Limit theorems for patterns in phylogenetic trees

Huilan Chang, Michael Fuchs*

*Corresponding author for this work

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

Studying the shape of phylogenetic trees under different random models is an important issue in evolutionary biology. In this paper, we propose a general framework for deriving detailed statistical results for patterns in phylogenetic trees under the Yule-Harding model and the uniform model, two of the most fundamental random models considered in phylogenetics. Our framework will unify several recent studies which were mainly concerned with the mean value and the variance. Moreover, refined statistical results such as central limit theorems, Berry-Esseen bounds, local limit theorems, etc., are obtainable with our approach as well. A key contribution of the current study is that our results are applicable to the whole range of possible sizes of the pattern.

Original languageEnglish
Pages (from-to)481-512
Number of pages32
JournalJournal of Mathematical Biology
Volume60
Issue number4
DOIs
StatePublished - 1 Jan 2010

Keywords

  • Central limit theorems
  • Moments
  • Patterns
  • Phylogenetic trees
  • Poisson approximations

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