A general comparison of relaxed molecular clock models
Open accessAbstract
Several models have been proposed to relax the molecular clock in order to estimate divergence times. However, it is unclear which model has the best fit to real data and should therefore be used to perform molecular dating. In particular, we do not know whether rate autocorrelation should be considered or which prior on divergence times should be used. In this work, we propose a general bench mark of alternative relaxed clock models. We have reimplemented most of the already existing models, including the popular lognormal model, as well as various prior choices for divergence times (birth-death, Dirichlet, uniform), in a common Bayesian statistical framework. We also propose a new autocorrelated model, called the "CIR" process, with well-defined stationary properties. We assess the relative fitness of these models and priors, when applied to 3 different protein data sets from eukaryotes, vertebrates, and mammals, by computing Bayes factors using a numerical method called thermodynamic integration. We find that the 2 autocorrelated models, CIR and lognormal, have a similar fit and clearly outperform uncorrelated models on all 3 data sets. In contrast, the optimal choice for the divergence time prior is more dependent on the data investigated. Altogether, our results provide useful guidelines for model choice in the field of molecular dating while opening the way to more extensive model comparisons.
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TL;DR
The paper benchmarks relaxed molecular clock models and divergence-time priors in a common Bayesian framework, adding a new autocorrelated CIR process. Across three eukaryotic protein data sets, autocorrelated rate models fit better than uncorrelated ones, while the best divergence-time prior depends on the data set.
Key findings
- The strict clock was strongly rejected relative to the unconstrained model on all data sets, with log Bayes factors ranging from about −157 to −3,072.
- Autocorrelated models, LOGN and CIR, had similar fit and clearly outperformed uncorrelated models (UEXP, UGAM, WN) on nearly all data sets; LOGN was slightly favored except on MITO100, where they were equivalent, and MITO150, where CIR was significantly preferred.
- The Dirichlet prior was generally close to the uniform prior, whereas the birth-death prior was rejected in most cases (ln BF < −6) but strongly favored on MITO100 and MITO150 (ln BF > 45).
- Dense taxonomic sampling was important for distinguishing autocorrelated from uncorrelated models; with only 10 taxa, the uncorrelated models were comparable to the autocorrelated ones.
Methods
- The authors reimplemented seven relaxed-clock models—STRICT, UEXP, UGAM, WN, LOGN, CIR, and an unconstrained reference—and combined them with uniform, Dirichlet, and birth-death priors on divergence times.
- Data sets were MOC (129 genes, 30,399 positions, 36 eukaryotes), MAM (3 nuclear genes, 3,700 positions, 60 mammals), and MITO (11 mitochondrial protein-coding genes, 3,220 positions, 155 osteichthyans plus 5 chondrichthyans, with ingroup subsamples of 10, 50, 100, and 150 taxa).
- Posterior sampling used MCMC in an extension of PhyloBayes under the normal approximation, and model fit was compared by Bayes factors computed with thermodynamic integration.
Limitations
- The paper states that no fossil calibrations were used, so only relative divergence times were examined and no conclusions about absolute dates or root age are provided.
- The analyses fixed the tree topology, used the normal approximation exclusively, and did not account for heterogeneity across sites or data partitions.
- The authors note that the reasons for the birth-death prior’s data-dependent performance are unclear, that sampling error in Bayes factor estimates was on the order of a few log units, and that substitution-model effects and other relaxed-clock models were not investigated.
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- Findingown data§ A General Comparison of Relaxed Molecular Clock Models · p. 2
The best choice of prior on divergence times depends more on the particular data set analyzed.
“In contrast, the optimal choice for the divergence time prior is more dependent on the data investigated.”
Quote in the paperSubstantial claim - Findingown data§ Introduction · p. 3
The results provide strong evidence favoring autocorrelated models, particularly under rich taxonomic sampling.
“Our results provide strong evidence in favor of autocorrelated models such as the lognormal and the CIR models, in particular under rich taxonomic sampling.”
Quote in the paperSubstantial claim - Findingown data§ Results and Discussion · p. 7
For all six data sets, the strict molecular clock is overwhelmingly rejected in favor of the unconstrained model, with Bayes factors ranging from 157 to 3,072.
“We see that for all data sets, the molecular clock is overwhelmingly rejected in favor of the unconstrained model, with Bayes factors ranging from 157 to 3,072.”
Quote in the paperSubstantial claim - Findingown data§ Results and Discussion · p. 7
For almost all data sets, the Bayes factors of the uncorrelated relaxed models (WN, UGAM, UEXP) are significantly inferior to those of the autocorrelated relaxed clock models (LOGN and CIR).
“For almost all data sets, the Bayes factors of the relaxed but completely uncorrelated models (WN, UGAM, UEXP) are significantly inferior to those of the autocorrelated relaxed clock models (LOGN and CIR)”
Quote in the paperSubstantial claim - Findingown data§ Results and Discussion · p. 7
Only when the number of taxa is small (MITO10) are the uncorrelated models comparable to the autocorrelated models.
“Only when the number of taxa is small (MITO10) are the uncorrelated models comparable to the autocorrelated models.”
Quote in the paperSubstantial claim
- Findingown data§ Results and Discussion · p. 7
Under dense taxonomic sampling (MITO150), the UEXP and WN models performed worse than the unconstrained model.
“under dense taxonomic sampling (MITO150), the UExp and the WN models were so bad that they performed even worse than the unconstrained model.”
Quote in the paperSubstantial claim - Findingown data§ Results and Discussion · p. 7
For most data sets, the two autocorrelated models, LOGN and CIR, have comparable Bayes factors.
“For most data sets, the 2 autocorrelated models, LOGN and CIR, have comparable Bayes factors.”
Quote in the paperSubstantial claim - Findingown data§ Comparison of Alternative Priors on Divergence Times · p. 8
On MITO100 and MITO150, the birth-death prior is strongly favored over the two alternatives (ln BF > 45).
“on which it is strongly favored over the 2 alternatives (ln BF . 45).”
Quote in the paperSubstantial claim - Findingown data§ Relative Divergence Times · p. 10
This trend is also observed under the birth-death prior but is less pronounced.
“This trend is also observed under the birth-death prior (fig. 3 b ) but is less pronounced.”
Quote in the paperSubstantial claim - Findingown data§ Relative Divergence Times · p. 10
For most nodes, the posterior standard errors are much smaller than the prior standard errors under both the uniform and birth-death priors.
“We observe in both cases that, for most nodes, the posterior standard errors (SEs) are much smaller than the prior SEs”
Quote in the paperSubstantial claim - Findingreasoning§ Dispersion Index and Rate Autocorrelation · p. 8
UGAM has a lower fit than LOGN and CIR.
“the fact that UGAM has a lower fit than LOGN and CIR”
Quote in the paperSubstantial claim - Findingown data§ Relative Divergence Times · p. 9
WN is closer to the strict molecular clock than CIR in terms of posterior mean estimates.
“first, WN is closer to the strict molecular clock than CIR in terms of posterior mean estimates (fig. 2 a and b ).”
Quote in the paperNot a substantial claim - Findingown data§ Relative Divergence Times · p. 8
The number of node age estimates under STRICT that significantly depart from their counterpart under WN, UEXP, and UGAM is 45, 33, and 53, respectively.
“We found only 45, 33, and 53 significantly departing nodes between the STRICT and the WN, UEXP, and UGAM models, respectively.”
Quote in the paperSubstantial claim - Findingown data§ Relative Divergence Times · p. 8
Both the STRICT and WN models seem to yield relative age estimates significantly at odds with those obtained under the CIR model.
“First, both the STRICT (fig. 2 a ) and the WN models (fig. 2 b ) seem to yield relative age estimates significantly at odds with those obtained under the CIR.”
Quote in the paperSubstantial claim - Findingown data§ Relative Divergence Times · p. 8
There is a higher discrepancy between CIR and STRICT than between WN and STRICT.
“Interestingly, there is a higher discrepancy between CIR and Strict than between WN and Strict (compare fig. 2 a and b ).”
Quote in the paperNot a substantial claim - Findingown data§ Relative Divergence Times · p. 8
Relative ages under LOGN and CIR are much more similar.
“In contrast, relative ages under LOGN and CIR are much more similar (fig. 2 c ).”
Quote in the paperSubstantial claim - Findingown data§ Comparison of Alternative Priors on Divergence Times · p. 8
For all data sets except MITO150, the Bayes factor between the Dirichlet and uniform priors is at most a few natural units above or below zero.
“For all data sets except MITO150, the Bayes factor between the DIR and UNIF ranges at most a few natural units above or below zero”
Quote in the paperSubstantial claim - Findingown data§ Relative Divergence Times · p. 10
The uniform prior tends to push old nodes further toward the root.
“In particular, it tends to push old nodes further toward the root (fig. 3 a ).”
Quote in the paperSubstantial claim - Findingown data§ Comparison of Alternative Priors on Divergence Times · p. 8
The birth-death prior is rejected in favor of the uniform prior in all cases (ln BF < -6) except on MITO100 and MITO150.
