PROCEEDINGS Open Access
Fast and accurate methods for phylogenomic
analyses
Jimmy Yang, Tandy Warnow*
From Ninth Annual Research in Computational Molecular Biology (RECOMB) Satellite Workshop on Com-
parative Genomics
Galway, Ireland. 8-10 October 2011
Abstract
Background: Species phylogenies are not estimated directly, but rather through phylogenetic analyses of different
gene datasets. However, true gene trees can differ from the true species tree (and hence from one another) due to
biological processes such as horizontal gene transfer, incomplete lineage sorting, and gene duplication and loss, so
that no single gene tree is a reliable estimate of the species tree. Several methods have been developed to
estimate species trees from estimated gene trees, differing according to the specific algorithmic technique used
and the biological model used to explain differences between species and gene trees. Relatively little is known
about the relative performance of these methods.
Results: We report on a study evaluating several different methods for estimating species trees from sequence
datasets, simulating sequence evolution under a complex model including indels (insertions and deletions),
substitutions, and incomplete lineage sorting. The most important finding of our study is that some fast and
simple methods are nearly as accurate as the most accurate methods, which employ sophisticated statistical
methods and are computationally quite intensive. We also observe that methods that explicitly consider errors in
the estimated gene trees produce more accurate trees than methods that assume the estimated gene trees are
correct.
Conclusions: Our study shows that highly accurate estimations of species trees are achievable, even when gene
trees differ from each other and from the species tree, and that these estimations can be obtained using fairly
simple and computationally tractable methods.
Background
With the increased availability of whole genome
sequence assemblies, the estimation of species trees
based upon the entire genome is now possible. The
most frequently used approaches for estimating species
phylogenies compute alignments on each gene, concate-
nate these alignments into one super-alignment, and
then estimate a tree from the super-alignment. However,
these “combined analysis” methods do not have good
statistical properties because different regions of the
genome can have different evolutionary histories. More
generally, it is increasingly clear that gene trees can be
different from species trees due to a number of biologi-
cal processes. One of the dominant causes for this
incongruence between gene and species trees is incom-
plete lineage sorting (ILS) [1], a population-level process
where lineages “coalesce” [2] deeply in the species phy-
logeny, so that the gene tree can be different from the
species tree. Thus, coalescence is a “backwards-in-time”
process, which is mathematically equivalent to a for-
wards-in-time process called “lineage sorting”, whereby
alleles within an ancient population diverge before a
speciation event, and then assort into the two sub-spe-
cies. ILS has been implicated in the different hypotheses
for the evolutionary tree on human, chimp, and gorilla
* Correspondence: tandy@cs.utexas.edu
Department of Computer Science, University of Texas at Austin, Austin TX
78712
Full list of author information is available at the end of the article
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© 2011 Yang and Warnow; licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited.

[3], but ILS is quite generally a major problem for spe-
cies tree estimation [4].
Several methods have been developed that estimate
species trees from estimated gene trees under the ILS
model. One main approach is to find the species tree
that implies the fewest number of deep coalescent
events, a computational problem called “MDC” (for
minimize deep coalescences [1]), a problem that is NP-
hard when the gene trees can be on different taxon sets
[5], but of unknown computational complexity when the
gene trees are constrained to be on the same taxon set.
Heuristics for MDC have been implemented in various
packages, including Phylonet [6], iGTP [7], and Mes-
quite [8]. Optimal solutions to MDC are not guaranteed
to be statistically consistent, meaning that even with
true trees for an unboundedly large number of genes,
the species tree optimizing the MDC criterion may not
converge to the true tree [9]. Similarly, standard consen-
sus tree methods have been shown to not be statistically
consistent [10] (however, see [11,12]).
Alternative techniques that are based upon statistical
models for ILS include GLASS [13], STEM [14],
*BEAST [15], BEST [16], and BUCKy [17,18] (see the
review article of Degnan and Rosenberg [19] for more
on these methods). GLASS is a polynomial time dis-
tance-based method (available in the Phylonet package
[6]) that is statistically consistent when all genes evolve
under the same rate; thus, when given a sufficient num-
ber of correct gene trees, GLASS will return a correct
species tree with high probability. STEM is a statistical
method that requires that all input gene trees be prop-
erly rooted, and also has statistical guarantees [14] when
the gene trees are correct. *BEAST, BEST, and BUCKy
[17] are Bayesian methods that produce a distribution of
species tree topologies based upon ILS from gene
sequence alignments; BUCKy also explicitly considers
causes of discord other than ILS (e.g., horizontal gene
transfer).
Other new methods have been developed and studied
for estimating species trees from incongruent gene trees,
among them the method by Yu et al. [20] (and available
in Phylonet) for a variant of the MDC approach, which
we call “constraint-MDC”. The input to constraint-
MDC is a set of estimated gene trees, where the trees
can be unrooted and only partially resolved, and the
objective is to find a species tree and rooted binary
refinements of these estimated gene trees so as to opti-
mize the MDC criterion with respect to the rooted bin-
ary refinements of the estimated gene trees. Thus, each
estimated gene tree topology is considered to be a con-
straint on the topology of the true gene tree.
