The DOI matches its Crossref record; 46 of the 46 references it cites were found in a registry or an index; none of the 27 sources its claims cite is checked for support yet.
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.
Overview
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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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37 Own interpretation · 24 Own result · 16 Not checked yet · 7 No basis given · 2 Own method
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“In contrast, the optimal choice for the divergence time prior is more dependent on the data investigated.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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“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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“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.”
plain- Asserted: passes — The authors put it forward as true.
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“on which it is strongly favored over the 2 alternatives (ln BF . 45).”
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“This trend is also observed under the birth-death prior (fig. 3 b ) but is less pronounced.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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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
- Probably not a substantial claim. 14
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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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“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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“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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“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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“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).”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“This contrasts with the linearly increasing variance of the lognormal model, which does not have a stationary behavior.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“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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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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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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In the paper
“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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“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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In the paper
“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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In the paper
“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 paper
“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 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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In the paper
“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.”
plaindirect- Asserted: passes — The authors put it forward as true.
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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.”
plaindirect- Asserted: passes — The authors put it forward as true.
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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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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
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).”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
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
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
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 ).”
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“Our conclusions are exclusively based on relative age estimates”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial 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?
The cited source says what the claim attributes to it.
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]
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.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ A General Comparison of Relaxed Molecular Clock Models · p. 2
“We find that the 2 autocorrelated models, CIR and lognormal, have a similar fit and clearly outperform uncorrelated models on all 3 data sets.”
§ Model Comparison · p. 7
“| 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] |”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ Comparison of Alternative Priors on Divergence Times · p. 8
“except on MITO100 and MITO150, on which it is strongly favored over the 2 alternatives (ln BF . 45).”
§ Dispersion Index and Rate Autocorrelation · p. 8
“| 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] |”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ Relative Divergence Times · p. 10
“We therefore checked that the optimal model (CIR þ BD) found under MITO150 (see fig. 1 b ) did not produce such patterns (fig. 4).”
§ Relative Divergence Times · p. 9
“( 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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Sorted by citations
MrBayes 3.2: Efficient Bayesian Phylogenetic Inference and Model Choice Across a Large Model Space
Ronquist, F., Teslenko, M., van der Mark, P., Ayres, D. L., Darling, A. E., Höhna, S., Larget, B. R., Liu, L., Suchard, M. A., & Huelsenbeck, J. P. (2012) · Systematic Biology · doi:10.1093/sysbio/sys029 · Cited by 28,399
“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
Lartillot, N., Lepage, T., & Blanquart, S. (2009) · Bioinformatics · doi:10.1093/bioinformatics/btp368 · Cited by 1,297
“Currently available molecular dating software programs propose either branch i.i.d. models of rate variations (Akerborg et al., 2008; Drummond et al., 2006), or autocorrelated model of rate variations (Kishino et al., 2001; Lepage et al., 2007; Rannala and Yang, 2007).”
Self-citationErwin, D. H., Laflamme, M., Tweedt, S. M., Sperling, E. A., Pisani, D., & Peterson, K. J. (2011) · Science · doi:10.1126/science.1206375 · Cited by 1,336
Upham, N. S., Esselstyn, J. A., & Jetz, W. (2019) · PLoS Biology · doi:10.1371/journal.pbio.3000494 · Cited by 1,235
Baele, G., Lemey, P., Bedford, T., Rambaut, A., Suchard, M. A., & Alekseyenko, A. V. (2012) · Molecular Biology and Evolution · doi:10.1093/molbev/mss084 · Cited by 1,145
“Hence, the approaches of Lepage et al. (2007) and Friel and Petitt (2008) both place most of the power values at points where the power posterior is changing rapidly.”
BackgroundMethodImproving Marginal Likelihood Estimation for Bayesian Phylogenetic Model Selection
Xie, W., Lewis, P. O., Fan, Y., Kuo, L., & Chen, M. (2010) · Systematic Biology · doi:10.1093/sysbio/syq085 · Cited by 1,061
“This approach generalizes the method suggested by Friel and Pettitt (2008), which corresponds to the special case α = 0.25, and is analogous to the sigmoidal function proposed by Lepage et al. (2007) in a model-switch TI framework.”
MethodInfluentialA metacalibrated time‐tree documents the early rise of flowering plant phylogenetic diversity
Magallón, S., Gómez‐Acevedo, S. L., Sánchez‐Reyes, L. L., & Hernández‐Hernández, T. (2015) · New Phytologist · doi:10.1111/nph.13264 · Cited by 1,043
“…models to estimate divergence times, it has been shown that under complex estimation conditions or molecular model misspecification, absolute molecular rates and divergence times may be erroneously estimated (e.g. Jansa et al., 2006; Hugall et al., 2007; Lepage et al., 2007; Brandley et al., 2011).”
