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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.”
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Items 201–300 of 544
Galtier, N., Blier, P. U., & Nabholz, B. (2008) · Mitochondrion · doi:10.1016/j.mito.2008.11.006 · Cited by 39
“Sophisticated methods of sequence analysis were recently developed to cope with these numerous problems (Thorne et al., 1998; Rannala and Yang, 2007; Lepage et al., 2007).”
MethodLinder, M., Britton, T., & Sennblad, B. (2011) · Systematic Biology · doi:10.1093/sysbio/syr009 · Cited by 39
“Although other priors for divergence times have been proposed (Thorne et al. 1998; Kishino et al. 2001; Drummond et al. 2006; Lepage et al. 2007), the birth–death process is the classic model for branching processes both in mathematics and in biology and is the natural null model choice for analyses above population l…”
BackgroundMethodInfluentialCascini, M., Mitchell, K. J., Cooper, A., & Phillips, M. J. (2018) · Systematic Biology · doi:10.1093/sysbio/syy080 · Cited by 38
Püschel, H. P., O'Reilly, J. E., Pisani, D., & Donoghue, P. C. J. (2019) · Palaeontology · doi:10.1111/pala.12443 · Cited by 39
“Branch rate variation was modelled with the independent gamma rate (IGR) relaxed-clock model (Lepage et al. 2007).”
MethodJouault, C., Legendre, F., Grandcolas, P., & Nel, A. (2021) · Systematic Entomology · doi:10.1111/syen.12477 · Cited by 39
Bruxaux, J., Gabrielli, M., Ashari, H., Prŷs‐Jones, R., Joseph, L., Milá, B., Besnard, G., & Thébaud, C. (2017) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2017.11.022 · Cited by 40
Jouault, C., Maréchal, A., Condamine, F. L., Wáng, B., Nel, A., Legendre, F., & Perrichot, V. (2021) · Zoological Journal of the Linnean Society · doi:10.1093/zoolinnean/zlab034 · Cited by 38
Timing the evolution of phosphorus-cycling enzymes through geological time using phylogenomics
Boden, J. S., Zhong, J., Anderson, R. E., & Stüeken, E. E. (2024) · Nature Communications · doi:10.1038/s41467-024-47914-0 · Cited by 36
“For the rest of this paper, we focus on estimates from the CIR clock model because it has been shown to outperformother clockmodels in termsof model fi t 43 and consistency between lineages participating in the same HGT events 40 .”
Tip-dated phylogeny of whirligig beetles reveals ancient lineage surviving on Madagascar
Gustafson, G. T., Prokin, A. A., Bukontaite, R., Bergsten, J., & Miller, K. B. (2017) · Scientific Reports · doi:10.1038/s41598-017-08403-1 · Cited by 37
Out of the Antilles: Fossil phylogenies support reverse colonization of bats to South America
Tavares, V. D. C., Warsi, O., Balseiro, F., Mancina, C. A., & Dávalos, L. M. (2018) · Journal of Biogeography · doi:10.1111/jbi.13175 · Cited by 36
“, 2000); IGR, independent gamma rates (Lepage et al., 2007); TK02, Thorne and Kishino (2002) model”
BackgroundDating placentalia: Morphological clocks fail to close the molecular fossil gap
Puttick, M. N., Thomas, G. H., & Benton, M. J. (2016) · Evolution · doi:10.1111/evo.12907 · Cited by 36
Tejada‐Lara, J. V., Antoine, P., Münch, P., Billet, G., Hautier, L., Delsuc, F., & Condamine, F. L. (2023) · Systematic Biology · doi:10.1093/sysbio/syad069 · Cited by 34
“However, analyses were carried out using both an uncorrelated gamma rate model (IGR model, Lepage et al. 2007), in which tree branches have their own evolutionary rates that follow a gamma distribution, and an autocorrelated lognormal rate model (TK02 model; Thorne and Kishino 2002) in which branch…”
