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CONSENSUS “general or widespread agreement”. Consensus tree – a tree depicting agreement among a set of trees a representation of a set of trees a phylogenetic inference from a set of trees Consensus methods can be characterised in terms of: Procedures - algorithms
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CONSENSUS“general or widespread agreement” • Consensus tree – a tree depicting agreement among a set of trees • a representation of a set of trees • a phylogenetic inference from a set of trees • Consensus methods can be characterised in terms of: • Procedures - algorithms • Axioms - desirable properties they satisfy • Objective functions - as trees that optimise some measure of fit between it and the input trees.
Conservative/Liberal CMs CMs characterised by Type of information/relationships (e.g. full splits) Condition for inclusion in consensus Conservative Strict Semi-strict Liberal Majority rule
Greatest Agreement Subtrees TWO INPUT TREES B D F G A G B C D E F A C E A G D E C B F B D F A C E Strict component consensus completely unresolved GAS/LCP TREE Taxon G is excluded
Reduced CMs • Focus is upon any relationships (splits) rather than only full splits • Occur in strict, majority-rule and semi-strict varieties • Uses polytomies (branch contractions) and pruning leaves or both to remove conflict • May be more sensitive than conventional methods focusing only on full splits
Strict component consensus A G D E C B F A D F C E B D F C E A D F B E Strict Reduced CM TWO INPUT TREES B D F G A G B C D E F A C E B D F A C E STRICT REDUCED CONSENSUS TREE Agreement Subtrees Taxon G is excluded
Parsimony analysis of poorly known fossils - an extreme case • Phylogenetic palaeontologists often have data sets that include very poorly known fossil taxa • Inclusion of such taxa is sometimes associated with a proliferation of most parsimonious tree and poorly resolved consensus trees • ‘Rogue’ taxa obfuscate consistent relationships among other taxa
Extending Support Measures • The same measures (BP, JP & DI) that are used for clades/splits can also be determined for triplets and quartets • This provides a lot more information because there are more triplets/quartets than there are clades • Furthermore....
The Decay Theorem • The DI of an hypothesis of relationships is equal to the lowest DI of the resolved triplets that the hypothesis entails • This applies equally to BPs and JPs as well as DIs • Thus a phylogenetic chain is no stronger than its weakest link! • and, measures of clade support may give a very incomplete picture of the distribution of support
A B C D E J I H G F A B C D E I H F J G Bootstrapping with Reduced Consensus X A B C D E F G I J H X A 1111100000 B 0111100000 C 0011100000 D 0001100000 E 0000100000 F 0000010000G 0000011000H 0000011100 I 0000011110 J 0000011111 X 1111111111 50.5 50.5 50.5 X 50.5 50.5 A B C D E F G H I J A B C D E I H F J G 99 100 98 99 98 100 100 100
Input Trees Consensus Trees More or less Conservative More or less Liberal
Input Trees SuperTrees More or less Conservative More or less Liberal