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Using Time-Structured Data to Estimate Evolutionary
Rates of Double-Stranded DNA Viruses
Submission: Research Article
Cadhla Firth1, Andrew Kitchen1, Beth Shapiro1, Marc A. Suchard2,3, Edward C.
Holmes1,4, Andrew Rambaut4,5
1Department of Biology, The Pennsylvania State University, University Park, PA, USA
2Departments of Biomathematics and Human Genetics, David Geffen School of Medicine,
University of California, Los Angeles, CA, USA
3Department of Biostatistics, School of Public Health, University of California, Los Angeles, CA,
4Fogarty International Center, National Institutes of Health, Bethesda, MD, USA
5Institute of Evolutionary Biology, University of Edinburgh, Edinburgh, UK
Corresponding Author: Cadhla Firth
Mailing Address: 722 W 168th St. 17th floor, Center for Infection and Immunity,
Columbia University, New York, NY 10032, USA
Keywords: double-stranded DNA viruses, nucleotide substitution rates, evolution, codivergence,
Running head: Evolutionary Rates of dsDNA Viruses
MBE Advance Access published April 2, 2010
Double-stranded (ds) DNA viruses are often described as evolving through long-term
codivergent associations with their hosts, a pattern that is expected to be associated with low
rates of nucleotide substitution. However, the hypothesis of codivergence between dsDNA
viruses and their hosts has rarely been rigorously tested, even though the vast majority of
nucleotide substitution rate estimates for dsDNA viruses are based upon this assumption. It is
therefore important to estimate the evolutionary rates of dsDNA viruses independent of the
assumption of host-virus codivergence. Here, we explore the use of temporally-structured
sequence data within a Bayesian framework to estimate the evolutionary rates for seven human
dsDNA viruses, including variola virus (the causative agent of smallpox) and herpes simplex
virus-1. Our analyses reveal that while the variola virus genome is likely to evolve at a rate of
approximately 1 x 10-5 substitutions/site/year, and hence approaching that of many RNA
viruses, the evolutionary rates of many other dsDNA viruses remain problematic to estimate.
Synthetic data sets were constructed to inform our interpretation of the substitution rates
estimated for these dsDNA viruses and the analysis of these demonstrated that given a
sequence data set of appropriate length and sampling depth, it is possible to use time-
structured analyses to estimate the substitution rates of many dsDNA viruses independently
from the assumption of host-virus codivergence. Finally, the discovery that some dsDNA
viruses may evolve at rates approaching those of RNA viruses has important implications for
our understanding of the long-term evolutionary history and emergence potential of this major
group of viruses.
The relationships between pathogens and their hosts are highly variable, ranging from newly
emergent zoonotic infections such as SARS coronavirus (Peiris et al. 2004), to codivergent
associations that span millions of years, like those seen in the papillomaviruses (Bernard et al.
2006). Recently, a concerted effort has been made to unravel the phylogenetic and
demographic contexts that have led to this diversity of relationships (Pérez-Losada et al. 2007,
Rector et al. 2007, Katzourakis et al. 2009, Smith et al. 2009). In particular, methodological
advances have enabled the incorporation of temporal information from time-structured
sequence data into strict or relaxed molecular clock models (Drummond et al. 2005, 2006,
Drummond and Rambaut 2007), which can then be used to estimate the timing of
epidemiologically important events (cross-species transmissions, epidemic outbreaks), as well
as historically important ones (the origin of multiple viral subtypes, host-pathogen
codivergence). RNA viruses are particularly well-suited to analyses of this type as their rapid
replication rate, large population sizes and error-prone polymerase result in large amounts of
genetic diversity being generated in measurable amounts of evolutionary time. Sequence
analysis programs such as BEAST (Bayesian Evolutionary Analysis by Sampling Trees) are of
particular importance in this regard as they utilize the genetic variation present in a sample to
simultaneously estimate both demographic and evolutionary parameters in the context of time
and space (Drummond et al. 2005, 2006, Drummond and Rambaut 2007, Lemey et al. 2009).
Codivergence with host species over thousands or millions of years has often been
invoked as the primary evolutionary mechanism shaping the diversity of many DNA (and some
RNA) viruses (Beer et al. 1999, Charrel et al. 1999, Sugimoto et al. 2002, Nemirov et al. 2004).
Importantly, inferences about key aspects of viral biology including the rate of evolutionary
change in the viral genome and the time-scale of speciation events, have often been made
based on the assumption of host-virus codivergence, which automatically places the evolution
of these viruses on the same scale as their hosts (Nakao et al. 1997, Hughes and Friedman
2000, Sugimoto et al. 2002, Nishimoto et al. 2006, Krumbholz et al. 2008). However, by
incorporating timing information from time-sampled (heterochronous) sequences into inferences
about the history of viral populations, it is possible to generate independent estimates of the rate
and time-scale of virus evolution, without requiring the strong assumption of codivergence.
Critically, analyses of this type have demonstrated that some host-virus systems that were once
thought to be examples of codivergence may in fact be the result of much more recent
evolutionary associations (Shackelton et al. 2006, Romano et al. 2008, Harkins et al. 2009,
Ramsden et al. 2009, Lewis-Rogers and Crandall 2009).
