2007
POINTS OF VIEW
trees are binary, split fit is co-Pareto on components (Wilkinson et al.,
2005a). When input trees have polytomies, an optimal splitfitsupertree
could include arbitrary resolutions that do not contradict any displayed
splits. In that case, split fit can fail to be co-Pareto (but not sub-Pareto)
on components. In contrast, the corresponding strict consensus, the
split fit* supertree, suppresses all arbitrary resolutions and must be
co-Pareto on components. A method that is co-Pareto on components
must also be co-Pareto (and sub-Pareto) on triplets and on nestings.
Our example confirms that triplet fit is not co-Pareto on components.
For example, of the 1677 triplet MRP supertrees, 339 include the component (DE). This is not present in either input tree but all the triplets
that it entails are present in at least one of the input trees. It also confirms that that the MinCut methods are not co-Pareto on components
337
(Semple and Steel, 2000). For example, D and K are grouped together
in the MinCut supertree (Fig. lc) and D and K nest within A-P in both
input trees but they are not a component in either input tree (Fig. 1).
Co-Pareto on triplets.—The triplet fit method is analogous to split fit,
and by analogy we might expect that triplet fit* is co-Pareto and thus
sub-Pareto on triplets, and that triplet fit is sub-Pareto on triplets and
co-Pareto on triplets when input trees are binary (in which case there
are no arbitrary resolutions). However, unlike full splits, combinations
of displayed triplets can entail triplets that are not displayed. Thus,
the analogy breaks down and there are, as yet, no proofs for any of
these conjectures, which remain open problems. Similarly, quartet fit'
is conjectured but has not been shown to be co-Pareto and sub-Pareto
on quartets.
Syst. Biol. 56(2):337-345,2007
Copyright © Society of Systematic Biologists
ISSN: 1063-5157 print / 1076-836X online
DOI: 10.1080/10635150701258795
Alarm Bells for the Molecular Clock? No Support for Ho et al.'s Model of
Time-Dependent Molecular Rate Estimates
BRENT C. EMERSON
Centre for Ecology, Evolution and Conservation, School of Biological Sciences, University of East Anglia, Norwich NR4 7TJ, UK; E-mail:
[email protected]
In a recent paper, Ho etal. (2005) appear to have
provided startling evidence for a relationship between
the rate of molecular evolution and sampling time that
they then describe with the fitting of vertically translated exponential decay curves. If correct, their results
carry major implications for molecular evolutionary biology (Penny, 2005), and their work follows from the observed disparity between mitochondrial DNA (mtDNA)
rate estimates directly measured from pedigree studies and those inferred from intraspecific and interspecific phylogenetic studies. A number of recent studies
of control region mtDNA from detailed human pedigrees have reported exceptionally high estimates of mutation rate, summarized in Howell et al. (2003). Pooling
data from two comparable Leber hereditary optic neuropathy studies (Howell et al., 1996,2003), Howell et al.
(2003) obtained a pedigree divergence rate of 1.0 mutations/bp/Myr (mutations per base pair per million
years) for the control region. Building on these data,
Howell et al. (2003) also combined data from a number of
unrelated pedigree studies (Bendall et al., 1996; Cavelier
et al., 2000; Heyer et al., 2001; Howell et al., 1996, 2003;
Mumm et al., 1997; Parsons and Holland, 1998; Parsons
etal., 1997; Sigurdardottir etal., 2000; Soodyall etal.,
1997) and obtained a broadly similar control-region pedigree divergence rate of 0.95 mutations/bp/Myr. Ho et al.
(2005) point out that this value is vastly greater (approximately 50 x) than the phylogenetically derived divergence rate of approximately 0.02 mutations/bp/Myr for
protein-coding mitochondrial DNA. However, it should
be acknowledged that, as deduced from comparative
phylogenetic studies, the control region evolves much
faster than the protein-coding regions within human mitochondrial DNA. Thus, in real terms, pedigree mutation
rates for the human mitochondrial control region appear
to be approximately 5- to 10-fold higher than phylogenetically derived divergence rates of 0.087 to 0.236 mutations/bp/Myr (Hasegawa et al., 1993; Stoneking et al.,
1992; Tamura and Nei, 1993).