BackgroundEstimating the timing of early eukaryotic diversification with multigene molecular clocks
Parfrey, L. W., Lahr, D. J. G., Knoll, A. H., & Katz, L. A. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1110633108 · Cited by 899
“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
The fossilized birth-death process for coherent calibration of divergence-time estimates
Heath, T. A., Huelsenbeck, J. P., & Stadler, T. (2014) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1319091111 · Cited by 834
“calibration of divergence-time estimates”
A Total-Evidence Approach to Dating with Fossils, Applied to the Early Radiation of the Hymenoptera
Ronquist, F., Klopfstein, S., Vilhelmsen, L., Schulmeister, S., Murray, D. L., & Rasnitsyn, A. P. (2012) · Systematic Biology · doi:10.1093/sysbio/sys058 · Cited by 930
“The IGR model is a continuous uncorrelated model, in which the branch rates are drawn independently from the same gamma distribution (Lepage et al. 2007).”
BackgroundMethodInfluentialAccounting for Calibration Uncertainty in Phylogenetic Estimation of Evolutionary Divergence Times
Ho, S. Y. W., & Phillips, M. J. (2009) · Systematic Biology · doi:10.1093/sysbio/syp035 · Cited by 906
“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).”
BackgroundMethodHöhna, S., Landis, M. J., Heath, T. A., Boussau, B., Lartillot, N., Moore, B. R., Huelsenbeck, J. P., & Ronquist, F. (2016) · Systematic Biology · doi:10.1093/sysbio/syw021 · Cited by 840
“…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
Tamura, K., Battistuzzi, F. U., Billing-Ross, P., Murillo, O. D., Filipski, A., & Kumar, S. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1213199109 · Cited by 674
Taxon sampling and the accuracy of phylogenetic analyses
(2008) · Journal of Systematics and Evolution · doi:10.3724/sp.j.1002.2008.08016 · Cited by 553
“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 526
Uncertainty in the Timing of Origin of Animals and the Limits of Precision in Molecular Timescales
dos Reis, M., Thawornwattana, Y., Angelis, K., Telford, M. J., Donoghue, P. C. J., & Yang, Z. (2015) · Current Biology · doi:10.1016/j.cub.2015.09.066 · Cited by 471
Total-Evidence Dating under the Fossilized Birth–Death Process
Zhang, C., Stadler, T., Klopfstein, S., Heath, T. A., & Ronquist, F. (2016) · Systematic Biology · doi:10.1093/sysbio/syv080 · Cited by 419
Vanneste, K., Baele, G., Maere, S., & de Peer, Y. V. (2014) · Genome Research · doi:10.1101/gr.168997.113 · Cited by 447
“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 438
“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
“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
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 369
“, 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 351
“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. A., Pisani, D., & Knoll, A. H. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1620089114 · Cited by 332
“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 321
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 310
“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
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
“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
“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 276
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 283
“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 282
Inoue, J. G., Donoghue, P. C. J., & Yang, Z. (2009) · Systematic Biology · doi:10.1093/sysbio/syp078 · Cited by 269
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
“[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
Lartillot, N., & Poujol, R. (2011) · Molecular Biology and Evolution · doi:10.1093/molbev/msq244 · Cited by 243
“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
“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 243
“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 246
“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 223
“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 226
“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 213
“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 217
“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 202
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 204
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 190
“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 197
“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 191
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
“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 194
“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
“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 177
“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
“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
“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 174
“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
“…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 167
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 167
“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
“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 164
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 162
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
“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 163
“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., Ortí, G., & Betancur‐R, R. (2014) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2014.10.011 · Cited by 151
“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 158
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 147
“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 147
Early Archean origin of Photosystem II
Cardona, T., Sánchez‐Baracaldo, P., Rutherford, A. W., & Larkum, A. W. (2019) · Geobiology · doi:10.1111/gbi.12322 · Cited by 144
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
“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
“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
“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
“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
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 134
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
(2016) · doi:10.1093/sysbio/syw041 · Cited by 120
“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 130
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
“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
Dornburg, A., Brandley, M. C., McGowen, M. R., & Near, T. J. (2011) · Molecular Biology and Evolution · doi:10.1093/molbev/msr228 · Cited by 128
“…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
“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
“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. B., Field, M. C., Buick, R., Eme, L., Gribaldo, S., Roger, A. J., Brochier‐Armanet, C., & Devos, D. P. (2016) · Journal of Cell Science · doi:10.1242/jcs.178566 · Cited by 131
“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 122
“…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 118
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
“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
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
“[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
A practical guide to molecular dating
Sauquet, H. (2013) · Comptes Rendus Palevol · doi:10.1016/j.crpv.2013.07.003 · Cited by 107
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
“…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
“…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
“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 103
“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
“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
“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 98
“…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
Cavalier-Smith, T., Chao, E., & Lewis, R. (2018) · Protoplasma · doi:10.1007/s00709-018-1241-1 · Cited by 79
“than by the lognormal model even though under simulation CIR appeared as reliable (Lepage et al. 2007).”
MethodInfluential
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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