Despite wide-spread interest in using novel statistical models that incorporate
heterochronous data to answer a wide range of biological questions, concerns have been raised
surrounding biases in evolutionary rate estimates that may be inherent to these methods (Ho et
al. 2005, Ho and Larson 2006, Emerson 2007, Ho et al. 2007b, Penny 2005, Navascues and
Emerson 2009). For example, a time-dependent relationship has been demonstrated to exist
for the molecular clock, such that molecular evolution is accelerated on short time-scales (Ho et
al. 2005, Ho and Larson 2006, Ho et al. 2007a,b). Concerns have also been raised regarding
the tendency of inference tools to recover substitution rates that are too rapid when population
structure in the data is unaccounted for, or when inappropriate calibration points are used (Ho et
al. 2008, Navascues and Emerson 2009). Ascribing times to samples and accommodating
these in analyses is effectively an assertion that these times span a consequential proportion of
the total evolutionary history of the taxa in question, and conditions the analysis on rates that
are sufficiently high that this is true. Such analyses have been used extensively to estimate the
evolutionary and epidemiological characteristics of a wide range of rapidly evolving RNA and
single-stranded (ss) DNA viruses, and appear to return estimates that accord well with the
known epidemiology of these pathogens (Shackelton et al. 2005, de Oliveira et al. 2006, Bryant
et al. 2007, Rambaut et al. 2008, Firth et al. 2009). However, the utility of these methods in
estimating the evolutionary dynamics of double-stranded (ds) DNA viruses, which may evolve
far more slowly than RNA viruses, has not yet been investigated. Indeed, the use of
heterochronous phylogenetic modeling has resulted in surprisingly high evolutionary rate
estimates for JC virus (Shackelton et al. 2006), variola virus (Li et al. 2007) and the bacterium
Neisseria gonorrhoeae (Pérez-Losada et al. 2007).
In this study, we examine the ability of current inference tools to estimate relatively low
evolutionary rates such as those thought to commonly characterize dsDNA viruses. Indeed,
Rector et al. (2007) suggest that dsDNA viruses are inappropriate for time-structured analyses
because their low mutation rates (~0.003 mutations/genome/replication, Drake 1991, Drake and
Hwang 2005, Duffy et al. 2008) will lead to immeasurable levels of genetic change over a given
sampling interval. This raises the possibility that the high rates of evolutionary change
previously reported for dsDNA viruses arise spuriously, and possibly inevitably, from the models
employed. However, if no measurable evolutionary change has occurred within a given
sampling period, we would expect any analytical outcomes to exhibit behavior consistent with a
lack of temporal structure in the data. Here, we use a variety of human dsDNA virus systems to
investigate the ability of heterochronous phylogenetic modeling to (i) accurately estimate the fit
of a molecular clock to dsDNA virus data sets with varying sample sizes and distributions, (ii)
recover the correct nucleotide substitution rate or reveal that there is a lack of temporal structure
in the data, and (iii) place the time to the most recent common ancestor (TMRCA) of these
viruses within the correct time frame (when known). To further assess the behavior of these
analytical tools, we created synthetic data sets under a variety of sampling schemes and
substitution rates, from an ‘RNA virus-like’ rate of 1x10-4 subs/site/year to a ‘dsDNA virus-like’
rate of 1x10-8 subs/site/year. Using these data we examined the ability of standard modeling
tools to recover the nucleotide substitution rate and TMRCA from a population when the true
evolutionary history of a sample is known.
We considered seven dsDNA viruses in our analysis. Human papillomavirus type-16
(HPV-16) is one of more than 100 human viruses within the large Papillomaviridae family of
dsDNA viruses with small genomes ranging from ~6 to 8 kbp. Many types of HPV (including
HPV-16) apparently exhibit strong patterns of codivergence with human populations, mirroring
the global movement of humans out of Africa, and clustering phylogenetically by ethnicity rather
than by current geographic distribution (Ong et al. 1993, Calleja-Macias et al. 2005, Bernard et
al. 2006, Chen et al. 2009). The rate of nucleotide substitution for HPV-18 has been estimated
at ~4.5x10-7 substitutions per site per year (subs/site/year) based on codivergence with human
populations, similar to estimates obtained for the feline papillomaviruses (1.95x10-8
subs/site/year), again assuming codivergence (Ong et al. 1993, Rector et al. 2007).
Two members of the Alphaherpesvirinae were also included in this analysis: Herpes
Simplex Virus-1 (HSV-1), and Varicella-Zoster virus (VZ). Herpesviruses are large dsDNA
viruses (genomes range from 125 to 240 kbp) that infect both vertebrates and invertebrates.
Phylogenies of the alphaherpesviruses show topologies highly congruent with those of their
diverse tetrapod hosts, and evolutionary rates for HSV-1 have been estimated at 3.5x10-8 to
3.0x10-9 subs/site/year based on the assumption of a codivergent history with their hosts
(Sakaoka et al. 1994, McGeoch et al. 2000). In contrast, the evolutionary history of VZ is less
conclusive, with evidence of both a codivergence relationship with humans (Wagenaar et al.
2003) and a more recent origin suggested by phylogenetic analyses (Muir et al. 2002).
BK virus is a human polyomavirus with a ~5 kbp genome that is closely related to JC
virus. Polyomaviruses were historically considered examples of human-virus codivergence, and
both BK and JC viruses have been used as markers for patterns of human evolution and
migration. However, more rigorous phylogenetic analyses of the relationship between a variety
of polyomaviruses and their primate hosts have suggested that no significant similarities in tree
topology or evolutionary time-scale exist between these groups (Pérez-Losada et al. 2006,
Shackelton et al. 2006, Zheng et al. 2007, Krumbholz et al. 2008). Estimates of the rate of
evolution of BK virus are greatly affected by the use of different calibration assumptions, ranging
from an intra-host rate estimate of 2-5x10-5 subs/site/year (Chen et al. 2004), to rates of
1.41x10-7 to 4x10-8 subs/site/year based on the assumption of codivergence between viral and
human populations (Yasunaga and Miyata 1982, Krumbholz et al. 2008).
Variola virus (VARV) is the etiological agent of the human-specific pathogen smallpox,
from the Poxviridae family (genome size = ~190 kbp). The first unequivocal description of
smallpox in human populations occurred in 4th Century A.D. in China, although cases have been
suspected as far back as 1122 B.C (Li et al. 2007). Previous estimates based on time-
structured sequence data have placed the origin of smallpox at 207-231 ybp using strict and
relaxed clocks, respectively (Li et al. 2007). However, this extremely recent estimate has been
disregarded as being at odds with both historical/epidemiological data and with the low genetic
diversity identified in serially-sampled sequences (Esposito et al. 2006, Li et al. 2007). As a
result, these authors have suggested that their evolutionary rate estimates may be upwardly
biased by the use of heterochronous phylogenetic models. In contrast, calibration with historical
records of smallpox infection (all of which are debatable) placed the TMRCA for VARV at 1,400
- 6,300 ybp, depending on the choice of calibration point, with correspondingly lower substitution
rates (Li et al. 2007, Babkin and Shchelkunov 2008, Hughes et al. 2009, Shchelkunov 2009).
