Shrinkage Effect in Ancestral Maximum Likelihood

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Shrinkage Effect in Ancestral Maximum Likelihood

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IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB) archive
Volume 6 , Issue 1 (January 2009) table of contents

Pages 126-133

Year of Publication: 2009

ISSN:1545-5963

Authors

Elchanan Mossel	UC Berkeley, Berkeley
Sebastien Roch	Microsoft Research, Redmond
Mike Steel	University of Canterbury, Christchurch

Publisher

IEEE Computer Society Press Los Alamitos, CA, USA

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DOI Bookmark:	10.1109/TCBB.2008.107

ABSTRACT

Ancestral maximum likelihood (AML) is a method that simultaneously reconstructs a phylogenetic tree and ancestral sequences from extant data (sequences at the leaves). The tree and ancestral sequences maximize the probability of observing the given data under a Markov model of sequence evolution, in which branch lengths are also optimized but constrained to take the same value on any edge across all sequence sites. AML differs from the more usual form of maximum likelihood (ML) in phylogenetics because ML averages over all possible ancestral sequences. ML has long been know to be statistically consistent - that is, it converges on the correct tree with probability approaching 1 as the sequence length grows. However, the statistical consistency of AML has not been formally determined, despite informal remarks in a literature that dates back 20 years. In this short note we prove a general result that implies that AML is statistically inconsistent. In particular we show that AML can 'shrink' short edges in a tree, resulting in a tree that has no internal resolution as the sequence length grows. Our results apply to any number of taxa.

REFERENCES

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