Choosing Appropriate Substitution Models for the Phylogenetic Analysis of
Beth Shapiro,1Andrew Rambaut,1and Alexei J. Drummond1,2
Department of Zoology, University of Oxford, Oxford, United Kingdom
Although phylogenetic inference of protein-coding sequences continues to dominate the literature, few analyses incor-
porate evolutionary models that consider the genetic code. This problem is exacerbated by the exclusion of codon-based
models from commonly employed model selection techniques, presumably due to the computational cost associated with
codon models. We investigated an efficient alternative to standard nucleotide substitution models, in which codon position
(CP) is incorporated into the model. We determined the most appropriate model for alignments of 177 RNA virus genes
and 106 yeast genes, using 11 substitution models including one codon model and four CP models. The majority of an-
alyzed gene alignments are best described by CP substitution models, rather than by standard nucleotide models, and
without the computational cost of full codonmodels. These results havesignificant implications for phylogenetic inference
of coding sequences as they make it clear that substitution models incorporating CPs not only are a computationally
realistic alternative to standard models but may also frequently be statistically superior.
The growing abundance of available molecular se-
quence data has inspired research across ecology and evo-
lutionary biology and continues to provide novel insights
into a range of biological questions. While the questions
are diverse, those using this information are linked by
a common challenge: to provide the best estimate of the
evolutionary history of their data. Probabilistic modeling
inference (Felsenstein 2001), dominated by maximum like-
lihood (ML) (Felsenstein 1981) and Bayesian (Yang and
Rannala 1997) estimation. While this statistical revolution
ers to select the model most appropriate for their data.
of evolutionary model can affect the outcome of any phy-
logenetic analysis, for example, by incorrectly estimating
tree topology (Penny et al. 1994; Bruno and Halpern
1999), influencing branch length estimation (Posada
2001), and biasing statistical support values (Buckley
and Cunningham 2002). Recently, free software packages
have provided a simple framework for choosing an evolu-
tionary model (e.g., Modeltest [Posada and Crandall 1998]
and variations). Using hierarchical likelihood ratio tests
(Goldman 1993) or Akaike information criterion (AIC)
tests (Posada and Buckley 2004), these programs iterate
the most appropriate model for a data set.
Such objective techniques for model choice have been
widely adopted in phylogenetics, to the extent that the use
of Modeltest, in particular, is sometimes regarded as a
prerequisite for publication of a phylogenetic analysis.
While this is an improvement in phylogenetic practice, it
has meant that the phylogenetics community has largely
overlooked models not included in the Modeltest hierarchy.
In particular, models such as GY94, proposed by Goldman
and Yang (1994) and Muse and Gaut (1994) and which
operate on codons rather than on individual nucleotides,
are not considered by Modeltest. Full codon models such
as GY94 are computationally expensive compared to stan-
dard nucleotide substitution models, which may have con-
tributed to their underrepresentation in the phylogenetic
literature. In fact, the use of codon-based models is essen-
tially restricted to parameter estimation on fixed trees for
purposes of detecting selection (Yang et al. 2000). Never-
models are becoming a realistic alternative to nucleotide
models for phylogenetic inference.
Codon-based models explicitly incorporate informa-
tion about the genetic code and as such are arguably among
the most biologically realistic models of the evolution of
coding sequences. Codon models can be divided into
two major categories: those like GY94 that specifically in-
corporate amino acid replacement rates (having codons
rather than nucleotides as their states) and those that parti-
tion a nucleotide-based model into categories based on
codon position (hereafter CP models). CP models are a spe-
cific form of the class of models that allow different models
of substitution for different partitions of the data (e.g., Yang
1996). While full codon models like the GY94 model bi-
ological reality more closely, the CP models are much more
To investigate whether CP models are more appropri-
ate than standard nucleotide substitution models such as
general time reversible with gamma distributed rate hetero-
geneity and a proportion of invariant sites (GTR 1 C 1 I),
we conducted a comparative survey of nucleotide, CP, and
codon substitution models on 283 multiple sequence align-
ments. Of these, 177 were RNA virus genes with align-
ments of 10–75 sequences (median 26) ranging from
468 to 2741 bp (median 940) in length (E. C. Holmes, per-
sonal communication). The remaining 106 were individual
gene alignments constructed using the published genomes
of seven Saccharomyces species and the outgroup Candida
albicans (Rokas et al. 2003).
We compared six commonly used nucleotide sub-
stitution models to four CP models (table 1) and GY94
1All authors contributed equally to this work.
2Present address: Department of Computer Science, University of
Auckland, Auckland, New Zealand.
Mol. Biol. Evol. 23(1):7–9. 2006
Advance Access publication September 21, 2005
? The Author 2005. Published by Oxford University Press on behalf of
the Society for Molecular Biology and Evolution. All rights reserved.