Importantly, any calibration of contemporary strains using historical records is potentially
problematic as selective sweeps and population bottlenecks can purge genetic diversity from
the population, resulting in a TMRCA that is far more recent than the historical association of the
virus with its host.
The origin(s) and emergence patterns of human adenoviruses (HAdV, genome sizes
range from ~26 to 45 kbp) are considerably more vague. The Adenoviridae form five distinct
clades, corresponding to their mammal, reptile, bird, amphibian and fish hosts. This
phylogenetic structure has led to the hypothesis that the five lineages codiverged along with the
host classes, with an estimated date for the split between human and chimpanzee adenoviruses
at ~5.5 mya (Benkö and Harrach 2003). Subsequent work has demonstrated that while some
HAdV groups may show cursory support for a codivergent history with primates (Subtype C),
other groups do not (Subtypes B and E). In addition, examination of the primate adenoviruses
shows that the majority of human and non-human adenoviruses are mixed throughout the tree
(Madisch et al. 2005, Roy et al. 2009).
Materials & Methods
Virus Data Sets
Data sets for each of the seven dsDNA viruses were compiled based on availability in GenBank.
Full genome sequences were used when available; otherwise, appropriate smaller gene
segments were used to maximize the size of the data sets. In all cases, the sampling year was
also collected for each sequence, and only samples that had not been exposed to extensive
laboratory manipulation were included. The details of all data sets are shown in table 1. Each
data set was aligned manually using Se-Al (v2.0a11 Carbon,
http://tree.bio.ed.ac.uk/software/seal) and examined for evidence of recombination using the
Bootscan, Chimaera, GENECONV, MaxChi, RDP, and SisScan methods with default
parameters, implemented in the RDP3 software package (Martin et al. 2005). Potential
recombinant sequences were identified when three or more methods within RDP3 were in
agreement with P<0.001. All potential recombinants were removed from further analysis.
Maximum likelihood (ML) phylogenies were estimated using PAUP* (4.0b, Swofford 2003) for
each alignment using the tree-bisection-reconnection method of branch swapping and the best
nucleotide substitution model as determined by Modeltest (v3.7, Posada and Crandall 1998).
The clock-like behavior of each data set was then assessed using a regression of root-to-tip
genetic distances inferred from the ML trees against sampling time in the program Path-O-Gen
(v1.1, http://tree.bio.ed.ac.uk/software/pathogen/; Drummond et al. 2003). Under this analysis
the correlation coefficient indicates the amount of variation in genetic distance that is explained
by sampling time. This provides a correlative measure of the goodness-of-fit of the data to a
strict molecular clock, and designates a root for the phylogeny that is most consistent with a
Phylogenies incorporating sampling time were then estimated for each data set using
the Bayesian Markov Chain Monte Carlo (MCMC) inference methods made available in BEAST
(v.1.4.8, Drummond and Rambaut 2007). These analyses were run using either the HKY or
GTR model of nucleotide substitution, and with or without an among-site rate heterogeneity
parameter (gamma) depending on the model that best fit the data. For protein coding genes,
the alignment was also partitioned into codon positions, while the full genome alignments also
included a parameter for invariant sites. Genealogies were estimated under (i) a strict
molecular clock, (ii) a relaxed molecular clock with an uncorrelated lognormal distribution
(UCLN) of rates, and (iii) a relaxed molecular clock with an uncorrelated exponential distribution
(UCED) of rates. A variety of prior probability distributions on the parameter characterizing the
rate of evolutionary change under a molecular clock were explored. These included both a
uniform distribution with boundaries at 0 and 100, and an exponential distribution with mean
expectations that ranged from 1.0x10-6 to 1.0. The evolutionary and coalescent parameters
were estimated under both the hypothesis of a constant population size, and using the less
constrained Bayesian skyline coalescent model (Pybus et al. 2000, Strimmer and Pybus 2001,
Drummond et al. 2005). A minimum of two independent MCMC simulations for each model-
clock combination were performed for no less than 100 million generations, sub-sampling every
10,000 generations to decrease auto-correlation between model parameter samples. The two
runs were combined for inspection after removing a 10% burnin from each, and statistical
confidence in the parameter estimates was assessed by reporting marginal posterior parameter
means and their associated 95% highest probability density (95% HPD) intervals.
To test the temporal signature present in these data sets, we used a tip-date
randomization technique (Duffy and Holmes 2009, Ramsden et al. 2009). Here, a null
distribution of mean substitution rates was generated by randomizing the sampling date
associated with each sequence, 20 times per alignment. The substitution rate was then re-
estimated in BEAST for each randomized data set under the best-fitting model for the true data,
as above. To assess the significance of the temporal structure present in the data, the mean
evolutionary rate estimate from the observed data was compared to the 95% HPDs estimated
from the randomized data sets. We also expect the lower tail of the 95% HPD of the
evolutionary rates from the randomized data to be large, and tend strongly towards zero.
