1. CONSENSUS “general or widespread agreement” Consensus tree – a tree depicting agreement among a set of treesConsensus 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: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.

2. Conservative/Liberal CMs CMs characterised by CMs characterised by Type of information/relationships (e.g. full splits) Type of information/relationships (e.g. full splits) Condition for inclusion in consensus Condition for inclusion in consensus Conservative Conservative Strict Strict Semi-strict Semi-strict Liberal Liberal Majority rule Majority rule

3. Types of Relationships

4. Greatest Agreement Subtrees A B C D E FG TWO INPUT TREES GAS/LCP TREE Taxon G is excluded AGBCDEF A B C D E F A B C DE F G Strict component consensus completely unresolved

5. Reduced CMs Focus is upon any relationships (splits) rather than only full splitsFocus is upon any relationships (splits) rather than only full splits Occur in strict, majority-rule and semi- strict varietiesOccur in strict, majority-rule and semi- strict varieties Uses polytomies (branch contractions) and pruning leaves or both to remove conflictUses polytomies (branch contractions) and pruning leaves or both to remove conflict May be more sensitive than conventional methods focusing only on full splitsMay be more sensitive than conventional methods focusing only on full splits

6. Strict Reduced CM A B C D E FG TWO INPUT TREES STRICT REDUCED CONSENSUS TREE Taxon G is excluded AGBCDEF A B C D E F A B C DE F G Strict component consensus B C D E F A C D E F A B D E F Agreement Subtrees

7. Parsimony analysis of poorly known fossils - an extreme case Phylogenetic palaeontologists often have data sets that include very poorly known fossil taxaPhylogenetic 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 treesInclusion 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‘Rogue’ taxa obfuscate consistent relationships among other taxa

8. Rhynchosaurs

9. Fossil & Recent Arthropods

11. Extending Support Measures The same measures (BP, JP & DI) that are used for clades/splits can also be determined for triplets and quartetsThe 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 cladesThis provides a lot more information because there are more triplets/quartets than there are clades Furthermore....Furthermore....

12. The Decay Theorem The DI of an hypothesis of relationships is equal to the lowest DI of the resolved triplets that the hypothesis entailsThe 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 DIsThis applies equally to BPs and JPs as well as DIs Thus a phylogenetic chain is no stronger than its weakest link!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 supportand, measures of clade support may give a very incomplete picture of the distribution of support

13. Bootstrapping with Reduced Consensus ABCDEF G HI J ABCDEF G HI J X ABCDEFGHIJX ABCDEFG H IJ ABC DEFGHIJ X 50.5 100 99 98 A 1111100000 B 0111100000 C 0011100000 D 0001100000 E 0000100000 F 0000010000 G 0000011000 H 0000011100 I 0000011110 J 0000011111 X 1111111111

15. Input Trees Consensus Trees More or less Conservative More or less Liberal

16. Input Trees More or less Conservative More or less Liberal SuperTrees