“it is rejected in favor of the uniform prior in all cases (ln BF , -6), except on MITO100 and MITO150”
Quote in the paperSubstantial claim - Findingcitation§ Relative Divergence Times · p. 10
The birth-death prior appears less informative in this study than in Aris-Brosou and Yang (2003), as noted by Welch et al. (2005).
“Note that the birth-death prior appears here less informative than in Aris-Brosou and Yang (2003), as noted by Welch et al. (2005).”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites Aris-Brosou and Yang 2003
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- cites Welch et al. 2005
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- Findingown data§ Relative Divergence Times · p. 10
The optimal model (CIR + BD) found under MITO150 did not produce such patterns.
“We therefore checked that the optimal model (CIR þ BD) found under MITO150 (see fig. 1 b ) did not produce such patterns (fig. 4).”
Quote in the paperSubstantial claim - Interpretationreasoning§ Materials and Methods · p. 5
As time goes to infinity, the CIR process has a stationary gamma distribution with mean one and variance r^2/(2h).
“In fact, as t goes to infinity, the process has a well-defined stationary distribution, which is a gamma distribution with mean one and variance r 2 /2 h .”
Quote in the paperNot a substantial claim - Premisecitation§ Introduction · p. 2
The choice of model has a nonnegligible influence on the resulting divergence dates.
“More generally, the model seems to have a nonnegligible influence on the resulting divergence dates (PerezLozada et al. 2004; Smith et al. 2006)”
Quote in the paperSubstantial claim0 of 2 sources checked- cites PerezLozada et al. 2004
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- cites Smith et al. 2006
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- Interpretationreasoning§ Materials and Methods · p. 4
UEXP and UGAM are uncorrelated only between branches, not within the time window of each branch.
“In particular, such a time process would display autocorrelations within the time window defined by each branch, so that, strictly speaking, UGAM and UEXP are uncorrelated only between branches.”
Quote in the paperNot a substantial claim - Interpretationown data§ Results and Discussion · p. 7
The strict molecular clock is not adapted to describing the evolution of real sequences.
“indicating that the strict molecular clock is not adapted to describing the evolution of real sequences.”
Quote in the paperSubstantial claim0 of 3 sources checked- cites Takezaki et al. 1995
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- cites Suchard et al. 2001
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- cites Douzery et al. 2004
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- Premisenone given§ Introduction · p. 3
Posterior Bayes factors underestimate the dimensionality penalty and favor unnecessarily complex models.
“In practice, they lead to an underestimation of the dimensionality penalty, hence favoring unnecessarily complex models.”
Quote in the paperSubstantial claim - Interpretationown data§ Results and Discussion · p. 7
The Bayes factors observed in this study tend to indicate that the theoretical shortcomings of the LOGN model do not really affect its performance in practice.
“Yet, the Bayes factors observed here tend to indicate that such theoretical shortcomings do not really affect the LogN model's performances in practice.”
Quote in the paperSubstantial claim - Premisecitation§ Dispersion Index and Rate Autocorrelation · p. 8
Under a Poisson process of constant rate, the dispersion index equals 1.
“It is equal to 1 in the case of a Poisson process of constant rate, which is why its measure has been used as a test of the molecular clock hypothesis, it considered as a corollary of the neutral theory (Kimura 1983; Gillespie 1991).”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Kimura 1983
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- cites Gillespie 1991
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- Premisecitation§ Dispersion Index and Rate Autocorrelation · p. 8
A pattern of increasing dispersion index with time can be reproduced only under processes of rate variation having sufficiently long-range autocorrelations.
“a pattern that can be reproduced only under processes of rate variations having sufficiently longrange autocorrelations (Bickel and West 1998).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Bickel and West 1998
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- Interpretationown data§ Results and Discussion · p. 7
The necessity of dense taxonomic sampling to discriminate between autocorrelated and nonautocorrelated models may explain previous results in which no significant rate autocorrelation was detected in real data sets.
“may explain previous results, in which no significant rate autocorrelation was detected in real data sets (Drummond et al. 2006).”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Drummond et al. 2006
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- Premisecitation§ Dispersion Index and Rate Autocorrelation · p. 8
The dispersion index seems to be an increasing function of time t.
“Furthermore, is seems to be an increasing function of t (Ohta 1995)”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Ohta 1995
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- Premisecitation§ Dispersion Index and Rate Autocorrelation · p. 8
Overdispersion is observed in real sequences, with the dispersion index significantly greater than 1 in many cases.
“Overdispersion is indeed observed in real sequences (Gillespie 1991): the dispersion index is significantly greater than 1 in many cases.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Gillespie 1991
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- Interpretationown data§ Results and Discussion · p. 7
Dense taxonomic sampling is necessary to discriminate between autocorrelated and nonautocorrelated models.
“The fact that dense taxonomic sampling is necessary to discriminate between autocorrelated and nonautocorrelated models”
Quote in the paperSubstantial claim - Interpretationown data§ Results and Discussion · p. 7
Autocorrelation is an important feature of the variation of evolutionary rates across time.
“indicating that autocorrelation is an important feature of the variation of evolutionary rates across time.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Relative Divergence Times · p. 10
Thanks to autocorrelation, the rate and time estimates at each node can rely on both local and distant information, which may help reduce their variance.
“This makes some sense: thanks to autocorrelation, the rate, and time estimates at each node can rely on both local and distant information, which may help them to reduce their variance.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Dispersion Index and Rate Autocorrelation · p. 8
The lower fit of UGAM compared with LOGN and CIR indicates the presence of autocorrelation over times spanning several successive branches, something UGAM is unable to capture.
“indicates the presence of autocorrelation over times spanning several successive branches, something UGAM is unable to capture.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Dispersion Index and Rate Autocorrelation · p. 8
UGAM implies an autocorrelated rate process within each time window defined by the branches of the tree.
“that UGam does indeed imply an autocorrelated rate process R ( t ) within each time window defined by the branches of the tree.”
Quote in the paperSubstantial claim - Interpretationown data§ Comparison of Alternative Priors on Divergence Times · p. 8
The Dirichlet prior is more or less equivalent to the uniform prior.
“indicating that the Dirichlet is more or less equivalent to the uniform prior (table 2).”
Quote in the paperSubstantial claim - Interpretationown data§ Relative Divergence Times · p. 10
The two priors are not excessively informative in general.
“indicating that the 2 priors are not excessively informative in general.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Dispersion Index and Rate Autocorrelation · p. 8
The relative ordering of WN, UGAM, LOGN, and CIR in the Bayes factor evaluations provides evidence for the presence of autocorrelation at both small and large scales.
“And the relative ordering of WN, UGAM, and LOGN and CIR in our Bayes factor evaluations provides evidence for the presence of autocorrelation at both the small and the large scales.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Relative Divergence Times · p. 10
The use of squared instead of direct OU processes and flexible enough hyperpriors on the parameters of the birth-death process does not seem to yield an excessively biased model for molecular datings.
“Altogether, these checks indicate that the use of squared, instead of direct, OU processes and flexible enough hyperpriors on the parameters of the birth-death process does not seem to yield an excessively biased model for molecular datings.”
Quote in the paperSubstantial claim - Interpretationown data§ Conclusion · p. 10
The Bayes factor evaluations give a nearly unanimous answer in favor of autocorrelated models.
“Concerning the relaxation process, our comparisons give a nearly unanimous answer in favor of autocorrelated models”
Quote in the paperSubstantial claim - Interpretationreasoning§ Conclusion · p. 11
The lesser variance observed under the autocorrelated models compared with the uncorrelated ones will probably also be observed for absolute dates.
“In this respect, the lesser variance observed under the autocorrelated models, compared with the uncorrelated ones (fig. 2 a and b ), will probably also be observed for absolute dates.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Conclusion · p. 11
The conclusions likely transpose to situations where one tries to estimate absolute ages using fossil calibrations.
“but they likely transpose to situations where one tries to estimate absolute ages using fossil calibrations.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Relative Divergence Times · p. 10
The greater informativeness and contradiction of the uniform prior for old nodes could explain the better fit of the birth-death prior over the uniform one found for MITO150.
“This could explain the better fit of the birth-death prior over the uniform one found in the case of MITO150 (table 2).”
Quote in the paperSubstantial claim - Interpretationown data§ Relative Divergence Times · p. 10
The prior has an influence on age estimates, but this influence is moderate compared with that of the rate process.
“Hence, the prior has an influence, but this influence is moderate, compared with that of the rate process (fig. 2).”
Quote in the paperSubstantial claim - Interpretationreasoning§ Conclusion · p. 11
Relying on autocorrelation, at least through a model correctly capturing its properties, has the advantage of letting calibrations effectively inform age estimates across larger distances over the tree.
“The reason is again quite simple: relying on autocorrelation, at least through a model correctly capturing its properties, has the advantage of letting calibrations effectively inform the age estimates across larger distances over the tree.”
