Syst. Biol. 63(1):31–54, 2014
© The Author(s) 2013. Published by Oxford University Press, on behalf of the Society of Systematic Biologists. All rights reserved.
For Permissions, please email: [email protected]
DOI:10.1093/sysbio/syt058
Advance Access publication August 20, 2013
Accelerated Rate of Molecular Evolution for Vittarioid Ferns is Strong
and Not Driven by Selection
CARL J. R OTHFELS1,2,∗ AND ERIC SCHUETTPELZ3,4
1 Department of Biology, Duke University, Box 90338, Durham, NC 27708, USA; 2 Department of Zoology, University of British Columbia,
#4200-6270 University Blvd., Vancouver, BC V6T 1Z4, Canada; 3 Department of Biology and Marine Biology, University of North Carolina Wilmington,
601 South College Road, Wilmington, NC 28403, USA; and 4 Department of Botany (MRC 166), National Museum of Natural History, Smithsonian
Institution, PO Box 37012, Washington DC 20013-7012, USA
∗ Correspondence to be sent to: Department of Zoology, University of British Columbia, #4200-6270 University Blvd., Vancouver, BC V6T 1Z4, Canada;
E-mail: [email protected].
Received 16 January 2013; reviews returned 26 March 2013; accepted 15 August 2013
Associate Editor: Roberta Mason-Gamer
Molecular evolutionary rate heterogeneity can take
many forms, ranging from variation among nucleotide
substitution types (Kimura 1980) to variation among
sites (Yang 1996), loci (Wolfe et al. 1989b; Small et al.
1998), genomic regions (Wolfe et al. 1989a), and genomic
compartments (Wolfe et al. 1987; Baer et al. 2007).
Perhaps most vexing, however, is lineage-specific rate
heterogeneity, whereby some lineages have significantly
different rates of molecular evolution than do their
close relatives. Such violations of a molecular clock
(Zuckerkandl and Pauling 1962, 1965) are ubiquitous
across the tree of life and have been characterized within
vertebrates (Bromham 2002; Hoegg et al. 2004; BinindaEmonds 2007), invertebrates (Hebert et al. 2002; Schon
et al. 2003; Shao et al. 2003; Thomas et al. 2006; Singh
et al. 2009), fungi (Lutzoni and Pagel 1997; Moncalvo
et al. 2000; Woolfit and Bromham 2003; Zoller and
Lutzoni 2003; Lumbsch et al. 2008), algae (Zoller and
Lutzoni 2003), bacteria (Woolfit and Bromham 2003),
liverworts (Lewis et al. 1997), seed plants (Bousquet et al.
1992; Muse 2000; Davies et al. 2004; McCoy et al. 2008;
Smith and Donoghue 2008; Xiang et al. 2008), and ferns
(Soltis et al. 2002; Des Marais et al. 2003; Schneider
et al. 2004; Schuettpelz and Pryer 2006; Korall et al.
2010; Li et al. 2011; Rothfels et al. 2012). Consequently,
this phenomenon has important implications for our
understanding of evolution, as well as for our ability to
infer and date evolutionary events.
Much of the research into molecular evolutionary
rate heterogeneity has focused on finding a correlation
between the rate of molecular evolution and some
natural history attribute of the organism in question,
using multiple independent comparisons (reviewed in
Lanfear et al. 2010). However, cases limited to a single
potential rate change, or where obvious candidate
correlated traits are lacking, are still tractable within a
model selection framework. Using this approach one
can ask if a potential rate discrepancy is significant by
comparing models that permit particular groups to have
individual rates (local clocks) to models that enforce a
global clock. This approach provides an elegant solution
to problems associated with the lack of independence
among branches and differing taxon sampling density,
does not require the a priori identification of a potential
correlated trait of interest, and has enjoyed considerable
popularity (Lutzoni and Pagel 1997, their “method 2”;
Yoder and Yang 2000; Bromham and Woolfit 2004;
Lanfear et al. 2007; Korall et al. 2010; Lanfear 2010;
Neiman et al. 2010); however, note the caveats described
by (Lanfear, 2010).
In this study, we use sequence data from all three plant
genomic compartments—nuclear, mitochondrial, and
plastid—to probe for signatures of rate heterogeneity
in a clade of ferns. We first utilize a maximum
likelihood (ML) method to look for rate heterogeneity
at the nucleotide level, which requires the a priori
Downloaded from http://sysbio.oxfordjournals.org/ by Carl Rothfels on January 9, 2014
Abstract.—Molecular evolutionary rate heterogeneity—the violation of a molecular clock—is a prominent feature of many
phylogenetic data sets. It has particular importance to systematists not only because of its biological implications, but also
for its practical effects on our ability to infer and date evolutionary events. Here we show, using both maximum likelihood
and Bayesian approaches, that a remarkably strong increase in substitution rate in the vittarioid ferns is consistent across
the nuclear and plastid genomes. Contrary to some expectations, this rate increase is not due to selective forces acting at
the protein level on our focal loci. The vittarioids bear no signature of the change in the relative strengths of selection and
drift that one would expect if the rate increase was caused by altered post-mutation fixation rates. Instead, the substitution
rate increase appears to stem from an elevated supply of mutations, perhaps limited to the vittarioid ancestral branch.
This generalized rate increase is accompanied by extensive fine-scale heterogeneity in rates across loci, genomes, and taxa.
Our analyses demonstrate the effectiveness and flexibility of trait-free investigations of rate heterogeneity within a modelselection framework, emphasize the importance of explicit tests for signatures of selection prior to invoking selection-related
or demography-based explanations for patterns of rate variation, and illustrate some unexpected nuances in the behavior
of relaxed clock methods for modeling rate heterogeneity, with implications for our ability to confidently date divergence
events. In addition, our data provide strong support for the monophyly of Adiantum, and for the position of Calciphilopteris in
the cheilanthoid ferns, two relationships for which convincing support was previously lacking. [Adiantum; Calciphilopteris;
codon models; divergence time dating; local clocks; model selection; molecular clock; mutation rate; nucleotide substitution
rate; Pteridaceae; rate heterogeneity; relaxed clocks; trigenomic analyses.]
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SYSTEMATIC BIOLOGY
MATERIALS AND METHODS
Taxon Sampling
We sampled 26 species, including 8 species from
each focal clade within the Pteridaceae (cheilanthoids,
vittarioids, and Adiantum), and 2 outgroup species
[13:56 4/12/2013 Sysbio-syt058.tex]
(Cryptogramma crispa and Pityrogramma austroamericana;
Appendix 1). The selected species span the phylogenetic
diversity of each clade, with at least one representative
included from each major subclade and were selected to
additionally capture the branch length variation in each
clade (Crane et al. 1995; Schuettpelz et al. 2007; Windham
et al. 2009; Lu et al. 2011b). Equal sampling across clades
was adopted to avoid the potential for node-density
effect artifacts (Fitch and Beintema 1990; Bromham 2002;
Venditti et al. 2006; Hugall and Lee 2007). The likelihood
of biases being introduced due to punctuated evolution
associated with speciation events (Pagel et al. 2006) is
also minimized, given that vittarioids—hypothesized to
have the fastest rates—constitute the smallest clade.
DNA Extraction, Amplification, and Sequencing
DNA was extracted from silica-dried leaf tissue
or herbarium fragments in the Fern Lab Database
(fernlab.biology.duke.edu) archive. Sequences were
obtained for three plastid loci (atpA, atpB, rbcL),
two mitochondrial loci (atp1, nad5), and one nuclear
locus (gapCp); note that plastids and mitochondria are
maternally inherited in this group of ferns (Gastony and
Yatskievych 1992). The three plastid loci were amplified
and sequenced using previously published protocols
(Pryer et al. 2004; Schuettpelz et al. 2006).
Most mitochondrial atp1 sequences were obtained
using primers F83-atp1 and R725-atp1 (Wikström
and Pryer 2005; full data for all primers used are
available in Supplementary Table S1), following the
protocol of Wikström and Pryer (2005). When reactions
failed, we amplified and sequenced atp1 with primers
CRATP1F1 and CRATP1R1, using a standard reaction
mix (Schuettpelz and Pryer 2007). Our thermal cycling
program consisted of an initial denaturation step (94◦ C
for 3 min), followed by 35 denaturation, annealing, and
elongation cycles (94◦ C for 45 s, 55◦ C for 30 s, 72◦ C
for 2 min), and a final elongation step (72◦ C for 10
min). Taxa with a type II intron (Cryptogramma and
Pityrogramma, see Results section) required additional
sequencing primers F328-atp1, F411-atp1, and R348-atp1
(Wikström and Pryer 2005).
Initial amplifications of nad5 were performed as
for atp1, but with primers K and L (Vangerow
et al. 1999) and a modified thermal cycling program
consisting of an initial denaturation step (94◦ C for
3 min), followed by 40 denaturation, annealing, and
elongation cycles (94◦ C for 45 s, 45◦ C for 30 s, 72◦ C
for 3 min), and a final elongation step (72◦ C for 10
min). The nad5 amplifications tended to be weak and
often resulted in multiple bands. These PCR products
were therefore cloned, and resulting colonies amplified,
following the protocol described by Schuettpelz et al.
(2008). We sequenced the colony amplifications using
primers K, L, KLEX, FLIN, LISEX, M13F, and M13R
(V.Knoop, unpublished data; Invitrogen; Vangerow et al.
1999). Particularly recalcitrant taxa were amplified
using primers CRNAD5F1 and CRNAD5R1 (using the
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selection of models to be compared from among a
near-infinite array of possible models. To explore the
impact of this requirement, we then employ a Bayesian
framework, utilizing two relaxed clock models. These
models explicitly incorporate rate variation across the
tree without the a priori division of the tree into
particular clades or classes. Finally, we conduct a series
of codon-based ML analyses to distinguish between
mutation-driven and fixation-driven causes of elevated
substitution rate.
Our focal group consists of the cheilanthoid ferns
(cheilanthoids), the genus Adiantum, and the vittarioid
ferns (vittarioids) in the family Pteridaceae. Each of
these subclades is fairly large (approximately 400, 200,
and 100 species, respectively; Crane 1997; Schuettpelz
et al. 2007; Lu et al. 2011b), and moderately old. The
divergence between the cheilanthoids and the vittarioids
+ Adiantum (collectively referred to as the adiantoids) is
estimated at approximately 90 Ma, and that between the
vittarioids and Adiantum at about 70 Ma (Schuettpelz
and Pryer 2009). Earlier molecular analyses inferred
considerably longer branch lengths for the vittarioids
than for the remainder of the Pteridaceae (Schuettpelz
and Pryer 2007; Schuettpelz et al. 2007), suggesting an
increase in the vittarioid rate of molecular evolution. This
increase may well be coupled with other changes, as the
vittarioids are very different from their relatives in terms
of their ecology, population biology, and morphology.
The vittarioids are obligate epiphytes in tropical habitats,
have dramatically simplified leaf morphologies (many
species are colloquially termed “shoestring ferns” and
others do not exceed lengths of a centimeter or two
or widths of more than two millimeters), and have
long-lived gametophytes that are capable of asexual
propagation via gemmae (Farrar 1974; Crane et al. 1995).
Here, we assess the nature and degree of molecular
rate heterogeneity in our focal group and identify
the pool of biological mechanisms that are tenable
explanations for the suggested vittarioid rate increase.
In doing so, we provide an example of a focused, traitfree analysis of molecular rates, demonstrate nuances
in the behavior of recently developed models that
accommodate rate variation, and show the utility and
importance of associated analyses of selection. Our
study aims to determine: (i) whether vittarioids have
elevated rates of molecular evolution compared with
those of their closest relatives; (ii) whether observed
rate differences are comparable across loci and genomic
compartments, and consistent with possible life-history
based explanations; and (iii) whether selection drove the
patterns observed.