MethodHe, M.-Q., Chen, J., Zhou, J.-L., Ratchadawan, C., Hyde, K., & Zhao, R.-L. (2017) · Scientific Reports · doi:10.1038/s41598-017-05203-5 · Cited by 53
Matschiner, M. (2018) · Hydrobiologia · doi:10.1007/s10750-018-3686-9 · Cited by 35
Lassalle, F., Dastgheib, S. M. M., Zhao, F. J., Zhang, J., Verbarg, S., Frühling, A., Brinkmann, H., Osborne, T. H., Sikorski, J., Balloux, F., et al. (2020) · Systematic and Applied Microbiology · doi:10.1016/j.syapm.2020.126165 · Cited by 35
A synopsis of rodent molecular phylogenetics, systematics and biogeography
Fabre, P., Hautier, L., & Douzery, E. (2015) · Cambridge University Press eBooks · doi:10.1017/cbo9781107360150.003 · Cited by 36
RelTime Rates Collapse to a Strict Clock When Estimating the Timeline of Animal Diversification
Lozano-Fernández, J., dos Reis, M., Donoghue, P. C. J., & Pisani, D. (2017) · Genome Biology and Evolution · doi:10.1093/gbe/evx079 · Cited by 32
Infectious Disease Dynamics Inferred from Genetic Data via Sequential Monte Carlo
Smith, R. A., Ionides, E. L., & King, A. A. (2017) · Molecular Biology and Evolution · doi:10.1093/molbev/msx124 · Cited by 32
“Various forms of such processes have been assumed in the literature (Ho and Duchne, 2014; Lepage et al., 2007), but not all of these are compatible with a mechanistic approach.”
Liu, S., Shen, L., Xu, T., Song, C., Gao, N., Wu, D., & Sun, Y. (2023) · Mycosphere · doi:10.5943/mycosphere/14/1/18 · Cited by 31
Reticulate evolution: Detection and utility in the phylogenomics era
Bjornson, S., Verbruggen, H., Upham, N. S., & Steenwyk, J. L. (2024) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2024.108197 · Cited by 36
Magallón, S. (2014) · Botanical Sciences · doi:10.17129/botsci.37 · Cited by 30
“Model misspecifi cation is a well-known source of error in relaxed clock analyses (e.g., Hugall et al., 2007; Lepage et al., 2007; Phillips, 2009; Brandley et al., 2011; Dornburg et al., 2012; Wertheim et al., 2012).”
BackgroundMethodA comparison of methods for estimating substitution rates from ancient DNA sequence data
Tong, K., Duchêne, D. A., Duchêne, S., Geoghegan, J. L., & Ho, S. Y. W. (2018) · BMC Evolutionary Biology · doi:10.1186/s12862-018-1192-3 · Cited by 28
“149 For each of the two rate schemes, we simulated three scenarios of among-lineage rate variation 150 under a white-noise model (Lepage et al. 2007), with variance along each branch of 0.”
MethodInfluentialMaul, K., Krug, M., Nickrent, D. L., Müller, K., Quandt, D., & Wicke, S. (2018) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2018.10.041 · Cited by 31
Beck, R. M. D., & Taglioretti, M. L. (2019) · Journal of Mammalian Evolution · doi:10.1007/s10914-019-09471-y · Cited by 32
“…the marginal likelihoods of four different clock model schemes: a single Independent Gamma Rates (IGR) model for the entire total evidence matrix (Lepage et al. 2007); a single Thorne and Kishino 2002 (TK02) model (Thorne and Kishino 2002); separate IGR models for the molecular and morphological…”
MethodOrigin of horsetails and the role of whole-genome duplication in plant macroevolution
Clark, J., Puttick, M. N., & Donoghue, P. C. J. (2019) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2019.1662 · Cited by 31
“A stepping stone analysis was used to test for the best-fitting clock model in MrBayes v. 3.2.6 [34,35]; this showed significant support for the correlated model [36] over the independent gamma rates [37] and strict clock models.”
