Estimating the rate of evolution of the rate of molecular evolution

“2009) using the default site-heterogeneous mixture model (CAT) and a log-normal autocorrelated relaxed clock (option -ln) (Thorne et al. 1998).”

“…speciation process (e.g., birth-and-death or birth-only process) and it allows for the incorporation of prior information on calibration times, including their minimum and maximum boundaries and the distribution of their uncertainties (Thorne et al. 1998; Kishino et al. 2001; Ho and Phillips 2009).”

“Then, by using these parameters, we estimated the maximum likelihood of the branch lengths of the rooted evolutionary tree together with a variance–covariance matrix of the branch length estimates by using the program Estbranches (Thorne et al., 1998).”

“Divergence ages were estimated using a relaxed molecular clock approach, as implemented in the PAML/MULTIDIVTIME package (Thorne et al., 1998; Kishino et al., 2001; Thorne and Kishino, 2002) and following Rutschmann (2005) instructions.”

“Relaxed molecular clocks were introduced by Sanderson (1997, 2002) and Thorne et al. (1998) to estimate the time to most recent common ancestor (tMRCA) in the absence of rate constancy.”

“Divergence times were estimated using two different Bayesian approaches which implement relaxed molecular clock models: the program MULTIDIVTIME (Thorne et al., 1998), following the protocol from the manual by Rutschmann (2005), and BEAST v1.”

“We used the MultiDivTime package (Thorne and Kishino, 2002; Thorne et al., 1998) to estimate the divergence times, based on nuclear sequences only.”

“A Bayesian estimation of divergence timeswas performed using Multidivtime (Thorne et al., 1998; Kishino et al., 2001; Thorne and Kishino, 2002).”

“…of relaxed clock models is based on ‘rate smoothing’, including non-parametric rate smoothing (Sanderson, 1997), penalized likelihood (Sanderson, 2002) and Bayesian autocorrelated relaxed clock methods (Thorne et al., 1998; Kishino et al., 2001; Aris-Brosou and Yang, 2002; Rannala and Yang, 2007).”

“Divergence times were estimated with the relaxed Bayesian molecular clock approach as implemented in the Multidistribute package (http://statgen.ncsu.edu/thorne/multidivtime. html; Thorne et al., 1998; Thorne and Kishino, 2002; individual programs mentioned below).”

“In this study we used a relaxed Bayesian approach for multilocus data as implemented in MULTIDIVTIME package (Thorne et al., 1998; Kishino et al., 2001; Thorne and Kishino, 2002).”

“Divergence date estimation was performed on the consensus MP topology using a Bayesian MCMC method as implemented in the program multidivtime (Thorne et al. 1998).”

“clock approach with the MULTIDISTRIBUTE program package (50, 51) (http://statgen.”

“In our study, the Bayesian relaxed clock analyses were carried out with the program beast 1.6.2 (Drummond & Rambaut, 2007), using the lognormal model of Thorne et al. (1998), which is uncorrelated in beast.”

“Unclock-like data are the rule, and many methods of estimating divergence times therefore relax the clock assumption (Rambaut and Bromham, 1998; Thorne et al., 1998; Aris-Brosou and Yang, 2002; Sanderson, 2002; Thorne and Kishino, 2002; Britton et al., 2007).”

“…show that the family taxonomic level explains 75% of this variance, while the order taxonomic level explains 21%, indicating that entire orders could all have (for example) low substitu-tion rates, which may be appropriately modeled using autocorrelated relaxed clock models (Thorne et al ., 1998).”

“Although other models have been considered (see Aris-Brosou and Yang, 2002) rate heterogeneity is usually modeled as drift in the logarithm of the rate over time (geometric Brownian motion: hereafter ‘‘rate-drift”) (Thorne et al., 1998).”

“B [ 45 ]. The covariance matrix of this multivariate normal distribution is estimated from the curvature of the log-likelihood surface (i.e., the inverse of the information matrix—[40], pp. 675–676).”

“haussa Chad Karal, 9 AJ875071 — 30 38 PR Veyrunes et al. (2004) Mali Ménaka, 10 Chevret et al.”

“Although methods for relaxing molecular clock models and using ‘local’ clocks are available (Thorne et al. 1998; Kishino et al. 2000; Sanderson 2003), the lack of reasonable calibration points for these locusts prevents our use of these approaches.”

“Such a dual function of elaiosomes has been previously reported (e.g., Pacini 1990; Bianchini and Pacini 1996; Lisci et al. 1996; Tiano et al. 1998).”

“Bayesian analysis of other types of among-taxon process heterogeneity has proven useful (e.g., the rate of sequence evolution; Huelsenbeck et al., 2000; Kishino et al., 2001; Thorne et al., 1998), and may be a fruitful approach to addressing the problem of base composition as well (Huelsenbeck et al.”

“These parameters were then used to estimate the branch lengths in the rooted evolutionary tree, in conjunction with a variance–covariance matrix of the branch lengths estimated using the program estbranches (Thorne et al., 1998).”

“: 1-907-474-6277; Fax: 1-907-474-5469. of a tree to have different rates (Rambaut & Bromham, 1998; Thorne et al., 1998; Yoder & Yang, 2000; Kishino et al., 2001; Rannala & Yang, 2007).”

“Divergence times estimated using the software Multidivtime ( Thorne et al. 1998 ) are shown at each of the key nodes with 95% confidence intervals.”

“…hypotheses, and molecular sequence age estimations have greatly enhanced our understanding of plant and animal distribution and movement (Thorne et al. 1998; Rambaut and Bromham 1998; Kishino et al. 2001; Thorne and Kishino 2002; Aris-Brosou and Yang 2002; Sanderson 2002, 2003; Drummond…”

“Nevertheless, we analyzed the supermatrix under two commonly deployed clock models, the lognormal (Thorne et al., 1998) and uncorrelated gamma multipliers (Drummond et al., 2006) models.”