Quote in the paperSubstantial claim - Interpretationown data§ Conclusion · p. 11
No clear guidelines can be deduced from the observations for the choice of the prior on divergence times, because the Bayes factors depend strongly on the data sets.
“On the other hand, concerning the choice of the prior on divergence times, no clear guidelines can be deduced from our observations as the Bayes factors turn out to depend strongly on the data sets.”
Quote in the paperSubstantial claim
- May combine two claims. 28
- Classified as probably not a substantial claim. 14
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Findingown data§ A General Comparison of Relaxed Molecular Clock Models · p. 2The two autocorrelated models, CIR and lognormal, fit similarly and clearly outperform uncorrelated models across all three data sets (eukaryotes, vertebrates, and mammals).
“We find that the 2 autocorrelated models, CIR and lognormal, have a similar fit and clearly outperform uncorrelated models on all 3 data sets.”
Quote in the paperSubstantial claimMay combine two claims.
Findingnone given§ Dispersion Index and Rate Autocorrelation · p. 7UGAM appears to be the best among the three branchwise models, although it is less fit than LOGN and CIR.
“Interestingly, UGAM, the uncorrelated gamma model (Drummond et al. 2006), appears to be the best among the 3 branchwise models, although it is less fit than LOGN and CIR.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Drummond et al. 2006
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Findingown data§ Results and Discussion · p. 7LOGN is slightly favored over CIR in all cases except MITO100, where they are equivalent, and MITO150, where CIR is significantly preferred over LOGN.
“LogN is slightly favored in all cases, except on MITO100 (where the 2 models have equivalent scores) and on MITO150 (where CIR is significantly preferred over LOGN, table 1, last row).”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ Relative Divergence Times · p. 10Nodes near the root are an exception, and more strikingly under the uniform prior: for old nodes, compared with the birth-death prior, the uniform prior appears to be both more informative and more in contradiction with posterior intervals.
“Nodes near the root are an exception, however, and more strikingly so under the uniform prior: for old nodes, and compared with the birth-death prior, the uniform prior appears to be both more informative and more in contradiction with posterior intervals.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ Relative Divergence Times · p. 8The higher discrepancy between CIR and STRICT is particularly true for nodes closer to the root (ages > 50), for which there is virtually no agreement between CIR and STRICT, whereas some overlap can be seen in the credibility intervals obtained under STRICT and WN.
“This is particularly true for the nodes closer to the root (ages . 50), for which there is virtually no agreement between CIR and STRICT (fig. 2 a ), whereas some overlapcanbeseeninthecredibility intervals obtained under Strict and WN (fig. 2 d ).”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ Relative Divergence Times · p. 8The number of departing nodes between STRICT and CIR is 100, and between STRICT and LOGN is 93.
“On the other hand, the number of departing nodes went up to 100 between STRICT and CIR and to 93 between STRICT and LOGN.”
Quote in the paperSubstantial claimMay combine two claims.
Findingnone given§ Comparison of Alternative Priors on Divergence Times · p. 8The MOC and MAM data sets display a tree shape characterized by an early interphyletic or interordinal diversification combined with low phylogenetic redundancy (few closely related taxa).
“In contrast, the other 2 data sets (MOC, MAM) display a tree shape characterized by an early interphyletic or interordinal diversification, combined with a low phylogenetic redundancy (few closely related taxa).”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationnone given§ Materials and Methods · p. 5The lognormal model has linearly increasing variance and does not have stationary behavior.
“This contrasts with the linearly increasing variance of the lognormal model, which does not have a stationary behavior.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S4 (based).
Interpretationnone given§ A General Comparison of Relaxed Molecular Clock Models · p. 2The CIR process has well-defined stationary properties.
“We also propose a new autocorrelated model, called the ''CIR'' process, with well-defined stationary properties.”
Quote in the paperNot a substantial claimMay combine two claims.
Interpretationcitation§ Materials and Methods · p. 5Using squared OU processes for the CIR model preserves positivity of the rate process and avoids the systematic bias of higher rates near the root found in the Aris-Brosou and Yang model.
“This makes more sense as it preserves the positivity of the rate process and avoids the systematic bias (rates tending to be higher near the root) that had been pointed out in the model of Aris-Brosou and Yang (2002) by Welch et al. (2005).”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Aris-Brosou and Yang (2002)
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Interpretationreasoning§ Materials and Methods · p. 5For the CIR process, the expected value of R(t) tends to 1 for large t, following an exponential decay with parameter h.
“We see here that the expected value of R ( t ) tends to 1 for large values of t . More precisely, it follows an exponential decay of parameter h ; h is, thus, the autocorrelation parameter of the CIR process (or equivalently, 1/ h is the decorrelation time of the process).”
Quote in the paperNot a substantial claimMay combine two claims.
Interpretationreasoning§ Materials and Methods · p. 6The birth-death process has a lack of identifiability among its three parameters, which the authors avoid by reparameterizing to two parameters.
“There is, however, a lack of identifiability between the 3 parameters, as evaluating the prior at ( k , l , q ) gives the same value as if evaluated at k þ k ; l þ k ; kq k þ k : We avoid such problems by restraining the parameter number to 2, with p 1 5 k -l and p 2 5 kq as our new parameterization.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Interpretationreasoning§ Materials and Methods · p. 5In the CIR process, h is the autocorrelation parameter, and 1/h is the decorrelation time.
“We see here that the expected value of R ( t ) tends to 1 for large values of t . More precisely, it follows an exponential decay of parameter h ; h is, thus, the autocorrelation parameter of the CIR process (or equivalently, 1/ h is the decorrelation time of the process).”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Interpretationreasoning§ Materials and Methods · p. 5For small t, the variance of R(t) in the CIR process is proportional to R(0) r^2, so r is the short-term variance.
“Finally, for small values of t , the variance of R ( t ) is proportional to R (0) r 2 , so that r will be designated as the ''short-term'' variance of the process.”
Quote in the paperNot a substantial claimMay combine two claims.
Interpretationreasoning§ Materials and Methods · p. 4The WN model has linear variance with time, whereas UGAM has quadratic variance, because averaging an uncorrelated process reduces variance over longer branches.
“In practice, the main difference between the WN model and the UGAM model lies in the variance of B i : whereas it is quadratic with time in the UGAM case, the WN has a linear variance, accounting for the fact that, by an averaging effect, the mean rate of an uncorrelated process is expected to have a smaller variance over longer branches.”
Quote in the paperNot a substantial claimMay combine two claims.
Premisenone given§ Introduction · p. 2A model's success on simulated data may not represent its relevance to real data, which is more directly assessed by statistical fit.
“However, the success of a model on simulated data may not always be representative of the model's relevance to the analysis of real data, which is more directly assessed by measuring the statistical fit of the model to the data at hand.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Interpretationnone given§ Introduction · p. 3The CIR process differs from the lognormal model mainly by having a stationary distribution.
“The CIR process mainly differs from the log normal in the fact that it possesses a stationary distribution.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Premisecitation§ Introduction · p. 3Posterior Bayes factors are regarded as very controversial.
“However, they are regarded as very controversial (see answers to Aitkin 1991).”
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Premisecitation§ Introduction · p. 3Thermodynamic integration has been used recently in several phylogenetic studies.
“One of these techniques, called thermodynamic integration (Ogata 1989), has been recently used in several phylogenetic studies (Lartillot and Philippe 2004, 2006; Blanquart and Lartillot 2006; Rodrigue et al. 2006).”
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- cites Lartillot and Philippe 2004, 2006
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Premisereasoning§ Introduction · p. 3Bayes factors implicitly penalize higher-dimensional models and allow general comparison among arbitrary numbers of non-nested models.
“Bayes factors present several advantages: they implicitly penalize models with higher dimensionality; furthermore, by using one single model as a global reference, they allow for a general comparison among an arbitrary number of models that are not necessarily nested.”
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Interpretationcitation§ Introduction · p. 3The CIR model resembles the OU model but avoids several limitations of the OU noted by Welch et al. (2005).
“The latter, CIR, is similar to the Ornstein-Uhlenbeck (OU) model (Aris-Brosou and Yang 2003) but without many of the shortcomings of the OU identified by Welch et al. (2005).”
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- cites Welch et al. (2005)
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Interpretationreasoning§ Dispersion Index and Rate Autocorrelation · p. 8Unlike WN, UGAM has a dispersion index that increases with time, which is a typical feature of autocorrelated models.
“Thus, unlike WN, UGAM has a dispersion index increasing with t , which is a typical feature of autocorrelated models.”
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Premisenone given§ Dispersion Index and Rate Autocorrelation · p. 8In the present case, the theoretical dispersion index is 1 + r for WN and 1 + r t for UGAM.
“In the present case, the theoretical dispersion index is equal to 1 þ r for WN and 1 þ r t for UGAM.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Interpretationreasoning§ Results and Discussion · p. 7LOGN may perform better on smaller data sets because it is simpler, having only one parameter controlling autocorrelation.