MethodInfluentialUsing multiple relaxed-clock models to estimate evolutionary timescales from DNA sequence data
Duchêne, S., & Ho, S. Y. W. (2014) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2014.04.010 · Cited by 29
Assessing the accuracy of phylogenetic rooting methods on prokaryotic gene families
Wade, T. E., Rangel, L. T., Kundu, S., Fournier, G. P., & Bansal, M. S. (2020) · PLoS ONE · doi:10.1371/journal.pone.0232950 · Cited by 29
Ritchie, A. M., Hua, X., Cardillo, M., Yaxley, K. J., Dinnage, R., & Bromham, L. D. (2020) · Diversity and Distributions · doi:10.1111/ddi.13179 · Cited by 30
“There are a large number of phylogenetic methods that allow rates of molecular evolution to vary over the phylogeny, such as “relaxed clock” models that allow limited random variation in rates among lineages (dos Reis et al., 2016; Ho, 2014; Kumar, 2005; Lepage et al., 2007).”
BackgroundBorths, M. R., & Stevens, N. J. (2017) · PLoS ONE · doi:10.1371/journal.pone.0185301 · Cited by 30
Bayesian Comparisons of Codon Substitution Models
Rodrigue, N., Lartillot, N., & Philippe, H. (2008) · Genetics · doi:10.1534/genetics.108.092254 · Cited by 30
Self-citationBoudinot, B. E., Khouri, Z., Richter, A., Griebenow, Z. H., van de Kamp, T., Perrichot, V., & Barden, P. (2022) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2022.02.20.480183 · Cited by 31
Pol, D., Baiano, M. A., Černý, D., Novas, F. E., Cerda, I. A., & Pittman, M. (2024) · Cladistics · doi:10.1111/cla.12583 · Cited by 28
“The analysis employed the white noise clock model of Lepage et al. (2007), as parameterized by Zhang and Wang (2019) and previously implemented in RevBayes by Sz ¨ oll ˝ osi et al. (2022).”
MethodRates and Rocks: Strengths and Weaknesses of Molecular Dating Methods
Guindon, S. (2020) · Frontiers in Genetics · doi:10.3389/fgene.2020.00526 · Cited by 28
Gene trees and species trees: irreconcilable differences
Swenson, K. M., & El-Mabrouk, N. (2012) · BMC Bioinformatics · doi:10.1186/1471-2105-13-s19-s15 · Cited by 28
“Thus, a great deal of effort has been put into finding accurate gene trees in the presence of variable rates of evolution and in the presence of horizontal gene transfer [9-18].”
BackgroundPhylogenetic estimates of diversification rate are affected by molecular rate variation
Duchêne, D. A., Hua, X., & Bromham, L. D. (2017) · Journal of Evolutionary Biology · doi:10.1111/jeb.13148 · Cited by 28
Mizuta, K., Tsukagoshi, H., Ikeda, T., Aoki, Y., Abiko, C., Itagaki, T., Nagano, M., Noda, M., & Kimura, H. (2014) · Journal of Medical Microbiology · doi:10.1099/jmm.0.068189-0 · Cited by 27
“The Bayesian Markov chain Monte Carlo (MCMC) method enables the evolutionary timescale to be estimated (Thorne et al., 1998; Lepage et al., 2007).”
MethodBorths, M. R., & Seiffert, E. R. (2017) · PLoS ONE · doi:10.1371/journal.pone.0173527 · Cited by 27
An 18S and 28S-based clock calibration for marine Proseriata (Platyhelminthes)
Scarpa, F., Cossu, P., Sanna, D., Lai, T., Norenburg, J. L., Curini-Galletti, M. C., & Casu, M. (2014) · Journal of Experimental Marine Biology and Ecology · doi:10.1016/j.jembe.2014.10.020 · Cited by 27
Porter, J. M., Johnson, L. A., & Wilken, D. H. (2010) · Systematic Botany · doi:10.1600/036364410790862542 · Cited by 27
Svenson, G. J., Brannoch, S. K., Rodrigues, H. M., O’Hanlon, J. C., & Wieland, F. (2016) · Scientific Reports · doi:10.1038/srep37753 · Cited by 29
A new method for inferring timetrees from temporally sampled molecular sequences
Miura, S., Tamura, K., Tao, Q., Huuki-Myers, L. A., Pond, S. L. K., Priest, J. M., Deng, J., & Kumar, S. (2020) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1007046 · Cited by 27
Evolving Perceptions on the Antiquity of the Modern Avian Tree
Brown, J. W., & van Tuinen, M. (2011) · Wiley eBooks · doi:10.1002/9781119990475.ch12 · Cited by 27
Convergent intron gains in hymenopteran elongation factor-1α
Klopfstein, S., & Ronquist, F. (2013) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2013.01.015 · Cited by 26
“(2012), and branch lengths were inferred under the independent gamma-rates relaxed-clock model (Lepage et al., 2007).”
