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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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“In contrast, the optimal choice for the divergence time prior is more dependent on the data investigated.”
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In the paper
“Our results provide strong evidence in favor of autocorrelated models such as the lognormal and the CIR models, in particular under rich taxonomic sampling.”
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In the paper
“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.”
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In the paper
“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)”
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“Only when the number of taxa is small (MITO10) are the uncorrelated models comparable to the autocorrelated models.”
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In the paper
“under dense taxonomic sampling (MITO150), the UExp and the WN models were so bad that they performed even worse than the unconstrained model.”
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In the paper
“For most data sets, the 2 autocorrelated models, LOGN and CIR, have comparable Bayes factors.”
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In the paper
“on which it is strongly favored over the 2 alternatives (ln BF . 45).”
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In the paper
“This trend is also observed under the birth-death prior (fig. 3 b ) but is less pronounced.”
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“We observe in both cases that, for most nodes, the posterior standard errors (SEs) are much smaller than the prior SEs”
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- It may state two separate claims as one. 28
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In the paper
“We find that the 2 autocorrelated models, CIR and lognormal, have a similar fit and clearly outperform uncorrelated models on all 3 data sets.”
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In the paper
“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.”
What the sources say
- Not checked yetcites Drummond et al. 2006
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In the paper
“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).”
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In the paper
“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.”
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In the paper
“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 ).”
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In the paper
“On the other hand, the number of departing nodes went up to 100 between STRICT and CIR and to 93 between STRICT and LOGN.”
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“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).”
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“This contrasts with the linearly increasing variance of the lognormal model, which does not have a stationary behavior.”
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“We also propose a new autocorrelated model, called the ''CIR'' process, with well-defined stationary properties.”
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In the paper
“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).”
What the sources say
- Not checked yetcites Aris-Brosou and Yang (2002)
- Not checked yetcites Welch et al. (2005)
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“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).”
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In the paper
“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.”
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In the paper
“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).”
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“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.”
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In the paper
“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.”
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“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.”
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In the paper
“The CIR process mainly differs from the log normal in the fact that it possesses a stationary distribution.”
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In the paper
“However, they are regarded as very controversial (see answers to Aitkin 1991).”
What the sources say
- Not checked yetcites Aitkin 1991
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In the paper
“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).”
What the sources say
- Not checked yetcites Ogata 1989
- Not checked yetcites Lartillot and Philippe 2004, 2006
- Not checked yetcites Blanquart and Lartillot 2006
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“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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In the paper
“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).”
What the sources say
- Not checked yetcites Aris-Brosou and Yang 2003
- Not checked yetcites Welch et al. (2005)
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“Thus, unlike WN, UGAM has a dispersion index increasing with t , which is a typical feature of autocorrelated models.”
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“In the present case, the theoretical dispersion index is equal to 1 þ r for WN and 1 þ r t for UGAM.”
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In the paper
“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).”
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In the paper
“In general, this absence of stationarity for a stochastic process is seen as a potential problem (Lepage et al. 2006).”
What the sources say
- Not checked yetcites Lepage et al. 2006
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“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.”
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In the paper
“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.”
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In the paper
“given that large discrepancies in the relative node ages between 2 models will probably imply large discrepancies in the absolute dates as well”
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In the paper
“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).”
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In the paper
“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.”
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In the paper
“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.”
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In the paper
“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.”
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In the paper
“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.”
What the sources say
- Not checked yetcites Ohta 1995
- Not checked yetcites Bickel and West 1998
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In the paper
“This may be simply due to the fact that our priors on hyperparameters are more vague.”
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In the paper
“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).”
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In the paper
“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.”
What the sources say
- Not checked yetcites Welch et al. 2005
- Not checked yetcites Aris-Brosou and Yang 2003
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In the paper
“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 ).”
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In the paper
“Our conclusions are exclusively based on relative age estimates”
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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.”
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In the citing paper
“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]
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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.”
Citations
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RetractedEquation of State Calculations by Fast Computing Machines
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Relaxed Phylogenetics and Dating with Confidence
Drummond, A. J., Ho, S. Y. W., Phillips, M. J., & Rambaut, A. (2006) · PLoS Biology · doi:10.1371/journal.pbio.0040088 · Cited by 6,463
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Items 301–400 of 544
Evolutionary Roots and Diversification of the Genus Aeromonas
Sanglas, A., Albarral, V., Farfán, M., Lorén, J. G., & Fusté, M. C. (2017) · Frontiers in Microbiology · doi:10.3389/fmicb.2017.00127 · Cited by 16
“…that although it is possible to infer phylogenies from molecular sequences, it is not possible to estimate molecular rates or divergence times, because the individual contribution of each one to molecular evolution cannot be separated (Felsenstein, 1981; Drummond et al., 2006; Lepage et al., 2007).”
