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New Zealand Mathematics Colloquium 1999
July 6-9, 1999
Department of Mathematics and Statistics, University of Canterbury
Christchurch, New Zealand

Organizers
Doris Barnard, Therese Boustead, Chris Price, Bruce Robson, Gunter Steinke, Graeme Wake, Allan Willms

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Distributions of Cherries for Two Models of Trees
by
Andy McKenzie
University of Canterbury
Coauthors: Mike Steel (University of Canterbury)

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.

Date received: May 15, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacc-22.