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QUARTETS AND PARAMETER RECOVERY FOR THE GENERAL MARKOV MODEL OF SEQUENCE MUTATION
 

Summary: QUARTETS AND PARAMETER RECOVERY FOR THE
GENERAL MARKOV MODEL OF SEQUENCE MUTATION
ELIZABETH S. ALLMAN 1 AND JOHN A. RHODES 2
Abstract. A quartet method of phylogenetic inference from biological se-
quence data might use only 4-dimensional marginal arrays of the joint distri-
bution array of bases in aligned sequences to infer 4-taxon tree topologies, and
then use these to infer an n-taxon tree. Since such methods have been advo-
cated as one way of dealing with the computational demands of deducing large
phylogenies, understanding the theoretical extent to which quartet methods
can ensure the appropriateness of a choice of a model of sequence mutation is
of interest. Unfortunately, quartet information cannot confirm that data is in
accord with the general Markov model on a tree relating n taxa. However, it
can confirm, under certain technical conditions, that there exists not only a
unique tree but also unique model parameters consistent with all quartet data.
These technical conditions can be phrased in terms of polynomial equalities
(phylogenetic invariants) and inequalities in the entries of the marginal arrays.
1. Introduction
Methods of inference of the evolutionary history leading to currently extant
species, or taxa, have been transformed in recent years by the ready availability of
biological sequence data such as that from DNA. While many approaches to this

  

Source: Allman, Elizabeth S. - Department of Mathematical Sciences, University of Alaska Fairbanks

 

Collections: Mathematics