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MBE Advance Access published online on March 10, 2004
Molecular Biology and Evolution, doi:10.1093/molbev/msh115
Molecular Biology and Evolution © Society for Molecular Biology and Evolution 2004; all rights reserved
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Accepted February 25, 2004
© 2004 Molecular Biology and Evolution © Society for Molecular Biology and Evolution 2004; all rights reserved.

Original Articles

On Counting Tandem Duplication Trees

Jialiang Yang 1 and Louxin Zhang 1*

1 Department of Mathematics, National University of Singapore, Singapore 117543

* To whom correspondence should be addressed. E-mail: matzlx{at}nus.edu.sg.


  Abstract

Large genomes are full of repeated DNA sequences. It was estimated that over half of the human DNA consists of repeated sequences (Baltimore, 2001; Eichler, 2002; Leem et al., 2002). Tandem duplication is one of the important evolutionary mechanisms for producing repeated DNA sequences, in which the copies that may or may not contain genes are adjacent along the genome. Fitch (1977) first observed that tandem duplication histories are much more constraint than speciation histories and proposed to model them assuming that unequal crossover is the biological mechanism from which they originate, and the corresponding trees are now called tandem duplication trees, the term tandem being sometimes omitted for the sake of conciseness. With more and more genomic sequences having been known, inferring tandem duplication history have redrawn researchers' attention recently (Benson and Dong, 1999; Tang, Waterman, and Yooseph, 2002; Elemento et al., 2002; Zhang et al., 2003).

The aim of this note is, first, to present a simple recurrence formula for the number of rooted duplication trees based on the recurrence formula proved in Gascuel et al. (2003). We also give a simple non-counting proof of the fact that the number of rooted duplication trees for n segments is exactly twice the number of unrooted duplication trees for n segments. Notice that this fact was proved based on a counting argument in Gascuel et al. (2003).

Key Words: Molecular phylogeny, tandem duplication history, duplication tree model


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