“A possible explanation is that LOGN may perform better on smaller data sets because it is simpler (it has only one parameter, controlling the autocorrelation).”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Premisecitation§ Results and Discussion · p. 7The absence of stationarity for a stochastic process is seen as a potential problem.
“In general, this absence of stationarity for a stochastic process is seen as a potential problem (Lepage et al. 2006).”
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Premisenone given§ Results and Discussion · p. 7In the long term, CIR has a stationary distribution, whereas the LOGN rate variance increases linearly with time.
“Note that, in the long term, the CIR has a well-defined behavior, that is, a stationary distribution, whereas in the LOGN model the rate has a variance that increases linearly with time.”
Quote in the paperSubstantial claimMay combine two claims.
Study design and conductreasoning§ Relative Divergence Times · p. 8No fossil records were used in this study, so dates are displayed on a relative scale where all leaves have an age of zero and the root an age of 100.
“No fossil records were used in this study, so dates are displayed on a relative scale where all leaves have an age of zero and the root an age of 100.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S4 (based).
Interpretationnone given§ Relative Divergence Times · p. 8Large discrepancies in relative node ages between two models will probably imply large discrepancies in absolute dates as well.
“given that large discrepancies in the relative node ages between 2 models will probably imply large discrepancies in the absolute dates as well”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Interpretationreasoning§ Comparison of Alternative Priors on Divergence Times · p. 8The lower fit of the birth-death prior for small data sets may be the result of a dimensional penalty, because the birth-death prior has one more parameter than the Dirichlet.
“the lower fit of the birth-death prior for small data sets may be the result of a dimensional penalty (the birth-death has one more parameter than the Dirichlet).”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Interpretationreasoning§ Comparison of Alternative Priors on Divergence Times · p. 8The large variation in fit could be due to the trees of MITO100 and MITO150 having long basal branches separating densely sampled vertebrate classes, a pattern that may be particularly well fitted by a birth-death process.
“Alternatively, this could be due to the fact that the trees of MITO100 and 150 have long basal branches, separating densely sampled vertebrate classes, a pattern that may be particularly well fitted by a birth-death process.”
Quote in the paperNot a substantial claimMay combine two claims.
Interpretationreasoning§ Relative Divergence Times · p. 8This study will not provide any information on the effect of models on absolute dates and, in particular, on the root age.
“As a consequence, this study will not provide any information on the effect of models on absolute dates and, in particular, on the root age.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationreasoning§ Dispersion Index and Rate Autocorrelation · p. 8Autocorrelation can be detected in two ways: between branches it can be directly observed, and within branches it can only be indirectly inferred through its net effect on the dispersion index.
“Altogether, autocorrelation can be detected in 2 different ways: between branches, it can be directly observed. Within branches, it can only be indirectly inferred, through its net effect on the dispersion index.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationcitation§ Dispersion Index and Rate Autocorrelation · p. 8UGAM is more in accordance with experimentally observed values for the dispersion index than WN, which may explain the better fit obtained for UGAM compared with WN.
“This also makes UGam more in accordance with experimentally observed values for the dispersion index (Ohta 1995; Bickel and West 1998), which may explain the better fit we obtain for UGAM, compared with WN.”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Ohta 1995
Not checked in the free run.
- cites Bickel and West 1998
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
Interpretationreasoning§ Relative Divergence Times · p. 10The lesser informativeness of the birth-death prior in this study may be due to the priors on hyperparameters being more vague.
“This may be simply due to the fact that our priors on hyperparameters are more vague.”
Quote in the paperNot a substantial claimMay combine two claims.
Interpretationown data§ Conclusion · p. 10The estimated dates are highly sensitive to the relaxation model used and, to a lesser extent, also to the prior on divergence times.
“In summary, our observations illustrate the high sensitivity of the estimated dates to the relaxation model used (fig. 2) and to a lesser extent also to the prior on divergence times (fig. 3).”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
Premisecitation§ Relative Divergence Times · p. 10The OU process, as implemented in Aris-Brosou and Yang (2003), imposes a general trend in the rate history.
“Another point raised by Welch et al. (2005) is that the OU process, as implemented in Aris-Brosou and Yang (2003), imposes a general trend in the rate history.”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Welch et al. 2005
Not checked in the free run.
- cites Aris-Brosou and Yang 2003
Not checked in the free run.
May combine two claims.
Interpretationown data§ Relative Divergence Times · p. 10Irrespective of the exact prior used, the data seem to at least partially override the prior information, providing age estimates that are quite robust, though not totally insensitive, to the exact choice of the prior.
“In any case, and irrespective of the exact prior used, the data seem to at least partially override the prior information as it provides age estimates that are quite robust (although not totally insensitive) to the exact choice of the prior (fig. 3 c and d ).”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
Study design and conductnone given§ Conclusion · p. 11The conclusions are exclusively based on relative age estimates.
“Our conclusions are exclusively based on relative age estimates”
Quote in the paperSubstantial claim
The authors state this as an assumption.
The rate process is Markovian.
“Assuming that the rate process is Markovian, the joint probability density of the values of the process at the nodes is given by:”
The paper relies on this without support.
The strict molecular clock is not biologically realistic and substitution rates change over time, requiring explicit accounting in molecular dating.
“However, it has become clear that the strict molecular clock hypothesis is not biologically realistic and that the rate at which substitutions accumulate with time is subject to changes that need to be explicitly accounted for in molecular dating techniques.”
The paper relies on this without support.
Few attempts have been made to compare the performance of available clock models.
“Remarkably, there have been few attempts thus far to compare the performances of available clock models.”
The paper relies on this without support.
The random subsampling of osteichthyans in the MITO data sets produces taxon samplings that differ only in number of taxa, so differences in model performance can be attributed to taxonomic sampling density.
“considered 4 different taxon samplings for the ingroup, obtained by randomly subsampling 10, 50, 100, and 150 osteichthyans.”
The paper relies on this without support.
The data sets used are representative of real sequence evolution, so conclusions about the strict molecular clock and autocorrelation generalize to real sequences.
“indicating that the strict molecular clock is not adapted to describing the evolution of real sequences.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Bayes factors have been used to decide between competing clock models in phylogenetic analysis.
“Bayes factors have been used to decide between competing clock models (such as the IR and AR models, e.g., [55]) in phylogenetic analysis.”
From Uncertainty in the Timing of Origin of Animals and the Limits of Precision in Molecular Timescales (2015) · cites this paper as [55]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Autocorrelated models do not outperform UGAM on MITO10
MinorThe abstract says both autocorrelated models clearly outperform uncorrelated models on all three data sets. For MITO10, table 1 gives UGAM a higher log Bayes factor (3.9-4.0) than either LOGN (3.2-3.7) or CIR (2.5-3.0).
“We find that the 2 autocorrelated models, CIR and lognormal, have a similar fit and clearly outperform uncorrelated models on all 3 data sets.”
“| UGAM | [26.6; 27.2] | [53.0; 55.7] | [3.9; 4.0] | [14.6;16.8] | [34.6; 36.2] | [4.5; 12.0] | | WN | [23.9; 24.6] | [48.8; 49.3] | [1.3; 1.6] | [9.0; 9.5] | [20.4; 21.3] | [ 4.3; 3.0] | | LOGN | [40.8; 43.1] | [61.1; 64.1] | [3.2; 3.7] | [23.5; 26.0] | [48.3; 56.8] | [36.7; 44.0] | | CIR | [36.7; 40.5] | [58.9; 60.6] | [2.5; 3.0] | [20.0; 22.8] | [51.6; 57.4] | [51.4; 60.2] |”
MITO100 birth-death Bayes factor is not above 45
MinorThe stated threshold holds for MITO150, but not MITO100. Table 2 reports MITO100 log Bayes factors of 13.3-17.4 for CIR and 13.3-17.1 for LOGN under the birth-death prior.
“except on MITO100 and MITO150, on which it is strongly favored over the 2 alternatives (ln BF . 45).”
“| CIR þ BD | [ 10.2; 8.1] | [ 9.6; 6.3] | [ 13.9; 12.9] | [ 8.8; 6.9] | [13.3; 17.4] | [46.4; 53.8] | | LOGN þ BD | [ 20.5; 19.0] | [ 10.3; 6.2] | [ 13.9; 13.1] | [ 8.4; 7.2] | [13.3; 17.1] | [46.6; 55.0] |”
Figure 1b uses a different prior from the cited model
MinorThe text points to figure 1b when discussing the CIR plus birth-death model, but the figure caption identifies its prior as uniform.
“We therefore checked that the optimal model (CIR þ BD) found under MITO150 (see fig. 1 b ) did not produce such patterns (fig. 4).”
“( b ) Relative divergence times under the MITO150 data set, under the CIR process and a uniform prior on divergence times.”
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MrBayes 3.2: Efficient Bayesian Phylogenetic Inference and Model Choice Across a Large Model Space
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“Three different relaxed clock models are available: the Compound Poisson Process (CPP; Huelsenbeck et al. 2000), the Thorne– Kishino 2002 (TK02; Thorne and Kishino 2002), and the Independent Gamma Rate (IGR; Lepage et al. 2007) models.”
