Literature DB >> 23117499

Exact formulas for the variance of several balance indices under the Yule model.

Gabriel Cardona1, Arnau Mir, Francesc Rosselló.   

Abstract

One of the main applications of balance indices is in tests of nullmodels of evolutionary processes. The knowledge of an exact formula for a statistic of a balance index, holding for any number n of leaves, is necessary in order to use this statistic in tests of this kind involving trees of any size. In this paper we obtain exact formulas for the variance under the Yule model of the Sackin, the Colless and the total cophenetic indices of binary rooted phylogenetic trees with n leaves.

Mesh：

Year:  2012        PMID： 23117499     DOI： 10.1007/s00285-012-0615-9

Source DB:  PubMed          Journal:  J Math Biol        ISSN： 0303-6812            Impact factor:   2.259


  8 in total

1.  Properties of phylogenetic trees generated by Yule-type speciation models.

Authors:  M Steel; A McKenzie
Journal:  Math Biosci       Date:  2001-03       Impact factor: 2.144

2.  Distributions of cherries for two models of trees.

Authors:  A McKenzie; M Steel
Journal:  Math Biosci       Date:  2000-03       Impact factor: 2.144

3.  Which random processes describe the tree of life? A large-scale study of phylogenetic tree imbalance.

Authors:  Michael G B Blum; Olivier François
Journal:  Syst Biol       Date:  2006-08       Impact factor: 15.683

4.  Optimization over a class of tree shape statistics.

Authors:  Frederick Matsen
Journal:  IEEE/ACM Trans Comput Biol Bioinform       Date:  2007 Jul-Sep       Impact factor: 3.710

5.  PATTERNS IN TREE BALANCE AMONG CLADISTIC, PHENETIC, AND RANDOMLY GENERATED PHYLOGENETIC TREES.

Authors:  Stephen B Heard
Journal:  Evolution       Date:  1992-12       Impact factor: 3.694

6.  SEARCHING FOR EVOLUTIONARY PATTERNS IN THE SHAPE OF A PHYLOGENETIC TREE.

Authors:  Mark Kirxpatrick; Montgomery Slatkin
Journal:  Evolution       Date:  1993-08       Impact factor: 3.694

7.  CENTRAL MOMENTS AND PROBABILITY DISTRIBUTION OF COLLESS'S COEFFICIENT OF TREE IMBALANCE.

Authors:  James S Rogers
Journal:  Evolution       Date:  1994-12       Impact factor: 3.694

8.  Phylogenetic analysis. Models and estimation procedures.

Authors:  L L Cavalli-Sforza; A W Edwards
Journal:  Am J Hum Genet       Date:  1967-05       Impact factor: 11.025
  8 in total
  3 in total

1.  A simple derivation of the mean of the Sackin index of tree balance under the uniform model on rooted binary labeled trees.

Authors:  Matthew C King; Noah A Rosenberg
Journal:  Math Biosci       Date:  2021-09-16       Impact factor: 2.144

2.  On Sackin's original proposal: the variance of the leaves' depths as a phylogenetic balance index.

Authors:  Tomás M Coronado; Arnau Mir; Francesc Rosselló; Lucía Rotger
Journal:  BMC Bioinformatics       Date:  2020-04-23       Impact factor: 3.169

3.  On the Colijn-Plazzotta numbering scheme for unlabeled binary rooted trees.

Authors:  Noah A Rosenberg
Journal:  Discrete Appl Math       Date:  2020-12-18       Impact factor: 1.139
  3 in total

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