BackgroundYin, Z., Lü, L., Yamamoto, S., Thayer, M. K., Newton, A. F., & Cai, C. (2020) · Cladistics · doi:10.1111/cla.12430 · Cited by 16
“Two relaxed models are available to morphological clock: autocorrelated lognormal distributions (“TK02”) model (Thorne and Kishino, 2002) and uncorrelated lognormal distributions (IGR) model (LePage et al., 2007).”
MethodModeling Substitution Rate Evolution across Lineages and Relaxing the Molecular Clock
Mello, B., & Schrago, C. G. (2024) · Genome Biology and Evolution · doi:10.1093/gbe/evae199 · Cited by 16
“Alternatively, Lepage et al. (2007) employed a Cox–Ingersoll–Ross (CIR) process (Cox et al. 1985; Lepage et al. 2007) to ensure stationarity of rates and model the evolution of rates in a correlated manner.”
BackgroundMethodInfluentialEarly–middle Permian Mediterranean gorgonopsian suggests an equatorial origin of therapsids
Matamales‐Andreu, R., Kammerer, C. F., Angielczyk, K. D., Simões, T. R., Mujal, E., Galobart, À., & Fortuny, J. (2024) · Nature Communications · doi:10.1038/s41467-024-54425-5 · Cited by 15
“We used the skyline fossilised birth-death tree model (SFBD) 43 in combination with new relaxed clock models recently implemented in the software Mr. Bayes 44 — see Methods.”
InfluentialEvolution is coupled with branching across many granularities of life
Douglas, J., Bouckaert, R., Harris, S. C., Carter, C. W., & Wills, P. R. (2025) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2025.0182 · Cited by 18
“…populations of either protocells or sets of proteins, respectively, initiated by the growth of a fluctuation (random change) away from a homogeneous ground state, through a dynamic instability where the bifurcation establishes a foothold, leading to its fixation in a new heterogeneous state.”
Kolibáč, J., Bocáková, M., Liebherr, J. K., Ramage, T., & Porch, N. (2020) · Zoological Journal of the Linnean Society · doi:10.1093/zoolinnean/zlaa064 · Cited by 15
Monte Carlo algorithms for Brownian phylogenetic models
Horvilleur, B., & Lartillot, N. (2014) · Bioinformatics · doi:10.1093/bioinformatics/btu485 · Cited by 15
“Typically, the Brownian process is explicitly sampled only at the internal nodes of the phylogeny, corresponding to cladogenetic events (Thorne et al., 1998; Lepage et al., 2007) or at the midpoints along the branches (Rannala and Yang, 2007).”
BackgroundMethodSelf-citationHimmelmann, L., & Metzler, D. (2009) · Bioinformatics · doi:10.1093/bioinformatics/btp417 · Cited by 15
“relaxed molecular clock models for the variation of mutation rates along the tree are currently discussed, cf. [ LBPL07 , Him09].”
Shrinkage-based Random Local Clocks with Scalable Inference
Fisher, A. A., Ji, X., Nishimura, A., Baele, G., Lemey, P., & Suchard, M. A. (2023) · Molecular Biology and Evolution · doi:10.1093/molbev/msad242 · Cited by 14
“Indeed, in a variety of settings, autocorrelation between clock rates appears crucial for accurate divergence-time estimation (Lepage et al. 2007).”
BackgroundDeep divergences among inconspicuously colored clades of Epipedobates poison frogs
López-Hervas, K., Santos, J. C., Ron, S. R., Betancourth‐Cundar, M., Cannatella, D. C., & Tarvin, R. D. (2024) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2024.108065 · Cited by 14
Barido‐Sottani, J., Żyła, D., & Heath, T. A. (2022) · Systematic Biology · doi:10.1093/sysbio/syac073 · Cited by 13
“…distribution of substitution rates among branches (such as “relaxed clock” models like those described by Thorne et al., 1998; Drummond et al., 2006; Lepage et al., 2007, and many others), these advances led to the introduction of new Bayesian approaches for jointly estimating phylogenetic…”
MethodClockstaRX: Testing Molecular Clock Hypotheses With Genomic Data
Duchêne, D. A., Duchêne, S., Stiller, J., Heller, R., & Ho, S. Y. W. (2024) · Genome Biology and Evolution · doi:10.1093/gbe/evae064 · Cited by 13
“13 Rates of molecular evolution were simulated for each gene tree under a white-noise molecular clock 478 model (Lepage et al. 2007), as implemented in NELSI (Ho et al.”