MethodPhyloBayes 3: a Bayesian software package for phylogenetic reconstruction and molecular dating
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MethodInfluentialA metacalibrated time‐tree documents the early rise of flowering plant phylogenetic diversity
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“The topology of the eukaryotic tree produced through coestimation of phylogeny and divergence times in BEAST is broadly consistent with other analyses (SI Text) (25, 26).”
BackgroundMethodInfluentialThe timescale of early land plant evolution
Morris, J. L., Puttick, M. N., Clark, J., Edwards, D., Kenrick, P., Pressel, S., Wellman, C. H., Yang, Z., Schneider, H., & Donoghue, P. C. J. (2018) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1719588115 · Cited by 926 · see citing works
The fossilized birth-death process for coherent calibration of divergence-time estimates
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“calibration of divergence-time estimates”
A Total-Evidence Approach to Dating with Fossils, Applied to the Early Radiation of the Hymenoptera
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“The available relaxed-clock methods have been compared in several reviews (Magallón 2004; Welch and Bromham 2005; Lepage et al. 2006; Rutschmann 2006), and their performance has been assessed in a number of studies (e.g., Ho et al. 2005; Drummond et al. 2006; Lepage et al. 2007).”
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“…be drawn from an autocorrelated process (Thorne et al. 1998; Thorne and Kishino 2002), any type of independent-rates model (Drummond et al. 2006; Lepage et al. 2007; Rannala and Yang 2007), a compound Poisson process (Huelsenbeck et al. 2000), a local-molecular clock model (Yang and Yoder 2003;…”
Self-citationEstimating divergence times in large molecular phylogenies
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“Current implementations of most of these methods require a fixed tree topology and sometimes fixed branch lengths (Thorne & Kishino, 2002; Sanderson, 2003; Lepage et al., 2007; for exceptions see Drummond et al., 2006).”
MethodBayesian Evolutionary Analysis with BEAST
Drummond, A. J., & Bouckaert, R. (2015) · Cambridge University Press eBooks · doi:10.1017/cbo9781139095112 · Cited by 518 · see citing works
Uncertainty in the Timing of Origin of Animals and the Limits of Precision in Molecular Timescales
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“correlated clocks (Lepage et al. 2007), while another study found that both resulted in similar posterior age estimates (Magallon et al.”
ResultFast Dating Using Least-Squares Criteria and Algorithms
To, T., Jung, M., Lycett, S., & Gascuel, O. (2015) · Systematic Biology · doi:10.1093/sysbio/syv068 · Cited by 415 · see citing works
“In all cases, very large input trees (>10,000 taxa) can easily be processed and transformed into time-scaled trees.”
Rota-Stabelli, O., Daley, A. C., & Pisani, D. (2013) · Current Biology · doi:10.1016/j.cub.2013.01.026 · Cited by 360 · see citing works
“Relaxed molecular clock analyses were performed under the best fitting molecular clock model for each considered data set, which was the autocorrelated CIR model [22] for all data sets but RNA (Table S2; Experimental Procedures).”
Bayesian molecular clock dating of species divergences in the genomics era
dos Reis, M., Donoghue, P. C. J., & Yang, Z. (2016) · Nature Reviews Genetics · doi:10.1038/nrg.2015.8 · Cited by 339 · see citing works
Molecular‐clock methods for estimating evolutionary rates and timescales
Ho, S. Y. W., & Duchêne, S. (2014) · Molecular Ecology · doi:10.1111/mec.12953 · Cited by 362 · see citing works
“, 2004), clock models (Lepage et al., 2007; Linder et al., 2011), and demographic models (Baele et al.”
BackgroundResultInfluentialChiari, Y., Cahais, V., Galtier, N., & Delsuc, F. (2012) · BMC Biology · doi:10.1186/1741-7007-10-65 · Cited by 340 · see citing works
“Despite the fact that autocorrelated models of clock relaxation have been shown to provide a significantly better fit than uncorrelated models on phylogenomic datasets [56,57], all analyses were conducted under both models of molecular clock relaxation for comparison purposes.”
BackgroundResultInfluentialEarly photosynthetic eukaryotes inhabited low-salinity habitats
Sánchez-Baracaldo, P., Raven, J., Pisani, D., & Knoll, A. (2017) · Proceedings of the National Academy of Sciences of the United States of America · doi:10.1073/pnas.1620089114 · Cited by 294 · see citing works
“Divergence times were estimated implementing three different relaxed molecular clock models: log normal (40), CIR (41), and UGAM (39) in Phylobayes 4.”
MethodInfluentialMagallón, S., Hilu, K. W., & Quandt, D. (2013) · American Journal of Botany · doi:10.3732/ajb.1200416 · Cited by 320 · see citing works
Li, H., Leavengood, J. M., Chapman, E. G., Burkhardt, D., Song, F., Jiang, P., Liu, J., Zhou, X. J., & Cai, W. (2017) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2017.1223 · Cited by 309 · see citing works
“We used Bayes factor (calculated using thermodynamic integration) in PhyloBayes to compare three widely used relaxed models, the autocorrelated Lognormal and Cox–Ingersoll–Ross (CIR) process and uncorrelated gamma multipliers (UGAM) [41].”
InfluentialPhylotranscriptomic consolidation of the jawed vertebrate timetree
Irisarri, I., Baurain, D., Brinkmann, H., Delsuc, F., Sire, J.-Y., Kupfer, A., Petersen, J., Jarek, M., Meyer, A., Vences, M., et al. (2017) · Nature Ecology & Evolution · doi:10.1038/s41559-017-0240-5 · Cited by 299 · see citing works
Self-citationOn the Age of Eukaryotes: Evaluating Evidence from Fossils and Molecular Clocks
Eme, L., Sharpe, S. C., Brown, M. W., & Roger, A. J. (2014) · Cold Spring Harbor Perspectives in Biology · doi:10.1101/cshperspect.a016139 · Cited by 287 · see citing works
“A number of different methods have been developed and debate continues as to which best captures biological reality (Drummond et al. 2006; Lepage et al. 2007; Ho and Phillips 2009; Linder et al. 2011).”
BackgroundMethodInfluentialDating the molecular clock in fungi – how close are we?
Berbee, M. L., & Taylor, J. W. (2010) · Fungal Biology Reviews · doi:10.1016/j.fbr.2010.03.001 · Cited by 285 · see citing works
“Rate variation is so clearly a feature of molecular evolution that most recent approaches to molecular clocks, as reviewed by Welch and Bromham (2005) and by Lepage et al. (2007), have been directed towards allowing rates to vary across different branches in a tree.”
BackgroundSo many genes, so little time: A practical approach to divergence-time estimation in the genomic era
Smith, S. A., Brown, J. W., & Walker, J. F. (2018) · PLoS ONE · doi:10.1371/journal.pone.0197433 · Cited by 282 · see citing works
Gibb, G. C., Condamine, F. L., Kuch, M., Enk, J. M., Moraes‐Barros, N., Superina, M., Poinar, H. N., & Delsuc, F. (2015) · Molecular Biology and Evolution · doi:10.1093/molbev/msv250 · Cited by 277 · see citing works
“However, it has been shown that autocorrelated rate models, such as the autocorrelated log-normal model (LN; Thorne et al. 1998), generally offer a better fit, especially with large data sets above the species level (Lepage et al. 2007; Rehm et al. 2011).”
BackgroundYang, Z. (2014) · doi:10.1093/acprof:oso/9780199602605.001.0001 · Cited by 273 · see citing works
Inoue, J. G., Donoghue, P. C. J., & Yang, Z. (2009) · Systematic Biology · doi:10.1093/sysbio/syp078 · Cited by 266 · see citing works
Evolution of parasitism in kinetoplastid flagellates
Lukeš, J., Skalický, T., Týč, J., Votýpka, J., & Yurchenko, V. (2014) · Molecular and Biochemical Parasitology · doi:10.1016/j.molbiopara.2014.05.007 · Cited by 255 · see citing works
“[99] Lepage T, Bryant D, Philippe H, Lartillot N.”
BackgroundThe origin of squamates revealed by a Middle Triassic lizard from the Italian Alps
Simões, T. R., Caldwell, M. W., Tałanda, M., Bernardi, M., Palci, A., Vernygora, O. V., Bernardini, F., Mancini, L., & Nydam, R. L. (2018) · Nature · doi:10.1038/s41586-018-0093-3 · Cited by 256 · see citing works
Lartillot, N., & Poujol, R. (2011) · Molecular Biology and Evolution · doi:10.1093/molbev/msq244 · Cited by 243 · see citing works
“This has been first proposed in the context of molecular dating methods, using Brownian diffusion processes (Thorne et al. 1998; Kishino et al. 2001; Thorne and Kishino 2002; Yang and Rannala 2006; Lepage et al. 2007; Rannala and Yang 2007).”