Synthetic Data Sets
Synthetic data sets were used to test the ability of heterochronous phylogenetic modeling to
correctly recover the true nucleotide substitution rates from a range of values that may exist in
DNA viruses (1.x10-4 to 1x10-8 subs/site/year), given the type of data used in the first part of this
study. Synthetic data sets were generated to reflect the evolutionary processes in two of the
seven dsDNA data sets analyzed, VARV and HSV-1, which represent the typical range one
might encounter in an analysis of temporally sampled data (table 1). The VARV-like synthetic
data consisted of 50 sequences of 100,000 bp sampled from 1946 to 1982 (similar to a full-
genome alignment), while the HSV-1-like synthetic data consisted of 84 sequences that were
1200 bp in length, sampled from 1981 to 2008 (a typical single-gene alignment). Sequences for
each data set were generated in the following manner. The year-of-sampling distribution
associated with the sequences was fixed to those values from the VARV and HSV-1 data sets
and random phylogenies were drawn from a coalescent process based on each group of taxa
(N = 50 or 84) using an MCMC algorithm and assuming a constant population size. The root
height for each phylogeny was fixed at one of the following intervals: 100 ybp, 1000 ybp, 10,000
ybp, 100,000 ybp, and 1,000,000 ybp. Sequences of the appropriate length were simulated
along each random tree following the HKY model of sequence evolution with data set-specific
base frequencies and transition/transversion ratios based on the ML estimate of these values
from the actual virus data sets. Gamma distributed rate variation was also initially added to the
HSV-1-like simulations, but as the inclusion of this parameter did not impact the results of the
simulations, it was removed from additional replications (data not shown). For the first set of
synthetic data, the rate of evolution followed a strict molecular clock (standard deviation around
the mean rate of 0.0) set at one of the following values corresponding to each specified value of
the root height: 1x10-4 subs/site/year (when the root height was 100 ybp), 1x10-5 subs/site/year,
1x10-6 subs/site/year, 1x10-7 subs/site/year and 1x10-8 subs/site/year (when the root height was
one million ybp). Twenty independent replicate data sets were created for each root
height/clock rate, and each virus-type. These synthetic data sets contained a similar number of
variant sites to the actual data sets, indicating that we were correctly modeling the true pattern
of evolution (data not shown). By co-varying the tree height and substitution rate in this manner,
the observed genetic diversity of each synthetic data set was held constant and similar to that
observed in the VARV and HSV-1 data sets. This allowed for a direct assessment of the power
of this method to estimate substitution rates under successive conditions in which smaller
proportions of overall genetic diversity can be attributed to the sampling interval. Posterior
inference was performed on each data set assuming a strict molecular clock, the HKY model of
nucleotide substitution and constant population size. MCMC simulations were run for 100
million generations, with sub-sampling every 10,000 generations. Convergence of all
parameters was verified visually using the program Tracer
An additional set of simulations was performed using both the HSV-1 and VARV-like
data, but incorporating branch-rate heterogeneity into the sequence simulation process. In this
case, sequences were evolved assuming a UCLN relaxed molecular clock with mean rates of
1x10-6, 1x10-7 and 1x10-8 subs/site/year and a standard deviation of 2.0 around the mean, with
corresponding root heights as above. Twenty replicate data sets were created with each
substitution rate for each virus type, and the posterior inferences were performed assuming a
strict clock, as above. The recovered estimates of the nucleotide substitution rates and TMRCA
(posterior mean and 95% HPD) from each group of simulations were then compared to the
known values of the simulated data. The number of simulations that included the true rate and
TMRCA estimates within the 95% HPDs was recorded for each clock rate/root height. In total,
320 MCMC analyses of simulated data were performed, 160 each for VARV- and HSV-1-like
data. A sample xml file for use in BEAST is included as Supplementary Information.
Inference of Substitution Rates
The Bayesian MCMC inference of each dsDNA virus data set converged efficiently on a
posterior mean value for all parameters with correspondingly narrow posterior distributions
around the mean rate and TMRCA. No substantial differences in the posterior estimates of the
mean evolutionary rates were observed when the initial values or prior distribution of the rate
parameter were varied. The mean evolutionary rates estimated for the seven dsDNA virus data
sets ranged from 10-6 to 10-3 subs/site/year (VARV/VZ and HPV-16, respectively) (table 2). The
95% HPDs ranged from 10-7 (HAdV-C) to 10-2 subs/site/year (HPV-16), and varied by no more
than an order of magnitude from their corresponding posterior mean in either direction (table 2).
Interestingly, with the exception of HPV-16, the mean evolutionary rates estimated were also
highly consistent across data sets, ranging from 6 x 10-6 to 8 x 10-5 subs/site/year. These
estimates were highly robust to choice of clock, rate distribution or demographic model
parameters, but were much higher than expected based on previous estimates of the
substitution rate of dsDNA viruses (table 2) (Duffy et al. 2008, Bernard 1994). In fact, the
evolutionary rates estimated for HPV-16, HSV-1, BK virus, HAdV-B and HAdV-C all approached
those measured in RNA viruses (Jenkins et al. 2002, Duffy et al. 2008). In addition, these high
rates were associated with extremely recent TMRCA estimates in all cases, ranging from ~10
ybp (HPV-16) to ~800 ybp (BK) (table 2).
Most dsDNA viruses are thought to evolve primarily through codivergence with their
hosts, and this process should be reflected in low rates of evolutionary change (Villarreal et al.
2000, Holmes 2004, Holmes and Drummond 2007). If we allow that the seven dsDNA viruses
used in this study do indeed evolve at a low rate consistent with a codivergent history (an
assumption that is not contentious in many cases), the possibility must be considered that the
high substitution rates estimated here are the result of estimation error, and do not reflect the
true evolutionary history of the data. As it is possible that such erroneous results are due to a
shallow sampling interval relative to the actual time scale of evolution (figure 1), we assessed
the strength of the temporal structure in our data sets by utilizing a randomization procedure.
The sequence-sampling time associations in each data set were randomized 20 times per virus
and the evolutionary rates were re-estimated from each of these data sets. The hypothesis of
significant temporal structure was rejected when the value of the mean evolutionary rate
estimated from the real data fell within the 95% HPDs of those estimated from the randomized
data. Comparisons between the actual and randomized estimates for each virus revealed
significant support for the presence of temporal structure in the data in all but two cases (HAdV-
C and VZ) (figure 2). Indeed, the 95% HPDs of the actual rate estimates fell outside the entire
distribution of the randomized data sets for HSV-1, BK, VARV and HAdV-B (figure 2).