Although there are insufficient data to provide robust estimates on pedigree divergence rates for proteincoding regions of human mitochondrial DNA, Howell
etal. (2003) have presented some suggestive data by
pooling data from three studies (Cavelier et al., 2000;
Howell etal., 1996, 2003), arriving at a divergence
rate of 0.06 mutations/bp/Myr, approximately three
times higher than the phylogenetic rate of 0.02 mutations/bp/Myr for protein-coding mitochondrial DNA
(but note that Howell et al., 2003, incorrectly assert that
the pedigree-derived estimate is approximately 30 times
higher than the phylogenetic rate). Thus, bearing in mind
the paucity of protein-coding pedigree data, current estimates place the mitochondrial DNA pedigree control
region and protein-coding rates to be approximately 5 to
10 times and 3 times higher than their respective phylogenetic rates.
To investigate further the transition between pedigree mutation rates and long-term mutation rates, Ho
et al. (2005) have estimated rates of change (c.f. rate of
divergence) from mitochondrial sequences of primate
(protein-coding and control region) and avian (proteincoding) taxa and compared these rates in the context of
338
VOL. 56
SYSTEMATIC BIOLOGY
the time points from which they were calibrated. In all
three cases it was found that there was a measurable transition between the high, short-term (<2 Myr) and the low,
long-term (>2 Myr) mutation rate. Furthermore, it was
found that the relationship between the age of the calibration and the rate of change can be described by a vertically translated exponential decay curve. On the basis
of their results, Ho et al. (2005) advocate that rate curves
may be used for correcting divergence date estimates by
taking the proposed rate decay into account.
The results of Ho et al. (2005) have far-reaching implications for any study involving the use of intra- or interspecific sequence data on a timescale less than 2 Myr, so it
is pertinent to assess their results critically. The robust nature of a study such as theirs relies primarily on four elements: (1) the reliability of the DNA sequence data, (2) the
ability of the methodology to accurately estimate genetic
divergence values, (3) the representative nature of the
sampling, and (4) the accuracy and validity of the calibration points. If we accept at face value the sequence data
obtained by Ho et al. (2005) from the published literature,
we are left with distance estimation, representative sampling, and calibration as potential sources of error within
the analyses of Ho et al. (2005). Here I provide a critical reanalysis of the data of Ho et al. (2005) in the context of these potential sources of error and demonstrate
that, beyond the pedigree data summarized by Howell
et al. (2003), there is no evidence for time dependency of
molecular rate estimates. Similar to Ho et al. (2005), rates
were estimated using Bayesian analysis as implemented
in the program BEAST vl.3 (Drummond etal., 2002;
Drummond and Rambaut, 2003) with a relaxed molecular clock. Analyses by Ho et al. (2005) were performed
with an unreleased version of BEAST (Ho, personal communication) that allowed rates to vary throughout the
tree in an autocorrelated manner, with the rate in each
0.20
TT
branch being drawn from an exponential distribution
whose mean was equal to the rate in its parent branch.
BEAST vl.3 uses an uncorrelated model of rate change,
and rates have been sampled from a lognormal distribution. Following a burn-in of 1,000,000 cycles, rates were
sampled once every 500 cycles from 10,000,000 Markov
chain Monte Carlo (MCMC) steps. I used the computer
program Tracer vl.2.1 (Rambaut and Drummond, 2005)
to ensure that (1) chains had converged to a stationary
distribution and (2) effective sample sizes were greater
than 100, as recommended (Drummond and Rambaut,
2003).
ESTIMATION OF GENETIC DIVERGENCE
The most extreme rate estimate Ho et al. (2005) obtained for primate protein-coding mtDNA comes from
their reanalysis of cytochrome b (cytb) sequence data
obtained for Mandrillus sphinx by Telfer etal. (2003)
(Fig. 1). Using a calibration date of 0.8 Mya (million
years ago) and applying Bayesian analysis with a relaxed clock model as implemented by the program
BEAST, they obtained a mean mutation rate estimate
of 0.116 mutations/bp/Myr. This is in fact a rather curious result. Ho et al. (2005) assert that, with three exceptions (chimpanzee-bonobo split, chimpanzee-human
split, and Neandertals), calibration dates used in their
study are based on either paleontological or biogeographical data. However, in the case of the mandrill data
set, the calibration date of 0.8 Mya is not of paleontological or biogeographical origin. Rather, it is derived from
Telfer et al. (2003) applying a phylogenetic nucleotide
substitution rate estimate (0.035 mutations/bp/Myr) for
silent sites within the primate cytb gene (Pesole et al.,
1999) to their six haplotypes to obtain an age estimate
for the most recent common ancestor (mrca) of M. sphinx.