BackgroundMethodInfluentialSelf-citationPhylogenetic rooting using minimal ancestor deviation
Tria, F. D. K., Landan, G., & Dagan, T. (2017) · Nature Ecology & Evolution · doi:10.1038/s41559-017-0193 · Cited by 241 · see citing works
“In the relaxed clock models approach, the evolutionary rate is allowed to vary among lineages, and the root position is optimized to produce an approximately equal time span between the LCA and all descendants 5 .”
MethodThe impact of taxon sampling on phylogenetic inference: a review of two decades of controversy
Nabhan, A. R., & Sarkar, I. N. (2011) · Briefings in Bioinformatics · doi:10.1093/bib/bbr014 · Cited by 237 · see citing works
“Some phylogenetic inference methods also make use of relaxed molecular clock models that do not assume a constant rate of molecular evolution across lineages [60–62].”
MethodWolfe, J. M., Breinholt, J. W., Crandall, K. A., Lemmon, A. R., Lemmon, E. M., Timm, L. E., Siddall, M. E., & Bracken‐Grissom, H. D. (2019) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2019.0079 · Cited by 232 · see citing works
“We compared the uncorrelated gamma multipliers (UGM) relaxed clock model [42], and the autocorrelated CIR model [43].”
MethodA phylogenomic framework and timescale for comparative studies of tunicates
Delsuc, F., Philippe, H., Tsagkogeorga, G., Simion, P., Tilak, M., Turón, X., López‐Legentil, S., Piette, J., Lemaire, P., & Douzery, E. (2018) · BMC Biology · doi:10.1186/s12915-018-0499-2 · Cited by 219 · see citing works
“However, it has been shown that autocorrelated rate models, such as the autocorrelated LN model, often provide a better fit with phylogenomic data [54, 72, 73].”
BackgroundSelf-citationLegendre, F., Nel, A., Svenson, G. J., Robillard, T., Pellens, R., & Grandcolas, P. (2015) · PLoS ONE · doi:10.1371/journal.pone.0130127 · Cited by 216 · see citing works
“Finally, autocorrelated models proved to have a higher statistical fit to the data than uncorrelated models [98,99].”
BackgroundBarba‐Montoya, J., dos Reis, M., Schneider, H., Donoghue, P. C. J., & Yang, Z. (2018) · New Phytologist · doi:10.1111/nph.15011 · Cited by 212 · see citing works
“The marginal likelihood is hard to calculate, but recently methods such as path-sampling (thermodynamic integration) and stepping-stones have been integrated within phylogenetics (Lartillot & Philippe, 2006; Lepage et al., 2007; Linder et al., 2011; Xie et al., 2011; Baele et al. 2012).”
BackgroundMethodInfluentialBayesian Estimation of Speciation and Extinction from Incomplete Fossil Occurrence Data
Silvestro, D., Schnitzler, J., Liow, L. H., Antonelli, A., & Salamin, N. (2014) · Systematic Biology · doi:10.1093/sysbio/syu006 · Cited by 211 · see citing works
“Because the model testing is focused on the number of rate shifts, only the birth–death term of Equation (16) is marginalized during the process to improve the performance of the MCMC sampling and reduce the computational cost (cf. Lepage et al. 2007).”
BackgroundHybridization of powdery mildew strains gives rise to pathogens on novel agricultural crop species
Menardo, F., Praz, C. R., Wyder, S., Ben‐David, R., Bourras, S., Matsumae, H., McNally, K. E., Parlange, F., Riba, A., Roffler, S., et al. (2016) · Nature Genetics · doi:10.1038/ng.3485 · Cited by 204 · see citing works
Model Selection and Parameter Inference in Phylogenetics Using Nested Sampling
Maturana‐Russel, P., Brewer, B. J., Klaere, S., & Bouckaert, R. (2018) · Systematic Biology · doi:10.1093/sysbio/syy050 · Cited by 198 · see citing works
dos Reis, M., Gunnell, G. F., Barba‐Montoya, J., Wilkins, A., Yang, Z., & Yoder, A. D. (2018) · Systematic Biology · doi:10.1093/sysbio/syy001 · Cited by 188 · see citing works
“With regard to clock model choice, an empirical study of three independent data sets showed that autocorrelated models outperform uncorrelated models, though the same study found a “high sensitivity” to the relaxation model employed (Lepage et al. 2007), while another empirical study found, however, that an independen…”
BackgroundResultInfluentialZhao, R.-L., Li, G., Ramirez, S. S., Stata, M., Yang, Z., Wu, G., Dai, Y., He, S., Cui, B., Zhou, J., et al. (2017) · Fungal Diversity · doi:10.1007/s13225-017-0381-5 · Cited by 194 · see citing works
“We used the uncorrelated lognormal relaxed clock model (Drummond et al. 2006; Lepage et al. 2007), specifying a gamma distribution prior (offset = 0, scale = 0.”
MethodInfluentialAdaptive dating and fast proposals: Revisiting the phylogenetic relaxed clock model
Douglas, J., Zhang, R., & Bouckaert, R. (2021) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1008322 · Cited by 184 · see citing works
Bayesian Inference of Species Networks from Multilocus Sequence Data
Zhang, C., Ogilvie, H. A., Drummond, A. J., & Stadler, T. (2017) · Molecular Biology and Evolution · doi:10.1093/molbev/msx307 · Cited by 186 · see citing works
“To extend to a re-laxed molecular clock model (e.g., Thorne and Kishino 2002; Drummond et al. 2006; Lepage et al. 2007; Rannala and Yang 2007), the molecular clock rate is variable across gene lineages following certain distributions with l as the mean.”
BackgroundThe evolutionary history of ferns inferred from 25 low‐copy nuclear genes
Rothfels, C. J., Li, F., Sigel, E. M., Huiet, L., Larsson, A. O., Bürge, D. O., Ruhsam, M., Deyholos, M. K., Soltis, P. S., Stewart, C. N., et al. (2015) · American Journal of Botany · doi:10.3732/ajb.1500089 · Cited by 191 · see citing works
“For the relaxed clock model, we used a uniform tree (branch lengths) prior and the " independent gamma rates " model, in which branch rates are drawn independently (no autocorrelation) from a scaled gamma distribution ( Lepage et al., 2007 ).”
SPERLING, E. A., ROBINSON, J. M., PISANI, D., & PETERSON, K. J. (2010) · Geobiology · doi:10.1111/j.1472-4669.2009.00225.x · Cited by 182 · see citing works
“Both the CIR and the lognormal models relax the molecular clock assumption by implying rate autocorrelation among the branches of the considered phylogeny (Lepage et al., 2007).”
BackgroundMethodInfluentialA multi-locus time-calibrated phylogeny of the siphonous green algae
Verbruggen, H., Ashworth, M. P., LoDuca, S. T., Vlaeminck, C., Cocquyt, E., Sauvage, T., Zechman, F. W., Littler, D. S., Littler, M. M., & Leliaert, F. (2008) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2008.12.018 · Cited by 181 · see citing works
“Taxa assigned to Dasycladales are both abundant and diverse in Ordovician strata, and include euspondyl (e.g., Chaetocladus) as well as aspondyl (e.g., Dasyporella) forms (Berger and Kaever, 1992; LoDuca, 1997; LoDuca et al., 2003).”
BackgroundBracken‐Grissom, H. D., Ahyong, S. T., Wilkinson, R., Feldmann, R. M., Schweitzer, C. E., Breinholt, J. W., Bendall, M. L., Palero, F., Chan, T., Felder, D. L., et al. (2014) · Systematic Biology · doi:10.1093/sysbio/syu008 · Cited by 180 · see citing works
“2006), others favoring autocorrelated models (Lepage et al. 2007) and some favoring both (autocorrelated and uncorrelated) depending on the data set (Ronquist et al.”
BackgroundParadis, E. (2013) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2013.02.008 · Cited by 177 · see citing works
“Since then, the Bayesian approach to molecular dating has flourished in a diversity of refinements (e.g., Drummond et al., 2006; Yang and Rannala, 2006; Lepage et al., 2007; Lartillot et al., 2009; Guindon, 2010; dos Reis and Yang, 2011; Wilkinson et al., 2011).”
BackgroundMethodThe Great Oxidation Event expanded the genetic repertoire of arsenic metabolism and cycling
Chen, S., Sun, G., Yan, Y., Konstantinidis, K. T., Zhang, S., Deng, Y., Li, X., Cui, H., Musat, F., Popp, D., et al. (2020) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2001063117 · Cited by 173 · see citing works
“Both the autocorrelated lognormal (-ln) and uncorrelated gamma multiplier (-ugam) relaxed clocks were applied to model the rate variation across lineages (41).”
MethodSilvestro, D., Cascales‐Miñana, B., Bacon, C. D., & Antonelli, A. (2015) · New Phytologist · doi:10.1111/nph.13247 · Cited by 166 · see citing works
“…the best-fitting distribution based on the Akaike Information Criterion (AIC; Akaike, 1974), we computed the estimated parameter values, which may be directly used for other studies as calibrations to date molecular phylogenetic trees using relaxed molecular clock models (e.g. Lepage et al., 2007).”