MethodInfluentialEnvironmental niche divergence among three dune shrub sister species with parapatric distributions
Chozas, S., Chefaoui, R. M., Correia, O. A., Bonal, R., & Hortal, J. (2017) · Annals of Botany · doi:10.1093/aob/mcx004 · Cited by 13
“In turn, specieslevel phylogenies estimated from DNA sequences (e.g. Pardo et al., 2008) allow the dating of speciation events via relaxed molecular clock methods (Lepage et al., 2007).”
BackgroundLabisko, J., Griffiths, R. A., Chong‐Seng, L., Bunbury, N., Maddock, S. T., Bradfield, K. S., Taylor, M. L., & Groombridge, J. J. (2018) · Biological Journal of the Linnean Society · doi:10.1093/biolinnean/bly183 · Cited by 13
Liu, H., Yang, Y., Sun, S., Kong, L., & Li, Q. (2020) · Zoologica Scripta · doi:10.1111/zsc.12412 · Cited by 13
Jouet, A., McMullan, M., & van Oosterhout, C. (2015) · Molecular Ecology · doi:10.1111/mec.13213 · Cited by 13
“To do so, we used an uncorrelated relaxed molecular clock to take into account lineage-specific rate heterogeneity (Lepage et al. 2007).”
MethodBattistuzzi, F. U., Filipski, A. J., & Kumar, S. (2011) · Wiley eBooks · doi:10.1002/9780470015902.a0001803.pub2 · Cited by 12
“This approach, however, obtains contrasting results based on the taxonomic sampling, the depth of the phylogeny, and the gene selection (Drummond et al., 2006; Lepage et al., 2007; Brown et al., 2008; Ho, 2009).”
ResultLindsey, C. R., Knoll, A. H., Herron, M. D., & Rosenzweig, F. (2024) · BMC Biology · doi:10.1186/s12915-024-01878-1 · Cited by 12
“Uncorrelated models (i.e., UGAM and WN) assume each branch of will have its own unique rate of evolution irrespective of rates across branches for closely and distantly related species [94, 95].”
BackgroundMethodInfluentialMolecular Evolution of Hemagglutinin (H) Gene in Measles Virus Genotypes D3, D5, D9, and H1
Saitoh, M., Takeda, M., Gotoh, K., Takeuchi, F., Sekizuka, T., Kuroda, M., Mizuta, K., Ryo, A., Tanaka, R., Ishii, H., et al. (2012) · PLoS ONE · doi:10.1371/journal.pone.0050660 · Cited by 12
“The time of the most recent common ancestor (tMRCA) with a 95% highest posterior density (HPD) was estimated by Bayesian molecular dating as described previously [9,10].”
MethodBaele, G., de Peer, Y. V., & Vansteelandt, S. (2009) · BMC Evolutionary Biology · doi:10.1186/1471-2148-9-87 · Cited by 12
“A referee remarked that Lepage et al. [24] have used a sigmoidal schedule for to circumvent this problem.”
A road map for phylogenetic models of species trees
Cornuault, J., & Sanmartín, I. (2022) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2022.107483 · Cited by 12
Ellis, E. A., Goodheart, J. A., Hensley, N. M., González, V. L., Reda, N. J., Rivers, T. J., Morin, J. G., Torres, E. P., Gerrish, G. A., & Oakley, T. H. (2022) · Systematic Biology · doi:10.1093/sysbio/syac057 · Cited by 13
“Along with node constraints, we used the Independent Gamma Rate (IGR) model (Lepage et al. 2007; Zhang 2016).”
MethodImpact of the Partitioning Scheme on Divergence Times Inferred from Mammalian Genomic Data Sets
Voloch, C. M., & Schrago, C. G. (2012) · Evolutionary Bioinformatics · doi:10.4137/ebo.s9627 · Cited by 12
Phylogeny of Anthospermeae of the Coffee Family Inferred Using Clock and Nonclock Models
Thureborn, O., Razafimandimbison, S. G., Wikström, N., Khodabandeh, A., & Rydin, C. (2019) · International Journal of Plant Sciences · doi:10.1086/703353 · Cited by 12
So many genes, so little time: a practical approach to divergence-time estimation in the genomic eraPreprint
Smith, S. A., Brown, J. W., & Walker, J. F. (2017) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/114975 · Cited by 13
“This is not an exhaustive list as other methods have been developed and new ones are continually released (e.g., Lepage et al. 2007; Tamura et al. 2012; Heath et al. 2014).”
