New Zealand Journal of Botany abstracts

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A complete family of phylogenetic invariants for any number of taxa under Kimura's 3ST model

MIKE STEEL

Mathematics Department
Massey University
Palmerston North, New Zealand*

LASZLO SZEKELY

Department of Mathematics
University of New Mexico
Albuquerque, NM 87131, U.S.A.

PETER L. ERDOS

Hungarian Academy of Science
and CWI, Amsterdam,
The Netherlands

PETER WADDELL

Plant Biology Department
Massey University
Palmerston North, New Zealand
*Present address: Department of Mathematics,
University of Canterbury, Private Bag 4800,
Christchurch, New Zealand.

Abstract We describe a new family of phylo- genetic invariants that arise from the recently developed spectral analysis approach to tree reconstruction. These invariants, which are valid for Kimura's 3ST model, possess four important properties—they are defined equally easily for any number of taxa, their description is tree-inde- pendent, they apply even when the distribution of the four nucleotides in the ancestral taxon is unknown, and they can be modified to deal with sequence sites that do not mutate independently with identical distribution. B93011 Received 19 January 1993; accepted 16 April 1993

Keywords genetic sequences; phylogenetic trees; phylogenetic invariants; Kimura's three-parameter model; convergence in probability

B93011 ; Received 19 January 1993; accepted 16 April 1993
New Zealand Journal of Botany, 1993, Vol. 31: 289-296
OO28-825X/93/3103-0289 $2.50/0 © The Royal Society of New Zealand 1993

PDF file of entire paper: medium quality (615K); (scanned from paper original: notes about this process)

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