Simulation studies to evaluate these methods have
examined performance on datasets in which the gene
trees can differ from the species tree due to ILS. These
studies have shown that the methods in Phylonet for
Constraint-MDC produce highly accurate species trees
[20], and that statistical species tree estimation (BEST,
*BEAST, BUCKy, and Stem) can produce more accurate
tree than the combined analysis method that computes
trees directly from the concatenated sequence alignment
[15]. They have also shown that *BEAST produces more
accurate trees than BEST [15], that BEST and BUCKy
produce more accurate trees than Stem [21], and that
Stem produces more accurate trees than MDC-based
analyses [22]. However, all these studies are substantially
limited because of the restriction to small datasets (with
at most 17 taxa), the use of only substitutions (i.e., no
indels) in the sequence evolution models, and the limita-
tion to ILS for causes of incongruence. A recent study
[23] addressed this last limitation, and compared BEST
and BUCKy on datasets in which the gene trees could
differ from the species tree due to HGT (horizontal
gene transfer) as well as ILS, and found cases where
BUCKy gave more accurate reconstructions.
However, the other restrictions are still too limiting,
for the following reasons. First, the restriction to small
datasets does not allow us to evaluate relative perfor-
mance on larger datasets, and does not help us under-
stand the computational limitations of the methods,
some of which are quite intensive. The restriction to
substitution-only sequence evolution models means that
alignments do not need to be estimated, and this
reduces errors in estimated gene trees (especially for
large datasets [24]). The two conditions together make
accurate gene tree estimation easier than for the general
case, and especially easier than for larger datasets with
high rates of indels and substitutions for which accurate
alignment estimation is particularly challenging.
In this paper we report on a simulation study using
ROSE [25] in which we explore the performance of a
large number of species tree estimation methods on
nucleotide sequence datasets with 17 to 500 taxa that
evolve with substitutions as well as indels. We report
results for two experiments. The first experiment
explored performance on datasets with multiple genes
on 17 or 100 taxa in which the true gene trees can differ
from the true species tree (and hence from each other).
In the second experiment, we explored performance on
datasets with multiple genes on 100 and 500 taxa in
which the true gene trees are topologically identical but
can have different branch lengths. Thus, the first experi-
ment evaluates performance when the estimated gene
trees can differ due to ILS as well as estimation error,
while the second experiment focuses on performance
when all incongruence between estimated gene trees is
due to estimation error.
Our simulation protocol is substantially more complex
(and more realistic) than most prior studies. Except for
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the 17-taxon datasets (the same ones used in [20], and
which evolve under the Jukes-Cantor [26] model, a sim-
ple substitution-only model in which all substitutions
are equally likely), all our datasets evolve under a model
that includes indels (insertions and deletions) as well as
substitutions. We use a more general substitution
model, GTR+Gamma (the General Time Reversible
model) [27], using GTR+Gamma parameters estimated
for a biological dataset (see [28] for details for this simu-
lation model), instead of Jukes-Cantor. We examine
100- and 500-taxon datasets, thus greatly exceeding the
maximum taxon dataset size (17) used in prior studies.
For datasets that evolve with indels, we estimate align-
ments using the default setting for MAFFT v. 6.717b
[29], a multiple sequence alignment method that is
established to be among the most accurate [24,28]. We
estimate gene trees using the default setting for Fas-
tTree [30] v. 2.1.3 to produce a fast and approximate
solution to maximum likelihood under GTR+Gamma.
We estimate distributions of gene trees using the
default setting for RAxML [31] v. 7.2.6 with 100 rapid
bootstrap replicates and a Bayesian method (MrBayes
[32] v. 3.1.2). The RAxML analysis includes a “best” ML
tree resulting from its search, as well as a set of gene
trees, allowing us to produce bootstrap support values
for the edges of its best tree. For our default MrBayes
analysis, we ran MrBayes for 1,000,000 generations with
a burn-in of 25% under the GTR+Gamma+I model; all
other options were left as defaults. With two runs and a
sampling ratio of 1:100, this is designed to produce
15,000 trees per gene sequence alignment input. We
varied the number of MCMC iterations used within
MrBayes analyses, and we also varied the number of the
sampled trees from the MrBayes analyses used in the
BUCKy analyses.
Although MrBayes and RAxML with rapid bootstrap-
ping produce a sample of different trees, we also use
them to produce point estimates of the gene tree for
those species tree estimation methods that require single
trees for each gene. In the case of the MrBayes (MB)
analysis, we output the majority consensus tree (MB-
maj) (that is, the tree containing all the splits that
appear in more than half of the trees that are sampled),
and the maximum a posteriori probability (MB-map)
tree. For the RAxML analysis, we use RAxML-75%, the
75%-bootstrap tree (i.e., the best ML tree found by
RAxML during the bootstrap search, with all branches
with support below 75% contracted). Finally, FastTree
outputs support values for every branch in the trees it
produces; thus, we can also use FT-75%, the tree pro-
duced by contracting all branches with support less than
75% in the FastTree output. Note that the MP-maj,
RAxML-75%, and FT-75% trees are not likely to be fully
resolved; therefore, these point estimations of gene trees
can only be used with species tree estimation methods
that permit unresolved gene tree inputs.
We explore seven methods for estimating species trees
from estimated gene trees or gene tree distributions.