BackgroundOberski, J. T., Sharma, P. P., Jay, K. R., Coblens, M. J., Lemon, K. A., Johnson, J. E., & Boyer, S. L. (2018) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2018.06.029 · Cited by 26
Zhan, S. H., Chen, L., Liao, C., Chang, W., Li, C., Tang, G., Liou, C., Wang, W., Wang, S., & Liu, S. (2022) · Molecular Ecology · doi:10.1111/mec.16455 · Cited by 26
“To infer the ultrametric phylogeny, we also applied a birth- death prior (Höhna et al., 2011) and independent gamma rate (IGR) to account for among- branch rate variation (Lepage et al., 2007).”
MethodBeetle bioluminescence outshines extant aerial predators
Powell, G. S., Saxton, N. A., Pacheco, Y. M., Stanger‐Hall, K. F., Martin, G. J., Kusy, D., da Silveira, L. F. L., Bocák, L., Branham, M. A., & Bybee, S. (2022) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2022.0821 · Cited by 25
“The age estimates for each clock model combination largely overlapped for the BD models; here we discuss the RCLN model, which assumes the branch rates are normally distributed and has been shown to more precisely estimate ages and therefore is widely used [78,79].”
MethodDiversity of HIV-1 Subtype B: Implications to the Origin of BF Recombinants
Leal, E. D. S., & Villanova, F. (2010) · PLoS ONE · doi:10.1371/journal.pone.0011833 · Cited by 26
“We also used a Bayesian Markov chain Monte Carlo (BMCMC) coalescent framework, implemented in the BEAST package [45], that uses DNA sequences to estimate ancestral genealogies using relaxed molecular clock models (lognormal) that have advantages over traditional clock models [46,47].”
Soares, A. E. R., & Schrago, C. G. (2012) · Bioinformatics and Biology Insights · doi:10.4137/bbi.s9677 · Cited by 25
López‐López, A., Aziz, A. A., & Galián, J. (2015) · Zoologica Scripta · doi:10.1111/zsc.12113 · Cited by 24
“Although the use of a strict molecular clock as the only way for calibrating phylogenetic trees is controversial (Thomas et al. 2006; Lepage et al. 2007), it does provide a method for estimating approximate divergence times and formulating preliminary biogeographic hypotheses (Burns 1997; Foley et…”
MethodJešovnik, A., González, V. L., & Schultz, T. R. (2016) · PLoS ONE · doi:10.1371/journal.pone.0151059 · Cited by 24
“Divergence dates were estimated using the Bayesian relaxed molecular clock approach as implemented in PhyloBayes v.3.3f [32] applying an auto-correlated model of clock relaxation [33,34].”
The age of insects and the revival of the minimum age tree
Klopfstein, S. (2020) · Austral Entomology · doi:10.1111/aen.12478 · Cited by 26
“lineages (Thorne et al. 1998; Drummond et al. 2006; Lepage et al. 2007; Lartillot et al. 2016), and sophisticated inference”
MethodBayesian Phylogenetic Inference using Relaxed-clocks and the Multispecies Coalescent
Flouri, T., Huang, J., Jiao, X., Kapli, P., Rannala, B. H., & Yang, Z. (2022) · Molecular Biology and Evolution · doi:10.1093/molbev/msac161 · Cited by 23
“The independent-rates model is implemented by Drummond et al. (2006) and Rannala and Yang (2007) (see also Lepage et al. 2007), which describes the variation in rate among lineages empirically without a mechanistic basis like the GBM.”