Ignoring the circularity in using a date derived from the
0.20
(a)
0.15
0.15
•0, o.io
o
O)
c
0.10
0.05
0.05
(b)
(0
o
o
a:
o
10
15
20
25
30
35
40
o
10
o
15
20
o
25
o
30
35
40
Age of calibration (Myr)
FIGURE 1. Estimated rate of change (in average nucleotide changes per site per million years) plotted against the date used to calibrate the
estimate for mtDNA protein-coding genes of primate taxa for (a) Ho et al. (2005) and (b) this study. Data points represent the mean value, and
error bars denote 95% credibility intervals. The open triangle represents cytb data for Mandrillus sphinx (Telfer et al., 2003). Open circles represent
cytb data compiled by Ho et al. (2005) for the following divergences (from left to right): chimpanzee-bonobo, chimpanzee-human, gorilla-human,
gibbon-hominidae, anthropoid-cercopithecoid, platyrrhine-catarrhine. Closed circles represent ND4 data compiled by Ho et al. (2005) for the
following divergences (from left to right): chimpanzee-human, gorilla-human, orangutan-human, gibbon-hominidae, anthropoid-cercopithecoid,
platyrrhine-catarrhine. The closed triangle represents the gorilla-human split (Horai et al., 1995).
2007
339
POINTS OF VIEW
same molecular data, simply through applying Bayesian
analysis with a relaxed clock model, Ho et al. (2005) have
obtained a mutation rate estimate among M. sphinx sequences substantially higher than the rate estimate of
Pesole et al. (1999). Given that all but one of the mandrill
substitutions occur at silent sites, one would expect the
rate estimate of Ho et al. (2005), estimated across all sites,
to be lower than that of Pesole et al. (1999), which is estimated across only silent sites. That the rate estimate of
Ho et al. (2005) is approximately three times higher than
that of Pesole et al. (1999) suggests that this is an artefact
of the Bayesian analysis.
This discrepancy between rate estimates may be due
to problems of parameter identifiability in the analysis
of Ho et al. (2005) that used an autocorrelated relaxed
clock. Unlike the uncorrelated model, the autocorrelated
model requires a prior probability distribution (prior)
on the rate at the root as well as a model of autocorrelated rate change. It is thus possible that there were
simply too many parameters in the analysis, given the
relatively low information content of the sequences (Ho,
personal communication). Parameter nonidentifiability
has the potential to confound rate estimates, and
Sullivan et al. (1999) have previously demonstrated
problems for parameter estimation related to the limited
information content of sequences. For the mandrill
analysis, as for all of their analyses, Ho et al. (2005)
estimated rates using the HKY+F+I model (Hasegawa
et al., 1985; Yang, 1994). Analysis of MCMC parameter
estimates for kappa (transition/transversion bias),
pinv (proportion of invariable sites), and alpha (the
gamma-distribution shape parameter) reveal these to be
distributed uniformly throughout the sampling interval,
particularly for kappa and alpha, irrespective of the
bounds placed upon the sampling interval. Although
this may be largely inconsequential for rate estimates
with regard to alpha and pinv, increased upper bounds
for kappa can lead to increased rate estimates (personal
observation). To avoid this problem, I used maximum
likelihood estimates using PAUP* as initial values for
parameters with lower and upper bounds of 80% and
120%, respectively, of their value. Within their original
analysis, Telfer et al. (2003) used the simpler HKY model
of sequence evolution (Hasegawa et al., 1985), and this
is in fact the model of sequence evolution selected by
the Akaike information criterion (AIC) for the mandrill
sequence data using PAUP* v4.0bl0 (Swofford, 1988) in
conjunction with Modeltest v3.7 (Posada and Crandall,
1998). The simpler but more appropriate HKY model of
sequence evolution, with appropriate parameterization
of kappa, yields a mutation rate estimate of 0.023 mutations/bp/Myr, a value not at odds with the traditional
phylogenetic estimate. For all subsequent analyses I
have used the model with the best AIC score for each
data set as determined with ModelTest, with each
parameter given lower and upper bounds of 80% and
120%, repectively, of the ML estimate of the initial value.
One of the two extreme rate estimates Ho et al. (2005)
obtained for primate noncoding mtDNA (0.37 mutations/bp/Myr) comes from their estimated mutation
rate for the control region in an analysis comprising four
contemporary human control region sequences and four
Neandertal ancient DNA sequences, with the rate estimate calibrated using the radiocarbon dates of the Neandertal sequences. Repeating the analysis of Ho et al.