Four of these are based upon ILS, and include Glass
(from Phylonet v. 2.3), Phylonet-MDC v. 2.3 (here called
“Phylonet”), iGTP-MDC v. 1.1, and BUCKy v. 1.4.0. The
other three methods are Greedy, iGTP-Dup v. 1.1 and
iGTP-Duploss v. 1.1. All of these methods, except
BUCKy, take as input a single tree for each gene. In
contrast, BUCKy operates in two steps: first it uses a
technique (the default is MrBayes) to produce a distri-
bution of estimated gene trees for each gene, and then
it uses these distributions to infer the species tree. In
fact, though, BUCKy produces two different trees–the
“concordance” tree (which we refer to as “BUCKy-con”)
and the population tree (which we refer to as “BUCKy-
pop”) [18]. The key difference between these two out-
puts is that the population tree is based upon a statisti-
cal model for incomplete lineage sorting while the
concordance tree is not, and thus the concordance tree
is designed to be used under more general conditions
than ILS. The three iGTP methods (iGTP-mdc, iGTP-
dup, and iGTP-duploss) each uses the same basic algo-
rithmic search strategy within iGTP but seek to opti-
mize different criteria (the number of deep coalescences,
number of duplications, or number of duplications and
losses, respectively). Finally, “Greedy” is the greedy con-
sensus technique (also called the “extended majority”
consensus) using PAUP* [33] v. 4.0b10; it begins by
computing the majority consensus (the tree whose edge-
induced taxon bipartitions are those that appear in
more than half of the input trees), and then adds bipar-
titions (if compatible) to the consensus tree, in an order
reflecting the frequency with which each bipartition
appears. Note that Phylonet and Greedy can be applied
to incompletely resolved gene trees, and that when we
use Phylonet on unresolved gene trees, it attempts to
find optimal solutions to the Constraint-MDC problem.
As discussed earlier, we produce incompletely resolved
gene tree estimations either by contracting low support
branches in fully resolved estimated gene trees, or by
computing the majority consensus tree of the distribu-
tion produced by MrBayes.
We describe methods for species tree estimation by
indicating the technique used to estimate the gene trees
(or their distributions) and the technique used to com-
pute the species tree from the gene trees. For example,
Greedy(FT-75%) refers to the method that computes the
FT-75% tree on every gene sequence alignment, and
then combines these (potentially unresolved) trees using
Greedy. Similarly, BUCKy-pop(MB-spa) refers to
BUCKy-pop run on a sparse sample of the MrBayes dis-
tributions for each gene, BUCKy-con(MB-full) refers to
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BUCKy-con run on the full sample of the MrBayes dis-
tributions, and Phylonet(MB-map) refers to Phylonet
run on the MAP trees from the MrBayes distributions.
Not all species trees we compute are fully resolved;
hence, the Robinson-Foulds distance (i.e., the bipartition
distance), is inappropriate for evaluating accuracy, as it
is biased in favor of unresolved trees [34]. Therefore, we
report tree error using the missing branch rate, which is
the proportion of internal branches in the true tree
defining bipartitions that are missing in the estimated
tree, also known as the “false negative” (FN) rate. How-
ever, many of the estimated species trees are fully
resolved, and for these trees, this measure is identical to
the Robinson-Foulds metric. These error rates range
from 0.0 - 1.0, with error of 0.0 indicating that the esti-
mated tree is identical to the true tree.
Results
Computational issues
We began by exploring the computational performance
of the methods we studied on 12 100-taxon datasets,
half with 25 genes and half with 50 genes. These studies
showed that these different pipelines (estimate gene
trees or distributions on gene trees, then use these to
estimate the species tree) vary substantially in terms of
computational effort.
The most computationally intensive methods we
explored use MrBayes or RAxML to estimate distribu-
tions on gene trees, but MrBayes analyses are particu-
larly expensive. Our analyses (data not shown)
indicated that enforcing a requirement that all
MrBayes analyses reach convergence was not achieved
on any dataset we examined, even after at least a week
for each alignment (and more than two weeks for
some alignments). Therefore, each 17-taxon 32-gene
dataset we examined could easily require a year (per-
haps several years) of analysis in order for each
MrBayes analysis to reach convergence.
Restricting the MrBayes runs so that each gene is ana-
lyzed in at most a day greatly reduces the running time,
and allows the first step (computing gene tree distribu-
tions for each gene) to complete in as many days as
there are genes (i.e., about a month for datasets with 32
genes, under two months for datasets with 50 genes).
These analyses will still be computationally intensive,
but not as intensive as waiting for all MrBayes analyses
to converge. However, early terminations of MrBayes
analyses are likely to make the analyses “invalid”, and
potentially therefore reduce the accuracy of the resultant
estimated species phylogeny. RAxML with bootstrapping
can also be computationally intensive, so that analyses
of single 100-taxon datasets with 1000 bootstrap repli-
cates took on average almost 10 hours, making an analy-
sis of 50 genes require 20 days just to obtain the initial
set of tree distributions. Limiting RAxML to only 100
bootstrap replicates greatly reduces the running time to
1.5 hours on average per sequence alignment with 100
taxa, thus making it possible to obtain RAxML distribu-
tions on 50 genes in about 3 days.
The only computationally intensive method for esti-
mating species trees from gene trees is BUCKy (all
others complete extremely quickly). BUCKy’s computa-
tional challenges are very much impacted by the total
number of taxa and total number of trees in its input.
We compared BUCKy analyses based upon sparse sam-
plings (at most 2000 trees per gene) from the MrBayes
distributions as input to BUCKy, in comparison to lar-
ger numbers of trees (7000 to 15,000 per gene) on six
100-taxon datasets with 25 and 50 genes. This modifica-
tion resulted a tremendous reduction in the computa-
tional effort, especially for the 50 gene datasets. The
BUCKy analyses of these 50 gene datasets with this
sparse sampling of MrBayes trees completed on average
in about one day and had peak memory usage averaging
33 GB, while BUCKy analyses using the “full” MrBayes
runs averaged one week per analysis and had average
peak memory usage of 150 GB. Several of the BUCKy
analyses of the full MrBayes sample used more than 200
GB of main memory, but no analysis of the sparse sam-
ple used more than 36 GB. The memory requirement
for these full MrBayes analyses is truly prohibitive, since
most investigators will not have computational resources
of this scale available, but the sparse MrBayes analyses
are computationally much less troublesome.
