The mean value of the squared path-difference distance for rooted phylogenetic trees

2009/06/13 by Arnau Mir, Mir, Arnau, Francesc Rossello +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #Discrete Mathematics (cs.DM) #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Mathematics #Populations and Evolution (q-bio.PE) #Quantitative Methods (q-bio.QM) #cs.DM #math.CA #q-bio.PE #q-bio.QM

paper · pdf · doi:10.48550/arxiv.0906.2470

16 pages

arxiv created 2009/06/13 · arxiv updated 2009/12/01

Abstract

The path-difference metric is one of the oldest distances for the comparison of fully resolved phylogenetic trees, but its statistical properties are still quite unknown. In this paper we compute the mean value of the square of the path-difference metric between two fully resolved rooted phylogenetic trees with n leaves, under the uniform distribution. This complements previous work by Steel and Penny, who computed this mean value for fully resolved unrooted phylogenetic trees.

Related

• The expected value under the Yule model of the squared path-difference distance
• Nodal distances for rooted phylogenetic trees
• The median of the distance between two leaves in a phylogenetic tree
• Distributions of topological tree metrics between a species tree and a gene tree
• An O(n \log n) time Algorithm for computing the Path-length Distance\n between Trees