Based on this analysis, it is clear that there is no support for a high substitution rate in
either HAdV-C or VZ. In contrast, the accuracy of the evolutionary rates for the remaining five
data sets cannot be discounted by this measure (figure 2). This latter result is surprising, given
the extremely rapid rate estimates that were recovered (table 2). If these sequences were
sampled over a time interval that was too narrow relative to the rate of viral evolution (i.e. recent
samples of slowly evolving/codiverging viruses), the dates at which the samples were taken
should confer little information about the evolutionary dynamics of the virus (figure 1).
Estimates of evolutionary rates from the actual and randomized data sets should then recover
comparable values, producing a pattern similar to that seen in HAdV-C and VZ (figure 2). One
caveat of this approach stems from the ability of the randomizations to break-up both temporal
and geographic structure in the data. Therefore, if hidden population substructure is
contributing to erroneous rate estimates (Navascues and Emerson 2009), it would be broken-up
by the temporal randomization process.
A conservative assessment of the degree of clock-like evolution present in a data set is
achieved by fitting a regression of the year-of-sampling against the root-to-tip genetic distance
of each sample, measured from an ML tree. When this regression was calculated for the seven
dsDNA virus data sets studied here, the resultant correlation strongly supported the presence of
molecular clock-like structure in VARV, weakly suggested the presence of clock-like evolution in
HAdV-B, HSV-1 and VZ, and revealed no support at all for this hypothesis in the HPV-16, BK
and HAdV-C data sets (figure 3). These results were not surprising for the HPV-16 data set
considering that the sequences were sampled over only a four-year interval (table 1), and are
consistent with the lack of temporal structure in the HAdV-C data identified by the randomization
analysis (figure 2).
Taken together, the heterochronous phylogenetic modeling analyses, randomization
procedure and regression analyses suggest the presence of high evolutionary rates in the HSV-
1, BK, VARV, and HAdV-B data sets, with varying levels of consistency. The VARV data set
was unique in that the relatively high rates of nucleotide substitution estimated by BEAST
(~9.32x10-6 subs/site/year, table 2) for this virus were strongly supported by both the
randomization and regression analyses (figures 2,3). In contrast, high substitution rates for the
HSV-1, BK, and HAdV-B data sets were supported by the randomization procedure, but showed
a weaker correlation between root-to-tip genetic distance and sampling time (R2 = 0.141, 0.004
and 0.327, respectively) than that found in VARV (R2 = 0.679).
When sequences were generated under a model approximating a strict molecular clock (i.e. all
branches of the tree evolve at the same rate), posterior inference was able to recover the
correct substitution rate with narrow 95% HPDs for all 20 replicates of both the VARV- and
HSV-1-like data sets when the rate was 10-4 subs/site/year (figure 4). The true substitution
rates were returned with similar accuracy and precision for the VARV-like data sets when the
rate was 10-5 or 10-6 subs/site/year (figure 4). However, at 10-7 and 10-8 subs/site/year the mean
substitution rates were consistently higher than the true values, but characterized by long-tail
posterior distributions tending towards zero (figure 4). For all VARV-like simulations, the true
substitution rate was contained within the 95% HPDs of the estimated rate, as were the
estimated TMRCAs (data not shown). We were considerably less successful at recovering the
true substitution rates for the HSV-1-like synthetic data sets. When the true substitution rate
was 10-5 subs/site/year, the posterior mean estimates were close to the true value; however,
some of the individual posterior distributions of the rate were highly skewed towards zero (figure
4). Similarly, when the set rate was 10-6 subs/site/year or lower, our tools were unable to
recover a mean rate that was close to the true value, and the 95% HPDs ranged from the
highest possible rate supported by the data, to a value approaching zero (figure 4). We
consider these widely skewed posterior distributions of the rate to signify a lack of significant
temporal structure in the data, an effect not seen in estimates based on our real data where
values close to zero were not observed.
To determine if the high substitution rates recovered for the dsDNA viruses analyzed in
the first part of this study could be a result of deviations from the molecular clock model coupled
with low temporal signal in the data, we added branch-rate heterogeneity (i.e. relaxed clock
behavior) to the synthetic data sets when the mean rate was set to 10-6, 10-7 and 10-8
subs/site/year, and re-estimated the rate of substitution. The posterior mean and 95% HPDs
estimated from these synthetic data sets were similar to those returned from the data simulated
under a strict clock (figure 5). When the true rate of the VARV-like data was set at 10-6
subs/site/year, the resultant estimates were close to the true values; however, substantial
deviations from the known values occurred when the rates were set to 10-7 or 10-8
subs/site/year, with correspondingly larger 95% HPDs (figure 5). The rates estimated from the
HSV-1-like data simulated with branch-rate heterogeneity also closely mirrored those from the
data simulated under a strict clock. The mean substitution rates estimated from all HSV-1-like
data were higher than the true values, and again associated with wide, long-tail posterior
distributions that tended towards zero (figure 5). As before, we consider these distributions to
indicate a lack of temporal structure in the data at these low evolutionary rates.
Based on the distribution of rates from our synthetic data sets, we are able to make a number of
general conclusions about the use of heterochronous data to estimate the substitution rates and
divergence times of potentially slowly evolving dsDNA viruses. In particular, given a data set
containing a large enough number of variable sites (such as the VARV data set), it is possible to
accurately estimate substitution rates that range from 10-4 to approximately 10-7 subs/site/year
using temporally sampled viruses, even if the data do not conform to a strict molecular clock
(figures 4, 5). This is dependent on the length of sequence, and for a data set containing only a
small number of informative nucleotide sites (as in the case of HSV-1), the temporal signal in
the data begins to break down at evolutionary rates below 1x10-5 subs/site/year (figures 4, 5).