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[13:56 4/12/2013 Sysbio-syt058.tex]
only two random-addition-sequence starting trees. This
analysis allowed us to phylogenetically discriminate
gapCp “short” sequences from gapCp “long” and gapC
sequences (Supplementary Fig. S1). The originally
targeted gapCp “short” locus was the best represented;
sequences from the other loci were discarded, along
with the gapCp “short” sequences from taxa outside
our focal sample. Among the remaining gapCp “short”
sequences were two copies from each of the four
sampled members of the Adiantum raddianum clade,
suggesting a duplication event had occurred on its stem
branch (Supplementary Fig. S1). To yield a nuclear
data set that was maximally comparable to the plastid
and mitochondrial data sets, we removed one set of
copies (the two copies have similar branch lengths and
preliminary analyses indicated no effect of retaining one
over the other). We were left with a single gapCp “short”
sequence from each of 22 (of 26) sampled taxa (gapCp
“short” sequences could not be obtained from four
vittarioid species). For simplicity, these gapCp “short”
sequences are hereafter referred to simply as gapCp
sequences.
In total, 117 sequences were newly obtained for
this study and deposited in GenBank (Appendix 1;
Supplementary Table S2). An additional 78 previously
published sequences were used to complete our data sets
(Appendix 1; Supplementary Table S2).
Sequence Alignment and Data Set Construction
The plastid and mitochondrial loci were aligned
individually, by eye, in Mesquite v2.72 (Maddison
and Maddison 2011). Ambiguous portions of each
alignment were excluded prior to subsequent analyses.
For mitochondrial nad5, unambiguous indels were
recoded following Simmons and Ochoterena’s (2000)
simple gap recoding method, to yield an additional data
set used in the topology searches, but not in subsequent
analyses.
The intron sequences within our retained gapCp data
were significantly divergent, making by-eye alignment
unreliable. In order to infer an objective alignment for
these regions, we used BAli-Phy v2.1.0 (Suchard and
Redelings 2006; Redelings and Suchard 2007; e.g., Gaya
et al. 2011), which coestimates alignment and phylogeny
in a Bayesian framework. These analyses were run
under a seven-partition scheme (one partition for each
of the three intron and four exon regions included in
the sequenced section; Schuettpelz et al. 2008), with
topologies and branch lengths linked across partitions
(a branch length scaling parameter was included to
allow intron and exon sequences to differ in their
global rates). Substitution parameters were estimated for
the exon partitions independently from those for the
intron partitions. All partitions were analysed under a
GTR+gwF substitution model (Tavaré 1986; Goldman
and Whelan 2002), with among-site rate heterogeneity
modeled by a five-state Dirichlet process for the exons
and a three-state process for the introns. The RS07
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program described above, but with 35 cycles and an
annealing temperature of 55◦ C) and direct sequenced
with CRNAD5F1, CRNAD5F2, CRNAD5F3, CRNAD5R1,
CRNAD5R2, CRNAD5R3, and LISIN (Supplementary
Table S1).
Nuclear gapCp sequences were obtained following
the protocol of Schuettpelz et al. (2008). For hard-toamplify vittarioid species, primer ESGAPCP11R1 was
replaced with CJRGAPVITR1 for both amplification
and sequencing. Although we attempted to target
gapCp “short” sequences through visualization of the
colony amplifications on agarose gels, we also obtained
sequences from the gapC and gapCp “long” paralogs
(Schuettpelz et al. 2008). Our total pool of sequences was
thus filtered in a stepwise manner to arrive at a set of
gapCp “short” sequences for subsequent analysis. From
the sequences obtained for each taxon, we first removed
any duplicates and all those sequences containing
indels in the exons (exon length is highly conserved
in this gene family and exons with indels are almost
certainly indicative of pseudogenes; Peterson et al. 2003;
Schuettpelz et al. 2008). We then manually screened
for and removed chimaeric sequences, presumably
resulting from PCR-mediated recombination (Cronn
et al. 2002). Because of the considerable phylogenetic
depth of our study (an ingroup sample of 24 species
selected from across a clade with a crown age of
approximately 90 myr; Schuettpelz and Pryer 2009), our
goal was not to identify each of the segregating alleles,
but rather to capture all of the major copy-types present
in each accession. We therefore constructed an exononly alignment of the sequences remaining from each
sample (independently for each sample) and inferred
from that alignment maximum parsimony trees through
a branch-and-bound search in PAUP* v4.0b10 (Swofford
2002). From the unrooted most parsimonious trees (or,
when multiple trees were found, consensus trees), we
designated as distinct all clusters of sequences that
differed from their nearest neighbors by more than 10
substitutions. The use of 10 substitutions was an ad hoc
cut-off based on preliminary examinations of the trees;
other cut-off values (from 5 to 20 substitutions) gave
similar results (data not shown). From each cluster we
selected the sequence that was closest to the geometric
center of the cluster (the least apomorphic sequence) and
discarded the others.
We then constructed a large exon-only alignment
comprising our partially filtered set of new sequences,
three well-characterized sequences from the fern genus
Cystopteris, and a set of previously published sequences
of known copy type from Martin et al. (1993), MeyerGauen et al. (1994), and Schuettpelz et al. (2008). We
analysed this data set using ML in PAUP* (Swofford
2002), under a GTR+I+G model with parameters fixed
at values obtained from jModeltest 0.1.1 (Posada 2008).
This search utilized TBR branch swapping, and was
repeated 100 times from independent random-additionsequence starting trees. To assess support, we also
performed 500 ML bootstrap replicates, with the same
settings as above, but with each search performed from
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SYSTEMATIC BIOLOGY
Tree Reconstruction
We analysed each of the six single-gene data sets
(atp1, atpA, atpB, gapCp, nad5, and rbcL), as well as the
nad5 recoded indels data set, using ML and Bayesian
approaches. ML analyses of the single-gene data sets
were conducted with RAxML v7.2.6 (Stamatakis 2006),
using the GTR+G model of sequence evolution and
the option to conduct a rapid bootstrap analysis (1000
replicates) and a search for the best-scoring tree in a
single program run (Stamatakis et al. 2008). The indel
data set was analysed in a similar fashion but utilizing
BINGAMMA, a likelihood model for binary data (Lewis
2001) that accommodates rate heterogeneity. Bayesian
analyses were executed in MrBayes v3.1.1 (Ronquist and
Huelsenbeck 2003), using the GTR+G model for genes
and the STANDARD+G model for recoded indels. We
ran 4 independent runs, each with 4 chains, for 10 million
generations. We sampled trees every 1000 generations
and assessed convergence by examining the standard
deviation of split frequencies within the output and by
plotting parameter values in Tracer v1.5 (Rambaut and
Drummond 2007). We very conservatively excluded the
first 2.5 million generations from each run as the burn-in
and computed a majority rule consensus from the pooled
trees using the “sumt” command. We analysed the
combined data sets (plastid data, mitochondrial data, all
genes, all data) as above, allowing for partition-specific
parameter estimates.
Likelihood Analysis of Nucleotide Models
To investigate lineage-specific rate heterogeneity in
our data, within and among loci and across genomic
[13:56 4/12/2013 Sysbio-syt058.tex]
compartments, we adopted a model comparison
approach using the program baseml of the PAML v4.4e
package (Yang 2007). We selected eight models of
particular biological interest for comparison (Table 1),
each of which incorporates a GTR+G substitution model
with independent parameter estimates for each included
partition. Our models vary in whether branch rates
are considered to be proportional (vs. independent)
among partitions, the presence of a molecular clock,
and (if present) how such a molecular clock is
enforced. All of our analyses utilized a fixed topology—
obtained via phylogenetic analysis of our combined data
set (Fig. 1c). Because we were interested in relative
rather than absolute rates, when a timescale was
necessary, we fixed the stem age of the ingroup at 10
arbitrary time units (rate estimates are thus in units
of substitutions per site per arbitrary time unit). We
repeated each analysis 10 times, independently, to avoid
results based on suboptimal peaks in the likelihood
surface. Here, we report results from the runs with the
highest likelihoods (results from all runs are available
at the Dryad repository (doi:10.5061/dryad.c5m42),
summarized from the PAML outputs using the Python
script PAMLparser (Supplementary Appendix S1).
Three of our chosen models do not incorporate a
molecular clock. The first, bas1, is the only model
investigated that links substitution parameters across
partitions; in addition, it requires that branch lengths
be proportional across partitions (Table 1). Model bas2
is the most parameter-rich model and is equivalent to
analysing each partition independently. Only the fixed
topology is shared among partitions and branch rates
are not required to be proportional. The third clockless
model (bas4) adds a proportionality requirement. Here,
there can be faster and slower partitions, but individual
branch lengths must remain proportional.
We also examined two models in which a global
molecular clock is enforced. The more complex of the
two (bas3, Table 1) is, as in bas2, equivalent to analysing
each partition independently, but here each partition
has a global clock. The simpler model (bas5, Table
1) additionally requires a shared set of branch times
while allowing the global clock rate to vary among
partitions.
Finally, we selected three models that incorporate local
molecular clocks. The most complex of these models
(bas8, Table 1) treats each partition as fully independent,
including branch times and rates. The simpler models
both require a shared set of branch times, but differ in
how local clock rates vary from partition to partition.
One (bas7) allows each partition to have its own unique
set of clock rates. The other (bas6) requires the local
clock rates to be proportional among partitions (if a
given local clock is fast in one partition, it must be fast
in all). In our local clock analyses (models bas6, bas7,
and bas8) we chose to compare four distinct regimes
(Fig. 2). Each regime assigns a unique rate parameter
(clock) to the outgroup branches and deep ingroup
branches following the “nuisance parameter” arguments
of Lanfear (2010). The first three regimes allocate a second
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indel model (Redelings and Suchard 2007) was applied
to the three intron partitions, which shared indel
model parameters (there were no gaps within the exon
partitions, so no indel model was applied to them;
Gaya et al. 2011). Priors were set at their default
values and seven independent chains were run, each for
100,000 generations, and sampled every 10 generations.
Inspection of parameter traces (Suchard and Redelings
2006; Rambaut and Drummond 2007) indicated that
each chain converged (to the same area of parameter
space) by 8000 generations. To be conservative, we
excluded the first 10,000 generations of each run, and
pooled the remaining generations across runs before
computing the posterior. For all parameters, the pooled
effective sample sizes were >2500. The maximum
posterior decoding alignment (the alignment that has
the maximum sum of column posteriors, weighted by
the number of nucleotides in that column; Redelings,
personal communication) from each partition was used
to produce an alignment for the complete included
region of gapCp. Sites for which only one taxon had a
character state other than a gap were excluded prior
to subsequent analyses; all other sites were retained.
The alignments, and associated trees, are available in
TreeBASE (accession S14194).
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Descriptions and parameter counts for the general nucleotide substitution models used in this study. NA, not applicable. For the parameter counts: n, number of tips (taxa); p, number of
partitions in the analysis; and c, number of predefined local clocks.
a Among partitions.
2n + 2p + 4
2np+6p
np+8p
2n+10p−4
n+10p−2
n+10p+c−3
cp+n+9p−2
np+cp+7p
p−1
0
0
p−1
p−1
(p−1)+(c−1)
c(p−1)+(c−1)
p(c−1)
2n−3
p(2n−3)
p(n−1)
2n−3
n−1
n−1
n−1
p(n−1)
3
3p
3p
3p
3p
3p
3p
3p
None
None
Global
None
Global
Local
Local
Local
bas1
bas2
bas3
bas4
bas5
bas6
bas7
bas8
Shared
Independent
Independent
Independent
Independent
Independent
Independent
Independent
Proportional
Independent
NA
Proportional
NA
NA
NA
NA
NA
NA
NA
NA
NA
Proportional
Independent
Independent
NA
NA
Independent
NA
Shared
Shared
Shared
Independent
0
1
1
4
4
4
4
1
0
0
1
0
1
2
3
2
5
5p
5p
5p
5p
5p
5p
5p
p
p
p
p
p
p
p
p
Rate
scalars
Branch
lengths
Gamma
shape
Base
frequency
Exchange
clock
Clock(s)
Model
Substitution
parametersa
Branch
lengthsa
Branch
ratesa
Branch
timesa
mgene
Time parameters
Substitution parameters
baseml settings
Nucleotide models used
TABLE 1.
