A Metric on the Space of Rooted Phylogenetic Trees

Background: The purpose of phylogenetic analysis is to not only show the evolutionary history of taxa, but also comprehend the origin of life. Rooted phylogenetic trees are employed to express the result of phylogenetic analysis. Objective: Computing the dissimilarity of rooted phylogenetic trees has been instrumental in our understanding of the evolutionary relationship of species and the analysis of the reconstruction method of phylogenetic trees. For example, in order to evaluate the method for constructing phylogenetic trees, we need to measure the differences among phylogenetic trees computed from different genes, or the differences between the constructed trees and the simulate trees or the true trees. Method: This paper proposes a new metric on the space of rooted phylogenetic trees that can be calculated in polynomial time in the size of the compared trees. The metric is based on the equivalence property of nodes. Results: Experimental results demonstrate the correlation of Triple distance with our distance is least and the correlation of Cluster distance and our distance is most. Conclusion: The metric proposed by this paper is very effective. This metric is defined for rooted phylogenetic trees, but can be carried over to unrooted phylogenetic trees by applying to an outgroup species appended the tree.