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Systematic Biology 2006 55(5):756-768; doi:10.1080/10635150600975218
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© 2006 Society of Systematic Biologists

Efficient Likelihood Computations with Nonreversible Models of Evolution

Bastien Boussau and Manolo Gouy

Laboratoire de Biométrie et Biologie Evolutive (UMR 5558); CNRS, Université Lyon 1 43 boulevard 11 nov 1918, 69622, Villeurbanne Cedex, France E-mail: boussau{at}biomserv.univ-lyon1.fr (B.B.)

Edited by Olivier Gascuel: Associate Editor


  Abstract

Recent advances in heuristics have made maximum likelihood phylogenetic tree estimation tractable for hundreds of sequences. Noticeably, these algorithms are currently limited to reversible models of evolution, in which Felsenstein's pulley principle applies. In this paper we show that by reorganizing the way likelihood is computed, one can efficiently compute the likelihood of a tree from any of its nodes with a nonreversible model of DNA sequence evolution, and hence benefit from cutting-edge heuristics. This computational trick can be used with reversible models of evolution without any extra cost. We then introduce nhPhyML, the adaptation of the nonhomogeneous nonstationary model of Galtier and Gouy (1998; Mol. Biol. Evol. 15:871–879) to the structure of PhyML, as well as an approximation of the model in which the set of equilibrium frequencies is limited. This new version shows good results both in terms of exploration of the space of tree topologies and ancestral G+C content estimation. We eventually apply it to rRNA sequences slowly evolving sites and conclude that the model and a wider taxonomic sampling still do not plead for a hyperthermophilic last universal common ancestor.

Keywords: Efficient algorithm; LUCA; maximum likelihood; molecular phylogeny; nonreversible model of evolution; PhyML; origin of life; root of life

Received October 17, 2006; Revised December 10, 2005; Accepted March 28, 2006
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