Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

Distributions of Tree Comparison Metrics-Some New Results

Mike A. Steel and David Penny
Systematic Biology
Vol. 42, No. 2 (Jun., 1993), pp. 126-141
DOI: 10.2307/2992536
Stable URL: http://www.jstor.org/stable/2992536
Page Count: 16
  • Download ($42.00)
  • Cite this Item
Distributions of Tree Comparison Metrics-Some New Results
Preview not available

Abstract

Measures of dissimilarity (metrics) for comparing trees are important tools in the quantitative analysis of evolutionary trees, but many of their properties are incompletely known. The present paper reports formulae for the distributions of three classes of tree comparison metrics: the partition (or symmetric difference) metric, the quartet metric (which compares subsets of four taxa), and a metric based on path-length differences between pairs of taxa. The properties studied include the mean and variance for several underlying distributions of trees, the range, the effect of the number of taxa, and methods of calculation. Three basic theorems and their proofs are reported, one for each class of tree comparison metric. The partition metric generates an asymptotic Poisson distribution for most distributions of trees (its mean is given for three tree distributions). Exact expressions are derived for the variance of the quartet metric and the mean square value of a metric based on path differences. Factors that affect the choice of a metric for a particular study include the degree of similarity of the trees being compared and the type of hypothesis being tested (e.g., whether the trees estimate the same underlying phylogeny or are simply related in some, perhaps unknown, way).

Page Thumbnails

  • Thumbnail: Page 
126
    126
  • Thumbnail: Page 
127
    127
  • Thumbnail: Page 
128
    128
  • Thumbnail: Page 
129
    129
  • Thumbnail: Page 
130
    130
  • Thumbnail: Page 
131
    131
  • Thumbnail: Page 
132
    132
  • Thumbnail: Page 
133
    133
  • Thumbnail: Page 
134
    134
  • Thumbnail: Page 
135
    135
  • Thumbnail: Page 
136
    136
  • Thumbnail: Page 
137
    137
  • Thumbnail: Page 
138
    138
  • Thumbnail: Page 
139
    139
  • Thumbnail: Page 
140
    140
  • Thumbnail: Page 
141
    141