MethodConvergent evolution of giant size in eurypterids
Ruebenstahl, A. A., Koch, N. M., Lamsdell, J. C., & Briggs, D. E. G. (2024) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2024.1184 · Cited by 10
López‐Antoñanzas, R., Simões, T. R., Condamine, F. L., Dirnberger, M., & Peláez‐Campomanes, P. (2024) · BMC Biology · doi:10.1186/s12915-024-02053-2 · Cited by 13
Lahr, D. J. G. (2021) · Memórias do Instituto Oswaldo Cruz · doi:10.1590/0074-02760200620 · Cited by 9
“These implementations of the Zuckerkandl and Pauling idea allow to explicitly parametrise all the biases that can interfere in the calculation of the molecular clock, especially those related to the rate variation over time, and along branches.(48) With the resurgence in studies of eukaryotic microorganisms, several r…”
MethodNucleotide Substitutions during Speciation may Explain Substitution Rate Variation
Janzen, T., Bokma, F., & Etienne, R. S. (2021) · Systematic Biology · doi:10.1093/sysbio/syab085 · Cited by 11
“For such cases, phylogenetic inference software allows one to use a relaxed molecular clock (Drummond et al. 2006; Lepage et al. 2007), which assumes that the substitution rate varies between lineages according to a statistical distribution such as a gamma or lognormal distribution.”
MethodBremer, N., Knopp, M. R., Martin, W. F., & Tria, F. D. K. (2022) · Life · doi:10.3390/life12070995 · Cited by 10
“Methods commonly used for rooting include: (i) the outgroup [1], including the special case of tree rooting with ancient gene duplications [2]; (ii) the midpoint criterion [3]; (iii) the minimal ancestor deviation (MAD) approach [4]; (iv) molecular clock models [5]; and (v) time-irreversible models [6].”
BackgroundGenetic and evolutionary perspectives on genogroup III, genotype 2 bovine noroviruses
Mauroy, A., Scipioni, A., Mathijs, É., Ziant, D., Daube, G., & Thiry, É. (2013) · Archives of Virology · doi:10.1007/s00705-013-1791-7 · Cited by 11
“uncorrelated relaxed lognormal molecular clock should be more efficient [18] and was the recommended relaxed”
BackgroundAn in silico comparison of reduced-representation and sequence-capture protocols for phylogenomicsPreprint
Collins, R. A., & Hrbek, T. (2015) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/032565 · Cited by 11
“Despite the findings of Lepage et al. (2007), where empirical data consistently departed from the strict clock in favor of autocorrelated or uncorrelated models, we found that none of our datasets could reject the null model of a single rate.”
ResultMolecular paleobiology — Progress and perspectives
Wörheide, G., Dohrmann, M., & Yang, Q. (2016) · Palaeoworld · doi:10.1016/j.palwor.2015.01.005 · Cited by 10
Relative Time Constraints Improve Molecular Dating
Szöllõsi, G. J., Höhna, S., Williams, T. A., Schrempf, D., Daubin, V., & Boussau, B. (2022) · Systematic Biology · doi:10.1093/sysbio/syab084 · Cited by 23
“These means and variances were given as input to a script that computes a posterior distribution of timetrees according to a birth–death prior on the tree topology and node ages, an UGAM prior on the rate of sequence evolution through time (Lepage et al. 2007), and using the calibrations and constraints gathered in pr…”
BackgroundMethodInfluentialKovacs, T. G. L., Walker, J., Hellemans, S., Bourguignon, T., Tatarnic, N. J., McRae, J. M., Ho, S. Y. W., & Lo, N. C. (2024) · Systematic Biology · doi:10.1093/sysbio/syae002 · Cited by 10
“There has also been varying support for uncorrelated and autocorrelated relaxed clocks, with substantial impacts on the inference of evolutionary histories (Lepage et al. 2007; Linder et al. 2011; Ho et al. 2015; dos Reis et al. 2018).”
BackgroundThe trunk replaces the longer mandible as the main feeding organ in elephant evolution
Li, C., Deng, T., Wang, Y., Sun, F., Wolff, B., Jiangzuo, Q., Ma, J., Xing, L., Fu, J., Zhang, J., et al. (2024) · eLife · doi:10.7554/elife.90908.3 · Cited by 10
Practical Guide and Review of Fossil Tip-Dating in Phylogenetics
Heckeberg, N. S., Capobianco, A., Khakurel, B., Darlim, G., & Höhna, S. (2025) · Systematic Biology · doi:10.1093/sysbio/syaf050 · Cited by 13
“…uncorrelated clocks such as UCLN and IGR should be generally preferred over other types of clock models, despite au-tocorrelated relaxed clock models being biologically often more realistic, but uncorrelated re-laxed clock models performing more robustly ( Lepage et al. 2007 ; Linder et al. 2011 ).”
Bakiu, R., Korro, K., & Santovito, G. (2015) · The European Zoological Journal · doi:10.1080/11250003.2015.1018352 · Cited by 10
“2000) and the independent gamma rates (IGR) model (Lepage et al. 2007).”