MethodMolecular Dating, Evolutionary Rates, and the Age of the Grasses
Christin, P., Spriggs, E. L., Osborne, C. P., Strömberg, C. A. E., Salamin, N., & Edwards, E. J. (2013) · Systematic Biology · doi:10.1093/sysbio/syt072 · Cited by 166 · see citing works
Tanner, A. R., Fuchs, D., Winkelmann, I. E., Gilbert, M. T. P., Pankey, M. S., Ribeiro, Â. M., Kocot, K. M., Halanych, K. M., Oakley, T. H., da Fonseca, R. R., et al. (2017) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2016.2818 · Cited by 166 · see citing works
“P HYLO B AYES 3.3f was used to infer molecular divergence times under the CIR [30] clock model, soft-bounds of 0.05 and a Yule-process birth–death model, with topology fixed to that inferred by P HYLO B AYES MPI v. 1.5a.”
InfluentialSimultaneous Bayesian gene tree reconstruction and reconciliation analysis
Åkerborg, Ö., Sennblad, B., Arvestad, L., & Lagergren, J. (2009) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0806251106 · Cited by 161 · see citing works
“Our choice is the iid-(cid:2) model (34, 36), where edge substitution rates are modeled as independent and identically (cid:2) -distributed variables with mean m and variance ν .”
MethodBracken‐Grissom, H. D., Cannon, M. E., Cabezas, P., Feldmann, R. M., Schweitzer, C. E., Ahyong, S. T., Felder, D. L., Lemaitre, R., & Crandall, K. A. (2013) · BMC Evolutionary Biology · doi:10.1186/1471-2148-13-128 · Cited by 162 · see citing works
The Archean origin of oxygenic photosynthesis and extant cyanobacterial lineages
Fournier, G. P., Moore, K. R., Rangel, L. T., Payette, J. G., Momper, L., & Bosak, T. (2021) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2021.0675 · Cited by 156 · see citing works
The impact of calibration and clock-model choice on molecular estimates of divergence times
Duchêne, S., Lanfear, R., & Ho, S. Y. W. (2014) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2014.05.032 · Cited by 156 · see citing works
“tistical support for models with rate autocorrelation (Lepage et al., 2007).”
BackgroundBayesian molecular dating: opening up the black box
Bromham, L. D., Duchêne, S., Hua, X., Ritchie, A. M., Duchêne, D. A., & Ho, S. Y. W. (2017) · Biological reviews/Biological reviews of the Cambridge Philosophical Society · doi:10.1111/brv.12390 · Cited by 152 · see citing works
“There is ongoing debate about whether uncorrelated or autocorrelated relaxed clocks provide a better fit to real molecular data, but this is likely to vary from one data set to another (Lepage et al., 2007; Ho, 2009; Ho, Duchêne & Duchêne, 2015; Lartillot, Phillips & Ronquist, 2016).”
BackgroundMethodInfluentialArcila, D., Pyron, R. A., Tyler, J. C., Ortı́, G., & Betancur‐R, R. (2014) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2014.10.011 · Cited by 152 · see citing works
“The IGR is a continuous uncorrelated model (also similar to the UCLN model) in which branch rates are drawn independently from the same gamma distribution (Lepage et al., 2007; Ronquist et al., 2012).”
MethodA molecular palaeobiological exploration of arthropod terrestrialization
Lozano-Fernández, J., Carton, R., Tanner, A. R., Puttick, M. N., Blaxter, M., Vinther, J., Olesen, J., Giribet, G., Edgecombe, G. D., & Pisani, D. (2016) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2015.0133 · Cited by 153 · see citing works
Model Averaging and Bayes Factor Calculation of Relaxed Molecular Clocks in Bayesian Phylogenetics
Li, W. L. S., & Drummond, A. J. (2011) · Molecular Biology and Evolution · doi:10.1093/molbev/msr232 · Cited by 145 · see citing works
“In phylogenetic estimation, it is often of interest as to whether rate of substitution is correlated between parent and child on a tree (Lepage et al. 2007; Ho 2009).”
BackgroundRapid Global Spread of wRi-like Wolbachia across Multiple Drosophila
Turelli, M., Cooper, B. S., Richardson, K. M., Ginsberg, P., Peckenpaugh, B., Antelope, C. X., Kim, K. J., May, M. R., Abrieux, A., Wilson, D. A., et al. (2018) · Current Biology · doi:10.1016/j.cub.2018.02.015 · Cited by 149 · see citing works
Early Archean origin of Photosystem <scp>II</scp>
Cardona, T., Sánchez‐Baracaldo, P., Rutherford, A. W., & Larkum, A. W. (2019) · Geobiology · doi:10.1111/gbi.12322 · Cited by 144 · see citing works
A New Malaria Agent in African Hominids
Ollomo, B., Durand, P., Prugnolle, F., Douzery, E., Arnathau, C., Nkoghe, D., Leroy, E. M., & François Renaud, A. (2009) · PLoS Pathogens · doi:10.1371/journal.ppat.1000446 · Cited by 140 · see citing works
“implemented in the PhyloBayes software [38,39], version 3.”
MethodRitchie, A. M., Lo, N. C., & Ho, S. Y. W. (2016) · Systematic Biology · doi:10.1093/sysbio/syw095 · Cited by 139 · see citing works
“Previous studies have indicated that the effects of tree priors are strongly dependent on characteristics of the data and the underlying phylogeny (Lepage et al. 2007).”
BackgroundMulcahy, D. G., Noonan, B. P., Moss, T. J., Townsend, T. M., Reeder, T. W., Sites, J. W., & Wiens, J. J. (2012) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2012.08.018 · Cited by 139 · see citing works
“The lognormal interval contains negative values, indicating that it often performed worse than the unconstrained model (Lepage et al., 2007).”
BackgroundMethodZhao, R.-L., Zhou, J., Chen, J., Margaritescu, S., Ramirez, S. S., Hyde, K. D., Callac, P., Parra, L. A., Li, G., & Moncalvo, J. (2016) · Fungal Diversity · doi:10.1007/s13225-016-0357-x · Cited by 139 · see citing works
“We used the uncorrelated lognormal relaxed clock model (Drummond et al. 2006; Lepage et al. 2007), specifying a gamma distribution for the ulcd.”
MethodInfluentialBlack, K. H., Archer, M., Hand, S. J., & Godthelp, H. (2012) · Springer eBooks · doi:10.1007/978-90-481-3428-1_35 · Cited by 138 · see citing works
Genealogical Working Distributions for Bayesian Model Testing with Phylogenetic Uncertainty
Baele, G., Lemey, P., & Suchard, M. A. (2015) · Systematic Biology · doi:10.1093/sysbio/syv083 · Cited by 133 · see citing works
Massive intracellular gene transfer during plastid genome reduction in nongreen Orobanchaceae
Cusimano, N., & Wicke, S. (2015) · New Phytologist · doi:10.1111/nph.13784 · Cited by 132 · see citing works
(2016) · doi:10.1093/sysbio/syw041 · Cited by 120 · see citing works
“An autocorrelated relaxed clock model was applied as it has been shown to provide a significantly better fit than uncorrelated models on phylogenomic data sets (Lepage et al. 2007; Rehm et al. 2011).”
MethodMaestri, R., Monteiro, L. R., Fornel, R., Upham, N. S., Patterson, B. D., & de Freitas, T. R. O. (2016) · Evolution · doi:10.1111/evo.13155 · Cited by 125 · see citing works
Dating the arthropod tree based on large-scale transcriptome data
Rehm, P., Borner, J., Meusemann, K., von Reumont, B. M., Simon, S., Hadrys, H., Misof, B., & Burmester, T. (2011) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2011.09.003 · Cited by 121 · see citing works
“Bayes factors were estimated using thermodynamic integration as implemented in PhyloBayes (Lepage et al., 2007) with 100,000 generations and a burn-in of 10,000.”
MethodResultInfluentialAncient dates or accelerated rates? Morphological clocks and the antiquity of placental mammals
Beck, R. M. D., & Lee, M. S. Y. (2014) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2014.1278 · Cited by 128 · see citing works
Dornburg, A., Brandley, M. C., McGowen, M. R., & Near, T. J. (2011) · Molecular Biology and Evolution · doi:10.1093/molbev/msr228 · Cited by 127 · see citing works
“…time methods that incorporate uncorrelated and autocorrelated models has been tested (Ho, Phillips, Drummond, et al. 2005; Drummond et al. 2006; Lepage et al. 2007), it is still unclear how either of these relaxed clock models perform in the presence of punctuated molecular rate shifts between…”
BackgroundMethodInfluentialClosing the gap between rocks and clocks using total-evidence dating
Ronquist, F., Lartillot, N., & Phillips, M. J. (2016) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2015.0136 · Cited by 120 · see citing works
“All relaxed clock analyses assumed an independent gamma rates (white noise) model [23] with the variance increase parameter having an exponential prior with rate 10 (expectation 0.1).”