Except where indicated, the analyses in this study are
based upon “fast” versions of MrBayes and RAxML with
bootstrapping, as follows. MrBayes analyses were per-
formed with only 1M iterations and we used only 100
bootstrap replicates for RAxML. Under these settings,
single 100-taxon sequence alignments could be analyzed
using MrBayes in under a day and using RAxML in
about 1.5 hours. Therefore, analyses of 50 gene
sequence alignments could be performed in 1-2 months
using MrBayes and in about 3 days using RAxML.
These settings made it possible to perform analyses of
multiple datasets, each with tens of genes, in reasonable
timeframes.
The fast methods we studied are all based upon Fas-
tTree, a method that is deterministic and very fast on
even very large datasets. In our studies, even on the
500-taxon datasets with 50 genes, all the fast methods
finished in under two hours and used less than 9 MB of
peak memory.
Figure 1 gives average running times of some repre-
sentative methods on 100-taxon datasets with 25 or 50
genes, in which we ran MrBayes for only 1,000,000
iterations, and RAxML with only 100 bootstrap repli-
cates. Even with these settings, however, methods based
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upon MrBayes are computationally intensive; BUCKy
(MB-full) is the most expensive, using a month on 25
genes and close to two months on 50 genes. BUCKy
(MB-spa) shaves about 4 days off that running time.
The next slowest is BUCKy(RAxML) which finishes in
under 4 days on 25 genes and about a week on 50
genes (note that these are analyses based upon 100
bootstraps, and that analyses using 1000 bootstraps
instead of 100 would have been much slower). Finally,
the methods based upon FastTree are extremely fast,
finishing in under an hour on 25 genes and under two
hours on 50.
Evaluation of algorithm design choices
We begin the study with examining two specific algo-
rithm design choices that were made in order to
improve topological accuracy and/or running time.
Recall that Phylonet was designed to solve the MDC
problem, and that when used with incompletely resolved
gene trees, it is designed to solve the Constraint-MDC
problem. The motivation for the Constraint-MDC pro-
blem is that low support edges are often not reflective
of true history [20]. The hypothesis is that contracting
the low support edges and solving Constraint-MDC will
improve accuracy. Since FT-75% refers to the result of
contracting all edges in the FastTree output with sup-
port below 75%, the hypothesis is that Phylonet(FT-
75%) should be more accurate than Phylonet(FT). This
is what we set out to test.
We also wished to evaluate the consequences of using
only a sparse subset of the MrBayes distribution as
input for BUCKy, instead of the full distribution. The
advantage of using the sparse distribution is the
decrease in running time and memory usage (as already
noted); however, the concern is that using a sparse dis-
tribution might reduce accuracy of BUCKy analyses. We
therefore wish to determine whether there is a statistical
difference between BUCKy(MB-full) and BUCKy(MB-
sparse).
In each experiment below, we began by comparing
Phylonet(FT-75%) to Phylonet(FT) to see if there was a
statistically significant difference. For those datasets in
which we ran BUCKy(MB) analyses, we also compared
BUCKy-con(MB-full) to BUCKy-con(MB-spa) and
BUCKy-pop(MB-full) to BUCKy-pop(MB-spa). These
pairwise comparisons were performed using Wilcoxon
signed-ranks tests. Other comparisons between methods
were performed using Wilcoxon signed-ranks tests, and
then corrected for multiple tests using Bonferroni’s
correction.
Phylonet(FT) vs. Phylonet(FT-75%)
We compared Phylonet(FT) to Phylonet(FT-75%) on
every dataset we generated, and there was a statistically
significant improvement obtained in every model condi-
tion (p < 0.01 for each condition, Wilcoxon signed-rank
test). We observed a statistically significant improve-
ment of Phylonet(FT-75%) over Phylonet(FT) on all the
datasets without ILS datasets for both true and MAFFT
alignments (n = 120 for each alignment type, p = 0.011
for the 500-taxon true alignments and and p < 0.0001
for all other datasets, Wilcoxon signed rank test). For
the ILS datasets, we observed a statistically significant
improvement for all 17-taxon ILS datasets (n = 500 for
each number of genes and alignment type, p < 0.0001
Wilcoxon signed-rank test). On the ten 100-taxon ILS
datasets, we also saw a statistically significant improve-
ment of Phylonet(FT-75%) over Phylonet(FT) (p = 0.002
for the true alignments and p = 0.001 for the MAFFT
alignments).
Since Phylonet(FT-75%) shows a statistically signifi-
cant improvement over Phylonet(FT) in every model
condition, it seems likely that contracting low support










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Figure 1 Running time on 100-taxon non-ILS datasets Average running time (y-axis given in log-scale) of methods on 100-taxon non-ILS
datasets with MAFFT alignments of (A) 25 and (B) 50 genes. MrBayes performed two runs of 1M MCMC iterations in each analysis, with an
average running time of 25 hours per sequence alignment. At the end of its analysis, MrBayes reported an average standard deviation of
bipartitions at 0.065, indicating that it was far from convergence. BUCKy used 15K trees per gene for the full MrBayes distribution and 2K trees
per gene on the sparse. RAxML performed 100 bootstrap replicates under GTRCAT. BUCKy analyses on RAxML used 100 trees per gene.
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edges in FastTree trees does improve the species tree
accuracy produced by Phylonet.