(2005) highlights an error in tree estimation that compromises the estimation of substitution rate from this data
set. Trees sampled from the post-burn-in chain are not
rooted with Neandertals and humans as sister groups;
instead a monophyletic group of human sequences is
nested within paraphyletic Neandertal sequences. Neither constraining both clades to be monophyletic nor
enforcing a strict clock resolved the problem. It would
appear that the sampling dates from the Neandertal sequences are confounding the tree construction as the removal of these dates does result in reciprocal monophyly
for both groups. Here I have undertaken a two-stage
analysis of the same sequence data set as Ho et al. (2005)
to obtain a control region mutation rate specific for Neandertals. In a first analysis I have derived an estimate for
the age of the mrca of the four Neandertals. In a second
analysis I have used this age to estimate the mutation
rate for the control region within Neandertals.
Age Estimate for the Neandertal Mrca
To estimate the age of the mrca of Neandertals, I have
included the four Neandertal sequences and sequences
from human, chimpanzee, and gorilla, with the appropriate sampling dates applied for each of the sequences,
and using the HKY mutation model. Inspection of tree
files from an initial analysis revealed that the majority
of topologies were incorrect, often to an alarming degree (e.g., Neandertals branching off basally, resulting in
greatly inflated estimates of mutation rate). Thus, for a
subsequent analysis, I imposed monophyly constraints
for (1) the four Neandertal sequences; (2) Neandertals
and humans; and (3) Neandertals, humans, and chimps.
Age constraints from the fossil record were also incorporated. The calibration age used by Ho et al. (2005) for the
split between the gorilla lineage and the lineage giving
rise to the other three taxa is 7.5 Myr, so I have constrained
the root to be no older than 8 Myr. The calibration age
used by Ho et al. (2005) for the split between the chimpanzee lineage and the human lineage is 5 Myr, so I have
constrained the age of this node to be between 4 and
6 Myr. Additionally I have constrained the age of the
human-Neandertal split to be no older than the 620 kya
(thousand years ago) age estimate of Krings et al. (1997).
Other age estimates exist (Krings et al., 1999; Ovchinnikov et al., 2000), but that of Krings et al. (1997) is the
oldest, and thus most conservative for a Neandertal control region rate estimate. No minimum age constraint
was imposed for this node, and a starting tree compatible with the constraints was used. The age estimate for
the Neandertal mrca from this analysis is 295 kya.
Estimated Mutation Rate for Neandertal Control Region
I performed two analyses to estimate the mutation rate
for a data set comprising the four Neandertal control
340
SYSTEMATIC BIOLOGY
VOL. 56
data as it incorporates all calibration points, including
the more important 1.5 Mya. Pan paniscus-Pan troglodytes
data point not included in the ND4 data set. I have parameterized the analysis using the best-fit model for the
primate cytb data set (GTR+F+I model) and constrained
the analysis so that for each of the calibration points,
the group of taxa associated with the calibration point is
monophyletic. It is clear from Figure 1 that, with a more
rigorous analytical approach, the trend described by Ho
et al. (2005) no longer exists for primate protein-coding
mitochondrial DNA.
The curvilinear relationship described by Ho et al.
(2005) for avian protein-coding mtDNA sequence data is
essentially driven by nine data points with calibrations
of 1 Myr or less. Among these nine data points there are
four phylogenetically independent divergence events for
three geologically independent calibration points. Eight
of the nine data points come from a study of Indian Ocean
sunbirds by Warren et al. (2003) where data from three
mitochondrial gene regions (ATPase6, cytb, and ND4)
were analyzed using a combined data approach to construct phylogenetic relationships. Warren et al. (2003)
identify three nodes from their phylogeny that can be
used as calibration points, and these are used in the reanalysis of Ho et al. (2005). However, Ho et al. (2005)
have converted these three nodes into eight data points
by analyzing the three mitochondrial regions individually. Given the obvious linkage between these three mitochondrial genes, and the fact that the same individual
birds were sequenced for each region, phylogenetic independence is compromised. Here, I have analyzed these
three divergence events using a combined data approach
(Fig. 2). The remaining data point of 1 Myr or less comes
from Krajewski and King's (1996) phylogenetic analysis of cranes. Krajewski and King (1996) identify four
calibration points encompassing nine phylogenetically
independent diversification events. Ho et al. (2005) have
sampled only four of these nine calibration points, but
here I include all nine, which includes an additional data
point of 1 Myr or less.