InfluentialSelf-citationMolecular phylogenetics unveils the ancient evolutionary origins of the enigmatic fairy armadillos
Delsuc, F., Superina, M., Tilak, M., Douzery, E., & Hassanin, A. (2011) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2011.11.008 · Cited by 125 · see citing works
“The log-normal rate-autocorrelated model was chosen to relax the molecular clock assumption because of its ability to reasonably fit various data sets (Lepage et al., 2007).”
MethodThe changing view of eukaryogenesis – fossils, cells, lineages and how they all come together
Dacks, J., Field, M. C., Buick, R., Eme, L., Gribaldo, S., Roger, A., Brochier-Armanet, C., & Devos, D. P. (2016) · Journal of Cell Science · doi:10.1242/jcs.178566 · Cited by 115 · see citing works
“However, variation in substitution rates has been widely documented, and ‘relaxed’ molecular clock methods have been developed that take into account that the rate of sequence evolution might vary across different branches (Ho and Phillips, 2009; Lepage et al., 2007; Welch and Bromham, 2005).”
BackgroundBayesian Phylogenetic Estimation of Clade Ages Supports Trans-Atlantic Dispersal of Cichlid Fishes
Matschiner, M., Musilová, Z., Barth, J. M. I., Starostová, Z., Salzburger, W., Steel, M., & Bouckaert, R. (2016) · Systematic Biology · doi:10.1093/sysbio/syw076 · Cited by 119 · see citing works
“…clock that accounts for the heritability of factors influencing rate variation (such as body mass, longevity, and generation time; Nabholz et al. 2008; Amster and Sella 2016) and may therefore model rate evolution more realistically than the uncorrelated molecular clock (Lepage et al. 2007).”
BackgroundThe changing face of the molecular evolutionary clock
Ho, S. Y. W. (2014) · Trends in Ecology & Evolution · doi:10.1016/j.tree.2014.07.004 · Cited by 116 · see citing works
Monocot fossils suitable for molecular dating analyses
Iles, W. J. D., Smith, S. Y., Gandolfo, M. A., & Graham, S. W. (2015) · Botanical Journal of the Linnean Society · doi:10.1111/boj.12233 · Cited by 117 · see citing works
“Although there are multiple sources of error in molecular dating (e.g. Magallón, 2004; Rutschmann, 2006; Lepage et al., 2007; Gandolfo, Nixon & Crepet, 2008; Parham & Irmis, 2008; Ho & Phillips, 2009; Clarke, Warnock & Donoghue, 2011; Parham et al., 2012; Dos Reis & Yang, 2013; Paradis, 2013; Sauquet, 2013), the large…”
BackgroundVinther, J., Sperling, E. A., Briggs, D. E. G., & Peterson, K. J. (2011) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2011.1773 · Cited by 111 · see citing works
Rate variation and estimation of divergence times using strict and relaxed clocks
Brown, R. P., & Yang, Z. (2011) · BMC Evolutionary Biology · doi:10.1186/1471-2148-11-271 · Cited by 114 · see citing works
“[18] compared the fit of several different models to three real datasets and argued for correlated rates particularly in large datasets (although their analyses did not use any calibrations and so did not fully reflect typical applications).”
ResultThe evolutionary history of bees in time and space
Almeida, E. A. B., Bossert, S., Danforth, B. N., Porto, D. S., Freitas, F. V., Davis, C. “., Murray, E. A., Blaimer, B. B., Spasojevic, T., Ströher, P. R., et al. (2023) · Current Biology · doi:10.1016/j.cub.2023.07.005 · Cited by 112 · see citing works
A practical guide to molecular dating
Sauquet, H. (2013) · Comptes Rendus Palevol · doi:10.1016/j.crpv.2013.07.003 · Cited by 107 · see citing works
A Dirichlet process prior for estimating lineage-specific substitution rates
Heath, T. A., Holder, M. T., & Huelsenbeck, J. P. (2012) · Molecular Biology and Evolution · doi:10.1093/molbev/msr255 · Cited by 105 · see citing works
“…stepping stone method (Xie et al. 2011) to perform Bayes factor comparisons of three different relaxedclock models: the independent gamma rates model also called the “white noise” model by Lepage et al. (2007), the CPP model (Huelsenbeck et al. 2000), and the AR-LN model (Thorne and Kishino 2002).”
BackgroundMethodInfluentialEstimating the Number of Subpopulations ( K ) in Structured Populations
Verity, R., & Nichols, R. A. (2016) · Genetics · doi:10.1534/genetics.115.180992 · Cited by 98 · see citing works
“…and has since been applied to a range of problems in phylogenetics and coalescent theory, including comparing models of demographics (Baele et al. 2012), migration (Beerli and Palczewski 2010), relaxed molecular clocks (Lepage et al. 2007), and sequence evolution (Blanquart and Lartillot 2006).”
BackgroundWright, D. F. (2017) · Journal of Paleontology · doi:10.1017/jpa.2016.141 · Cited by 102 · see citing works
“uncorrelated ‘relaxed clock’models where branch-specific rates are independently drawn from the same underlying parametric distribution (Lepage et al., 2007; Heath and Moore, 2014).”
BackgroundThe Past Sure is Tense: On Interpreting Phylogenetic Divergence Time Estimates
Brown, J. W., & Smith, S. A. (2017) · Systematic Biology · doi:10.1093/sysbio/syx074 · Cited by 102 · see citing works
“In this vein, we note that the fit (Lepage et al. 2007; Ho et al. 2015) and adequacy (Duchêne et al.”
BackgroundA Bayesian framework to estimate diversification rates and their variation through time and space
Silvestro, D., Schnitzler, J., & Zizka, G. (2011) · BMC Evolutionary Biology · doi:10.1186/1471-2148-11-311 · Cited by 100 · see citing works
“Alternatively, researchers could choose to run molecular clock analyses in which the prior on the node ages is not based on a birth-death process, but modeled using uniform or Dirichlet distributions [55,56], as implemented in e.”
MethodThe impact of the rate prior on Bayesian estimation of divergence times with multiple Loci
Dos Reis, M., Zhu, T., & Yang, Z. (2014) · Systematic Biology · doi:10.1093/sysbio/syu020 · Cited by 93 · see citing works
“Usually information from the fossil record is used to calibrate molecular trees and estimate clade ages (Thorne et al. 1998; Drummond et al. 2006; Yang and Rannala 2006; Lepage et al. 2007).”
MethodA Hierarchical Bayesian Model for Calibrating Estimates of Species Divergence Times
Heath, T. A. (2012) · Systematic Biology · doi:10.1093/sysbio/sys032 · Cited by 97 · see citing works
“…θa), can be characterized by nonbiological parametric distributions such as the Dirichlet distribution (Kishino et al. 2001) or uniform distribution (Lepage et al. 2007), or by branching processes describing lineage diversification, including the Yule model (Yule 1924; Sanderson 1997; Thorne et…”
BackgroundVea, I. M., & Grimaldi, D. A. (2016) · Scientific Reports · doi:10.1038/srep23487 · Cited by 97 · see citing works
Cavalier-Smith, T., Chao, E., & Lewis, R. (2018) · Protoplasma · doi:10.1007/s00709-018-1241-1 · Cited by 79 · see citing works
“than by the lognormal model even though under simulation CIR appeared as reliable (Lepage et al. 2007).”
MethodInfluential
- Authors
- Lepage, T., Bryant, D., Philippe, H., & Lartillot, N.
- Affiliations
- McGill University (CA)
- University of Auckland (NZ)
- Université de Montréal (CA)
- Centre National de la Recherche Scientifique (FR)
- Venue
- Molecular Biology and Evolution
- Publisher
- Oxford University Press (OUP)
- Published
- 2007-06-29
- Volume
- 24
- Issue
- 12
- Pages
- 2669-2680
- ISSN
- 0737-4038 (ISSN-L)
- 1537-1719
- OpenAlex
- W2116474217
- Cited by
- 546
- References
- 46
- Citations by year
- 2026: 27 · 2025: 28 · 2024: 24 · 2023: 33 · 2022: 39 · 2021: 34 · 2020: 38 · 2019: 29 · 2018: 43 · 2017: 33 · 2016: 32 · 2015: 38 · 2014: 50 · 2013: 18 · 2012: 19
- FWCI
- 4.98
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Molecular Biology and Evolution (publishedVersion)
- PubMed (publishedVersion)
- HAL (submittedVersion, cc-by)
- Funders
- Génome Québec
- Centre National de la Recherche Scientifique
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Genomics and Phylogenetic Studies
- Physical Sciences › Earth and Planetary Sciences › Paleontology › Evolution and Paleontology Studies
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Evolution and Genetic Dynamics
- Keywords
- relaxed molecular clock, divergence time estimation, CIR process, Dirichlet prior, model comparison, Bayes factor, thermodynamic integration, protein sequence data
- MeSH terms
- Bayes Theorem, Models, Molecular, Phylogeny, Time Factors, Genetic Variation
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