In these cases, the sampling interval is probably too small relative to the rate of evolution of the
virus. Therefore, any substitution rate estimated using these types of data will likely not
converge on the true rate, but will instead return a wide posterior distribution of the rate that
tends towards zero (figure 5). This behavior is also likely to be robust to a poor fit to the
molecular clock (e.g. the use of a strict clock with highly rate-variable data), and can be
interpreted as an indication that the data are not appropriate for a temporal analysis by a
program such as BEAST.
Interestingly, the shape and lower tails of the posterior distributions estimated from our
synthetic data at low rates were similar to those returned from analyzing the HPV-16, HAdV-C
and VZ data sets (table 2). This strongly suggests that there is insufficient temporal structure in
these data to undertake an analysis of the nucleotide substitution rate in the absence of external
calibration points. However, a very different pattern was seen in the HSV-1, BK, VARV and
HAdV-B data sets (figure 4). Here, analysis of the observed data sets resulted in high
substitution rate estimates associated with tight 95% HPDs, a pattern that we were unable to
reproduce using the synthetic data even with the inclusion of large amounts of branch-rate
heterogeneity (i.e. when applying a standard deviation of 2.0log10 to the mean clock rate). As
such, extensive rate heterogeneity across the phylogeny is unlikely to explain the high
substitution rates observed in these viruses, and we are therefore unable to justify the high rates
of evolution measured for some of these dsDNA viruses by simply invoking estimation error.
The analysis of contemporaneously sampled, slowly evolving viruses results in a posterior
distribution that reveals the lack of structure in the data, a phenomenon unlike the posterior
distributions recovered from the analysis of these viruses. Hence, our simulations support the
conclusion that VARV is evolving at a rate close to 1x10-5 subs/site/year, and indicates that
there is no obvious flaw in the analysis of the HSV-1, BK and HAdV-B data sets that could result
in erroneous substitution rate estimates. Therefore, we accept high rates of evolution in VARV,
and tentatively suggest that high substitution rates may also occur in the thymidine kinase gene
of HSV-1, the HAdV-B hexon (capsid) gene, and potentially in BK virus, although further work is
clearly needed. It is also possible that these high rates are the result of model
misspecification(s) that have not yet been identified. We now consider the case of some of
these viruses in more detail.
The rate of nucleotide substitution in VARV obtained from our analysis (~1x10-5 subs/site/year),
accords well with rates previously estimated (and discarded) using a variety of methods.
Multiple attempts have been made to use historical documentation of the (potentially) first
smallpox outbreaks in endemically infected regions as calibration points to estimate the
divergence dates and substitution rate of VARV (Li et al. 2007, Babkin and Shchelkunov 2008,
Shchelkunov 2009). Accordingly, the choice of calibration points has dramatically influenced
many of these estimates, resulting in an approximate TMRCA for VARV ranging from 200 to
6000 ybp, with correspondingly variable substitution rates (Li et al. 2007, Babkin and
Shchelkunov 2008, Shchelkunov 2009). In most cases, these externally-calibrated estimates
are orders of magnitude lower from those achieved using temporally sampled sequences (Li et
al. 2007, this study). In an attempt to clarify the timescale of VARV evolution, Hughes et al.
(2009) estimated the substitution rate using the synonymous sites of 132 protein-coding genes
distributed throughout the genome, and scaled the rate around the two dates previously
suggested for the introduction of the P-II clade into South America (the 16th Century African
slave trade or the 18th Century West African slave trade). The use of either of these calibration
points had little impact on the overall rate estimate, which ranged from 4 - 6x10-6 subs/site/year
and was similar to both our rate estimate and that of Babkin and Shchelkunov (2008) (2 - 3x10-6
Two primary pieces of information have been used to support the idea that VARV is a
slowly evolving virus with a long history of association with human populations. The first is that
epidemiologically linked isolates appear to accumulate no mutational changes over the period of
one year (Li et al. 2007). However, it is also theoretically possible to explain this observation by
invoking selective sweeps or severe population bottlenecks during transmission, which act to
reduce the variability accrued during replication in a single individual. The second factor
opposing high evolutionary rates for VARV is the suggestion of congruence between historical
records of the introduction and spread of the virus in various locations, and the TMRCAs
estimated for the major VARV clades. However, as noted above, the use of historical records
as calibration points from which the rate and divergence times of viruses are estimated is
problematic. In particular, these epidemiological records do not necessarily correlate with the
true origin or introduction of a pathogen, as revealed by the different dates used for the same
introductions of VARV in multiple locations, and the last common ancestor of any
contemporaneously sampled set of viruses may be of more recent origin than the common
ancestor of the entire species (Hughes et al. 2009, Shchelkunov 2009). Calibrating evolutionary
analyses using a time point that predates the age of the most recent common ancestor of a
sample will bias the substitution rate and divergence date estimates towards a much older
history (and correspondingly lower substitution rates). In contrast, the current analysis only
estimates the TMRCA of the sample, not of VARV itself, and may therefore return TMRCA
estimates more recent than the known age of this human pathogen, particularly if there has
been a large-scale reduction in diversity (i.e. selective sweep or population bottleneck) in the
recent history of VARV. Although we cannot exclude all estimation errors in the case of VARV,
the high level of genetic variation in our data explained by temporal sampling (R2 = 0.68) lends
support to the existence of rapid evolutionary rates in VARV (Hughes et al. 2009, this study).
Herpes Simplex Virus-1
The cases of HSV-1 and HAdV-B are considerably more perplexing than that of VARV. The
estimated substitution rates for these viruses were highly consistent between models (table 2)
and were supported by the randomization test of temporal structure in the data (figure 2). In
addition, we were unable to reproduce similarly high estimates of the substitution rate from viral
data sets known to be slowly evolving through the analysis of synthetic data. In particular, the
possibility that genes within herpesviruses such as HSV-1 could be evolving at a rate of 10-5
subs/site/year is perhaps one of the most difficult results of this study to reconcile with the
biology of the virus as it is presently understood.
