Comparison of Undirected Phylogenetic Trees Based on Subtrees of Four Evolutionary Units

A method to measure how similar are two phylogenetic trees for the same collection of evolutionary units (EUs) is described. The measure does not change with changes in the direction of evolution in either of the two trees being compared, and thus it depends only on the convexity and proximity of the groups of EUs within the collection under study. It can also be used with only partially resolved phylogenetic trees. The measure is based on the idea that a group of four EUs is the smallest group for which there is more than one possible distinct undirected phylogenetic tree. For a given phylogenetic tree, the undirected subtree inherited by a group of four EUs is the tree that results when all the branches containing only EUs not in this group of four are removed. Every group of four EUs either inherits one of three distinct types of undirected phylogenetic trees, or is unresolved. Two phylogenetic trees can be com- pared on the basis of which groups of four EUs inherit the same type of undirected phylogenetic tree. The ideas can be extended to comparisons of three or more trees. (Phylogenetic trees; compatibility; subtree.)