Computing quadratic entropy in evolutionary trees

Drago Bokal (Author), Matt DeVos (Author), Sandi Klavžar (Author), Aki Mimoto (Author), Arne Ø. Mooers (Author)

Abstract

We note here that quadratic entropy, a measure of biological diversity introduced by Rao, is a variant of the weighted Wiener index, a graph invariant intensively studied in mathematical chemistry. This fact allows us to deduce some efficient algorithms for computing the quadratic entropy in the case of given tip weights, which may be useful for community biodiversity measures. Furthermore, on ultrametric phylogenetic trees, the maximum of quadratic entropy is a measure of pairwise evolutionary distinctness in conservation biology, introduced by Pavoine. We present an algorithm that maximizes this quantity in linear time, offering a significant improvement over the currently used quadratic programming approaches.

Keywords

teorija grafov;evolucijsko drevo;filogenetsko drevo;Wienerjev indeks;graph theory;evolutionary tree;phylogenetic tree;quadratic entropy;originality;distinctness;Wiener index;

Data

Language:	English
Year of publishing:	2011
Typology:	0 - Not set
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	519.17:54
COBISS:	16009817
ISSN:	2232-2094
Parent publication:	Preprint series
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Other data

Secondary language:	English
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 1-18
Volume:	ǂVol. ǂ49
Issue:	ǂšt. ǂ1160
Chronology:	2011
ID:	68893