Herpesviruses are prototypic examples of host-pathogen codivergence, and comparing
the phylogeny of their vertebrate hosts with that of the virus indeed reveals strong topological
congruence (McGeoch and Cook 1994, McGeoch et al. 1995, 2000, Jackson 2005). However,
the substitution rate for herpesviruses such as HSV-1 has not previously been measured
independently from the hypothesis of codivergence. A key measure of the evolutionary rate of
herpesviruses originated from the analysis of 63 variable restriction endonuclease sites in 242
HSV-1 samples from three human populations represented by six countries: Asian (Korea,
Japan and China), African (Kenya) and European (Sweden and the USA) (Sakaoka et al. 1994).
Based on rough estimates of the divergence times between these ethnic groups (110,000 years
for the split between African and European/Asian populations, and 50,000 years for the split of
Asian from European groups) and the nucleotide differences between them, a substitution rate
of 3.5x10-8 subs/site/year was estimated (Sakaoka et al. 1994). This rate is two-to-three orders
of magnitude lower than any of the substitution rates we estimate here, including that of HSV-1
and VARV (table 2). Hughes et al. (2009) suggested previously that the HSV-1 rate of Sakaoka
et al. (1994) might be too low given the substitution rates estimated for VARV. However, a
gene-specific mutation rate of approximately 2x10-8 mutations/site/replication has been
experimentally derived for the thymidine kinase gene of HSV-1 (the same gene analyzed here),
an estimate congruent with both the substitution rate estimated by Sakaoka et al. (1994), and
for dsDNA viruses generally (Drake 1991, Lu et al. 2002, Drake and Hwang 2005).
If the mutation rate of HSV-1 is 2x10-8 mutations/site/replication, we must then ask if it is
possible for this rate to be translated into the substitution rate of 10-5 subs/site/year we
estimated? The most likely mechanism through which such an inflated substitution rate could
occur is through strong and continuous positive selection. To test for the presence of positive
selection within our HSV-1 thymidine kinase gene alignment, the overall ratio of
nonsynonymous to synonymous substitutions per site (dN/dS) was estimated using the program
HyPhy (Kosakovsky Pond et al. 2005). The dN/dS ratio for this data set was 0.700, consistent
with either localized positive selection on some codons or perhaps a substantial relaxation of
purifying selection on this gene, as has been previously suggested (Drake and Hwang 2005).
Hence, although positive selection may be contributing to the high substitution rates estimated
for this gene, it seems highly unlikely that such adaptive evolution could result in a substitution
rate that is three orders of magnitude higher than expected. We are therefore unable to
conclusively reconcile the high substitution rates estimated here for HSV-1 (and potentially the
related VZ virus), with what is known about the background mutation rate and biology of
herpesviruses. At the very least, our HSV-1 analysis strongly suggests that future research
should focus on acquiring sufficient herpesvirus data to allow for a rigorous estimate of the
substitution and replication rates of these viruses, independent from any assumption of
High Rates of Evolution in dsDNA viruses?
Clearly, the high rates of molecular evolution we have measured here for all seven dsDNA
viruses are not easily explained by the understood biology of these (and other) dsDNA viruses.
However, we cannot simply attribute the remarkably similar rate estimates across the seven
viruses to an error in the method of estimation, as we were unable to recover comparably high
estimates from the analysis of our synthetic data sets. While we have little confidence in the
rates estimated for some of our data sets (HAdV-C, VZ, HPV-16), others are suggestive of high
substitution rates in dsDNA viruses (VARV, HAdV-B, and perhaps HSV-1 and BK) and clearly
merit further investigation. It is possible to identify two general mechanisms that may be driving
the substitution rate of these viruses above the background mutation rate (~2x10-8 to 7x10-7
mutations/site/replication, Drake et al. 1998). First, as the rate of viral replication directly
impacts the long-term substitution rate (this parameter is analogous to generation time), very
high replication rates have the potential to inflate the substitution rates of dsDNA viruses
(McLysaght et al. 2003, Gubser et al. 2004, Esposito et al. 2006, Hughes et al. 2009). The
impact of high replication rates may be particularly important for those viruses that are highly
transmissible and/or result in acute infections in humans (VARV, HAdV-B), but are unlikely to
have a similar effect in those viruses causing asymptomatic, latent and/or chronic infections
(BK, HSV-1) in the host. Unfortunately, the replication rates of these viruses during natural
infections in the host are unknown. Second, as discussed in the context of HSV-1, strong
(diversifying) positive selection could also act to increase the substitution rate above the
(neutral) mutation rate. Positive selection is most likely to be observed in viruses that cause a
strong immune response in the host, or are the target of intense vaccination or intervention
campaigns. However, as with replication rates, relatively little is known about the extent and
nature of adaptive evolution in dsDNA viruses, although to date positive selection has not been
identified in the protein coding genes of VARV (Hughes et al. 2009).
More generally, understanding the mechanisms of dsDNA virus evolution is central to
the accurate assessment of these infectious agents as potentially emerging diseases of both
humans and animals, particularly as the focus thus far has been primarily directed toward RNA
viruses. Investigating the rates and processes of dsDNA virus evolution independent of the
hypothesis of codivergence therefore constitutes an important avenue for future research.
CF received funding from the Natural Sciences and Engineering Research Council of Canada.
MAS is support by United States Public Health Service grant GM086887. We thank the
National Evolutionary Synthesis Center for hosting the working group “Software for Bayesian
Evolutionary Analysis by Sampling Trees”, from which this project profited.
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Table 1. The gene, number of sequences, length (number of base pairs) and sampling interval
for each of the dsDNA virus used in this analysis.