BUCKy(MB-spa) vs. BUCKy(MB-full)
We now evaluate the statistical significance of changes
in tree error that result from using BUCKy to analyze a
sparse subset of the MrBayes distribution instead of the
full distribution. These comparisons were done on only
a few datasets (25 17-taxon datasets with 32 genes, 25
17-taxon datasets with 8 genes, and six 100-taxon data-
sets with 25 genes). Of these three model conditions,
there was only one condition (17 taxa with 32 genes) in
which there was any statistically significant difference
for BUCKy-con (p = 0.002, Wilcoxon signed-rank test),
and no condition that resulted in a statistically signifi-
cant change for BUCKy-pop.
This suggests that neither BUCKy-con nor BUCKy-
pop is particularly impacted by using a sparse subset of
the MrBayes distributions, and that the computational
advantages of using the sparse distributions may be
worth the risk involved in using fewer trees. However, it
is also possible that the lack of statistical significance is
a result of the small sample size, and that more exten-
sive testing will demonstrate that the difference is statis-
tically significant; thus, further research will need to
investigate the impact of sparse sampling.
Experiment 1: gene trees that can differ from the species
tree due to ILS
We continue with the experiments we performed on 17-
taxon and 100-taxon datasets where the true gene trees
can differ from the true species trees due to ILS.
17-taxon datasets
We begin the discussion with the results for 17-taxon
datasets with 8 and 32 genes per dataset. These data
evolved under Jukes-Cantor, the simplest substitution-
only model (all substitutions are equally likely), and so
there was no need to estimate the alignment on any
dataset.
We begin with a discussion of Glass’s performance.
First, Glass can be run on distance matrices estimated
directly from an alignment or from a tree computed
on an alignment. We evaluated the accuracy for trees
returned by Glass on 25 datasets, each with 32 genes
per dataset, using three different ways of calculating
distances on 25 datasets: the logdet [35] distances,
computed using DNADIST from the PHYLIP package
(v3.69) [36], calculated directly from the alignment,
and distances computed on the FastTree and MAP
tree from the MrBayes analysis. The best results were
obtained from the logdet distance matrix (66.6% FN
error) with the other two distances having much
higher error rates (76.9% for FastTree and 85.4% for
the MAP tree). These results are all very poor, indicat-
ing that although Glass gives the best results on logdet
distances, it is much worse than the other methods.
Therefore, we omit Glass from any further discussion
in this section.
Figure 2 shows results for all methods on 25 of the
17-taxon datasets with 32 genes, and we describe the
differences between 8 and 32 genes. Although relative
performance differs depending on the number of genes,
some trends are consistent across the data. First, the
topological accuracy is to a large extent predicted by the
technique used to estimate the gene trees, with methods
based upon MrBayes or RAxML distributions typically
having less error than methods that use FastTree. For
example, on 32 genes, methods based upon MrBayes
(but not including the MB-map tree) or RAxML have
error rates that range from 8.3-12.9%, while methods
based upon FastTree have error rates that range from
13.7-22.6%. On 8 genes, methods based upon MrBayes
range from 20-22.6%, methods based upon RAxML
range from 19.4-24.9%, while methods based upon Fas-
tTree range from 21.7-32.0%. Thus, there is substantial
overlap for results based upon MrBayes or RAxML (and
even FastTree can produce fairly accurate trees for 8
genes), but clearly using better methods for gene tree
estimation has an impact on the final species phylogeny.
The best performing method differs for 8 and 32 genes
(BUCKy-con(MB-full) is the most accurate for 32 genes,
and BUCKy-con(RAxML) is the most accurate on 8
genes), but in general all BUCKy analyses do very well
for both numbers of genes. Using a sparse subset of the
MrBayes distribution reduces accuracy for BUCKy-con
and BUCKy-pop under both numbers of genes, in some
cases substantially (e.g., for 32 genes, BUCKy-con(MB-
full) has 8.3% error but BUCKy-con(MB-spa) has 12.9%
error).
Among the “fast” methods (i.e., the methods that use
FastTree to estimate gene trees), Phylonet(FT-75%),
Greedy(FT), and Greedy(FT-75%) are the best three for
both numbers of genes, and iGTP-dup the least accurate
for both numbers of genes. Finally, for both numbers of
genes, the most accurate of the iGTP methods was
iGTP-duploss.
We now compare six representative methods, BUCKy-
con(MB-spa), BUCKy-con(MB-full), BUCKy-con
(RAxML), Phylonet(FT-75%), Greedy(FT-75%), and
iGTP-duploss(FT). The difference in error rate between
the best fast method and the best slow method is about
5%, which in relative terms is large – but for datasets of
this size, this is about 0.7 of an edge on average (since a
17-taxon tree has only 14 internal edges).
After using Bonferroni’s correction for multiple tests,
we observed that only one pair of representative meth-
ods (iGTP-duploss(FT) and BUCKy-con(MB-spa)) had a
statistically significant difference on 8 genes. For 32
genes, we saw some additionally statistically significant
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pairwise comparisons, all involving BUCKy-con(MB-spa)
or BUCKy-con(MB-full). However, all the other methods
could not be distinguished from each other. Further-
more, three fast methods–greedy(FT-75%), Phylonet(FT-
75%), and iGTP-duploss(FT)–were statistically indistin-
guishable from BUCKy-con(MB-spa), BUCKy-pop(MB-
spa), and BUCKy-pop(MB-full).