MethodUpham, N. S., & Borroto‐Páez, R. (2017) · Journal of Mammalogy · doi:10.1093/jmammal/gyx077 · Cited by 24
Selecting and averaging relaxed clock models in Bayesian tip dating of Mesozoic birds
Zhang, C. (2021) · Paleobiology · doi:10.1017/pab.2021.42 · Cited by 23
“…(Kishino and Hasegawa 1990; Huelsenbeck et al. 2000; Yoder and Yang 2000; Kishino et al. 2001; Thorne and Kishino 2002; Drummond et al. 2006; Lepage et al. 2007; Rannala and Yang 2007), and have been widely used in phylogenetics for estimating divergence times and evolutionary rates (Heath…”
MethodAssessing the relative performance of fast molecular dating methods for phylogenomic data
Costa, F. P. D. F., Schrago, C. G., & Mello, B. (2022) · BMC Genomics · doi:10.1186/s12864-022-09030-5 · Cited by 20
“Therefore, it assumes autocorrelation of evolutionary rates, which has been suggested as pervasive across the tree of life [36, 37].”
BackgroundThe origin of Rhinocerotoidea and phylogeny of Ceratomorpha (Mammalia, Perissodactyla)
Bai, B., Meng, J., Zhang, C., Gong, Y.-X., & Wang, Y. (2020) · Communications Biology · doi:10.1038/s42003-020-01205-8 · Cited by 23
Dohrmann, M., Vargas, S., Janussen, D., Collins, A. G., & Wörheide, G. (2013) · Paleobiology · doi:10.1666/0094-8373-39.1.95 · Cited by 23
“Among-site rate variation was modeled with the Dirichlet process of Huelsenbeck and Suchard (2007), and among-lineage rate variation was accounted for by employing a log-normal autocorrelated relaxed molecular clock model (see Lepage et al. 2007 for details and justification).”
MethodModeling the Evolution of Rates of Continuous Trait Evolution
Martin, B. S., Bradburd, G. S., Harmon, L. J., & Weber, M. G. (2022) · Systematic Biology · doi:10.1093/sysbio/syac068 · Cited by 20
“Notably, there is also no known rate evolution process that would produce independent, log-normally distributed branchwise rates (Lepage et al., 2006, 2007).”
BackgroundThe affinities of the Late Triassic Cryptovaranoides and the age of crown squamates
Brownstein, C. D., Simões, T. R., Caldwell, M. W., Lee, M. S. Y., Meyer, D. L., & Scarpetta, S. G. (2023) · Royal Society Open Science · doi:10.1098/rsos.230968 · Cited by 22
“We employed the uncorrelated independent gamma rate clock model [52] as in previous iterations of this dataset.”
Flightless scaly‐tailed squirrels never learned how to fly: A reappraisal of Anomaluridae phylogeny
Fabre, P., Tilak, M., Denys, C., Gaubert, P., Nicolas, V., Douzery, E., & Marivaux, L. (2018) · Zoologica Scripta · doi:10.1111/zsc.12286 · Cited by 22
Deep time diversity and the early radiations of birds
Yu, Y., Zhang, C., & Xu, X. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2019865118 · Cited by 23
Foley, S., Krehenwinkel, H., Cheng, D.-Q., & Piel, W. H. (2021) · PeerJ · doi:10.7717/peerj.11162 · Cited by 21
Garzón‐Orduña, I. J., Menchaca-Armenta, I., Contreras‐Ramos, A., Liu, X., & Winterton, S. L. (2016) · BMC Evolutionary Biology · doi:10.1186/s12862-016-0746-5 · Cited by 21
“As mentioned previously, the principal difference between the two models is in their assumptions of heritability of substitution rates [41], the LN allowing for substitution rates to be inherited (i.”