[13:56 4/12/2013 Sysbio-syt058.tex]
35
rate to the cheilanthoids, Adiantum, and the vittarioids,
respectively, leaving the third rate to be shared by the
remaining two clades. The fourth regime gives each of
the major clades its own rate.
For each of the eight general models, the data were
analysed according to an unpartitioned scheme, a threepartition scheme (one partition for each of the three
genomic compartments) and a six-partition scheme (one
partition for each locus). Model fit was evaluated using
the small-sample correction for the Akaike Information
Criterion (AICc: Akaike 1974; Hurvich and Tsai 1989),
which converges to the AIC as sample size increases
and has a reduced propensity for selecting unduly
parameterized models when sample size is small
(Burnham and Anderson 2004). Smaller AICc scores
indicate better fit and, as a general rule of thumb, any
model with an AICc score four or more points above
the best-fitting model has considerably less support
(Burnham and Anderson 2002). For all models, sample
size for the AICc calculation was considered to be
the number of nucleotide characters (sites) in the
alignment.
Likelihood Analysis of Codon Models
To evaluate whether any lineage-specific rate
heterogeneity might be explained by the effects of
selection (at the protein level) on our focal loci, we
also performed a series of analyses using the program
codeml of the PAML v4.4e package (Yang 2007). We
selected four codon models (Goldman and Yang
1994) of particular biological interest for comparison
(Table 2), each with a parameter () representing
the transition:transversion ratio, a second parameter
(ω) representing the nonsynonymous:synonymous
substitution ratio (i.e., dn:ds), and codon frequencies
calculated from the nucleotide frequencies at the three
codon positions. This basic model forms the foundation
for our models cod1 through cod4 (Table 2), all of
which utilize the fixed (unrooted) topology obtained
via phylogenetic analysis of our combined data set
(Fig. 1c).
The first model (cod1, Table 2) is a basic branch
model (Yang 1998; Yang and Nielsen 1998), in which the
phylogeny is divided, a priori, into groups of branches
that are each allocated their own ω parameter. We
evaluated four versions of this model, each with a
different clade regime (Fig. 2). Our second model (cod2)
is equivalent to model M2a of Wong et al. (2004) and
Yang et al. (2005) and is a basic site model (Nielsen and
Yang 1998; Yang et al. 2000), in which the likelihood
of the data is computed given a certain number of
site classes (analogous to the site classes of the gamma
distribution of rates in nucleotide models incorporating
this parameter), each of which has its own ω parameter.
Model cod2 has three site classes (with ω0 < 1; ω1 = 1;
and ω2 > 1, respectively), and four ω-related parameters
(a proportion of sites fitting ω0 , a proportion of sites
fitting ω1 , and the ω0 and ω2 parameters themselves;
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Parameter counts
Total
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a)
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b)
c)
FIGURE 1. ML phylograms. a) From the individual loci: (i) atpA; (ii) atpB; (iii) rbcL; (iv) gapCp; (v) atp1; and (vi) nad5. b) From the data combined
by compartment: (i) plastid; and (ii) mitochondrion. c) All data. Branch lengths are in substitutions/site. Bold branches are strongly supported
(≥70% ML bootstrap support and ≥0.95 posterior probability). Bootstrap support values are shown above the branch and posterior probabilities
below. Asterisks (*) indicate 100% bootstrap support or 1.0 posterior probability.
since the proportions have to sum to 1, the proportion
of sites fitting ω2 is not a free parameter, nor is the ω1
parameter fixed at 1). The third model (cod3; model M3
in codeml) is very similar, but allows ω1 to vary between
[13:56 4/12/2013 Sysbio-syt058.tex]
zero and infinity, rather than being fixed at 1, and thus
has an additional free parameter.
The final model we considered (cod4) is model D
of Bielawski and Yang (2004). This clade model is a
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37
ROTHFELS AND SCHUETTPELZ—VITTARIOID RATES
i
Outgroup
C
V
Regime 1
Regime 2
Regime 3
Regime 4
A
Outgroup
ii
C
A
Regime nu1
Regime nu2
Regime nu3
Regime nu4
Local Clock 2
Local Clock 3
Local Clock 0
Local Clock 1
FIGURE 2. Clock/clade regimes. The four “clock” (for nucleotide analyses) or “clade” (for the codon analyses) regimes used for the plastid
and mitochondrial data (i) and the nuclear data (ii). For each regime, branches of a given shade share rate or ω parameters (depending on the
analysis), whereas branches with different shades get their own individual parameters. Regimes 1–3 each have three rate or ω parameters; regime
4 has four. Clade name abbreviations follow Figure 1c.
TABLE 2.
Codon models used
Parameter counts
codeml settings
Model
ω variability
cod1
cod2
cod3
cod4
Among branches
Among sitesa
Among sitesb
Among branches and sites
Substitution parameters
model
nssites
Exchange
Codon frequency
Branch lengths
Total
2
0
0
3
NA
2
3
3
p(c+1)
5p
6p
p(c+5)
9p
9p
9p
9p
p(2n−3)
p(2n−3)
p(2n−3)
p(2n−3)
p(2n+c+7)
p(2n+11)
p(2n+12)
p(2n+c+11)
Descriptions and parameter counts for the general codon models used in this study. NA = not applicable. For the parameter counts: n, number
of tips (taxa); p, number of partitions in the analysis; c, number of predefined “clades” for the branch-site analyses.
a With two free ω parameters (ω < 1; ω = 1; ω > 1).
0
1
2
b With three free ω parameters (ω < 1; ω ≥ 0; ω > 1).
0
1
2
variation of the general branch-site family of models
(Yang and Nielsen 2002) that allow heterogeneous dn:ds
ratios across codons and also across branches of the
phylogeny. With three site classes, cod4 incorporates
two parameters corresponding to the proportion of sites
optimized under the first two site classes (as in cod2, the
third proportion is not a free parameter). The ω for the
first site class is allowed to take any value between 0 and
1; the ω for the second class can take any value between
zero and infinity. Both of these site classes are applied
across the full phylogeny. However, the ω parameter for
the third site class is independently optimized for each
of the predesignated clades and can also take any value
between zero and infinity. We ran four versions of this
[13:56 4/12/2013 Sysbio-syt058.tex]
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V
model, each under a different clade regime, as we did
for cod1 (Fig. 2).
Because is not possible to directly perform partitioned
analyses in codeml, it was necessary to run each partition
individually and sum log-likelihoods and parameter
counts. To avoid basing conclusions on results from
suboptimal likelihood peaks, we repeated each analysis
10 times independently and we report the run with the
highest likelihood (results from all runs are available at
the Dryad repository, doi:10.5061/dryad.c5m42). Data
were again summarized from the PAML outputs using
PAMLparser (Supplementary Appendix S1). Each model
was run on the unpartitioned data, under a threepartition scheme (one partition for each of the three
Page: 37
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38
genomic compartments) and a six-partition scheme (one
partition for each locus). Model fit was evaluated as for
the nucleotide models above.
RESULTS
Character Data
The single-gene alignments ranged from 1342 bp
(atpB) to 2544 bp (nad5), with the 6-gene data set
comprising 10,487 bp (Supplementary Table S3). An
additional 82 characters were obtained through the
scoring of the nad5 indels, resulting in a combined
data set of 10,569 bp. In atp1 there is a group II intron
(studied by Wikström and Pryer (2005)) that is present
in Cryptogramma and Pityrogramma but absent in all other
sampled species (apparently due to a single loss on the
branch leading to the adiantoids and cheilanthoids); this
intron was excluded prior to analysis. The nad5 group II
intron identified by Vangerow et al. (1999), however, is
present in all members of our sample, and was included
in our analyses.
Phylogeny
Among the phylogenies inferred from the six
individual loci (the indel characters were included with
the nad5 sequence characters), there are only two wellsupported conflicts, both involving atp1 (Fig. 1a(v)). This
gene places two species of Adiantum (A. peruvianum
and A. tetraphyllum) as sister to the remainder of
the ingroup, with strong support, rather than with
the other species of Adiantum. This gene also places
Rheopteris (rather than Anetium) as sister to Vittaria. These
incongruences are not the result of a misidentification
(the same extractions were used for all loci), or of a
lab error (the sequences involved are clearly adiantoid
and all sequenced members of that clade are uniquely
represented in the tree). We therefore considered the
incongruence to be due to stochastic variation in the
atp1 signal (e.g., see Weisrock 2012; Rothfels et al. 2013b),
and concatenated the loci to infer the compartment
specific (Fig. 1b) and global (Fig. 1c) ML phylograms
(see Materials and Methods section). All nodes in the
phylogeny resulting from ML analysis of the combined
data set are well supported by both ML bootstrapping
(≥ 70% bootstrap support) and by Bayesian inference
(≥ 0.95 posterior probability; Fig. 1c). This includes
strong support for each of the three major subclades
of interest—cheilanthoids, vittarioids, and Adiantum
(labeled C, V, and A, respectively; Fig. 1c)—with
Adiantum and the vittarioids sister to each other, and
that clade sister to the cheilanthoids.
Downloaded from http://sysbio.oxfordjournals.org/ by Carl Rothfels on January 9, 2014
Bayesian Analysis
To further dissect patterns of rate heterogeneity,
while avoiding the need to assign local clocks or
even a topology a priori, we analysed our data in a
Bayesian framework using BEAST v1.6.1 (Drummond
and Rambaut 2007; Drummond and Suchard 2010).
BEAST offers two relaxed clock models that are
of particular interest here: one with uncorrelated
lognormally distributed branch rates and another with
randomly assigned local clocks (Drummond et al.
2006; Drummond and Suchard 2010). The six loci (the
nad5 indel data set was not included) were analysed
individually and in combination using each of these
two models. For the partitioned analyses, substitution
parameters were unlinked across partitions, while clock
parameters and topologies were linked. Monophyly
was enforced for four taxon sets: (i) all taxa except
for Cryptogramma (in effect, rooting the tree); (ii) all
taxa except for Cryptogramma and Pityrogramma; (iii) the
cheilanthoids; and (iv) Adiantum (it was never necessary
to enforce the monophyly of the vittarioids). In all
cases, we employed a GTR+G substitution model and
a birth–death tree prior, with the average clock rate
fixed at 1.0. Priors were left at their default values
with the exception of birthDeath.meanGrowthRate,
which was given a uniform prior between 1 and 100,
and birthDeath.relativeDeathRate, which was given a
uniform prior between 0 and 2. Convergence and
effective sample sizes were assessed in Tracer v1.5
(Rambaut and Drummond 2007).
For each data set, the lognormal uncorrelated
relaxed clock (LURC) analyses were run four times
independently, for 50 million generations each, with
the chain sampled every 2000 generations. These
runs converged relatively rapidly. The first 10 million
generations were discarded (very conservatively) as
burn-in prior to summarizing the posterior. The random
local clock (RLC) analyses generally took longer to
converge and were run 7 times independently for 100
million generations, with chains sampled every 25,000
generations. Nevertheless, some individual runs failed
to converge. Of the 7 runs per data set, at least 5
converged in all cases, and the burn-in period for the
converged runs ranged from 20 million to 80 million
generations. The total post-burn-in sample sizes ranged
from 10,400 samples (for the concatenated mitochondrial
data) to 19,000 samples (for the concatenated full data).
[13:56 4/12/2013 Sysbio-syt058.tex]
VOL. 63
SYSTEMATIC BIOLOGY
Likelihood Analysis of Nucleotide Models
Optimizations of branch lengths for the individuallocus data sets (Fig. 3a–c) and the individualcompartment data sets (Fig. 3c–e) on the combined
topology reveal a clear trend toward longer branches
for the vittarioid taxa. However, this trend is not
absolute (Fig. 3a,e) and there is substantial branch length
variation within each of the major clades.