100-taxon datasets
For the 100-taxon datasets, in order to run the compu-
tationally intensive methods, we explored performance
on only 10 datasets, each with 25 genes. Because these
datasets are large, we only evaluated BUCKy(MB-spa),
terminating MrBayes at 1M iterations, and giving a
sparse sample of 2000 trees for each gene to BUCKy.
These datasets evolved under a model with substitutions
as well as indels, and so we discuss results for both the
true and MAFFT alignment on each dataset.
Glass, run on the logdet distance matrix computed
directly from the sequence alignments, had very high
error rates for both true and MAFFT alignments (73.4%
and 74.2%, respectively), much higher than any other
method (none of which had error rate above 9%). Error
rates did not vary much between the MAFFT and true
alignments, so that with the exception of Glass, error
rates did not change by more than half a percent.
Therefore, we focus our discuss on the results for the
true alignment, and omit results for Glass. On the true
alignments (see Fig. 3) all the methods had relatively
low error rates that varied between 5.0% and 8.8%.
Interestingly, there were several methods with error
rates in the 5.0-5.2% range, each based upon a different
technique for estimating the gene trees–BUCKy-pop
(RAxML) with 5.0%, BUCKY-con(MB-spa) with 5.2%,
and greedy(FT-75%) with 5.1% error. These observations
suggest that these gene trees were relatively easy to esti-
mate, in contrast to the 17-taxon datasets we studied
earlier, where even the most accurate species trees
based upon FastTree had distinctly higher error than
the most accurate trees based upon either RAxML or
MrBayes. Several fast methods have very good accuracy
(errors in the 5.1%-5.9% range), including Greedy(FT),
Greedy(FT-75%), and Phylonet(FT-75%), the three fast















 





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Figure 2 Missing branch rates on 17-taxon 32-gene datasets with ILS Average missing branch rates of methods on 25 17-taxon 32-gene
datasets with incomplete lineage sorting. (A) shows results for the slow methods, (B) shows results for the fast methods, and (C) shows
representative methods of both types. Bars indicate standard error.
Yang and Warnow BMC Bioinformatics 2011, 12(Suppl 9):S4
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methods that had the least error for the 17-taxon
datasets.
After correcting for multiple tests using Bonferroni’s
correction, there were no statistically significant differ-
ences between the representative methods on the true
alignments for these datasets, and only one statistically
significant difference on the MAFFT alignment (between
Phylonet(RAxML-75%) and BUCKy-pop(RAxML)).
Experiment 2: analyses when no ILS occurs
Since a systematist will not always know the cause for
incongruence between estimated gene trees, species tree
estimation methods that are designed to handle ILS
need to be able to reconstruct species trees when incon-
gruence is due to other causes. Here we examine the
case where all incongruence between estimated gene
trees is due to estimation error.
The true gene trees for these datasets have identical
topologies but different branch lengths, thus allowing us
to investigate the ability of methods to reconstruct the
true species tree from gene tree estimates when no ILS
occurs. These datasets evolved with indels as well as
substitutions, thus requiring the estimation of align-
ments for the gene sequence datasets. When alignments
are not highly accurate, however, gene trees will also
have error, leading to the estimated gene trees exhibit-
ing increased incongruence. We explored this question
on datasets with 100 and 500 taxa. Trends for 500 taxa
were very similar to those we observed for 100 taxa, and
so we focus our discussion on the 100 taxon datasets.
As before, Glass(logdet) had very high error, and we
omit Glass from further discussion. The most striking
observation is that the error rates of fast methods on
the MAFFT alignment are much higher than error rates
on the true alignment (Fig. 4) suggesting that alignment
estimation error greatly impacted gene tree estimation
error. The other general observation is that iGTP-dup
(FT) has the highest error rates of all fast methods on
both true and MAFFT. Therefore, for the rest of this
discussion, we will only address the remaining methods.
All fast methods (besides iGTP-dup(FT)) have excel-
lent accuracy on the true alignment, with error rates
that vary from 3.4-4.9%; thus, the difference between the
most accurate method (greedy(FT)) and the other fast
methods (except for iGTP-dup(FT)) is very small. How-
ever, we note that the three fast methods with best
accuracy are the usual ones – greedy(FT) with 3.4%
error followed by greedy(FT-75%) with 3.6% error and
Phylonet(FT-75%) with 4.0% error. After correcting for
multiple tests, all but two comparisons are statistically















 






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Figure 4 Missing branch rates of fast methods on 100-taxon datasets without ILS Average missing branch rate of fast methods on 120
100-taxon datasets without incomplete lineage sorting for 25 and 50 genes. (A) shows results for the true alignments and (B) shows results for
the MAFFT alignments. Bars indicate standard error.















 





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Figure 3 Missing branch rates on true alignments of 100-taxon 25-gene datasets with ILS Average missing branch rate of methods on
ten (10) 100-taxon 25-gene datasets with incomplete lineage sorting on true alignments. (A) shows results for the slow methods, (B) shows
results for the fast methods, and (C) shows results for representative methods of both types. Bars indicate standard error.
Yang and Warnow BMC Bioinformatics 2011, 12(Suppl 9):S4
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Page 8 of 12

significant; the only ones that aren’t are Greedy(FT) vs.
Greedy(FT-75%) and iGTP-duploss(FT) vs. Phylonet(FT-
75%).
