Computing quadratic entropy in evolutionary trees

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

Abstract

Kvadratična entropija, ki jo je vpeljal Rao, je mera za biološko raznolikost. V članku opazimo, da je kvadratična entropija inačica uteženega Wienerjevega indeksa, ki je po drugi strani intenzivno raziskovana grafovska invarianta v matematični kemiji. To dejstvo omogoča izpeljavo nekaj učinkovitih algoritmov za izračunavanje kvadratične entropije v primeru danih listnih uteži. Na ultrametričnih drevesih je Pavoine vpeljal maksimum kvadratičnih entropij kot mero za paroma evolucijsko različnost v ohranitveni biologiji. Predstavljamo algoritem, ki maksimizira to količino v linearnem času, kar je pomembna izboljšava glede na obstoječe kvadratične programske pristope.

Keywords

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

Data

Language:	English
Year of publishing:	2011
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	519.17:54
COBISS:	16059481
ISSN:	0898-1221
Views:	294
Downloads:	32
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Računanje kvadratične entropije v evolucijskih drevesih
Secondary 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.
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 3821-3828
Volume:	Vol. 62
Issue:	no. 10
Chronology:	2011
ID:	1475858