Our model comparison analyses are more
illuminating than a simple inspection of branch
lengths. The best performing model, by far, is the
most heavily parameterized (bas2), partitioned by
locus (Table 3; Fig. 4), despite a strong penalty by the
AICc. After bas2, the best fitting of the non-local clock
Page: 38
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2014
39
ROTHFELS AND SCHUETTPELZ—VITTARIOID RATES
a)
atpA
b)
atpB
rbcL
atp1
c)
nad5
d)
e)
gapCp “short”
vittarioids
cheilanthoids
Adiantum
FIGURE 3. Branch lengths optimized on consensus topology. Branch lengths of the mitochondrial loci (a), the plastid loci (b), the nuclear locus
(c), and the combined plastid (d) and combined mitochondrial (e) data, optimized on the topology from the combined data (Fig. 1c). Branch
length bars each indicate 0.03 substitutions/site/arbitrary time unit.
TABLE 3.
Model
bas1
bas3
bas1
bas2
bas3
bas4
bas5
bas1
bas2
bas3
bas4
bas5
bas6
bas6
bas6
bas6
bas7
bas7
bas7
bas7
bas8
bas8
bas8
bas8
Fit of the full data on the nucleotide models
Partitioning
None
None
By locus
By locus
By locus
By locus
By locus
By compartment
By compartment
By compartment
By compartment
By compartment
By compartment
By compartment
By compartment
By compartment
By compartment
By compartment
By compartment
By compartment
By compartment
By compartment
By compartment
By compartment
Clock Parameter
count
regimea
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
1
2
3
4
1
2
3
4
1
2
3
4
58
34
68
348
204
108
83
62
174
102
78
53
56
56
56
57
60
60
60
63
108
108
108
111
lnL
AICc
–41,813.15
–42,229.79
–41,199.80
–40,515.34
–41,156.48
–40,995.03
–41,436.10
–41,208.81
–40,722.08
–41,286.15
–41,058.03
–41,501.64
–41,361.23
–41,446.50
–41,275.96
–41,238.62
–41,350.65
–41,331.80
–41,167.16
–41,095.55
–41,121.89
–41,188.82
–41,037.67
–40,984.41
83,743.19
845,27.90
82,536.84
81,766.80
82,734.52
82,209.16
83,040.04
82,542.64
81,804.69
82,780.57
82,273.67
83,110.04
82,835.29
83,005.84
82,664.75
82,592.10
82,822.26
82,784.57
82,455.29
82,318.16
82,462.89
82,596.74
82,294.46
82,195.87
NA, not applicable.
a Clock regimes correspond to those in Figure 2.
models is bas4, which is followed by bas1, bas3, and
finally bas5 (Fig. 4). The differences in fit among these
models are dramatic. On average, each model had an
improvement of more than 300 points in AICc score
over the next best performing model—nearly two orders
of magnitude greater than the rule of thumb difference
for a “considerable” AICc improvement (Burnham
[13:56 4/12/2013 Sysbio-syt058.tex]
and Anderson 2002). The three best performing
models are all clockless (tips are not constrained to
be contemporaneous), differing from each other only
in the degree to which parameters are shared across
partitions. The best performing model (bas2) has no
shared parameters, the next best (bas4) has no shared
parameters except that branch lengths are constrained to
be proportional across partitions, and the worst fitting
of the clockless models (bas1) has proportional branch
lengths and shared substitution parameters (Table 3;
Fig. 4).
Under a given model, the unpartitioned runs had
very poor fit, and partitioning by locus (six partitions)
always resulted in better fit than did partitioning by
compartment (three partitions; Fig. 4(i)). With regard
to partitioning, the smallest AICc difference (5.80)
was for bas1, which includes relatively few additional
parameters for each new partition (Tables 1, 3) but is
nonetheless above the “considerable” improvement cutoff of four AICc points. Overall, the effect of altering
the partitioning scheme was much smaller than that
of changing the model. For example, the six-partition
version of a model never outperforms the three-partition
version of the next best model (such models differ by an
average of over 250 AICc points; Fig. 4(ii)).
Both of the local clock models (bas6 and bas7),
partitioned by compartment, fit the combined data
better than a comparable global clock model (bas5)
and worse than a comparable clockless model (bas4;
Table 3; Fig. 5). The more highly parameterized bas7
consistently outperformed bas6, which forces branch
lengths to be proportional across partitions (Fig. 5). The
effects of the different local clock regimes on the two
models are very similar (Fig. 5), with only one notable
deviation: clock regime 2 (cheilanthoids and vittarioids
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“outgroup”
31–54
40
VOL. 63
SYSTEMATIC BIOLOGY
i
ii
85000
83200
83100
bas5
AICc (smaller for better models)
84000
83500
83000
82500
83000
82800
bas3
82700
82600
bas1
82500
82300
bas4
82200
81900
82000
81800
bas2
81700
81500
a
b
bas1
c
Partitioned by
compartment
bas2
bas3
Partitioned by
locus
bas4
bas5
FIGURE 4.
Model fit of the full data on the general nucleotide models. Units are in AICc points; smaller values indicate better fit. i) Fit
of unpartitioned data (a) versus the same data partitioned by compartment (three partitions; b), and by locus (six partitions; c). ii) Fit of the
partitioned analyses. The small tree icons in part (ii) indicate whether the model is clockfree (unrooted), or has some form of molecular clock
enforced.
sharing a local clock) was a worse fit than clock regime
1 (Adiantum and vittarioids sharing a local clock) under
bas6, but a better fit under bas7. That said, local clock
regimes 1 and 2 are both very poorly performing for the
combined data and there is a strong increase in model
fit (decrease in AICc) moving to regime 3, the first to
allow the vittarioids their own clock (Fig. 2). A smaller
(but still considerable) improvement of fit is seen under
clock regime 4, which gives each of the major clades its
own clock.
Model fit for the compartment-level data, individually
optimized, reveals that much of the difference in fit
under the local clock regimes is driven by the strong
improvement in fit of the plastid data under clock
regimes 3 and 4 (Table 4; Fig. 6). The nuclear data show
a similar pattern but the mitochondrial data are very
different, fitting worst under clock regime 3 (which gives
the vittarioids their own clock, lumping Adiantum and
the cheilanthoids together), and best under regime 1
(giving cheilanthoids their own clock, Adiantum and the
vittarioids together; Table 4; Fig. 6).
[13:56 4/12/2013 Sysbio-syt058.tex]
The local clock rate estimates under clock regime 4
(each major clade given its own clock) help explain
the discrepancy in fit among the compartments. In the
plastid and nuclear genomes, the cheilanthoids have
the slowest rate, followed by Adiantum, and finally
the vittarioids, with a particularly high rate (Table 4;
Fig. 7). The vittarioids have a plastid rate that is
2.73 and 5.82 times greater than Adiantum and the
cheilanthoids, respectively. For the nuclear data, the
numbers are similar: the vittarioids are 2.46 times
faster than Adiantum and 3.08 times faster than the
cheilanthoids. The mitochondrial data, however, show
nearly identical rates for Adiantum and the vittarioids,
with both being faster than the cheilanthoids (3.16 and
3.07 times faster, respectively; Table 4; Fig. 7). The rate
increase seen for the vittarioids in the plastid and nuclear
data thus also includes Adiantum in the mitochondrial
data, explaining the better fit of the mitochondrial
data to the local clock regime that allows Adiantum
and the vittarioids to share a clock (regime 1). These
rate estimates are derived from data that, within a
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AICc (smaller for better models)
84500
31–54
2014
83200
Improvement in fit (AICc) vs. global clock
AICc (smaller for better models)
83100
83000
82900
82800
82700
82600
bas4
bas5
bas6
bas7
82500
82400
82300
82200
clock regime
2
clock regime
3
450
350
300
250
200
150
100
50
0
clock regime
4
FIGURE 5. Comparison of the fit of the local clock models (bas6 and
bas7) to the global clock (bas5) and clockfree (bas4) models. Units are
in AICc points; smaller values indicate better fit. The data under all
models are partitioned by compartment (three partitions). The clock
regimes follow Figure 2.
given compartment, were not partitioned. To ensure
that heterogeneity among codon positions within a
compartment is not biasing our estimates (Brandley et al.
2005; Shapiro et al. 2005; Lanfear et al. 2012; Rothfels
et al. 2013a), we additionally ran these analyses with
the data partitioned by codon position (one partition for
each codon position, and one for noncoding characters,
if present). The two model types (unpartitioned vs.
partitioned by codon position) gave very similar rate
estimates for all compartments (data not shown).
Likelihood Analysis of Codon Models
As with the nucleotide models, the introduction of
partitions in the codon models had a strong effect
mitochondrial
plastid
nuclear
400
clock regime
1
clock regime
2
clock regime
3
clock regime
4
FIGURE 6. Fit of the compartment data to the local clock models
(under bas8). For each combination of compartment and clock regime,
the fit scores are standardized against the fit of the same data under
the global clock model. Units are in AICc points, with larger values
indicating bigger improvements in fit for the local clock model. The
clock regimes follow Figure 2.
on AICc scores (Table 5; Fig. 8(i)). However, threepartition schemes (by compartment) generally fit better
for the codon models than do more complex six-partition
schemes (by locus; Table 5; Fig. 8(i),(ii)). That said, the
effect of the model (e.g., cod1 vs. cod2) was still much
stronger than that of the partitioning scheme (three vs.
six partitions).
The branch model (cod1)—the only model that
did not allow for differences in selection pressure
among codons—performed very poorly (at least 1500
AICc points worse than the other models; Table 5;
Fig. 8(ii)), even though it accommodates lineagespecific differences. The three remaining models each
incorporate three site classes to accommodate selection
differences among codons. The worst performing of
these site models was the simplest (cod2), which was
Downloaded from http://sysbio.oxfordjournals.org/ by Carl Rothfels on January 9, 2014
clock regime
1
TABLE 4.
41
ROTHFELS AND SCHUETTPELZ—VITTARIOID RATES
Fit of the compartment data and rate estimates under local clocks
Local clock ratesa
Partition
Plastid
Plastid
Plastid
Plastid
Mitochondrion
Mitochondrion
Mitochondrion
Mitochondrion
Nuclear
Nuclear
Nuclear
Nuclear
Clock regimeb
Parameter count
1
2
3
4
1
2
3
4
1
2
3
4
36
36
36
37
36
36
36
37
36
36
36
37
lnL
−24,722.411
−24,762.292
−24,629.441
−24,612.159
−9271.300
−9295.614
−9305.914
−9271.283
−7128.177
−7130.909
−7102.319
−7100.970
AICc
clock 0
clock 1
clock 2
49,517.480
49,597.241
49,331.538
49,299.012
18,615.601
18,664.228
18,684.829
18,617.623
14,331.477
14,336.942
14,279.761
14,279.240
0.006381
0.006618
0.006919
0.006363
0.003151
0.003283
0.003269
0.003120
0.027437
0.028789
0.027964
0.027612
0.029328
0.018745
0.008387
0.007547
0.007748
0.003935
0.005141
0.002544
0.032859
0.030989
0.020127
0.017868
0.007585
0.010018
0.025738
0.016098
0.002504
0.006357
0.006218
0.008053
0.017725
0.019710
0.051948
0.022348
clock 3
NA
NA
NA
0.043965
NA
NA
NA
0.007822
NA
NA
NA
0.055020
All values obtained using the bas8 nucleotide model. NA, not applicable.
a Rates are in number of substitutions per site per arbitrary time unit.
b Clock regimes correspond to those in Figure 2.
[13:56 4/12/2013 Sysbio-syt058.tex]
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Substitution rate (per site per time unit)
42
SYSTEMATIC BIOLOGY
0.06
plastid
mitochondrial
nuclear
0.05
0.04
0.03
0.02
0.01
0
clade 0
(outgroup)
clade 1
(cheilanth.)
clade 2
(Adiantum)
clade 3
(vittarioids)
TABLE 5.