Additional calibration points of 1 Myr or less exist
within the data set of Fleischer et al. (1998) but were not
analyzed by Ho et al. (2005).. Fleischer et al. (1998) present
molecular phylogenetic data for the drepanidines of the
Hawaiian Islands and illustrate an apparent relationship
between separation time and molecular divergence for
three calibration points derived from the geological ages
REPRESENTATIVE SAMPLING
of the Hawaiian Islands. Ho et al. (2005) incorporate only
In addition to the Mandrillus sphinx data set, Ho et al. two of these calibration points when in fact a total of
(2005) have used seven hominid calibrations for their pri- five can be identified using the criteria of Fleischer et al.
mate protein-coding analyses. Some of these are from the (1998). The additional two are (1) the Kauai and Hawaii
fossil record, whereas others are derived from molecu- akepa split and (2) the Kauai and Oahu/Maui/Hawaii
lar data combined with paleontological estimates. Most amakihi split. Here I include all five calibration points,
of these calibration points are represented by two mi- which include two additional data points of 1 Myr or
tochondrial genes, cytb and ND4, for the same lineage less. Additional avian mtDNA data calibration points,
divergence event, but given the linkage of these genes all greater than 10 Myr, come from Randi's (1996) phythere is an inherent lack of phylogenetic independence. logenetic analysis of Alectoris partridges and Nunn and
Thus, a more appropriate strategy is for either the analy- Stanley's (1998) study of tube-nosed seabirds. As with
sis of a single region, or the combination of both mtDNA the other analyses, I have parameterized with the approprotein-coding regions. Here, I have analyzed the cytb priate mutation model and the necessary monophyly
region sequences and using the HKY model. For the first
analysis I circumvented using the sampling ages associated with the sequences by reducing the age of the mrca
to 253 kya. This treats the Neandertal sequences as if
they had been sampled contemporaneously by reducing
the age of the mrca by the maximum sampling age of
the sequences. This will, if anything, provide an overestimate of the mutation rate because whereas two of
the sequences have sampling dates of 42 kya, the other
two sequences have sampling dates of 40 kya and 29
kya. This analysis gave an estimated mutation rate of
0.05 mutations/bp/Myr, a value compatible with traditional phylogenetic estimates. For the second analysis, I incorporated the sampling ages for each of the
sequences and obtained a mutation rate estimate of 0.79
mutations/bp/Myr, a value more than 10 times higher
than the previous estimate.
The only sensible explanation for the much higher
rate estimate when sampling dates are incorporated is
that, rather than reflecting the time dependency of the
control-region mutation rate, it is an artefact resulting
from a limitation with incorporating noncontemporaneous sequence samples for BEAST analyses. Repeating the
analysis of the human-Neandertal sequence data set with
the mutation parameters of Ho et al. (2005), I arrived at
an even higher rate estimate (1.98 mutations/bp/Myr)
and could only obtain a value close to the published estimate (0.37 mutations/bp/Myr) by placing an upper
bound on the mutation rate so that it did not exceed the
pedigree rate estimate of Howell et al. (2003; 0.475 mutations/bp/Myr). It would appear that the rate estimate
obtained by Ho et al. (2005) is flawed, due primarily to
a problem associated with the BEAST software for the
analysis of non-contemporaneous sequence samples.
For all subsequent analyses, I have enforced monophyly constraints such that a group of taxa associated
with the calibration point is monophyletic. This appears
to be a critical constraint, as BEAST does not require a
user-specified tree topology (Drummond and Rambaut,
2003), and if trees are sampled where the group of interest is not monophyletic, this will result in exaggerated
rate estimates. This problem was particularly apparent
for the primate control region data, where sampled trees
in the absence of monophyly constraints were often topologically incorrect.
2007
POINTS OF VIEW
20
Age of calibration (Myr)
FIGURE 2. Estimated rate of change (in average nucleotide changes per site per million years) plotted against the date used to calibrate the
estimate for mtDNA protein-coding genes of avian taxa for (a) Ho et al. (2005) and (b) this study. Data points represent the mean value, and
error bars denote 95% credibility intervals, (a) Open circles, grey filled circles, and filled circles represent cytb, ATPase6, and ND4 divergences,
respectively, among sunbirds of the Indian Ocean (Warren et al., 2003). In (b) these data have been combined and are represented by open circles.
Open diamonds represent cytb divergences among Hawaiian drepanidines (Fleischer et al., 1998). Filled triangles represent cytb divergences
among cranes (Krajewski and King, 1996). The open triangle represents the divergence between chickens and partridges (Randi, 1996). Filled
diamonds represent divergences within the Procellariiformes (Nunn and Stanley, 1998).
constraints have been applied. Although two out of
seven rate reestimates generated from recent time points
are notably higher than the rest (Fig. 2), both can be adequately explained without recourse to arguments of time
dependency.