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(see Methods). For each alignment analyzed, we used AIC
as the model selection criterion to choose the best fitting of
the nucleotide substitution models. We found that models
superior to standard nucleotide models in both RNA virus
and yeast protein-coding sequences. All four CP models
performed better on average for the 283 alignments ana-
lyzed than did GTR 1 C 1 I. The HKY1121 CP1121
C112 model was the best nucleotide model for all but
one of the 106 yeast genes, despite having two less param-
eters thanGTR1C1I.Theremainingyeast genewasbest
described by GTR 1 CP123. CP models were chosen above
other nucleotide models in 174/177 virus alignments (99%;
table 1). Taken together, this strongly suggests that biolog-
ical information about CP should be used when choosing
a substitution model for phylogenetic analysis of protein-
A strong log-log relationship was observed between
the rate of evolution in the third position relative to the rest
of the codon and the ratio of nonsynonymous to synony-
mous substitutions (x) estimated under the GY94 model
(fig. 1). The strength of this relationship demonstrates that
the CP model of nucleotide evolution captures the essential
characteristics of the full codon model. Further, it suggests
that it may be possible to use this model as an approximate
estimator of x instead of the much more computationally
demanding full codon models.
We have not attempted a systematic investigation of
the full range of potential CP models, and it remains likely
that superior models to those described here exist. Instead,
we have attempted to demonstrate that biologically moti-
vated CP models that are superior to the standard range
of nucleotide substitution models can be constructed, with
no increase in parametric complexity. We are aware that
with only limited effort, the models introduced here can
be used in Bayesian phylogenetic inference packages such
as MrBayes (Huelsenbeck and Ronquist 2001; Ronquist
and Huelsenbeck 2003) and BEAST (available at http://
Although the performance of the CP models was im-
pressive, one of the striking results of this analysis was the
performance of the GY94 model, which was chosen ahead
of all other models in all 106 yeast genes and in 119/177
(67%) virus genes analyzed (table 2). Unfortunately, the
options for performing a phylogenetic analysis under the
GY94 model are still quite limited. Currently, only
MrBayes (Huelsenbeck and Ronquist 2001; Ronquist
and Huelsenbeck 2003) caters for this, and its speed is typ-
ically two orders of magnitude slower than for nucleotide
models. Realistically, use of this model is currently feasible
only for small data sets of fewer than 50 taxa. Nevertheless,
in light of its excellent fit to real data, the GY94 model
should be an obvious choice in situations where computa-
tional resources and data size permit.
The Classes ofSubstitutionModels Analyzedand theNumber
of Data Sets for Which a Model in the Class Was the Best
the GY94 model and the relative rate of the third CP in CP models. Closed
squares represent virus gene alignments, and open diamonds represent
yeast gene alignments. Both axes are plotted in log space, and the black
lines are the best fitting power law for the two sets of data. This plot shows
that the relative rate of the third CP is a good predictor of the x parameter.
The Nucleotide Models Analyzed
ModelParametersCP Model?In Modeltest?
HKY 1 I
HKY 1 C
HKY 1 C 1 I
HKY 1 CP123
HKY1121 CP1121 C112
GTR 1 I
GTR 1 C
GTR 1 C 1 I
GTR 1 CP123
GTR 1 CP1121 C
8 Shapiro et al.
by guest on October 17, 2015
Methods Download full-text
Throughout the study, a single tree topology was as-
sumed for each alignment. For virus data, ML phylogenies
were estimated under the GTR 1 C 1 I model using
PAUP* (Swofford 2003). For yeast genes, the tree esti-
mated from the combined data and reported in Rokas
et al. (2003) was used. We tested an array of nucleotide
substitution models and GY94 (using codeml from the
PAML package; Yang 1997). For each model and align-
ment, the branch lengths of the respective phylogeny
were reestimated along with parameters of the substitution
model. PAUP* was used to estimate a nested hierarchy of
models commonly used for phylogenetic inference and
which are found among those in Modeltest (Posada and
Crandall 1998). These include combinations of the
HKY85 (Hasegawa, Kishino, and Yano 1985) and GTR
(Lanave et al. 1984) models of nucleotide substitution,
the discrete gamma model of heterogeneity among sites
(Yang 1994), and the invariant site model. We label these
models by combining acronyms of the components, for
example, GTR 1 C 1 I in the case of GTR with gamma
rate heterogeneity and invariant sites. In addition, we con-
sidered models in which the CP are allowed different rates
relative to each other, resulting in models we labeled
HKY 1 CP123and GTR 1 CP123, with the subscript indi-
catingthe rate categoryfor each CP.Althoughthese models
areoccasionallyusedinphylogeneticstudies, often referred
to as site-specific rate models, they are much less common
than standard nucleotide substitution models.
Using baseml from the PAML package (Yang 1997),
we constructed two additional models that we believed
might better represent the biological reality of codon evo-
lution. For these, we grouped first and second CPs into a
single partition with respect to third CPs, allowing the latter
to have a different rate. For the first model, we assumed that
all three CPs shared the same GTR model of substitution
and the same shape parameter (a) of the gamma model
ber of parameters as GTR 1 C 1 I and is labeled GTR 1
CP1121 C. The final nucleotide model was a combination
of HKY 1 C with a different transition-transversion and a
parameter along with a relative rate between partitions, re-
sulting in fewer parameters than GTR 1 C 1 I. This model
We would like to thank E. Holmes for the collection
and curation of the 177 virus data sets used in this anal-
ysis. This work was funded by the Wellcome Trust and
the Royal Society.
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