BackgroundA Kolmogorov-Smirnov test for the molecular clock based on Bayesian ensembles of phylogenies
Antoneli, F., Passos, F. M., Lopes, L. R., & Briones, M. R. S. (2018) · PLoS ONE · doi:10.1371/journal.pone.0190826 · Cited by 21
“We performed the 2KS test for the unconstrained ensemble against the strict clock-constrained ensemble and the uncorrelated rates log-normal relaxed clock model [40].”
MethodAncient balancing selection on heterocyst function in a cosmopolitan cyanobacterium
Sano, E. B., Wall, C. A., Hutchins, P. R., & Miller, S. R. (2018) · Nature Ecology & Evolution · doi:10.1038/s41559-017-0435-9 · Cited by 21
Local and relaxed clocks: the best of both worlds
Fourment, M., & Darling, A. E. (2018) · PeerJ · doi:10.7717/peerj.5140 · Cited by 22
“For a broader overview on the topic we direct the reader to reviews (Ho & Duchêne, 2014; Dos Reis, Donoghue & Yang, 2016) and performance benchmark studies (Ho et al., 2005; Lepage et al., 2007).”
BackgroundMethodInfluentialSperling, E. A. (2013) · The Paleontological Society Papers · doi:10.1017/s1089332600002692 · Cited by 22
“The most important advance is that modern molecular divergence estimation methods now explicitly take into account the fact that rates of molecular evolution vary between lineages (Drummond and Rambaut, 2007; Lepage et al., 2007; Lartillot et al., 2009).”
BackgroundZhang, Y., Yu, J., Xia, M., Chi, X., Khan, G., Chen, S., & Zhang, F. (2021) · Ecology and Evolution · doi:10.1002/ece3.8274 · Cited by 20
Why should we compare morphological and molecular disparity?
van den Ende, C., Puttick, M. N., Urrutia, A. O., & Wills, M. A. (2023) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.14166 · Cited by 21
“Relaxed clock models applying various rate smoothing functions at different scales are an acknowledgement of this phenomenon (Lartillot et al., 2016; Lepage et al., 2007; Tiley et al., 2020; Yang, 1994).”
BackgroundSaclier, N., Duchemin, L., Konecny‐Dupré, L., Grison, P., Eme, D., Martin, C., Callou, C., Tristan, L., Francois, C. M., Issartel, C., et al. (2023) · Molecular Ecology Resources · doi:10.1111/1755-0998.13882 · Cited by 20
Barden, P., Boudinot, B. E., & Lucky, A. (2017) · Invertebrate Systematics · doi:10.1071/is16067 · Cited by 20
“…et al. (2012), four node- and all tip-dating analyses assumed a uniform clock with the clock prior set to an independent gamma rates (IGR) model (Lepage et al. 2007)where each branch is allowed an independent rate that is drawn from a gamma distribution (i.e. we employed a ‘relaxed clock’…”
MethodJäger, G., & List, J. (2018) · Language Dynamics and Change · doi:10.1163/22105832-00801002 · Cited by 20
“Regarding the tree prior, we assumed a relaxed molecular clock model (more and Change 8 (2018) 22–54 specifically, the Independent Gamma Rates model (cf. Lepage et al., 2007), with an exponential distribution with rate 200 as prior distribution for the variance of rate variation).”
MethodSvenson, G. J., Medellín, C., & Sarmiento, C. E. (2015) · Systematic Entomology · doi:10.1111/syen.12151 · Cited by 20
“For character rate shift analysis, we obtained a time-calibrated phylogeny using mrbayes with an independent gamma rate (IGR) modelled clock (LePage et al., 2007).”