Assumption 3: Divergence Events Do Not
Predate Island Ages
Two phenomena can lead to the violation of this assumption, and thus the overestimation of mutation rate
estimates. The first involves population genetic variation within the ancestral island population (Fig. 3). If
CALIBRATION ACCURACY
haplotype and nucleotide diversity are appreciable in
The two high avian rate estimates come from the In- the ancestral population, then the greater is the probdian Ocean island archipelago-based analysis of Warren ability that the gene coalescent time between descenet al. (2003), who expand on the work of Fleischer et al. dent lineages on different islands predates the island
(1998) to identify eight assumptions, which when vio- age. This may be controlled for by using contemporary
lated will lead to incorrect rate estimates when dating intra-specific levels of variation as a proxy (Wilson et al.,
nodes from island ages. Excluding assumptions regard- 1985), but sampling in the sunbird and drepanidine studing lineage rate variation and branch length estimation, ies is not adequate to do this. Importantly, the inflation
two of these assumptions, and an additional assumption of the rate estimate due to ancestral population variation
(Emerson, 2002), will lead to elevated rate estimates if will be greater for more recent time points. The second
they are violated.
phenomenon that can lead to overestimation of mutation rate estimates is lineage extinction (Fig. 4), and island archipelagos are perhaps the one system where the
Assumption 1: K-Ar Dates of Earliest Subaerial Lavas and
pervasive role of extinction has been best documented
Island Ages Are Correctly Estimated
(e.g., Emerson, 2003; Emerson and Kolm, 2005; Emerson
Clearly, if island ages are underestimated, this will lead
and Oromi, 2005; Gillespie, 2004; MacArthur and Wilson,
to an overestimation of mutation rate estimates.
1967; Ricklefs and Bermingham, 2001).
Given these assumptions, it seems unlikely that the
Assumption 2: Subaerial Lavas Representing the First
two high rate estimates reflect a general trend of time
Emergence of the Island above Sea Level Are Accessible to
dependency for molecular rate estimates, particularly so
Geologists and Have Not Been Deeply Buried by More
when five other rate estimates for time points of 1 Myr
Recent Strata
or less do not deviate from rate estimates generated from
Similar to assumption 1, if the earliest lavas are buried, older time points.
The final extreme rate estimate presented by Ho et al.
then island ages will be underestimated, leading to an
overestimation of mutation rate estimates. Recent arthro- (2005) comes from an analysis of Amerindian control repod analyses on the Canary Islands have demonstrated gion sequences from the Nuu-Chah-Nulth tribe (Kolman
the use of molecular phylogenetic data to corroborate et al., 1995; Ward et al., 1991). For their analysis, Ho
geological speculation of older lavas lying hidden be- et al. (2005) have calibrated the mrca of this sequence
data set with a date of 24,000 years, representing the
neath younger terrain (Emerson et al., 2006).
342
SYSTEMATIC BIOLOGY
Divergence predates colonisation
VOL. 56
Simultaneous colonisation and divergence
' divergence
• colonisation
colonisation <
time
divergence <
source island
colonised island
source island
colonised island
FIGURE 3. Ancestral population genetic variation, island colonization, speciation, and genetic divergence. In the first diagram, the two
contemporary taxa carry alleles that diverged prior to island colonization, and this would lead to the overestimation of mutation rate by
calibrating with the age of the colonized island. In the second diagram, genetic divergence is coincident with island colonization. The potential
effect of ancestral population genetic variation on the overestimation of mutation rate is greater for more recent colonization events.
Moheli
Moheli
Moheli
1 t
(a)
I Grande Comore
1 Grande Comore
Madagascar
Madagascar
Africa
•Africa
Africa
•Africa
Grande Comore
Grande Comore
(b)
I Madagascar
• Madagascar
Africa
Africa
Africa
Africa
j Moheli
1
Moheli
Moheli
I Anjouan
J*
I Anjouan
(c)
I Grande Comore
• Grande Comore
Madagascar
Madagascar
Africa
Africa
Africa
-Africa
FIGURE 4. Lineage extinction and incomplete sampling of extant taxa are important considerations when estimating the ages of colonization
events from a molecular phylogeny. (a) Phylogenetic relationships among island subspecies oiNectarinia notata and mainland species of Nectarinia
(modified from Warren et al., 2003). The filled circle denotes the node assigned an age of 0.5 Myr for calibrating the divergence between the
Moheli and Grande Comore subspecies, under the assumption that the youngest island of Grande Comore (maximum age 0.5 Myr) is the most
recently colonized, (b) In the event of the extinction of the subspecies on Moheli, the same calibration strategy would result in an overestimate
of the substitution rate, (c) An extinct sister taxa of the Gran Comore subspecies (in this case a hypothetical species on Anjouan) would lead to
an overestimate of the substitution in (a).