Model
cod1
cod1
cod1
cod1
cod1
cod1
cod1
cod1
cod1
cod1
cod1
cod1
cod2
cod2
cod2
cod3
cod3
cod3
cod4
cod4
cod4
cod4
cod4
cod4
cod4
cod4
cod4
cod4
cod4
cod4
Fit of the full data on the codon models
Partitioning
By compartment
By compartment
By compartment
By compartment
By locus
By locus
By locus
By locus
None
None
None
None
By compartment
By locus
None
By compartment
By locus
None
By compartment
By compartment
By compartment
By compartment
By locus
By locus
By locus
By locus
None
None
None
None
Clade Parameter
regimea
count
1
2
3
4
1
2
3
4
1
2
3
4
NA
NA
NA
NA
NA
NA
1
2
3
4
1
2
3
4
1
2
3
4
178
178
178
181
364
364
364
370
62
62
62
63
181
370
63
184
375
64
190
190
190
193
388
388
388
394
66
66
66
67
lnL
AICc
–31,125.31
–31,124.32
–31,123.62
–31,121.95
–30,917.42
–30,917.68
–30,914.27
–30,911.70
–32,204.70
–32,198.30
–32,194.52
–32,193.72
–30,334.41
–30,133.79
–31,363.83
–30,264.73
–30,077.03
–31,331.96
–30,256.20
–30,255.01
–30,254.78
–30,255.59
–30,042.64
–30,056.63
–30,051.57
–30,051.41
–31,329.96
–31,330.26
–31,325.76
–31,324.74
62,617.53
62,615.55
62,614.16
62,617.20
62,609.87
62,610.39
62,603.57
62,612.04
64,534.72
64,521.90
64,514.35
64,514.80
61,042.12
61,056.23
62,855.01
60,909.14
60,954.07
62,793.31
60,904.87
60,902.49
60,902.02
60,910.05
60,914.93
60,942.92
60,932.79
60,946.21
62,793.40
62,794.02
62,785.02
62,785.01
NA, not applicable.
a Clade regimes correspond to those in Figure 2.
over 100 AICc points poorer than either of the other two
models. Those remaining models (cod3 and cod4) had
very similar AICc scores on the full data, regardless of
partitioning scheme (Table 5; Fig. 8).
[13:56 4/12/2013 Sysbio-syt058.tex]
Using the cod4 model, the three genomic
compartments have approximately parallel responses
in fit to the different clade regimes (Table 6; Fig. 9). In
each case, clade regime 4—the one that gives each clade
its own ω parameter—was the worst fitting, with the
other three regimes being very close in performance.
This is yet another example of the data not supporting
the most parameter-rich models (clade regime 4 has
an additional parameter over the other three regimes;
Fig. 2). The mitochondrial data, if analysed separately,
showed considerable support for the inclusion of
lineage effects under most of the clade regimes (most
of the mitochondrial AICc improvements are greater
than 4; Fig. 9). In contrast, the nuclear data showed
considerable support for the simpler, lineage-effect free
model (differences are greater than 4 AICc points). The
plastid data did not show considerable support for
either model over the other (Fig. 9).
For both the nuclear and plastid data, most sites were
optimized by the software under site class 1 (the class
constrained to have ω values <1; see Methods section),
indicating strong purifying selection. In fact, the ML
estimates of ω for those data were near zero (Table 6;
Fig. 10). For each of the three compartments, relatively
few codon sites were optimized under site class 2 (ω
between zero and infinity), additional evidence for a
preponderance of purifying selection. However, those
few mitochondrial and nuclear sites that were optimized
under site class 2 had ML ω estimates considerably above
1, suggesting strong positive selection at a small number
of sites across the tree (Table 6; Fig. 10(ii)).
The estimates for the ω parameters that were allowed
to have different values for each clade (those for site
class 3) are marked by two main patterns. The first is
that the biggest ω differences are between the outgroup
and the ingroup clades for both the mitochondrial data
(a decrease in ω) and the plastid data (an increase in ω;
Fig. 10(iii)). Presumably, a strong difference in selective
pressure between the ingroup and outgroup is driving
the high proportion of mitochondrial sites optimized
under this site class (slighter over 50% of the codons;
Fig. 10(i)). The second broad pattern is that there is
little change in the signature of selection among the
three ingroup clades. The mitochondrial and nuclear loci
have ω estimates for site class 3 of approximately 0.3,
regardless of the clade. The plastid data site class 3 ω
estimate is approximately 1.25 (regardless of clade), but
very few sites are allocated to this site class (Table 6;
Fig. 10(i), (iii)).
Downloaded from http://sysbio.oxfordjournals.org/ by Carl Rothfels on January 9, 2014
FIGURE 7.
Lineage-specific rates of evolution for each genomic
compartment. Inferred substitution rates of the compartment data for
each of the clades of clock regime 4 (Fig. 2), calculated under the bas8
model. Units are in substitutions per site per arbitrary time unit.
VOL. 63
Bayesian Analyses
The Bayesian analyses under the LURC and RLC
models yielded results that were complementary to
those obtained through the likelihood analyses. For each
of the LURC compartmental analyses, the vittarioid
branches are generally reconstructed as having higher
rates of molecular evolution (Fig. 11(i)). However, this
increase is against a very heterogeneous background of
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ROTHFELS AND SCHUETTPELZ—VITTARIOID RATES
i
ii
64750
43
62750
AICc (smaller for better models)
63750
63250
62750
62250
61750
62550
61150
60950
61250
cod1
cod3
cod2
cod4
60750
60750
a
b
c
Partitioned by
compartment
Partitioned by
locus
FIGURE 8. Model fit of the full data on the general codon models. Units are in AICc points; smaller values indicate better fit. i) Fit under
unpartitioned data (a) versus the same data partitioned by compartment (three partitions; b), and by locus (six partitions; c). ii) Zoomed-in view
of the fit of the partitioned analyses.
rate variation (within each of the major clades there are
both unusually fast branches, and particularly slow ones)
and much of the rate increase in the vittarioids maps to
a single branch (the stem branch of the clade). The RLC
analyses reconstruct much more homogenous patterns
of rate variation (Fig. 11(ii)). Here, the vittarioids are
uniformly fast, the cheilanthoids are generally slow, and
Adiantum is somewhat intermediate. However, within
that broad pattern, it is actually a cheilanthoid terminal
branch (the one leading to Hemionitis) that has the
highest rate. For the RLC analyses, the mean number
of reconstructed rate shifts across the posterior sample is
8.06 ± 0.018, despite half the prior density for the number
of rate changes being on 0.
DISCUSSION
Phylogenetic Relationships
The most significant phylogenetic result of this
study is the very strong support for a monophyletic
Adiantum (Fig. 1c). Adiantum has an unusual degree
of morphological consistency compared to other large
[13:56 4/12/2013 Sysbio-syt058.tex]
fern genera and is defined by a unique character state—
sporangia born on, and limited to, the false indusium
(Tryon et al. 1990). However, molecular phylogenetic
studies have struggled to find support for its monophyly
with respect to the vittarioid ferns, which are strikingly
different, morphologically (Gastony and Rollo 1995;
Schuettpelz and Pryer 2007; Schuettpelz et al. 2007;
Ruhfel et al. 2008; Bouma et al. 2010; Lu et al. 2011a,b).
Our six-locus data set strongly supports the monophyly
of Adiantum, with 94% ML bootstrap support and 1.0
posterior probability (Fig. 1c).
Other relationships within the adiantoids (Adiantum
plus the vittarioids) were mostly in accordance with
earlier studies (Crane et al. 1995; Crane 1997; Schuettpelz
et al. 2007; Ruhfel et al. 2008; Lu et al. 2011a,b), but better
supported. We find novel support for a clade uniting the
enigmatic Rheopteris (the least morphologically reduced
of the vittarioids) and Monogramma acrocarpa, one of
the most reduced species, a result that suggests a
pattern of convergent morphological simplification in
the vittarioids (Crane et al. 1995; Schuettpelz et al.
2007; Ruhfel et al. 2008). Broad relationships within
the cheilanthoid ferns are becoming increasingly well
understood (Gastony and Rollo 1995; Gastony and Rollo
1998; Kirkpatrick 2007; Prado et al. 2007; Schuettpelz
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AICc (smaller for better models)
64250
31–54
44
VOL. 63
SYSTEMATIC BIOLOGY
Improvement in fit (AICc) vs. site model (Cod3)
NA
NA
NA
NA
NA
NA
1.130
NA
NA
NA
0.328
NA
NA
NA
0.252
NA NA
NA NA
NA NA
NA NA
NA NA
NA NA
0.004 0.203
NA NA
NA NA
NA NA
0.000 4.832
NA NA
NA NA
NA NA
0.017 1.923
NA
NA
NA
1.274
1.296
1.130
1.307
0.418
0.129
0.150
0.336
0.352
0.338
0.251
0.333
NA
NA
NA
NA
NA
NA
0.004 0.201
0.004 0.200
0.004 0.204
0.004 0.203
0.000 4.831
3.195 15.104
3.230 15.195
0.000 4.832
0.018 1.923
0.018 1.913
0.017 1.923
0.017 1.923
NA
NA
NA
1.191
1.176
1.297
1.284
0.333
0.168
0.146
0.418
0.302
0.302
0.337
0.342
6
4
2
0
mitochondrial
plastid
-2
nuclear
-4
-6
-8
-10
NA
NA
NA
NA
NA
NA
0.004 0.201
0.004 0.200
0.004 0.204
0.004 0.203
0.000 4.831
3.195 15.104
3.230 15.195
0.000 4.832
0.018 1.923
0.018 1.913
0.017 1.923
0.017 1.923
clade regime
1
clade regime
2
clade regime
3
clade regime
4
0.841
0.865
0.730
0.838
0.837
0.839
0.839
0.404
0.117
0.116
0.404
0.731
0.727
0.721
0.722
0.119
0.125
0.239
0.122
0.122
0.121
0.121
0.087
0.010
0.010
0.087
0.031
0.031
0.031
0.031
0.040
0.011
0.031
0.041
0.041
0.040
0.040
0.509
0.873
0.874
0.509
0.238
0.242
0.247
0.247
0.004 0.207
0.174 3.060
0.018 0.320
0.004 0.201
0.004 0.200
0.004 0.204
0.004 0.203
0.000 4.831
3.195 15.104
3.230 15.195
0.000 4.832
0.018 1.923
0.018 1.913
0.017 1.923
0.017 1.923
1.148
14.217
1.919
0.672
0.673
0.675
0.675
1.048
0.457
0.459
1.049
0.328
0.324
0.315
0.315
FIGURE 9. Fit of the compartment data to the branch-site (“clade”)
models. The fit scores are standardized against the fit of the same data
under the site model (values plotted are AICc score under cod3 minus
AICc score under cod4). Units are thus in AICc points, but with larger
(more positive) values indicating bigger improvements in fit for the
branch-site model over the site model, and thus the magnitude of the
influence of lineage effects. The entire line for the nuclear data is below
zero because cod3 was a better fit for those data than was cod4 (and
thus the AICc scores for cod4 were larger). The clade regimes follow
Figure 2.
NA, not applicable.
a Clade regimes correspond to those in Figure 2.
46,436.9
9842.1
4652.8
46,433.9
46,433.6
46,433.1
46,435.2
9836.7
9834.5
9835.1
9838.9
4658.8
4658.9
4658.3
4661.4
−23,153.4
−4854.4
−2256.9
−23,149.8
−23,149.7
−23,149.5
−23,149.5
−4849.5
−4848.4
−4848.7
−4849.5
−2256.8
−2256.9
−2256.6
−2256.6
64
64
56
66
66
66
67
66
66
66
67
58
58
58
59
Plastid
Mitochondrial
Nuclear
Plastid
Plastid
Plastid
Plastid
Mitochondrial
Mitochondrial
Mitochondrial
Mitochondrial
Nuclear
Nuclear
Nuclear
Nuclear
cod3
cod3
cod3
cod4
cod4
cod4
cod4
cod4
cod4
cod4
cod4
cod4
cod4
cod4
cod4
NA
NA
NA
1
2
3
4
1
2
3
4
1
2
3
4
3
2
1
3
2
1
3
2
1
3
2
1
Genome
Model
Clade Parameter
regimea
count
lnL
AICc
1
2
3
Omegas for clade 0
Site classes
Proportions
Site classes
Fit of the compartment data and parameter estimates for codon models
TABLE 6.
