Majority-rule reduced consensus trees and their use in bootstrapping

Bootstrap analyses are usually summarized with majority-rule component consensus trees. This consensus method is based on replicated components and, like all component consensus methods, it is insensitive to other kinds of agreement between trees. Recently developed reduced consensus methods can be used to summarize much additional agreement on hypothesised phylogenetic relationships among multiple trees. The new methods are "strict" in the sense that they require agreement among all the trees being compared for any relationships to be represented in a consensus tree. Majority-rule reduced consensus methods are described and their use in bootstrap analyses is illustrated with a hypothetical and a real example. The new methods provide summaries of the bootstrap proportions of all n-taxon statements/partitions and facilitate the identification of hypotheses of relationships that are supported by high bootstrap proportions, in spite of a lack of support for particular components or clades. In practice majority-rule reduced consensus profiles may contain many trees. The size of the profile can be reduced by constraints on minimal bootstrap proportions and/or cardinality of the included trees. Majority-rule reduced consensus trees can also be selected a posteriori from the profile. Surrogates to the majority-rule reduced consensus methods using partition tables or tree pruning options provided by widely used phylogenetic inference software are also described. The methods are designed to produce more informative summaries of bootstrap analyses and thereby foster more informed assessment of the strengths and weaknesses of complex phylogenetic hypotheses.