2007
POINTS OF VIEW
30
0
5
10
15
20
25
Age of calibration (Myr)
FIGURE 5. Estimated rate of change (in average nucleotide changes per site per million years) plotted against the date used to calibrate the
estimate for mtDNA control region sequences of primate taxa for (a) Ho et al. (2005) and (b) this study. Data points represent the mean value,
and error bars denote 95% credibility intervals. Open circles represent data compiled by Ho et al. (2005) for the following divergences (from
left to right): Neandertals, chimpanzee-bonobo (represented twice), chimpanzee-human, orangutan-human, anthropoid-cercopithecoid. The
closed circle represents data for Amerindians (Ward et al., 1991). The filled triangle represents an additional estimate for the chimpanzee-human
divergence (Vigilant et al., 1991). The open triangle represents the gorilla-human divergence taken from the data of Ho et al. (2005). The pedigree
estimate of Howell et al. (2003) has been excluded.
2003) compared with the more moderate mutation rates
typically inferred from phylogenetic studies. This begs
the question of when the apparent high rate estimate derived from pedigree data falls to a level compatible with
traditional phylogenetic estimates, and this is a fundamentally important question for molecular evolutionary
biologists. Ho et al. (2005) have presented data suggesting that for time points up to 2 Mya, rate estimates may
be inflated above traditionally held values, but analyses presented here leave little, if any, cause for concern.
That is not to say that the phenomenon that Ho et al.
(2005) have attempted to address is neither an important
nor interesting one. However, it would seem likely that
the time-scale upon which the pedigree rate converges
to the evolutionary rate is very much shorter than the
timescale Ho et al. (2005) have focused on, and it is debatable whether this convergence would follow an exponential distribution, or if such a pattern existed, whether
it could not be equally explained by coalescent effects.
The present study does highlight some concerns with
the use of Metropolis-Hastings Markov chain Monte
Carlo (MCMC) integration to estimate both mutation
rates and divergence dates. Several factors can lead to
the exaggeration of mutation rate and divergence date
estimates. Adequate parameterization is clearly needed,
particularly when divergences between sequences are
low (personal observation), and care must be taken to
ensure that sampled trees are not at odds with the
specific hypotheses being tested. Finally, the incorporation of noncontemporaneously sampled sequences in
the analyses conducted here has also led to erroneous
results. The findings presented here carry implications
for recent studies, many of which incorporate ancient
DNA sequences, where MCMC integration has been carCONCLUSIONS
ried out for the estimation of divergence dates (e.g.,
Studies based on pedigree data have produced re- Bunce et al., 2003; Weinstock et al., 2005), mutation rates
markably high estimates of mutation rate (Howell et al., (e.g., Lambert et al., 2002; Ritchie et al., 2004; Shapiro
midpoint between the estimates of 15,000 (Morrell, 1990)
and 33,000 (Dillehay and Collins, 1988) years for the entrance of humans into the Americas. The flaw in the
analysis of this data point is that it assumes that NuuChah-Nulth tribe mtDNA diversity is derived from a
single founding mitochondrial lineage. This is clearly
not the case, as Nuu-Chah-Nulth haplotypes are not
monophyletic when placed in reference to other mtDNA
sequences from outside the Americas. In their original
paper, Ward et al. (1991) pointed out that the magnitude
of sequence divergence within the Nuu-Chah-Nulth suggests that the origin of this diversity predates the entry of
humans into the Americas. The Nuu-Chah-Nulth are genetically quite diverse, representing much of the genetic
diversity present across both Amerind and Na-Dene
tribes (Kolman et al., 1995), which belongs to four founding haplotypes groups (Schurr, 2004). As such, there is
no reliable date for calibrating the mrca of this data set
and it must be removed from the analysis.
For the remaining control region rate estimates (Fig. 5),
I have used the same sequence data as Ho et al. (2005) and
the same calibration points, with one exception. The deep
time point of 25.85 Myr representing the anthropoidcercopithecoid split has been removed (the age of this
event is clearly outside of the time frame for which the
control region can be considered phylogenetically useful) and the more recent time point of 7.5 Myr representing the split between the gorilla lineage and the chimpanzee/human lineage has been added. It is clear from
Figure 5 that with a more rigorous analytical approach
the trend described by Ho et al. (2005) no longer exists
for primate noncoding mitochondrial DNA.
