Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T16:54:45.116Z Has data issue: false hasContentIssue false
  • English
  • Français

Unrooted trees for numerical taxonomy

Published online by Cambridge University Press:  14 July 2016

Annette J. Dobson
Annette J. Dobson*
Affiliation:
James Cook University of North Queensland
Get access Rights & Permissions [Opens in a new window]

Abstract

It is common to represent taxonomic hierarchies of related objects (such as similar plant or animal species or languages of the same family) by rooted trees with labelled terminal vertices which represent the objects. The multivariate data comparing numerous characteristics of the objects is first reduced to indices of similarity (or more often of dissimilarity) between each pair of objects. These are used to classify the objects into groups which are then depicted on a tree.

This paper shows that an unrooted tree with labelled terminal vertices may provide a better representation of the relationships between the objects because the similarity indices are required to conform to fewer restrictions. Also for a given number of terminal vertices, there are fewer unrooted than rooted trees so that studies using probability distributions of trees or seeking the most suitable tree to represent the data are more practicable.

Keywords

NUMERICAL TAXONOMYGRAPH THEORYSIMILARITYFAMILY TREESREPRESENTATIONNUMBERS OF TREESPROBABILITIES OF TREES
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 1 , March 1974 , pp. 32 - 42
Copyright
Copyright © Applied Probability Trust 1974 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Cavalli-Sforza, L. L. and Edwards, A. W. F. (1967) Phylogenetic analysis models and estimation procedures Amer. J. Hum. Genet. 19, 233–257.Google ScholarPubMed
Cormack, R. M. (1971) A review of classification J. R. Statist. Soc. A 134, 321–367.CrossRefGoogle Scholar
Farris, J. S. (1970) Methods for computing Wagner trees Syst. Zool. 19, 83–92.Google Scholar
Harary, F. and Prins, G. (1959) The number of homeomorphically irreducible trees, and other species Acta Math. 101, 141–162.CrossRefGoogle Scholar
Harding, E. F. (1971) The probabilities of rooted tree-shapes generated by random bifurcaation Adv. Appl. Prob. 3, 44–77.CrossRefGoogle Scholar
Hartigan, J. A. (1967) Representation of similarity matrices by trees J. Amer. Statist. Ass. 62, 1140–1158.Google Scholar
Jardine, N. and Sibson, R. (1971) Mathematical Taxonomy. Wiley, New York.Google Scholar
Johnson, S. C. (1967) Hierarchical clustering schemes Psychometrika 32, 241–254.Google Scholar