Trees of trees: an approach to comparing multiple alternative phylogenies.

Phylogenetic analysis very commonly produces several alternative trees for a given fixed set of taxa. For example, different sets of orthologous genes may be analyzed, or the analysis may sample from a distribution of probable trees. This article describes an approach to comparing and visualizing multiple alternative phylogenies via the idea of a "tree of trees" or "meta-tree." A meta-tree clusters phylogenies with similar topologies together in the same way that a phylogeny clusters species with similar DNA sequences. Leaf nodes on a meta-tree correspond to the original set of phylogenies given by some analysis, whereas interior nodes correspond to certain consensus topologies. The construction of meta-trees is motivated by analogy with construction of a most parsimonious tree for DNA data, but instead of using DNA letters, in a meta-tree the characters are partitions or splits of the set of taxa. An efficient algorithm for meta-tree construction is described that makes use of a known relationship between the majority consensus and parsimony in terms of gain and loss of splits. To illustrate these ideas meta-trees are constructed for two datasets: a set of gene trees for species of yeast and trees from a bootstrap analysis of a set of gene trees in ray-finned fish. A software tool for constructing meta-trees and comparing alternative phylogenies is available online, and the source code can be obtained from the author.