DOI: 10.5061/dryad.9h6h8
title: Data from: Mixture models of nucleotide sequence evolution that account for heterogeneity in the substitution process across sites and across lineages

description: Molecular phylogenetic studies of homologous sequences of nucleotides
 often assume that the underlying evolutionary process was globally
 stationary, reversible and homogeneous (SRH), and that a model of
 evolution with one or more site-specific and time-reversible rate matrices
 (e.g., the GTR rate matrix) is enough to accurately model the evolution of
 data over the whole tree. However, an increasing body of data suggests
 that evolution under these conditions is an exception, rather than the
 norm. To address this issue, several non-SRH models of molecular evolution
 have been proposed, but they either ignore heterogeneity in the
 substitution process across sites (HAS) or assume it can be modelled
 accurately using the Γ distribution. As an alternative to these models of
 evolution, we introduce a family of mixture models that approximate HAS
 without the assumption of an underlying predefined statistical
 distribution. This family of mixture models is combined with non-SRH
 models of evolution that account for heterogeneity in the substitution
 process across lineages (HAL). We also present two algorithms for
 searching model space and identifying an optimal model of evolution that
 is less likely to over- or under-parameterize the data. The performance of
 the two new algorithms was evaluated using alignments of nucleotides with
 10,000 sites simulated under complex non-SRH conditions on a 25-tipped
 tree. The algorithms were found to be very successful, identifying the
 correct HAL model with a 75% success rate (the average success rate for
 assigning rate matrices to the tree's 48 edges was 99.25%) and, for
 the correct HAL model, identifying the correct HAS model with a 98%
 success rate. Finally, parameter estimates obtained under the correct
 HAL-HAS model were found to be accurate and precise. The merits of our new
 algorithms were illustrated with an analysis of 42,337 second codon sites
 extracted from a concatenation of 106 alignments of orthologous genes
 encoded by the nuclear genomes of Saccharomyces cerevisiae, S. paradoxus,
 S. mikatae, S. kudriavzevii, S. castellii, S. kluyveri, S. bayanus, and
 Candida albicans. Our results show that second codon sites in the
 ancestral genome of these species contained 49.1% invariable sites, 39.6%
 variable sites belonging to one rate category (V1), and 11.3% variable
 sites belonging to a second rate category (V2). The ancestral nucleotide
 content was found to differ markedly across these 3 sets of sites, and the
 evolutionary processes operating at the variable sites were found to be
 non-SRH and best modelled by a combination of 8 edge-specific rate
 matrices (4 for V1 and 4 for V2). The number of substitutions per site at
 the variable sites also differed markedly, with sites belonging to V1
 evolving slower than those belonging to V2 along the lineages separating
 the 7 species of Saccharomyces. Finally, sites belonging to V1 appeared to
 have ceased evolving along the lineages separating S. cerevisiae, S.
 paradoxus, S. mikatae, S. kudriavzevii, and S. bayanus, implying that they
 might have become so selectively constrained that they could be considered
 invariable sites in these species.
description: Supplementary_material.tar.bz2This supplementary material contains three files: 1 - a README file, with further details about the other two files. 2 - Rokas_2.phy (an alignment of a data set used to illustrate the methods). 3 - Yeast_tree.nwk (the corresponding tree used to illustrate the methods).HAL-HAS SoftwareHAL-HAS is a program package, comprising HAL-BU, HAL-TD, and HAS, that was written to allow users to infer an optimal model of evolution for a given data set, a given tree.Hetero SoftwareHetero was written to facilitate the development and testing of phylogenetic methods.