Distributions of cherries for two models of trees

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Publisher's DOI/URI
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Degree name
Research Report
Publisher
University of Canterbury. Dept. of Mathematics
Journal Title
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Date
1999
Authors
McKenzie, Andrew Cameron
Steel, M. A.
Abstract

Null models for generating binary phylogenetic trees are useful for testing evolutionary hypotheses and reconstructing phylogenies. We consider two such null models

  • the Yule and uniform models - and in particular the induced distribution they generate on the number Cn of cherries in the tree, where a cherry is a pair of leaves each of which is adjacent to a common ancestor. By realizing the process of cherry formation in these two models by extended Polya urn models we show that Cn follows a normal distribution. We also give exact formulas for the mean and standard deviation of the Cn in these two models. This allows simple statistical tests for the Yule and uniform null hypotheses.
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Ngā upoko tukutuku/Māori subject headings
ANZSRC fields of research
Fields of Research::49 - Mathematical sciences::4901 - Applied mathematics::490102 - Biological mathematics
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Copyright Andrew Cameron McKenzie