MethodGargiulo, R., Guacchio, E. D., & Caputo, P. (2015) · Taxon · doi:10.12705/644.7 · Cited by 20
Volcanic events coincide with plant dispersal across the Northern Andes
Sanín, M. J., Cardona, A., Valencia‐Montoya, W. A., Jiménez, M. F. T., Carvalho-Madrigal, S., Gómez, A. C., Bacon, C. D., Tangarife, T. R., Jaramillo, J. S., Zapata, S., et al. (2022) · Global and Planetary Change · doi:10.1016/j.gloplacha.2022.103757 · Cited by 19
A timeline of bacterial and archaeal diversification in the ocean
Martínez-Gutiérrez, C. A., Uyeda, J. C., & Aylward, F. O. (2023) · eLife · doi:10.7554/elife.88268 · Cited by 22
Three tree priors and five datasets
Rama, T. (2018) · Language Dynamics and Change · doi:10.1163/22105832-00802005 · Cited by 18
Model-Based Inference of Punctuated Molecular Evolution
Manceau, M., Marin, J., Morlon, H., & Lambert, A. (2020) · Molecular Biology and Evolution · doi:10.1093/molbev/msaa144 · Cited by 23
Paleogene mammalian fauna exchanges and the paleogeographic pattern in Asia
Ni, X., Li, Q., Zhang, C., Samiullah, K., Zhang, L., Yang, Y., & Cao, W. (2019) · Science China Earth Sciences · doi:10.1007/s11430-019-9479-1 · Cited by 19
“The changes of the evolutionary rate along a phylogenetic tree are described with the independent Gamma rate model (Lepage et al., 2007): The means of the evolutionary rates are identical on different clades and the deviations are positively correlated with the branch lengths.”
BackgroundImpacts of Taxon-Sampling Schemes on Bayesian Tip Dating Under the Fossilized Birth-Death Process
Luo, A., Zhang, C., Zhou, Q., Ho, S. Y. W., & Zhu, C. (2023) · Systematic Biology · doi:10.1093/sysbio/syad011 · Cited by 18
“If the uncorrelated lognormal relaxed clock (Drummond et al. 2006) is used to analyze an empirical data set for which, for example, a white-noise model (Lepage et al. 2007) fits better, interaction between taxon-sampling density and among-lineage rate variation could be possible.”
MethodInaccurate fossil placement does not compromise tip‐dated divergence times
Koch, N. M., Garwood, R. J., & Parry, L. A. (2023) · Palaeontology · doi:10.1111/pala.12680 · Cited by 18
“An uncorrelated relaxed morphological clock (IGR) was implemented (Lepage et al .”
MethodRamírez‐Reyes, T., Piñero, D., Flores-Villela, O. A., & Vázquez‐Domínguez, E. (2017) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2017.07.008 · Cited by 18
“Next, for the comparison of the three relaxed molecular models, we selected the independent gamma rate (IGR), because it is a non-correlated continuous model, where each branch has an independent rate from a gamma distribution (Lepage et al., 2007; Ronquist et al., 2012).”
MethodThe molecular clock and evolutionary timescales
Luo, A., & Ho, S. Y. W. (2018) · Biochemical Society Transactions · doi:10.1042/bst20180186 · Cited by 19
Léveillé‐Bourret, É., Eggertson, Q., Hambleton, S., & Starr, J. R. (2021) · Journal of Systematics and Evolution · doi:10.1111/jse.12740 · Cited by 18
Villanova, F., Cui, S., Ai, X., & Leal, E. D. S. (2016) · Archives of Virology · doi:10.1007/s00705-015-2744-0 · Cited by 18
Dating the Bacterial Tree of Life Based on Ancient Symbiosis
Wang, S., & Luo, H. (2024) · Systematic Biology · doi:10.1093/sysbio/syae071 · Cited by 17
“This method can be used to find the best-fitting clock model by calculating the marginal likelihood using either the stepping-stone method (Xie et al. 2011) or the thermodynamic integration (Lartillot and Philippe 2006; Lepage et al. 2007).”
Molecular and morphological clocks for estimating evolutionary divergence times
Barba‐Montoya, J., Tao, Q., & Kumar, S. (2021) · BMC Ecology and Evolution · doi:10.1186/s12862-021-01798-6 · Cited by 17
“The Independent Gamma Rate (IGR) model, in which the rates of evolution on branches varied independently from a gamma distribution [45], was used as a rate prior.”