[13:56 4/12/2013 Sysbio-syt058.tex]
8
et al. 2007; Zhang et al. 2007; Rothfels et al. 2008;
Windham et al. 2009; Eiserhardt et al. 2011; Johnson
et al. 2012) and our results are consistent with these
studies. A notable finding for cheilanthoids here,
however, is the strong support for Calciphilopteris
ludens as a member of this clade (Fig. 1c). Earlier
studies that included this taxon typically resolved it
as sister to the rest of the cheilanthoids, but without
support (Schuettpelz et al. 2007; Zhang et al. 2007),
making it unclear as to whether it was more closely
related to the cheilanthoids, or to the adiantoids.
Certainly, morphology would place Calciphilopteris in
the cheilanthoids (Tryon 1942), and that is where it was
treated in a recent classification of the genus (Yesilyurt
and Schneider 2010).
Downloaded from http://sysbio.oxfordjournals.org/ by Carl Rothfels on January 9, 2014
Omegas for clade 1
Site classes
Omegas for clade 2
Site classes
Omegas for clade 3
Site classes
10
Patterns of Substitution Rate Heterogeneity
In our analyses, we find rates of molecular evolution
to vary among taxa, loci, and genomic compartments.
Consistent with other studies of vascular plants (Wolfe
et al. 1987; Wolfe et al. 1989b), our mitochondrial data
are more slowly evolving than are our plastid data
(Supplementary Fig. S2), despite the fact that the plastid
loci are all coding and much of the nad5 alignment is
intron sequence. In turn, the plastid loci are themselves
much more slowly evolving than is our low-copy nuclear
locus (Supplementary Fig. S2). However, these results
are coarse—the nuclear rate, in particular, is inferred
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45
1
2
3
1
3
2
1
4
3.5
3
2.5
2
1.5
1
0.5
0
mitochondrial
nuclear
1.25
1
0.75
0.5
0.25
0
clade 0
(outgroup)
clade 1
(cheil.)
clade 2
(Adiant.)
clade 3
(vittar.)
FIGURE 10. Inferences of selection pressure on genomic compartments, across taxa. i) Proportion of sites allocated to each site class, for each
genomic compartment, under cod4 (a “clade” branch-site model). Estimates for ω (the ratio of nonsynonymous to synonymous substitutions)
for (ii) site classes 1 and 2, and (iii) site class 3. The ω values for site class 3 are permitted to vary across predefined “clades” in the tree, in this
case, by the four clades of clade regime 4 (Fig. 2).
from a single short locus, with a high proportion of
missing data in the intron portions (Supplementary
Table S3).
The lineage-specific and partition-specific differences
we observe are strong, and their intersection—the
variation (across data sets) of the variation (across
taxa) of the rate of molecular evolution—is especially
interesting. Overall, the vittarioids show a dramatically
elevated rate of molecular evolution, evolving 4.3 times
faster on average than the cheilanthoids (under a local
clock model with all data linked—bas6 with clock
regime 4; Dryad doi:10.5061/dryad.c5m42). This rate
acceleration is even more pronounced when the plastid
data are considered alone (Table 4; Fig. 7). Adiantum is
also faster than the cheilanthoids, but generally much
slower than the vittarioids. Local clock models that
force the cheilanthoids and Adiantum to share a rate
(vittarioids get their own) have a much better fit than
those that force the vittarioids to share a rate with either
the cheilanthoids or Adiantum (by 367 and 329 AICc
points, respectively; bas7; Fig 5; Table 3). However, it
is important to note that local clock models that give
each of the three major clades its own rate are still
preferred over those that force any two to share a rate
(clock regime 4 vs. clock regimes 1, 2, or 3, Fig. 2), by a
minimum of 137 AIC points (Fig. 5; Table 3). Although
within-clade rate variation can result in the superior fit
of local clock models even when there is no difference
in expected rates among the clades in question (Lanfear
2010), this is not driving our results. Under the Local
Clock Permutation Test (Lanfear 2010; 1000 permutations
used) both the plastid and nuclear data reject the null
model of no rate differences among the focal clades (p <
0.001 and < 0.015, respectively), but the mitochondrial
data do not.
[13:56 4/12/2013 Sysbio-syt058.tex]
From the Bayesian analyses, we reconstruct the
vittarioid stem branch to have an average substitution
rate that is 2.16 or 2.30 times that of the branch that
gave rise to it (under the LURC and RCL models,
respectively; Fig. 11). This acceleration for vittarioids is
noteworthy in that for the subset of previous studies
where polarity could be established, rate accelerations
were less frequent than were slowdowns (e.g., Soltis et al.
2002; Schuettpelz and Pryer 2006; Bininda-Emonds 2007;
Korall et al. 2010; Li et al. 2011).
The strong, broad lineage effects we see in our data
set occur in the context of extensive fine-grained rate
variation. In all cases, clockless (unrooted) models fit
the data much better than do local clock models (Fig. 5;
Table 3), despite the greatly increased parameter number
of the former. The fine-grained effects are best exhibited
by the Bayesian LURC analyses (Fig. 11(i)). Under this
uncorrelated model of rate variation, which lacks any
a priori division of the tree into focal clades, the data
prefer many rate changes, spread across the tree. Most
of the vittarioid branches are slower than at least one
branch in each of the other clades (Fig. 11(i)) and the
vittarioid rate increase, under this model, appears to
be largely attributable to a single very fast branch—
the stem branch of the clade. Even under the RLC
model, which strongly favors very few rate changes
(half the prior density is on zero rate changes), the
mean number of rate changes across the tree is above
eight, and three rate changes (the number necessary
to give each of the major clades their own rates with
no further changes) is outside the 95% credibility
interval for the rateChangeCount parameter. Inferences
under this model do, however, suggest rather uniformly
elevated rates across the vittarioids, instead of a single
fast branch at the base of the clade as inferred under
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plastid
4.5
1.5
Increasing purifying selection Incr. positive selection
2
iii
5
Non-synonymous to synonymous (dn/ds) substitution ratio
ii
3
Incr. pur. sel. Increasing positive selection
i
Non-synonymous to synonymous (dn/ds) substitution ratio
ROTHFELS AND SCHUETTPELZ—VITTARIOID RATES
31–54
46
VOL. 63
SYSTEMATIC BIOLOGY
0.33
0.78
0.54
0.42
0.41
0.38
0.41
0.5
0.52
0.43
0.69
0.55
0.97
0.7
2.02
1.11
0.84
0.99
2.83
i) LURC
0.83
1.64
1.16
0.9
0.84
0.84
1.63
1.25
1.26
1.04
1.31
0.97
1.2
0.97
1.29
0.97
0.62
1.25
0.57
0.62
0.72
a
b
Downloaded from http://sysbio.oxfordjournals.org/ by Carl Rothfels on January 9, 2014
0.66
1.03
0.67
0.84
0.77
0.68
0.95
0.59
0.9
0.54
0.21
0.87
0.52
0.51
0.52
0.51
0.51
0.51
0.57
1.08
1.08
2.87
1.08
1.08
2.21
0.51
0.87
0.51
0.55
0.87
ii) RLC
2.15
All vittarioid branches
have a rate of 2.13
unless indicated
1.58
2.17
2.15
2.04
2.03
2.04
0.87
1.43
All Adiantum
branches have
a rate of 0.87
unless indicated
0.92
b
a
10
9
8
7
6
5
4
3
2
1
0
Arbitrary time units from present
FIGURE 11. Comparison of Bayesian relaxed clock models: rate and divergence time contrasts. Results from the full data, partitioned by
compartment, analysed under a lognormal uncorrelated relaxed clock (LURC; i) and a random local clock (RLC; ii) model. Branch thickness and
shading are both proportional to inferred median rate for the branch; median rate estimates are presented above the branches. Two discrepancies
between the models are highlighted: the difference between the inferred ages of the ingroup (arrow a) and between the inferred crown age of
the vittarioids (arrow b).
the LURC model. Under the RLC model, all vittarioid
branches have faster median rates than do any other
branches, save that of the cheilanthoid Hemionitis, which
is reconstructed as fastest of all.
The pattern of variation across our data sets is
similar to that seen across taxa, with some strong,
coarse patterns in the context of considerable finescaled variation. In our analyses, the “variation in rate
variation” is partitioned much more strongly among
[13:56 4/12/2013 Sysbio-syt058.tex]
compartments than among loci (Fig. 4). Generally,
the loci within a compartment behave similarly. This
result contrasts with, for example, Moncalvo et al.
(2000), who found significantly different patterns of
rate variation among loci within compartments. The
differences among compartments we observe compose
perhaps the most difficult set of results to interpret. Both
the plastid and the nuclear data strongly support an
accelerated rate of evolution for the vittarioids compared
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ROTHFELS AND SCHUETTPELZ—VITTARIOID RATES
[13:56 4/12/2013 Sysbio-syt058.tex]
regimes (Fig. 5), and the strongly elevated rates inferred
for the vittarioids under those same models (Fig. 7)
demonstrate that the rate acceleration of the vittarioids
is a prominent feature of these data. The general
consistency of this acceleration—across the plastid
and nuclear loci (Fig. 7)—is most compatible with
demographic (selection and drift related) and/or lifehistory based explanations. Changes in polymerase
proof reading accuracy (c.f. Cho et al. 2004; Parkinson
et al. 2005), for example, can be discounted—since
the compartments have their own polymerases, such a
change would affect only a single compartment.
Patterns of Selection
Our results with codon models showed a pattern
somewhat opposed to that of the nucleotide models.
Whereas the fit of the nucleotide models improved
with model complexity (the best-fitting model was the
most highly parameterized one, with the finest grained
partition scheme), codon model fit was maximized with
models of intermediate complexity. The unpartitioned
codon models fit very poorly (Fig. 8(i)), but the threepartition (by compartment) scheme outperformed the
more complex six-partition (by locus) scheme (Fig. 8(ii)).
This result is in contrast to earlier studies (Eyre-Walker
and Gaut 1997; Muse and Gaut 1997; Muse 2000) that
found selective effects (nonsynonymous substitution
rate differences, in their case) to be largely locus specific.
The intermediate-is-best pattern is also seen among the
main model types. Model cod1, which does not include
site effects, fits very poorly. The site models (cod2 and
cod3) fit much better, but the further addition of branch
effects (in the branch-site model cod4) has a negligible
effect (Fig. 8(ii); Table 5). The lack of a lineage effect
in the fit of the codon models is among our most
interesting results. In marked contrast to the nucleotidebased analyses, our codon-based analyses show no
significant evidence of fine-scale differences across data
partitions or strong differences among lineages (Figs. 9
and 10). Differences in selective signatures, when they
do appear (i.e., the evidence for strong positive selection
in a subset of the mitochondrial sites but not for those
of the plastid; Fig. 10(ii)), extend across the tree, and
thus cannot explain the heterogeneity in evolutionary
rates that is so striking in this group. Finally, the only
indications of lineage effects (e.g., ML estimates of ω
for site class 3 of cod4) are weak, and occur between
the outgroup and ingroup, rather than among ingroup
clades (Fig. 10(iii)).
These results further limit the pool of biological
mechanisms that might explain the vittarioid rate
increase. While our nucleotide-based results are
consistent with life-history or demography-based
explanations, the subset of explanations that depend
on altered post-mutation fixation rates, including those
that invoke changes in the relative strength of selection
and drift (e.g., reduced efficacy of selection in small
populations; Woolfit and Bromham 2003; Bromham and
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to either other major clade, but the degree of the
increase differs (in the plastid data, vittarioids are 5.8
times faster than cheilanthoids and 2.7 times faster than
Adiantum; in the nuclear data, those values are 3.1 and
2.5, respectively; Fig. 7; Table 4). The mitochondrial
data, in contrast, show a rate increase for both Adiantum
and the vittarioids, versus the cheilanthoids, but no
subsequent increase from Adiantum to the vittarioids
(vittarioids:cheilanthoids = 3.1; Adiantum:cheilanthoids
= 3.2; vittarioids:Adiantum = 0.97; Fig. 7; Table 4).