Admixture of evolutionary rates across a butterfly hybrid zone
Xiong, T., Li, X., Yago, M., & Mallet, J. (2022) · eLife · doi:10.7554/elife.78135 · Cited by 10
“As such variation affects how fast the molecular clock ticks, reconstructing gene genealogies among different species some-times accounts for species-specific rates of evolution ( Lepage et al., 2007 ).”
BackgroundDerouiche, L., Irzagh, A., Rahmouni, R., Tahri, R., Hadjeloum, M., Bouhadad, R., & Fernandes, C. (2020) · Gene · doi:10.1016/j.gene.2020.144510 · Cited by 10
Guterres, D. C., Galvão-Elias, S., de Souza, B. C. P., Pinho, D. B., dos Santos, M. D. D. M., Miller, R. G., & Dianese, J. C. (2018) · Mycologia · doi:10.1080/00275514.2018.1465774 · Cited by 10
“Branch ages were modeled using the uncorrelated lognormal relaxed clock (Drummond et al. 2006; Lepage et al. 2007), specifying a gamma distribution for the ulcd.mean parameter with a shape of 1.0, scale of 0.003, and offset of 0.0, with unlinked rates for clock and substitution models.”
MethodInfluentialZhang, R., Wang, L., Tian, S., Liu, Y., Jiang, Y., Zhou, X., Yang, D., Liu, X., & Wang, Y. (2025) · Systematic Entomology · doi:10.1111/syen.12684 · Cited by 10
“Numerous studies have been conducted on the effects of substitution models (Abadi et al., 2019; Tao et al., 2020), molecular clock models (Ho & Duchene, 2014; Lepage et al., 2007) and fossil sampling (Inoue et al., 2010; O ’ Reilly & Donoghue, 2020; Tamura et al., 2018).”
Molecular Dating of Phylogeny of Sturgeons (Acipenseridae) Based on Total Evidence Analysis
Shedko, S. V. (2022) · Russian Journal of Genetics · doi:10.1134/s1022795422060084 · Cited by 9
Darriba, D., Aberer, A. J., Flouri, T., Heath, T. A., Izquierdo-Carrasco, F., & Stamatakis, A. (2013) · IEEE International Symposium on Parallel & Distributed Processing, Workshops and Phd Forum · doi:10.1109/ipdpsw.2013.267 · Cited by 9
“Special cases of this model are (i) the so-called global molecular clock that only has one single rate category [5], (ii) the local molecular clock model, where closely related lineages (subtrees) share the same substitution rate [6], [7], and (iii) the independent rates model, where the rate for…”
Jin, H., Yonezawa, T., Zhong, Y., Kishino, H., & Hasegawa, M. (2016) · Genes & Genetic Systems · doi:10.1266/ggs.16-00003 · Cited by 9
Kiyota, N., Kobayashi, M., Tsukagoshi, H., Ryo, A., Harada, S., Kusaka, T., Obuchi, M., Shimojo, N., Noda, M., & Kimura, H. (2013) · Infection Genetics and Evolution · doi:10.1016/j.meegid.2013.10.024 · Cited by 9
“Another technique, the Bayesian Markov chain Monte Carlo (MCMC) method, enables the time-scaled phylogeny of viral genes to be estimated (Lepage et al., 2007; Thorne et al., 1998).”
MethodAsymmeTree: A Flexible Python Package for the Simulation of Complex Gene Family Histories
Schaller, D., Hellmuth, M., & Stadler, P. F. (2022) · Software · doi:10.3390/software1030013 · Cited by 12
Mu, T., Lin, Y., Pu, H., Keyhani, N. O., Dang, Y., Lv, H., Zhao, Z.-Y., Heng, Z., Wu, Z., Xiong, C., et al. (2024) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2024.108211 · Cited by 8
Wang, C.-G., Wu, Y.-D., Zhang, X. Y., Dai, Y., Li, Z., & Yuan, Y. (2025) · IMA Fungus · doi:10.3897/imafungus.16.161336 · Cited by 8
Oberlander, K., Roets, F., & Dreyer, L. L. (2014) · Journal of Biogeography · doi:10.1111/jbi.12304 · Cited by 8
“Similarly, we tested the fit of a strict clock, relaxed clock under the IGR model (Lepage et al., 2007), and a model where rates across branches were free to vary, using Bayes factors (Kass & Raftery, 1995) computed in Tracer with the marginal likelihood values from the stepping stone MrBayes runs.”
MethodA test of Generalized Bayesian dating: A new linguistic dating method
Rama, T., & Wichmann, S. (2020) · PLoS ONE · doi:10.1371/journal.pone.0236522 · Cited by 8
“There are multiple relaxed clock rate models [54] employing different assumptions for deriving the multiplicative factor.”