The situation changes for the MAFFT alignments,
where error rates for the fast methods are much higher
(ranging from 18.0-21.4%, if we omit iGTP-dup(FT)
which has 29% error), and the differences between
methods somewhat greater. On these alignments, the
most accurate method is Greedy(FT) at 18.0%, followed
by iGTP-duploss at 18.4%, and then by Greedy(FT-75%)
at 18.5%. Phylonet(FT-75%) is in fourth place with
20.0% error. Thus, the results for the MAFFT alignment
are similar, but show greater differences between meth-
ods, and also show that iGTP-duploss(FT) can give very
good results as well. After correcting for multiple tests,
we find that the top three methods, Greedy(FT), Greedy
(FT-75%), and iGTP-duploss(FT), cannot be distin-
guished statistically, nor can iGTP-mdc(FT) be distin-
guished from Phylonet(FT-75%) or Phylonet(FT).
In order to evaluate the computationally intensive
methods, we used a subset of 12 datasets (half with true
alignments and half with MAFFT alignments, and with
half on 25 genes and half on 50 genes). Average error
rates on the six datasets with the true alignment ranged
from 2.2-3.0% when based upon MrBayes distributions
(full or sparse), from 2.7-4.5% when based upon RAxML
bootstrapping analyses, and from 3.3-7.0% when based
upon FastTree (see Fig. 5). Thus, using MrBayes and
RAxML instead of FastTree did improve the error, but
not dramatically. The best accuracy for methods that
use MrBayes was obtained by Greedy(MB-maj) (2.2%
FN), followed closely by BUCKy-con(MB) at 2.5%. The
best accuracy for methods based upon RAxML was
BUCKy-pop(RAxML) at 2.7% FN, followed closely by
BUCKy-con(RAxML) at 2.8%. The most accurate meth-
ods that use FastTree were Phylonet(FT-75%), Greedy
(FT-75%), and Greedy(FT), with error rates of 3.5%,
3.5%, and 3.3%, respectively. iGTP-duploss(FT) had the
lowest error of the three iGTP methods (3.7% FN rate),
and iGTP-dup(FT) had the worst accuracy of all
methods (7.0% FN rate). Not surprisingly, after correct-
ing for multiple tests, none of the differences were sta-
tistically significant.
Results for the six datasets with the MAFFT alignment
were much higher, but showed similar relative perfor-
mance (data not shown). The best results for MrBayes
analyses were obtained by BUCKy-con(MB-full) (14.0%),
the best results for RAxML-based analyses were
obtained by BUCKy-con(RAxML) (also at 14%), and the
best results for FastTree-based analyses were obtained
by Greedy(FT-75%) (at 14.8% FN rate). Here, too, iGTP-
dup(FT) had the worst accuracy (29.5% FN rate) of all
methods, and iGTP-duploss(FT) had the least error of
all three iGTP methods (15.3% FN rate). Again, not sur-
prisingly, after correcting for multiple tests, none of
these differences were statistically significant.
Overall summary of performance
The experiments we reported have datasets that range
in terms of the causes for incongruence between esti-
mated gene trees (some involve ILS, while others only
involve estimation error), rates of evolution (the 17-
taxon and 100-taxon non-ILS datasets have higher rates
than the 100-taxon ILS datasets), presence of indels,
number of taxa, and type of alignment (true or
MAFFT). Thus, the relative performance between meth-
ods varies with the models. However, certain trends
hold throughout.
The first observation is that BUCKy analyses of
MrBayes or RAxML distributions produces highly accu-
rate trees, either tied with the best or close to the best,
even for the suboptimal way in which we ran these
methods (stopping MrBayes analyses well before conver-
gence, using only 100 bootstrap replicates for RAxML,
and only using a sparse subset of the full MrBayes
distributions).
The second observation is that several fast methods
(notably, Greedy(FT-75%), Phylonet(FT-75%), and
Greedy(FT)) provide very good results, coming close to
BUCKy analyses of MrBayes and RAxML distributions















 





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Figure 5 Missing branch rates on true alignments for 100-taxon datasets without ILS Average missing branch rate of methods on six (6)
100-taxon datasets without incomplete lineage sorting on true alignments for 25 and 50 genes. (A) shows results for the slow methods, (B)
shows results for the fast methods, and (C) shows results for representative methods of both types. Bars indicate standard error.
Yang and Warnow BMC Bioinformatics 2011, 12(Suppl 9):S4
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(often without any statistically significant differences to
these methods), and with greatly reduced computational
requirements. Furthermore, these fast trees have very
low computational requirements, completing in at most
two hours and with peak memory usage of at most 9
MB, even on our largest datasets containing 50 genes
and 500 taxa. Therefore, there are feasible alternatives
to methods like BUCKy, which offer statistically-based
estimation and high accuracy but at a computational
cost that may be prohibitive.
The fast methods we studied are all based upon
FastTree, a heuristic for ML that uses a deterministic
hill-climbing heuristic to find locally optimal solu-
tions to ML, and thus is likely to end up “stuck” in
local optima. It is therefore possible that even better
accuracy might be obtained, albeit at a computational
cost. The remaining observations have to do with
algorithm design. First, our study shows that methods,
like Phylonet and BUCKy, that by design explicitly
accommodate error in the input gene trees can pro-
duce more accurate trees than methods that assume
all the input gene trees are correct. We have also
shown that modifications to MrBayes (such as sparsi-
fication of its output distribution) can be made with-
out compromising the accuracy of BUCKy’s estimated
trees. These, and other approaches, could easily result
in additional improvements for species tree estima-
tion methods.
