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
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