MethodInfluentialRazafimandimbison, S. G., Wikström, N., Khodabandeh, A., & Rydin, C. (2022) · Annals of Botany · doi:10.1093/aob/mcac121 · Cited by 8
“…we performed relaxed-clock analyses using three alternative relaxed-clock models, the Brownian motion model (TK02) described by Thorne and Kishino (2002), the white noise model (WN) described by LePage et al. (2007) and the independent lognormal model (ILN) described by Drummond et al. (2006).”
MethodGülay, A., Fournier, G. P., Smets, B. F., & Girguis, P. R. (2023) · Molecular Biology and Evolution · doi:10.1093/molbev/msad161 · Cited by 9
“1c (Lepage et al. 2007) under the CAT20 model, BD and UNI tree priors, and uncorrelated gamma distributed (UGM), autocorrelated lognormal (LN), and autocorrelated CIR process rate models.”
MethodHancock, Z. B., & Blackmon, H. (2020) · Journal of Heredity · doi:10.1093/jhered/esaa042 · Cited by 8
“…centered around questions of how to appropriately apply fossil calibrations (e.g., Heath et al. 2014; Brown and Smith 2018), rate heterogeneity (Pond and Muse 2005), rate of morphological evolution (Lynch 1990), and selecting an adequate clock model (Douzery et al. 2004; Lepage et al. 2007).”
Vilarino, A., Dias, E. S., & Bispo, P. C. (2021) · Zoological Journal of the Linnean Society · doi:10.1093/zoolinnean/zlab077 · Cited by 8
Total-Evidence Dating and the Fossilized Birth–Death Model
Gavryushkina, A. “., & Zhang, C. (2020) · Springer eBooks · doi:10.1007/978-3-030-60181-2_11 · Cited by 8
Li, H., Zhuo, D., Wáng, B., Nakamine, H., Yamamoto, S., Zhang, W., Jepson, J. E., Ohl, M., Aspöck, U., Aspöck, H., et al. (2024) · Systematic Biology · doi:10.1093/sysbio/syae068 · Cited by 8
Bayesian modelling of the fossil record enlightens the evolutionary history of Hemiptera
Boderau, M., Fu, Y., Jiang, H., Guan, S., Peng, A., Nel, A., & Jouault, C. (2025) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2025.1133 · Cited by 7
Fau, M., Wright, D. F., Ewin, T. A. M., Gale, A. S., & Villier, L. (2024) · PeerJ · doi:10.7717/peerj.18169 · Cited by 7
“To account for rate variation among lineages throughout the tree, we applied an uncorrelated morphological clock where branch rates vary according to an independent gamma rates model ( Lepage et al., 2007 ).”
MethodParameterizing Pantherinae: De Novo Mutation Rate Estimates from Panthera and Neofelis Pedigrees
Armstrong, E. E., Carey, S. B., Harkess, A., Lazzari, G. Z., Solari, K. A., Maldonado, J. E., Fleischer, R. C., Aziz, N., Walsh, P., Koepfli, K., et al. (2025) · Genome Biology and Evolution · doi:10.1093/gbe/evaf060 · Cited by 8
Rubinoff, D., Jose, M. S., & Kawahara, A. Y. (2012) · Pacific Science · doi:10.2984/66.1.2 · Cited by 7
“We realize that this method of divergence estimation has problems (Britten 1986, Roger and Hug 2006, Lepage et al. 2007), but it provides a starting point for future work. results”
MethodUsing Trees to Capture Reticulate Evolution
Tofigh, A. A. (2009) · Cited by 7
Payri, C. E., & Verbruggen, A. H. (2009) · Journal of Phycology · doi:10.1111/j.1529-8817.2009.00717.x · Cited by 7
“The initial, justified critique of the molecular clock has led to the development of more realistic models that relax the assumption of the molecular clock by allowing rate heterogeneity across lineages (Lepage et al. 2007).”
BackgroundRubinoff, D., Jose, M. S., Johnson, P. J., Wells, R., Osborne, K., & Roux, J. J. L. (2015) · Biological Conservation · doi:10.1016/j.biocon.2015.01.023 · Cited by 7
McGill, L. M., Fitzpatrick, D. A., Pisani, D., & Burnell, A. M. (2017) · Nematology · doi:10.1163/15685411-00003096 · Cited by 7
“Cross-validation assays indicated that for our dataset the CIR (Lepage et al., 2007) and LogNormal (Thorne et al., 1998) autocorrelated molecular clock models outperformed the uncorre- 908 Nematology Downloaded from Brill.com09/18/2019 03:16:11PM via Maynooth University lated gamma multipliers…”
BackgroundMethodInfluentialMaiti, A. K. (2022) · Virus Research · doi:10.1016/j.virusres.2022.198712 · Cited by 6
Relative time constraints improve molecular datingPreprint
Szöllősi, G. J., Höhna, S., Williams, T. A., Schrempf, D., Daubin, V., & Boussau, B. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.10.17.343889 · Cited by 7
Koch, N. M., Thompson, J. R., Mooi, R., & Rouse, G. W. (2025) · Systematic Biology · doi:10.1093/sysbio/syaf055 · Cited by 9
“…model (TK02; Thorne and Kishino 2002 ), which assumes evolutionary rates are inherited across lineages following a Brownian motion; and an un-correlated independent gamma model (IGR; Lepage et al. 2007 ), according to which the evolutionary rates of ancestors and descendants are uncoupled.”