Conclusions
Our study evaluating the computationally intensive
methods was necessarily limited in number and in
scope. Nevertheless, the experiments we performed
show that some very fast methods for estimating species
trees from gene sequence alignments can come close to
the accuracy of the best methods, while taking dramati-
cally less time (two hours instead of months of analysis),
and with much smaller peak memory requirements (a
few MB instead of potentially hundreds of GB). Further-
more, while we observed differences in accuracy
between methods, some of which were substantial, the
data suggests that in many cases, the differences
between the best fast methods and the best computa-
tionally intensive methods we studied are not statisti-
cally significant. Additional experiments are clearly
needed in order to evaluate whether this is true, or
whether this is a consequence of the limited number of
datasets we evaluated. It is also important to determine
if these trends hold generally, or if there are conditions
where the computationally intensive methods offer sub-
stantially improved accuracy.
Our study has many ramifications for simulation stu-
dies. Because alignment estimation error has an impact
on both the absolute and relative performance of
methods, future simulation studies should include indels
in their models and use both estimated and true align-
ments. Gene tree estimation error has a very large
impact on species tree estimation, and so the best meth-
ods for estimating gene trees should be used. This study
shows that relative and absolute performance is also
impacted by the number of taxa, and so datasets with
larger numbers of taxa ought to be included. Finally,
since simple methods (like the greedy consensus of esti-
mated gene trees) are often quite accurate, these meth-
ods should be included in the methods that are
compared.
Although we initiated the study in order to evaluate
methods for estimating species trees in the presence of
ILS, the observations in this study are also relevant to
estimating species trees in the presence of gene duplica-
tion and loss. In particular, the poor performance of
iGTP-dup for non-ILS datasets, in comparison to simple
methods like Greedy, suggests that there is need for
substantial improvement in methods for estimating spe-
cies trees in the presence of gene duplication and loss.
Perhaps the improvements for species tree estimation
we observed by developing methods that explicitly han-
dle error (either in a Bayesian framework, or by con-
tracting low support edges in estimated gene trees) can
be obtained for gene duplication and loss scenarios as
well.
Materials and methods
All datasets (true trees and true alignments) used in this
study are available at http://www.cs.utexas.edu/users/
phylo/datasets/ILS.
Simulated datasets
17-taxon datasets with ILS
The 17-taxon datasets with 8 and 32 genes are from
[37], and were provided to us by Yun Yu and Luay
Nakhleh. These datasets were generated by simulating
Jukes-Cantor evolution (i.e., only with substitutions)
down gene trees that evolved within species trees under
a coalescent process, and each alignment contained
DNA sequences of length 1000.
100-taxon datasets with ILS
We simulated ten 100-taxon 25-gene datasets that
evolve with ILS as follows. A single 100-taxon model
tree from [28] was used as the species tree. We uni-
formly scaled down its branch lengths by 0.05 to pro-
duce a model tree with short enough branches so that
ILS would occur. We evolved 25 trees within this spe-
cies tree using MS [38], starting with an island model of
100 separate taxa, and then joining the lineages back-
wards in time based on the species tree. The MS com-
mand we used is:
ms 100 25 -T -I 100 1 1 ... 1 -ej <t> <from> <to> ...
Yang and Warnow BMC Bioinformatics 2011, 12(Suppl 9):S4
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This produces 25 gene trees, each with branch
lengths. We simulated sequence evolution down each
gene tree under a GTR+Gamma+Gap model (with para-
meters derived from the model tree in [28]) using
ROSE, with the root sequence having length 1000. The
GTR+Gamma+Gap parameters of model trees in [28]
are based upon biological datasets, and the tree topolo-
gies and branch lengths are based upon a random birth-
death model, and are generated using r8s [39].
100- and 500-taxon datasets without ILS
We used model species trees from [28] (see discussion
above). Each dataset contained 25 or 50 genes. Half of
the datasets were generated by model trees that were
identical to the species tree, and half were generated by
model trees that were identical topologically but had dif-
ferent branch lengths. To produce the modified gene
trees, each branch length in the species tree was multi-
plied by a different random number with expected value
1, and then rescaled so that all trees had the same total
treelength. We then generated sequences on each model
gene tree under GTR+Gamma+Gap using ROSE [25],
using the model parameters given in [28], and with
sequence length 1000 at the root.
Acknowledgements
This research was supported by the National Science Foundation (DEB-
0733029 and DBI-1062335) and by a fellowship from the John Simon
Guggenheim Foundation to TW. We thank Luay Nakhleh and Yun Yu for
making the 17-taxon datasets available to us for this study. We thank Cecile
Ané, Luay Nakhleh, Noah Rosenberg, and the anonymous referees for very
helpful suggestions, and Steve Evans for discussions about statistical tests.
This article has been published as part of BMC Bioinformatics Volume 12
Supplement 9, 2011: Proceedings of the Ninth Annual Research in
Computational Molecular Biology (RECOMB) Satellite Workshop on
Comparative Genomics. The full contents of the supplement are available
online at http://www.biomedcentral.com/1471-2105/12?issue=S9.
Authors’ contributions
TW conceived and designed the study; JY implemented the analysis tools,
produced the data, and created the figures and tables; TW and JY analyzed
the data; TW wrote the paper.
Competing Interests
The authors declare that they have no competing interests.
Published: 5 October 2011
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doi:10.1186/1471-2105-12-S9-S4
Cite this article as: Yang and Warnow: Fast and accurate methods for
phylogenomic analyses. BMC Bioinformatics 2011 12(Suppl 9):S4.
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Yang and Warnow BMC Bioinformatics 2011, 12(Suppl 9):S4
http://www.biomedcentral.com/1471-2105/12/S9/S4
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