosuchus

5

Mesodapedon

S. sanjaunensis

H. gordoniH. huxleyiS. fischeri

R. spenceriR. brodeiR. articepsStenaulorhynchusHowesiaMesosuchus

6

S. sanjaunensis

Fossil & Recent Arthropods

Fossil & Recent Arthropods

Extending Support Extending Support MeasuresMeasures

• The same measures (BP, JP & DI) The same measures (BP, JP & DI) that are used for clades/splits can that are used for clades/splits can also be determined for triplets and also be determined for triplets and quartetsquartets

• This provides a lot more This provides a lot more information because there are information because there are more triplets/quartets than there more triplets/quartets than there are cladesare clades

• Furthermore....Furthermore....

The Decay TheoremThe Decay Theorem• The DI of an hypothesis of relationships is The DI of an hypothesis of relationships is

equal to the lowest DI of the resolved triplets equal to the lowest DI of the resolved triplets that the hypothesis entailsthat the hypothesis entails

• This applies equally to BPs and JPs as well as This applies equally to BPs and JPs as well as DIsDIs

• Thus a phylogenetic chain is no stronger than Thus a phylogenetic chain is no stronger than its weakest link!its weakest link!

• and, measures of clade support may give a and, measures of clade support may give a very incomplete picture of the distribution of very incomplete picture of the distribution of supportsupport

Bootstrapping with Reduced Bootstrapping with Reduced ConsensusConsensus

A B C D E FGHIJ

A B C D E FGHIJ

X

A B C D E FGHIJX

A B C D E F G H I J

A B C D E F G H I J

X

50.5

50.5

50.550.5

50.5

100

100 100

100

99

99

98

98

A 1111100000B 0111100000C 0011100000D 0001100000E 0000100000F 0000010000G 0000011000H 0000011100I 0000011110J 0000011111X 1111111111

Gbrev

Gram

Pcoop

Galt

GlarvGsech

Hrost

GaltGlarv

Gsech

Pcoop

Gram

Gbrev

Hrost Hrost

Gram

Pcoop

Galt

GlarvGsech

Gbrev

Galt

Gram

Pcoop

Gbrev

HrostGsech

Glarv

Hrost

Gram

Pcoop

Gbrev

GlarvGsech

Galt

Hrost

Gram

Pcoop

Gbrev

GlarvGsech

Galt

Hrost

Gram

Pcoop

Gbrev

GlarvGsech

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Input Trees

Consensus Trees

More or lessConservative

More or lessLiberal

GbrevPcoop

Galt

Glarv

Galt

Pcoop

Gram

Gbrev

Gram

Galt

GlarvGsech

Pcoop

Gbrev

HrostGsech

Hrost

Gbrev

Glarv

Galt

Hrost

Gram

Pcoop

Gbrev

GlarvGsech

Hrost

Gram

Pcoop

Gbrev

GlarvGsech

GaltGalt

Input Trees

More or lessConservative

More or lessLiberal

SuperTrees