Ge, S., Jiang, Z.-H., Ren, L., van Achterberg, C., & Tan, J.-L. (2023) · Arthropod Systematics & Phylogeny · doi:10.3897/asp.81.e107579 · Cited by 6
“The analyses were computed with an Mkv + G unordered model (Lewis 2001) and an independent gamma relaxed clock model (Lepage et al., 2007; lset rates = gamma, prset clockvarpr = IGR, prset igrvarpr = exp(10); no rate variation was computed with lset rates = equal).”
MethodDirnberger, M., Bauer, E., & Reichenbacher, B. (2024) · Journal of Systematic Palaeontology · doi:10.1080/14772019.2024.2340498 · Cited by 6
Hidden introductions of freshwater red algae via the aquarium trade exposed by DNA barcodes
Zhan, S. H., Hsieh, T., Yeh, L. S., Kuo, T., Suda, S., & Liu, S. (2020) · Environmental DNA · doi:10.1002/edn3.139 · Cited by 6
Quintet Rooting: rooting species trees under the multi-species coalescent model
Tabatabaee, Y., Sarker, K., & Warnow, T. J. (2022) · Bioinformatics · doi:10.1093/bioinformatics/btac224 · Cited by 6
Anderson, B. M., Pisani, D., Miller, A. I., & Peterson, K. J. (2011) · Geology · doi:10.1130/g32413.1 · Cited by 6
Distinguishing Between Convergent Evolution and Violation of the Molecular Clock for Three Taxa
Mitchell, J., Sumner, J. G., & Holland, B. R. (2018) · Systematic Biology · doi:10.1093/sysbio/syy038 · Cited by 6
History Can Matter: Non-Markovian Behavior of Ancestral Lineages
Cartwright, R. A., Lartillot, N., & Thorne, J. L. (2011) · Systematic Biology · doi:10.1093/sysbio/syr012 · Cited by 6
“This possibility could explain findings that rate autocorrelation over time is small (e.g., Drummond et al. 2006; but see Lepage et al. 2007).”
BackgroundSelf-citationTofigh, A. A., Sjöstrand, J., Sennblad, B., Arbestad, L., & Lagergren, J. (2009) · KTH Publication Database DiVA (KTH Royal Institute of Technology) · Cited by 6
Panchaksaram, M., Freitas, L. A., & dos Reis, M. (2024) · Systematic Biology · doi:10.1093/sysbio/syae066 · Cited by 6
Lin, Q., Hu, S., Wu, Z., Huang, Y., Wang, S., Shi, W., & Zhu, B. (2025) · Scientific Reports · doi:10.1038/s41598-025-95789-y · Cited by 5
“A strict molecular clock was implemented to accommodate rate variation across branches 64 .”
Phylogenetics in space: How continuous spatial structure impacts tree inference
Hancock, Z. B., Lehmberg, E. S., & Blackmon, H. (2022) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2022.107505 · Cited by 5
Pu, H., Yang, J., Keyhani, N. O., Yang, L., Zheng, M., Qiu, C., Mao, Y., Shang, J., Lin, Y., Xiong, C., et al. (2025) · Journal of Fungi · doi:10.3390/jof11010028 · Cited by 5
Davolos, D., Pietrangeli, B., Persiani, A. M., & Maggi, O. (2019) · INTERNATIONAL JOURNAL OF SYSTEMATIC AND EVOLUTIONARY MICROBIOLOGY · doi:10.1099/ijsem.0.003275 · Cited by 5
Testing the ancient marine redox record from oxygenic photosynthesis to photic zone euxina
French, K. L. (2015) · Open Access Server of the Woods Hole Scientific Community (Woods Hole Scientific Community) · doi:10.1575/1912/7126 · Cited by 5
Models of nucleotide substitution
Yang, Z. (2014) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780199602605.003.0001 · Cited by 5
Confidence intervals in molecular dating by maximum likelihood
Paradis, E., Claramunt, S., Brown, J. W., & Schliep, K. P. (2022) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2022.107652 · Cited by 5
No phylogenomic support for a Cenozoic origin of the “living fossil” Isoetes
Wikström, N., Larsén, E., Khodabandeh, A., & Rydin, C. (2022) · American Journal of Botany · doi:10.1002/ajb2.16108 · Cited by 4
“It has been repeatedly shown that node age estimation is highly sensitive to the relaxation model used (e.g., Ho et al., 2005; LePage et al., 2007; Battistuzzi et al., 2010; Crisp et al., 2014; Ho, 2014).”
