The Annals of Statistics

Invariants of Some Probability Models Used in Phylogenetic Inference

Steven N. Evans and T. P. Speed

Full-text: Open access

Abstract

The so-called method of invariants is a technique in the field of molecular evolution for inferring phylogenetic relations among a number of species on the basis of nucleotide sequence data. An invariant is a polynomial function of the probability distribution defined by a stochastic model for the observed nucleotide sequence. This function has the special property that it is identically zero for one possible phylogeny and typically nonzero for another possible phylogeny. Thus it is possible to discriminate statistically between two competing phylogenies using an estimate of the invariant. The advantage of this technique is that it enables such inferences to be made without the need for estimating nuisance parameters that are related to the specific mechanisms by which the molecular evolution occurs. For a wide class of models found in the literature, we present a simple algebraic formalism for recognising whether or not a function is an invariant and for generating all possible invariants. Our work is based on recognising an uderlying group structure and using discrete Fourier analysis.

Article information

Source
Ann. Statist., Volume 21, Number 1 (1993), 355-377.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349030

Digital Object Identifier
doi:10.1214/aos/1176349030

Mathematical Reviews number (MathSciNet)
MR1212181

Zentralblatt MATH identifier
0772.92012

JSTOR
links.jstor.org

Subjects
Primary: 62H05: Characterization and structure theory
Secondary: 60K99: None of the above, but in this section 62F99: None of the above, but in this section

Keywords
Invariant phylogenetic inference discrete Fourier analysis random walk on a group

Citation

Evans, Steven N.; Speed, T. P. Invariants of Some Probability Models Used in Phylogenetic Inference. Ann. Statist. 21 (1993), no. 1, 355--377. doi:10.1214/aos/1176349030. https://projecteuclid.org/euclid.aos/1176349030


Export citation