344
SYSTEMATIC BIOLOGY
VOL. 56
Horai, S., K. Hayasaka, R. Kondo, K. Tsugane, and N. Takahata. 1995.
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Howell, N., I. Kubacka, and D. A. Mackey. 1996. How rapidly does the
ACKNO WLEDG EMENTS
human mitochondrial genome evolve? Am. J. Hum. Genet. 59:501509.
I would like to thank Tammy Steeves, Melanie Pierson, and Neil
Gemmell for stimulating discussion and helpful comments on an ear- Howell, N., C. B. Smejkal, D. A. Mackey, P. F. Chinnery, D. M. Turnball,
and C. Herrnstadt. 2003. The pedigree rate of sequence divergence
lier version of the manuscript, and two anonymous referees and Simon
in the human mitochondrial genome: There is a difference between
Ho for helpful comments and suggestions. Particular thanks to Simon
phylogenetic and pedigree rates. Am. J. Hum. Genet. 72:659-670.
Ho for providing additional detail not contained within the original
manuscript. Thank you also to Neil Gemmell and the University of Kolman, C. J., E. Bermingham, R. Cooke, R. H. Ward, T. D. Arias, and F.
Guionneau-Sinclair. 1995. Reduced mtDNA diversity in the Ngobe
Canterbury for providing office space and facilities during a sabbatical
Amerinds of Panama. Genetics 140:275-283.
visit.
Krajewski, C, and D. G. King. 1996. Molecular divergence and phylogeny: Rates and patterns of cytochrome b evolution in cranes. Mol.
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Syst. Biol. 56(2):345-355,2007
Copyright © Society of Systematic Biologists
ISSN: 1063-5157 print / 1076-836X online
DOi: 10.1080/10635150701286549
Seeing the Trees for the Network: Consensus, Information Content, and Superphylogenies
OLIVIER GAUTHIER AND FRANCOIS-JOSEPH LAPOINTE
Departement de sciences biologiques, Universite de Montreal, C.P. 6128, Succursale Centre-Ville, Montreal (Quebec) H3C 3J7, Canada;
E-mail: [email protected];[email protected]
Phylogenetic inference often leads to solutions made
up of multiple trees on a given set of leaves or taxa. These
competing hypotheses might be the equally optimal
trees obtained from the analysis of a single matrix
using maximum parsimony (Hennig, 1979) or maximum likelihood (Felsenstein, 1981) or the set of most
probable trees produced by Bayesian analysis (Rannala
and Yang, 1996; Larget and Simon, 1999; Mau et al.,
1999). They might also have been inferred independently from different data sets or even be the result
of resampling methods such as the bootstrap or the
jackknife (Felsenstein, 1985; Penny and Hendy, 1985,
1986). Consensus methods are commonly used to identify areas of conflict and agreement among such multiple trees; they can represent the relationships that
are supported either unanimously or by a majority of
trees while discarding other, less supported relationships (Bryant, 2003). Thus, a consensus method is usually defined as a function that takes as input a set,
or profile, of trees on the same set of taxa and returns a single tree on the same set of taxa (Leclerc and
Cucumel, 1987; Steel et al., 2000; Bryant, 2003). This
function can take different forms, and many consensus
methods have been proposed (see Swofford, 1991;
Bryant, 2003, for reviews), amongst which the strict consensus (Sokal and Rohlf, 1981) and majority-rule consensus (Margush and McMorris, 1981) are perhaps the
most widely used and understood. These various functions differ in two major respects: (1) the kind of information they preserve and (2) the way they deal with
conflict among input trees. Indeed, the information contained in a tree can be considered in terms of nesting,
three- or four-taxon statements, components, and branch
lengths, while conflict can be left unresolved or dealt
with using different criteria (Bryant, 2003). Notwithstanding these differences, most methods abide to the
prevailing phylogenetic model: that of a tree embedding
a hierarchy of descent. This model puts forward a fully
resolved, or binary, tree as the ideal representation of
evolution. In practice, consensus trees are seldom binary
and they embed—i.e., are compatible with—multiple
binary trees. Indeed, because it is often impossible to
distinguish between hard and soft polytomies (Nelson
and Platnick, 1980; Maddison, 1989) and because the latter can be resolved in a number of different ways, an
unresolved tree can be refined by a set of binary trees