InfluentialFossilization processes have little impact on tip‐calibrated divergence time analyses
O’Reilly, J. E., & Donoghue, P. C. J. (2021) · Palaeontology · doi:10.1111/pala.12564 · Cited by 5
“The independent gamma rate (IGR) clock model (Lepage et al. 2007) was used and assigned a variance parameter prior of exp(10).”
MethodBakiu, R., Tolomeo, A. M., & Santovito, G. (2015) · The European Zoological Journal · doi:10.1080/11250003.2015.1071437 · Cited by 5
“2000) and the independent gamma rates (IGR) model (Lepage et al. 2007).”
Molecular and morphological clocks for estimating evolutionary divergence timesPreprint
Barba‐Montoya, J., Tao, Q., & Kumar, S. (2021) · Research Square · doi:10.21203/rs.3.rs-29165/v2 · Cited by 5
A Timeline of Bacterial and Archaeal Diversification in the OceanPreprint
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Meregalli, M., Menardo, F., Klass, K., & Cervalla, P. (2013) · Arthropod Systematics & Phylogeny · doi:10.3897/asp.71.e31765 · Cited by 4
Origin and Evolution of Human Immunodeficiency Viruses
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The Estimated Pacemaker for Great Apes Supports the Hominoid Slowdown Hypothesis
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COI Barcoding of the Shorebirds: Rates of Evolution and the Identification of Species
Elbourne, R. (2011) · TSpace (University of Toronto) · Cited by 4
A new method for detecting autocorrelation of evolutionary rates in large phylogeniesPreprint
Tao, Q., Tamura, K., Battistuzzi, F. U., & Kumar, S. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/346635 · Cited by 4
“We chose BF-SS because the harmonic mean estimator has many statistical shortcomings (Lepage et al. 2007; Xie et al. 2011; Baele et al. 2013) and thermodynamic integration (Silvestro et al.”
BackgroundMethodMixture Models for Dating with ConfidencePreprint
Darlim, G., & Höhna, S. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.09.25.614964 · Cited by 5
“…process (Lepage et al., 2006), the uncorrelated lognormal model (UCLN; Drummond et al., 2006), the uncorrelated exponential model (UCE; Drummond et al., 2006), and the independent gamma rates model (IGR; Lepage et al., 2007) — where the UCLN, UCE and IGR are today the most widely used clock models.”
BackgroundMethodCole, S. R., Wright, D. F., & Hopkins, M. J. (2025) · Journal of Paleontology · doi:10.1017/jpa.2025.10110 · Cited by 4
“However, we also accounted for rate variation among lineages throughout the tree by applying an uncorrelated morphological clock where branch rates vary according to an independent gamma rates model (Lepage et al., 2007).”
Late Cretaceous origins for major nightshade lineages from total-evidence timetree analysis
González-Ramírez, I. S., Deanna, R., & Smith, S. D. (2026) · Annals of Botany · doi:10.1093/aob/mcag011 · Cited by 3
Hardies, S. C., Cho, B. C., Jang, G. I., Wang, Z., & Hwang, C. Y. (2023) · Viruses · doi:10.3390/v15071475 · Cited by 3
“6) [27] with the BLOSUM replacement matrix as the amino acid prior, a four-category gamma correction, and the independent gamma rates relaxed clock model, also called the “white noise” model [28], with 4 chains and 1,000,000 generations and 50% reserved for burnin, unless the convergence statistics indicated a need fo…”
MethodTotal-evidence dating and the phylogenetic affinities of early fossil passerines
Lowi‐Merri, T. M., Gjevori, M., Bocheński, Z. M., Wertz, K., & Claramunt, S. (2024) · Journal of Systematic Palaeontology · doi:10.1080/14772019.2024.2356086 · Cited by 5
Factors influencing the accuracy and precision in dating single gene trees
Louvel, G., & Crollius, H. R. (2025) · Peer Community Journal · doi:10.24072/pcjournal.556 · Cited by 3
“In the uncorrelated case, the branch-wise rates are most commonly modeled as a lognormal, gamma or exponential, but alternatively the “white noise” model has the interesting property that the variance of the rate is smaller on longer branches (Lepage et al. 2007).”
Metadata
- 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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