The mitochondrial data therefore stand out, even by
visual inspection (Figs. 1, 3). The two mitochondrial
loci clearly differ from the other compartments, but
also from each other, and both are evolving relatively
slowly, on average (Supplementary Fig. S2). It is tempting
to attribute the anomalous mitochondrial pattern to
stochastic variation in the substitution process, given
the generally weak signal present in the mitochondrial
data sets. However, the model selection analyses
demonstrate that the variation is nonetheless significant:
the mitochondrial data fit much better under a local
clock regime that forces Adiantum and the vittarioids
to share a rate and gives the cheilanthoids their own
clock, than under either of the alternatives (e.g., the clock
regime that has a single rate for the cheilanthoids and
Adiantum, and a different rate for the vittarioids, is 69
AIC points worse; Fig. 6; Table 4). In addition, unlike
the plastid or nuclear data, the mitochondrial data do
not favor the four-rate local clock model (clock regime
4, Fig. 2). Giving each of the major clades (plus the
outgroup) its own rate results in a small reduction in
fit (of 2.0 AIC points) over the three-rate clock regime
1 (in which Adiantum and the vittarioids share a rate;
Fig. 6; Table 4).
One of the noteworthy results of the nucleotide model
selection analyses was the strong preference of the
data for the most highly parameterized model (bas2),
which is not only clockless, with unlinked substitution
parameters, but additionally lacks a proportional branch
length constraint. In effect, bas2 treats each partition
as coming from a separate evolutionary process. This
model is a much better fit for the data than are any
of the other general models, and bas2 partitioned
by locus outperforms the same model partitioned by
compartment (by 37.9 AIC points; Fig. 4; Table 3). Thus,
fine-scale, locus-specific variation in the variation of
rate is one of the dominant features of these data.
Even among the local clock models, those which permit
each clock to vary freely across partitions (e.g., if the
rate for clock 1 is twice that of clock 2 in the first
partition, it need not be so for the second partition)
fit considerably better than do the corresponding local
clock models where the clocks are constrained to be
proportional across partitions (bas6 vs. bas7; Fig. 5;
Table 3).
Overall, the results of our analyses eliminate the
possibility that the apparent rate acceleration of the
vittarioids is simply due to stochastic variation in
the substitution process. The differences in fit among
the local clock models under the different local clock
47
31–54
48
SYSTEMATIC BIOLOGY
Methods of Investigating Rate Heterogeneity
We found our model-fitting approach, using the
AICc, to be an effective means of investigating rate
heterogeneity. Model-fitting analyses allowed us to
establish the pattern of rate variation without requiring
multiple independent observations, and to evaluate the
assumption that rate is an organism-level phenomenon
influenced by some component of that organism’s life
history and thus manifest across loci and genomic
compartments (e.g., Bousquet et al. 1992; Nikolaev et al.
2007; Bromham 2009; Lanfear et al. 2010). In addition,
our approach allowed us to avoid the challenges
of phylogenetic non-independence, which have been
prevalent in the history of rate heterogeneity research
(reviewed in Bromham 2002). Typically, the issue of
non-independence is accommodated by examining a
series of independent pair-wise comparisons—informed
by, for example, a particular phenotypic change of
choice—evaluated with a sign test or similar approach
[13:56 4/12/2013 Sysbio-syt058.tex]
(e.g., Sarich and Wilson 1967; Muse and Weir 1992;
Bromham et al. 1996; Bromham and Woolfit 2004;
Lanfear et al. 2010). Phylogenetic non-independence
is much more difficult to account for in cases, like
ours, that lack repeated examples of a rate change
correlated with a plausible external factor. There has
been a temptation in such cases to approach evolutionary
rate itself as a trait and to reconstruct the evolution
of that trait on a phylogeny (e.g., Lutzoni and Pagel
1997, their “method 1”). However, if one attempts to
do so in a likelihood or Bayesian framework, then
the quantity being reconstructed (rate) is itself part
of the model used in the reconstruction (the branch
lengths). Other approaches also potentially run subtly
afoul of the issue of independence. Many analyses that
explicitly model rate variation do so in a manner that
assumes a degree of correlation among parent and child
branches (e.g., r8s; Sanderson 2002, 2003), rendering
branch rates dependent (c.f. Hoegg et al. 2004; Korall
et al. 2010). Finally, even if a model does not assume
autocorrelation (e.g., some of the models in BEAST;
Drummond et al. 2006; Drummond and Rambaut 2007)
those branches are still embedded within the hierarchy
of the phylogenetic tree. Different branches each have
a role in accommodating the same data, and thus a
rate reconstructed for a given branch is not independent
of the rates reconstructed for the others. It remains to
be seen whether these issues have practical effects in
real data sets; preliminary comparisons suggest that
they do not (e.g., Nabholz et al. 2008; Welch et al.
2008). Much future progress is likely to come from
recent approaches that model rate variation explicitly
as a trait, or at least, as “trait dependent” (Lartillot and
Poujol 2010; Mayrose and Otto 2011). By coestimating
rate and divergence time, these methods avoid the
circularity and non-independence problems; related
models can then be compared using likelihood ratio tests
or model selection approaches, in a manner similar to
this study.
Our model-fitting analyses, under likelihood, did
require the a priori identification of models to compare,
which was not trivial. The number of possible
parameterizations of a partitioned analysis increases
rapidly with the number of partitions. Our data
set of six loci can be divided into groups of loci
203 different ways. In a simplified scenario, where
for each of the 203 different partitioning regimes
we allow parameters of each “type” (exchangeability;
base frequency; gamma shape; clock regime—unrooted,
global, or one of four local clock regimes) to be either
shared across the full data set or allocated individually
to each of the partitions, there are 9744 different
possible models. However, even with the requirement
of a priori identification of models, the ML modelfitting approach described here will remain attractive.
In our case, it allowed us to elucidate complex patterns
of rate variation, in the absence of any associated
correlation-based hypotheses, and the same approach
was readily extendable to our investigations of complex
heterogeneous patterns of selection.
Page: 48
Downloaded from http://sysbio.oxfordjournals.org/ by Carl Rothfels on January 9, 2014
Leys 2005; Woolfit and Bromham 2005) are undermined
by the absence of lineage-specific signatures of selection
in our codon-based analyses. Selection may still be
ultimately responsible for the elevated rates, but only
indirectly (e.g., through selection for increased mutation
rates in the vittarioids). It is possible that lineage-specific
effects were undetectable by our methods (there are
one-third as many codons as nucleotide sites, so the
codon models may lack some of the power of their
nucleotide counterparts). However, the strong contrast
between the two model types (vittarioids having very
strong lineage effects in the nucleotide models vs. none in
the codon models) argues that selective effects, if present,
are too weak to explain the observed rate discrepancy.
The remaining subset of explanations, then, is limited
to those that invoke changes in the supply of mutations,
rather than changes in the rate of post-mutation fixation.
Because only those explanations with organism-wide
effects are tenable, given the bigenomic nature of the rate
increase, life history or related environmental factors are
considered to be the most likely agent.
Reports of molecular rate heterogeneity caused by
changes in environment-driven mutation rates are rare
in the literature. To our knowledge, such effects have
been found only in lichen-forming fungi (Lutzoni and
Pagel 1997) and halophytic crustaceans (Hebert et al.
2002). That said, it is important to note that the rate
increase for the vittarioids may be driven substantially
by a single elevated rate on the clade’s stem branch
(Fig. 11(i)). If this one branch is responsible for the rate
increase, looking for environmental correlates among
extant vittarioids could be unproductive. Instead, one
would need to ask what was so unusual about the
environment of the ancestor of the vittarioids that
could cause mutation rates high enough to yield a
rate of substitution approaching six times that of the
background, even when spread across all descendent
branches?
VOL. 63
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ROTHFELS AND SCHUETTPELZ—VITTARIOID RATES
Implications for Topology Inference and Divergence
Time Dating
Questions about the patterns and causes of rate
variation aside, our results are also relevant to recent
debates concerning the influence of rate heterogeneity,
and the way it is modeled, on phylogenetic inference.
Drummond et al. (2006) make the case that standard
“unrooted” (or “no-clock”; Yang and Rannala 2006;
Wertheim et al. 2010) models are flawed, in that they
do not require contemporaneity of the tips. Given that
we know that the tips are contemporaneous (in most
cases), is it reasonable to ignore that information when
inferring phylogeny? Might our inferences be more
accurate if such data were included explicitly in the
model via “relaxed clock” approaches (Drummond et al.
2006)? Recent studies failed to find any significant
improvement of relaxed clock over unrooted models
(Wertheim et al. 2010; Rothfels et al. 2012), but were
generally inconclusive: “The question remains whether,
in practice, modeling rate variation among branches can
improve phylogenetic inference” (Wertheim et al. 2010).
In our case, the inference of ingroup relationships was
largely insensitive to the choice of model (at least, among
those investigated, which included both unrooted and
relaxed clock models). However, when unconstrained,
both relaxed clock models failed to root the tree correctly,
placing the root along the fastest branch (separating
the vittarioids from the rest of the tree) rather than
between the ingroup and outgroup (results not shown).
This placement renders the adiantoids paraphyletic,
and strongly conflicts with the results obtained from
[13:56 4/12/2013 Sysbio-syt058.tex]
expanded taxon samples (e.g., Gastony and Rollo 1995;
Schuettpelz and Pryer 2007; Schuettpelz et al. 2007;
Bouma et al. 2010). At least for these data, then, the
relaxed clock models (with our choices of priors and
parameterization) are not yet fully capable of accurately
modeling rate variation such that they are able to root
this tree correctly without additional information.
While the effects of model choice on topology are
perhaps modest, their effects on inferences of timing
(the dating of evolutionary events) are strong. The two
relaxed clock models (LURC and RLC) we employed not
only made different inferences about the location and
scale of rate changes, but also inferred correspondingly
strong differences in the relative timing of divergences
(Fig. 11). The RLC model inferred events to be generally
younger than the LURC, by over 10% of the total tree
height for the base of the ingroup (Fig. 11, arrow a), and
by over 20% of the tree height for the crown clade of
the vittarioids (Fig. 11, arrow b). These discrepancies
are potentially the result of a worst-case scenario
(very strong rate heterogeneity in a phylogeny without
internal time constraints—our sole constraint is at the
base of the tree) but are nonetheless dramatic and
potentially worrisome. A closer inspection of the results
of the two models shows that, as expected, the branch
rates inferred under one model are strongly correlated
with those inferred under the other (Supplementary
Fig. S3). However, the stem branch for the vittarioids
is an outlier—it is inferred to have a much higher
rate under the LURC model than under the RLC
model, whereas the other vittarioid branches have a
much lower rate under the LURC model than under
the RLC model (the vittarioid stem branch is below
the diagonal in Supplementary Fig. S3, vs. the other
vittarioid branches, which are above the diagonal). In
effect, the tendency of the RLC model to penalize
frequent rate changes causes it to prefer to distribute
the substitutions that the LURC model loaded onto
the single stem branch, and spread them across the
entire clade. The LURC model correspondingly infers
a shorter (but faster) stem branch, whereas the RLC
model infers a longer, slower branch (Fig. 11), and
thus very different divergence times. A similar complex
model-mediated effect is apparent in Hemionitis, which
is on a sufficiently long terminal branch that it is
given its own rate under both models. The RLC model
prefers to force all the neighboring branches to share a
single rate—especially Mildella, the slow sister lineage to
Hemionitis—and thus the rate change on the Hemionitis
branch is particularly extreme (Fig. 11, Supplementary
Fig. S3). As with the vittarioids, a single deeper branch
is inferred to have a much higher rate under the LURC
than RLC models (Supplementary Fig. S3, arrow), with
the more distal tips showing the opposite pattern,
for the overall result of a small number of ancestral
branches below the diagonal in Supplementary Fig. S3,
and many more (typically terminal) branches above the
diagonal. In effect, the RLC prefers rate homogeneity,
but when heterogeneity is necessary, the degree of
the change is unimportant. The LURC model, with its
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Understanding the patterns of selection proved critical
in this study, to evaluating the potential causes of
the vittarioid rate increase. Given the vittarioids’
idiosyncratic biology, there are many potential correlates
for their elevated rate of evolution (e.g., changes
associated with their reduced morphologies, with their
gametophyte generation, or induced by their epiphytic
habit). However, any explanation for their elevated
rates, based on these correlates, should be interpreted
with caution to ensure that mutation, rather than
fixation, is invoked. This danger of inferring causation
from correlation is perhaps best illustrated, and most
intriguing, in studies of rate heterogeneity in plants,
where many studies have found a correlation between
generation time and evolutionary rate (Bousquet et al.
