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© 2007 Society of Systematic Biologists
Alarm Bells for the Molecular Clock? No Support for Ho et al.'s Model of Time-Dependent Molecular Rate Estimates
Edited by Jack Sullivan: Associate Editor
1 Centre for Ecology, Evolution and Conservation, School of Biological Sciences, University of East Anglia Norwich, NR4 7TJ, UK E-mail: b.emerson{at}uea.ac.uk
Received March 6, 2006; Revised June 6, 2006; Accepted September 28, 2006 In a recent paper, Ho et al. (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 et al., 1997; Sigurdardottir et al., 2000; Soodyall et al., 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 50x) 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 protein-coding regions of human mitochondrial DNA, Howell et al. (2003) have presented some suggestive data by pooling data from three studies (Cavelier et al., 2000; Howell et al., 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 (protein-coding) taxa and compared these rates in the context of 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 v1.3 (Drummond et al., 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 branch being drawn from an exponential distribution whose mean was equal to the rate in its parent branch. BEAST v1.3 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 v1.2.1 (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).
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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 et al. (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 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.
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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+
+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* v4.0b10 (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 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.
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In addition to the Mandrillus sphinx data set, Ho et al. (2005) have used seven hominid calibrations for their primate protein-coding analyses. Some of these are from the fossil record, whereas others are derived from molecular data combined with paleontological estimates. Most of these calibration points are represented by two mitochondrial genes, cytb and ND4, for the same lineage divergence event, but given the linkage of these genes there is an inherent lack of phylogenetic independence. Thus, a more appropriate strategy is for either the analysis of a single region, or the combination of both mtDNA protein-coding regions. Here, I have analyzed the cytb 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+
+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.
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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 of the Hawaiian Islands. Ho et al. (2005) incorporate only two of these calibration points when in fact a total of five can be identified using the criteria of Fleischer et al. (1998). The additional two are (1) the Kauai and Hawaii akepa split and (2) the Kauai and Oahu/Maui/Hawaii amakihi split. Here I include all five calibration points, which include two additional data points of 1 Myr or less. Additional avian mtDNA data calibration points, all greater than 10 Myr, come from Randi's (1996) phylogenetic analysis of Alectoris partridges and Nunn and Stanley's (1998) study of tube-nosed seabirds. As with the other analyses, I have parameterized with the appropriate mutation model and the necessary monophyly 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.
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The two high avian rate estimates come from the Indian Ocean island archipelago–based analysis of Warren et al. (2003), who expand on the work of Fleischer et al. (1998) to identify eight assumptions, which when violated will lead to incorrect rate estimates when dating nodes from island ages. Excluding assumptions regarding lineage rate variation and branch length estimation, two of these assumptions, and an additional assumption (Emerson, 2002), will lead to elevated rate estimates if they are violated.
Assumption 1: K-Ar Dates of Earliest Subaerial Lavas and Island Ages Are Correctly Estimated
Clearly, if island ages are underestimated, this will lead to an overestimation of mutation rate estimates.
Assumption 2: Subaerial Lavas Representing the First Emergence of the Island above Sea Level Are Accessible to Geologists and Have Not Been Deeply Buried by More Recent Strata
Similar to assumption 1, if the earliest lavas are buried, then island ages will be underestimated, leading to an overestimation of mutation rate estimates. Recent arthropod analyses on the Canary Islands have demonstrated the use of molecular phylogenetic data to corroborate geological speculation of older lavas lying hidden beneath younger terrain (Emerson et al., 2006).
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 haplotype and nucleotide diversity are appreciable in the ancestral population, then the greater is the probability that the gene coalescent time between descendent lineages on different islands predates the island age. This may be controlled for by using contemporary intra-specific levels of variation as a proxy (Wilson et al., 1985), but sampling in the sunbird and drepanidine studies is not adequate to do this. Importantly, the inflation of the rate estimate due to ancestral population variation will be greater for more recent time points. The second 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 pervasive role of extinction has been best documented (e.g., Emerson, 2003; Emerson and Kolm, 2005; Emerson and Oromí, 2005; Gillespie, 2004; MacArthur and Wilson, 1967; Ricklefs and Bermingham, 2001).
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Given these assumptions, it seems unlikely that the two high rate estimates reflect a general trend of time dependency for molecular rate estimates, particularly so when five other rate estimates for time points of 1 Myr or less do not deviate from rate estimates generated from older time points.
The final extreme rate estimate presented by Ho et al. (2005) comes from an analysis of Amerindian control region sequences from the Nuu-Chah-Nulth tribe (Kolman et al., 1995; Ward et al., 1991). For their analysis, Ho et al. (2005) have calibrated the mrca of this sequence data set with a date of 24,000 years, representing the 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 Nuu-Chah-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 anthropoid-cercopithecoid 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.
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Conclusions |
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Studies based on pedigree data have produced remarkably high estimates of mutation rate (Howell et al., 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 carried out for the estimation of divergence dates (e.g., Bunce et al., 2003; Weinstock et al., 2005), mutation rates (e.g., Lambert et al., 2002; Ritchie et al., 2004; Shapiro et al., 2004), and demography (e.g., Biek et al., 2006; Drummond et al., 2005), and these may need to be reevaluated.
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Acknowledgements |
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I would like to thank Tammy Steeves, Melanie Pierson, and Neil Gemmell for stimulating discussion and helpful comments on an earlier version of the manuscript, and two anonymous referees and Simon Ho for helpful comments and suggestions. Particular thanks to Simon Ho for providing additional detail not contained within the original manuscript. Thank you also to Neil Gemmell and the University of Canterbury for providing office space and facilities during a sabbatical visit.
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References |
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