THE CHARACTERIZATION OF TOPOLOGY - A COMPARISON OF 4 TOPOLOGICAL INDEXES FOR ROOTED BINARY-TREES

Authors
Citation
Gm. Berntson, THE CHARACTERIZATION OF TOPOLOGY - A COMPARISON OF 4 TOPOLOGICAL INDEXES FOR ROOTED BINARY-TREES, Journal of theoretical biology, 177(3), 1995, pp. 271-281
Citations number
39
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Biology Miscellaneous
ISSN journal
0022-5193
Volume
177
Issue
3
Year of publication
1995
Pages
271 - 281
Database
ISI
SICI code
0022-5193(1995)177:3<271:TCOT-A>2.0.ZU;2-O
Abstract
The quantification of the topological features of binary trees has bee n applied in several branches of biology, from botany to neurobiology to animal behaviour. The methods available for quantifying tree topolo gy differ, both in how they are applied and how they relate to one ano ther. In this paper, I study the behaviour of four commonly used topol ogical indices in relation to Shreve's random model for binary trees ( Shreve, 1966) and a variety of simple growth rules. The goals of these exercises include the following: (i) Derivation of expected values fo r each of the topological indices over a range of tree sizes (magnitud es) of relevance to biological trees. (ii) Derivation of confidence li mits for these expected values. (iii) Calculation of pairwise correlat ion coefficients for all the indices from the Monte Carlo simulations. And (iv) to explore the relationships between each of the indices and to develop an understanding about what aspects of branching each of t he different indices reflects. From these analyses I suggest that care needs to be taken when comparing different topological indices becaus e they are poorly correlated with one another and because they all sho w high dependence on the size of the examined tree. Independent of suc h considerations, the use of the total pathlength (Pe) is advocated, b ecause it shows consistent and easily characterized behaviour in relat ion to the random model and relatively robust behaviour in relation to the growth simulations. (C) 1995 Academic Press Limited