Virus Gene No. of taxa Length (bp) Sampling
2005 - 2008
1981 - 2008
1983 - 2007
1986 - 2007
1970 - 2007
1946 - 1977
1978 - 2007
Genome (coding only)
Table 2. Mean and 95% highest probability density (HPD) of the Bayesian posterior estimates of substitution rate (subs/site/year)
and time to most recent common ancestor (TMRCA) (ybp) for seven dsDNA viruses: Human Papillomavirus Type-16, Herpes
Simplex Virus-1, Variola Virus (VZ), BK virus (BK), Variola virus (VARV), Human Adenovirus Subtype B (HAdV-B) and Human
Adenovirus Subtype C (HAdV-C). Estimates were made under a variety of molecular clock models (strict, relaxed with a lognormal
distribution of rates, and relaxed with an exponential distribution of rates), as well as under two demographic models (constant
population size and Bayesian Skyline (BS)). The best model was chosen as the one with the highest marginal likelihood (Suchard et
al. 2001), and is indicated with an asterisk (*).
Virus Clock Model Demographic
0.7490 – 9.812x10-4
0.0953 – 9.194x10-4
0.0001 – 14.91x10-3
0.0175 – 14.23x10-3
0.0494 – 2.164x10-3
0.0009 – 1.856x10-3
0.4995 – 1.264x10-4
0.5727 – 1.208x10-4
0.5027 – 1.274x10-4
0.5457 – 1.215x10-4
0.4386 – 1.398x10-4
0.4387 – 1.269x10-4
2.192 – 5.531x10-6
2.010 – 5.480x10-6
1.764 – 8.435x10-6
7 – 46
6 – 67
3 – 27
3 - 15
4 - 44
3 – 53
83 – 212
84 – 191
81 - 226
79 – 202
66 – 356
62 – 387
186 – 452
183 – 466
92 - 546
1.859 – 9.487x10-6
0.0697 – 2.050x10-5
0.0694 – 1.235x10-5
2.307 – 4.311x10-5
0.8400 – 3.466x10-5
2.515 – 5.371x10-5
1.344 – 4.681x10-5
2.877 – 6.700x10-5
2.416 – 6.411x10-5
7.847 – 10.20x10-6
7.772 – 10.16x10-6
5.889 – 10.53x10-6
5.905 – 10.48x10-6
5.157 – 13.09x10-6
4.977 – 13.84x10-6
0.3949 – 1.019x10-4
3.877 – 9.981x10-5
0.3479 – 1.043x10-4
0.3661 – 1.113x10-4
0.383 – 1.066x10-4
0.4087 – 1.125x10-4
0.5132 – 6.299x10-5
0.1006 – 5.146x10-5
0.9117 – 8.236x10-5
0.3472 – 8.545x10-5
1.009 – 7.528x10-5
0.0139 – 6.798x10-5
74 – 431
70 – 1031
51 – 741
734 - 1386
791 – 3180
436 - 1511
442 - 2200
303 - 1394
286 - 1550
167 - 218
168 - 220
136 – 313
136 - 309
85 - 366
76 – 372
31 - 68
27 - 62
28 - 111
24 - 98
29 – 91
25 – 75
71 – 591
62 – 937
32 – 441
22 - 503
45 - 444
37 - 628
Figure 1. Tree diagrams with identical taxa numbers sampled over identical time intervals.
When the sampling interval is similar to the time frame over which sequence evolution occurs
(10-4 subs/site/year), it is possible to assess the long-term rate of evolution with high precision
(a). When the sampling interval is small relative to the time frame of sequence evolution (10-8
subs/site/year), it may become difficult to accurately estimate substitution rates (b). The scale
bars indicate the branch lengths in number of years.
Figure 2. Posterior mean and 95% HPDs of the substitution rates estimated from the actual
data sets (far left value for each virus) and the 20 tip-date randomizations for the dsDNA viruses
Human Papillomavirus Type-16 (HPV-16), Herpes Simplex Virus-1 (HSV-1), BK virus (BK),
Variola virus (VARV), Human Adenovirus Subtype-B (HAdV-B), Human Adenovirus Subtype-C
(HAdV-C) and Varicella Zoster virus (VZ). The mean rates estimated for the HAdV-C and VZ
data sets were not significantly different from those estimated from the randomized data sets.
Figure 3. Genetic distance versus sampling year for the dsDNA viruses (clockwise from top
left): Human Papillomavirus Type-16 (HPV-16), Herpes Simplex Virus-1 (HSV-1), BK Virus
(BK), Variola Virus (VARV), Human Adenovirus Subtype B (HAdV-B), Human Adenovirus
Subtype C (HAdV-C), and Varicella Zoster Virus (VZ). The regression coefficient (R2) estimates
the fit of the data to a strict molecular clock by testing the degree of influence sampling time has
over the amount of pairwise diversity in the data. This analysis supports the presence of
temporal structure in the data for VARV and HAdV-B, while suggesting the presence of
temporal structure for HSV-1 and VZ. No evidence for temporal structure within the sampled
period was found for the HPV-16, BK and HAdV-C data sets using this method.
Figure 4. Substitution rates (posterior mean and 95% HPD) estimated from synthetic data sets
based on the VARV and HSV-1 data sets from the first part of this study. Twenty replicates of
both the VARV- and HSV-1-like data sets were generated under strict molecular clocks evolving
at each of 10-4, 10-5, 10-6, 10-7 and 10-8 subs/site/year. The dashed lines show the true mean
evolutionary rate for each group of simulations of the corresponding color. The mean and 95%
HPDs of the substitution rates for VARV and HSV-1 under the best evolutionary model are
shown for comparison.
Figure 5. Substitution rates (posterior mean and 95% HPD) estimated from simulated data sets
based on the VARV and HSV-1 data sets from the first part of this study. Twenty replicates of
both the VARV- and HSV-1-like data sets were generated under relaxed molecular clocks
evolving at each of 10-6, 10-7 and 10-8 subs/site/year. The dashed lines show the true mean
evolutionary rate for each group of simulations of the corresponding color. The mean and 95%
HPDs of the substitution rates for VARV and HSV-1 under the best evolutionary model are
shown for comparison.
Substitution Rate (log(subs/site/year)
Substitution Rate (log(subs/site/year))
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Substitution Rate (log(subs/site/year))