1992; Gaut et al. 1992; Laroche et al. 1997; Smith and
Donoghue 2008; Korall et al. 2010), a pattern well
documented in animals. However, plants do not have
a segregated germ line, and thus should show no
correlation between the number of generations and the
number of potentially mutation-inducing replications in
the history of their gametes, which is the explanation
typically proffered for the “generation time hypothesis”
(Mooers and Harvey 1994; Li et al. 1996). As Muse (2000)
notes, while such a correlation may exist in plants, the
mechanism is unclear (but see Lanfear et al. 2013).
49
31–54
50
SYSTEMATIC BIOLOGY
SUPPLEMENTARY MATERIAL
Data files and/or other supplementary information
related to this paper have been deposited at Dryad
(http://datadryad.org/) under doi:10.5061/dryad.
c5m42.
FUNDING
This work was supported by the Society for Systematic
Biologists (Graduate Student Research Award to C.J.R.),
the Natural Sciences and Engineering Research Council
of Canada (a Julie Payette PGS M and PGS D to C.J.R.),
and the National Science Foundation (DEB-1145925
to E.S.).
ACKNOWLEDGMENTS
Our great thanks to the individuals who made this
project possible: Kathleen Pryer, who had a pivotal
role in initiating and guiding this project; Layne
Huiet, who assisted in the lab and provided critical
materials and unpublished information regarding the
phylogeny of Adiantum; Ben Redelings for guidance
through (and execution of) the BAli-Phy analyses; Ester
Gaya and Casey Dunn for assistance with PAMLparser;
Volker Knoop for supplying unpublished nad5 primer
[13:56 4/12/2013 Sysbio-syt058.tex]
sequences; and Joe Bielawski, Fay-Wei Li, Nimrod
Rubinstein, and Dave Swofford, for assistance with the
complexities of parameter counting, model selection,
and codon models. Maarten Christenhusz, Jim Croft,
Layne Huiet, Thomas Janssen, Nathalie Nagalingum,
Tom Ranker, Harald Schneider, Alan Smith, and Paul
Wolf contributed plant materials used in this study;
we thank the staff of A, COLO, DUKE, GOET, P, TUR,
UC, and UTC for curating the associated vouchers.
This manuscript was greatly improved through the
thoughtful comments of Rob Lanfear, Sally Otto, Editorin-Chief Frank Anderson, Associate Editor Roberta J.
Mason-Gamer, and an anonymous reviewer.
APPENDIX 1
List of accessions sampled in this study, presented
in the following format: Species, Fern Lab database
number (http://fernlab.biology.duke.edu/), Voucher
(HERBARIUM), Provenance: GenBank numbers (with
citations for previously published sequences) for atpA,
atpB, rbcL, atp1, nad5, gapCp (in that order). Missing data
are indicated by “–”. Herbarium acronyms follow Index
Herbariorum (Thiers [continuously updated]).
Adiantum aethiopicum L., 3895, N.Nagalingum 24
(DUKE), Australia, New South Wales: KC984436,
KC984441, KC984519, KC984409, KC984493, KC984450.
Adiantum formosum R.Br., 4602, A.R.Smith s.n. (UC),
Cult. (wild provenance unknown): KC984437, KC984442,
KC984520, KC984410, KC984494, KC984453. Adiantum
hispidulum Sw., 4603, L.Huiet 101 (UC), Cult. (wild
provenance unknown): KC984438, KC984443, KC984521,
KC984411, KC984495, KC984455. Adiantum malesianum
J.Ghatak, 2506, L.Huiet 111 (UC), Cult. (wild provenance
unknown): EF452068 (Schuettpelz et al. 2007), EF452011
(Schuettpelz et al. 2007), EF452132 (Schuettpelz et al.
2007), KC984412, KC984496, EU551257 (Schuettpelz et al.
2008). Adiantum peruvianum Klotzsch, 2507, L.Huiet
103 (UC), Cult. (wild provenance unknown): EF452070
(Schuettpelz et al. 2007), EF452013 (Schuettpelz et al.
2007), EF452133 (Schuettpelz et al. 2007), KC984413,
KC984497, KC984456. Adiantum raddianum C.Presl, 638,
P.G.Wolf 717 (UTC), Cult. (wild provenance unknown):
EF452071 (Schuettpelz et al. 2007), U93840 (Wolf 1997),
KC984522, KC984414, KC984498, KC984458. Adiantum
tenerum Sw., 2504, L.Huiet 107 (UC), Cult. (wild
provenance unknown): EF452072 (Schuettpelz et al.
2007), EF452014 (Schuettpelz et al. 2007), EF452134
(Schuettpelz et al. 2007), KC984415, KC984499,
KC984459. Adiantum tetraphyllum Humb. & Bonpl. ex
Willd., 2505, L.Huiet 105 (UC), Cult. (wild provenance
unknown): EF452073 (Schuettpelz et al. 2007), EF452015
(Schuettpelz et al. 2007), EF452135 (Schuettpelz et al.
2007), KC984416, KC984500, KC984460. Anetium
citrifolium (L.) Splitg., 3339, M.Christenhusz 4076
(TUR), France, Guadeloupe: EF452075 (Schuettpelz et al.
2007), EF452017 (Schuettpelz et al. 2007), KC984523,
KC984417, KC984501, KC984461. Antrophyum latifolium
Page: 50
Downloaded from http://sysbio.oxfordjournals.org/ by Carl Rothfels on January 9, 2014
tendency toward many smaller rate changes, is able to
“accommodate” some of the additional substitutions
on the deeper ancestral branches, resulting in rate
changes that are less dramatic but more frequent (Fig. 11,
Supplementary Fig. S3).
While all of our rate and divergence time inferences
are model dependent (we do not know the “true rates”),
the concordance between the pattern of rate variation
in the LURC results and the strong preference of the
data for ML models with the maximum number of
permitted rate parameters (Fig. 4; Table 3) suggests
that fine-scale rate heterogeneity may be dominant in
our data. Contrary to the position of Drummond and
Suchard (2010) that “in any given tree there exist a small
number of rate changes … in general, the numerous
small changes arise as a modeling consequence, and are
not necessarily data-driven” (see also Yoder and Yang
2000), our data suggest the opposite: it may be the few,
large changes inferred under the RLC model that are a
model consequence.
An appealing avenue for future research is to compare
the fit of complex relaxed clock models on diverse data
sets, using Bayes factors. Unfortunately, Bayes factors are
frequently calculated from the harmonic mean, which
is an unreliable method (Lartillot and Philippe 2006;
Fan et al. 2011; Xie et al. 2011); more reliable methods
are just now becoming available (Lewis et al. 2010;
Baele et al. 2012). Regardless of the ultimate truth,
one conclusion is clear—inferences of rate, and thus of
divergence times, are critically dependent on the model
adopted.
VOL. 63
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ROTHFELS AND SCHUETTPELZ—VITTARIOID RATES
[13:56 4/12/2013 Sysbio-syt058.tex]
2007), KC984431, KC984515, KC984472. Pityrogramma
austroamericana Domin, 2561, E.Schuettpelz 301
(DUKE), Cult. (wild provenance unknown): EU268769
(Rothfels et al. 2008), EF452050 (Schuettpelz et al. 2007),
EF452166 (Schuettpelz et al. 2007), KC984432, KC984516,
KC984473. Rheopteris cheesemaniae Alston, 3373, Croft
1749 (A), Papua New Guinea: EF452126 (Schuettpelz
et al. 2007), EF452063 (Schuettpelz et al. 2007), EF452176
(Schuettpelz et al. 2007), KC984433, KC984517, –.
Vittaria graminifolia Kaulf., 2395, E.Schuettpelz 227
(DUKE), Ecuador, Zamora-Chinchipe Prov.: EF452128
(Schuettpelz et al. 2007), EF452064 (Schuettpelz et al.
2007), U21295 (Crane et al. 1995), KC984434, KC984518, –.
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Blume, 3078, T.Ranker 1774 (COLO), Papua New
Guinea: EF452076 (Schuettpelz et al. 2007), EF452018
(Schuettpelz et al. 2007), EF452138 (Schuettpelz et al.
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KC984422, KC984506, KC984465. Cheilanthes covillei
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2008), KC984444, EU268782 (Rothfels et al. 2008),
KC984420, KC984504, EU551267 (Schuettpelz et al.
2008). Cryptogramma crispa (L.) R.Br. ex Hook.,
2949, M.Christenhusz & F.Katzer 3871 (DUKE),
United Kingdom, Scotland: EU268740 (Rothfels et al.
2008), EF452027 (Schuettpelz et al. 2007), EF452148
(Schuettpelz et al. 2007), KC984421, KC984505,
KC984464. Haplopteris elongata (Sw.) E.H.Crane,
2546, L.Huiet 112 (UC), New Caledonia: EF452096
(Schuettpelz et al. 2007), EF452035 (Schuettpelz et al.
2007), EF452153 (Schuettpelz et al. 2007), KC984423,
KC984507, KC984466. Hecistopteris pumila (Spreng.)
J.Sm., 3278, M.Christenhusz 3976 (TUR), France,
Guadeloupe: EF452097 (Schuettpelz et al. 2007),
EF452036 (Schuettpelz et al. 2007), KC984524, KC984424,
KC984508, –. Hemionitis palmata L., 2557, E.Schuettpelz
297 (DUKE), Cult. (wild provenance unknown):
EU268743 (Rothfels et al. 2008), EF452037 (Schuettpelz
et al. 2007), KC984525, KC984425, KC984509, KC984467.
Mildella intramarginalis (Kaulf. ex Link) Trevis, 3513,
H.Schneider s.n. (GOET), Cult. (wild provenance
unknown): EF452085 (Schuettpelz et al. 2007), EF452025
(Schuettpelz et al. 2007), EF452146 (Schuettpelz et al.
2007), KC984426, KC984510, KC984468. Monogramma
acrocarpa (Holttum) D.L.Jones, 3375, T.Ranker 1778
(COLO), Papua New Guinea: KC984435, KC984439,
EF452156 (Schuettpelz et al. 2007), KC984427,
KC984511, –. Monogramma graminea (Poir.) Schkuhr,
3548, T.Janssen 2692 (P), France, Reunion: EF452102
(Schuettpelz et al. 2007), EF452040 (Schuettpelz et al.
2007), EF452157 (Schuettpelz et al. 2007), KC984428,
KC984512, KC984469. Notholaena grayi Davenp., 3187,
E.Schuettpelz et al. 480 (DUKE), USA, Arizona, Cochise
Co.: EU268749 (Rothfels et al. 2008), JF832173 (Rothfels
et al. 2012), EU268794 (Rothfels et al. 2008), KC984429,
KC984513, KC984470. Pellaea atropurpurea (L.) Link,
2957, E.Schuettpelz 312 (DUKE), Cult. (originally
collected from Virginia, USA): JQ855925 (Johnson
et al. 2012), KC984440, EF452162 (Schuettpelz et al.
2007), KC984430, KC984514, KC984471. Pentagramma
triangularis (Kaulf.) Yatsk., Windham & E.Wollenw.,
3152, E.Schuettpelz et al. 445 (DUKE), USA, Arizona,
Gila Co.: EU268768 (Rothfels et al. 2008), EF452049
(Schuettpelz et al. 2007), EF452165 (Schuettpelz et al.
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