MethodCranial and mandibular anatomy of Plastomenus thomasii and a new time-tree of trionychid evolution
Evers, S., Chapelle, K. E. J., & Joyce, W. G. (2023) · Swiss Journal of Palaeontology · doi:10.1186/s13358-023-00267-5 · Cited by 17
“For the clock model, we specified a relaxedclock that allows rates to vary over time with each branch having an independent rate drawn from a gamma distribution (independent gamma rate, or IGR; Lepage et al., 2007).”
MethodMolecular Biogeography: The Intersection between Geographic and Molecular Variation
Mantooth, S. J., & Riddle, B. R. (2011) · Geography Compass · doi:10.1111/j.1749-8198.2009.00297.x · Cited by 17
Log Transformation Improves Dating of Phylogenies
Mai, U., & Mirarab, S. (2020) · Molecular Biology and Evolution · doi:10.1093/molbev/msaa222 · Cited by 19
“2000) or allow correlated rates across branches (Thorne et al. 1998; Kishino et al. 2001; Sanderson 2002; Lepage et al. 2007; Drummond and Suchard 2010; Snir et al. 2012; Tamura et al. 2012).”
BackgroundRitchie, A. M., Hua, X., & Bromham, L. D. (2022) · BMC Ecology and Evolution · doi:10.1186/s12862-022-02015-8 · Cited by 17
“time estimates under the Bayesian methodology to the choice of rate prior, provided that 99 enough separate rate parameters are allowed and sufficient calibrating information is 100 provided (27-33); but see (34).”
MethodLorén, J. G., Farfán, M., & Fusté, M. C. (2014) · PLoS ONE · doi:10.1371/journal.pone.0088805 · Cited by 21
“This implies 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 [15]–[17].”
BackgroundPaleozoic diversification of terrestrial chitin-degrading bacterial lineages
Gruen, D. S., Wolfe, J. M., & Fournier, G. P. (2019) · BMC Evolutionary Biology · doi:10.1186/s12862-019-1357-8 · Cited by 19
“The uniform prior considers every possible topology to be equal and favors divergences that are evenly spaced across the tree from the root to tip [55, 56].”
BackgroundShafir, A., Azouri, D., Goldberg, E. E., & Mayrose, I. (2020) · Evolution · doi:10.1111/evo.14036 · Cited by 17
“The IGR relaxed clock model (Lepage et al. 2007) was used to account for clock variation across lineages in the relaxed uncorrelated model, and the TK02 autocorrelated model was used for the relaxed autocorrelated model (Thorne and Kishino 2002).”
BackgroundMethodWang, X., Zhang, Y., Liu, Y., Li, H., Jia, L., Han, J., Li, T., Wang, X., Li, J., Wen, H., et al. (2021) · AIDS Research and Human Retroviruses · doi:10.1089/aid.2020.0190 · Cited by 16
“30 The GTR + I + G nucleotide substitution model, 31 a flexible Bayesian Skyline coalescent tree prior, 32 and a re-laxed uncorrelated lognormal molecular clock model 33 were selected in BEAUTi v.1.7.5.”
InfluentialRydin, C., Blokzijl, R., Thureborn, O., & Wikström, N. (2021) · Taxon · doi:10.1002/tax.12493 · Cited by 16
Loria, S. F., Ehrenthal, V. L., Nguyen, A. D., & Prendini, L. (2022) · Insect Systematics and Diversity · doi:10.1093/isd/ixac028 · Cited by 16
Liu, S., Zhou, J., Song, J., Sun, Y.-F., Dai, Y., & Cui, B. (2023) · Frontiers in Microbiology · doi:10.3389/fmicb.2023.1115761 · Cited by 16
“The clock model was set to an uncorrelated lognormal relaxed clock (Drummond et al., 2006; Lepage et al., 2007).”
MethodCalculations for multi-type age-dependent binary branching processes
Jones, G. (2010) · Journal of Mathematical Biology · doi:10.1007/s00285-010-0362-8 · Cited by 16
“It is easier and more natural to deal with the case of rooted trees with a strict or relaxed molecular clock (as used in [13,30] for example) and so this article concentrates on rooted trees with node times (divergence times) measured in years.”
Background
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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