Analysis of Quartet Dissimilarity Measures Between Undirected Phylogenetic Trees

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Abstract
An undirected phylogenetic tree is an unrooted tree with labeled leaves in which no interior vertex has just two incident edges; the labels associated with the tree''s leaves identify organisms or evolutionary units in a study collection. Any subset of four leaf labels is called a quartet. Each quarter inherits from the phylogenetic tree a subtree providing basic information about branching relationships among the quartet''s organisms within the phylogenetic tree. Consequently, quartets can be used to measure resolution of, and to construct measures of structure and dissimilarity between, such trees. I report empirical and theoretical investigations of six quartet dissimilarity measures. The empirical study provides information about frequency distributions of quartet dissimilarities when trees are randomly sampled from the set of all phylogenetic trees of given size. The theoretical study analyzes expectations of quartet dissimilarity measures when trees are randomly sampled; for this model, expectations of quartet dissimilarity measures are determined by the expectation of a measure of tree resolution.