“First three relaxed clock models, the lognormal autocorrelated clock model (LOG) [38], the Cox-IngersollRoss process (CIR) [39] and uncorrelated gamma multipliers (UGM) [40] were compared by tenfold cross-validation with eight replicates, as specified in PhyloBayes 3.3.”

“To obtain an estimate of the time of divergence of Rhinolophus taxa we applied the relaxed Bayesian clock method using the MULTIDIVERGENCE software package (Thorne et al., 1998; Thorne and Kishino, 2002).”

“…and testing hypotheses on vicariance Selecting a calibration point that matches the true age of lineage divergence is absolutely essential for obtaining accurate divergence time estimates (e.g. Thorne et al., 1998; Bromham & Penny, 2003; Heads, 2005; Ho et al., 2008; Ho & Phillips, 2009).”

“…of relative rates of molecular evolution between lineages often show strong departure from a molecular clock, an observation that has prompted the development of several new approaches of divergence time estimation in the absence of rate homogeneity (Sanderson 1997, 2002; Thorne et al. 1998).”

“MCMCTree implements the approximate likelihood method for clock dating proposed by Thorne et al. 73 and implemented in MCMCtree 74 that reduces computation time signi fi cantly and enables the analysis of large alignments such as ours.”

“As an alternative approach to PL, we used Bayesian divergence time estimation, which also allows relaxing the clock assumption ( Thorne et al., 1998; Thorne and Kishino, 2002; analyses relied on the program package available from J. Thorne’s webpage: http://statgen.ncsu.edu/thorne/ multidivtime.html).”

“Molecular dating analyses were carried out using the paml/multidivtime package (Thorne et al., 1998; Kishino et al., 2001; Thorne & Kishino, 2002) following the instructions of Rutschmann (2005).”

“These authors used a Bayesian MCMC method (Thorne et al. 1998; Thorne & Kishino 2002) and a biogeographical hypothesis for the origin of the genus Craugastor to estimate divergence times of all species groups within Craugastor based on mitochondrial (ND2”

“, as in relaxed molecular clock models for estimating divergence times (Thorne et al. 1998; Rannala and Yang 2007).”

“More importantly, the differences in isolation dates, under the assumption of rate constancy, provide information of isolation (Thorne et al. , 1998).”

“The program estbranches (Thorne et al., 1998) was then used to calculate branch lengths and their variance, given the sequence data [82 ITS sequences of a length of 805 nucleotides (nt)], the model parameter values from paml, and the specified rooted topology.”

“This software was implemented using a Bayesian approach that incorporated the variations of substitution rates among genes and among lineages (Thorne et al., 1998; Kishino et al., 2001; Thorne and Kishino, 2002).”

“Most of the studies on species with disjunct distributions in these two areas have focused on estimating phylogenetic relationships among EA and ENA taxa and estimating divergence times, yet few have rigorously analyzed patterns of morphological variation among the disjunct taxa.”

“To estimate divergence time, the Bayesian relaxed-clock method varying the molecular rate among lineages in an autocorrected manner was used (Thorne et al., 1998).”

“The most parsimonious cladogram of the combined data was specified and used in PAML v. 3.14 (Yang 1997) to create the output files needed for the Multidivergence package developed by Thorne et al. (1998) and Kishino et al. (2001).”

“In Bayesian rate autocorrelation dating, rates are drawn from a log normal distribution and assigned to different branches in the tree, and a parameter called the Brownian motion constant describes the amount of autocorrelation [132-134].”

“We estimated the age of the coastal clade using a Bayesian approach that does not assume constant evolutionary rates, as implemented in the software package ‘multidistribute’ (Thorne et al., 1998; Thorne & Kishino, 2002).”

“9/25/03, was used (Thorne et al., 1998; Kishino et al., 2001) following the guidance published by Rutschmann (2005).”

“The third generation of clocks allowed rates to vary over all branches in the phylogeny, whether randomly or correlated across related branches [73,74].”

“The CI was calculated using a likelihood interpretation (see Materials and Methods) of the cost function residual analogous to the method used in Multidivtime [31].”

“…relationships between the African, Madagascan and Indian plates, when combined with recent techniques for estimating divergence times from DNA sequence data (e.g. Thorne et al., 1998; Sanderson, 2002), provide an excellent opportunity to assess dispersal abilities for taxa that span these areas.”

“We used the Bayesian approach [66] as implemented in the MULTIDIVTIME program package [52], which relaxes the molecular clock by allowing continuous autocorrelation of substitution rates among the branches of the phylogenetic tree.”

“We implemented a geometric Brownian motion (GBM) prior on the duplication and loss rates (Thorne et al. 1998; Rannala and Yang 2007) to model correlated rates across the species tree.”

“Divergence time estimates We used the Bayesian molecular dating method implemented in multidivtime (Thorne et al. 1998; Kishino et al. 2001; Thorne & Kishino 2002; Thorne 2003).”

“The Bayesian method (Thorne et al. 1998) provides a powerful general framework for integrating such different sources of information.”

“We estimated divergence times based on a Bayesian relaxed molecular clock approach, using the MULTIDISTRIBUTE package (Kishino et al., 2001; Thorne and Kishino, 2002; Thorne et al., 1998).”

“Several relaxed-clock models have been developed in the past decade, some of which have been implemented in Bayesian settings (Thorne et al. 1998; Aris-Brosou and Yang 2002; Drummond et al. 2006; Lepage et al. 2007; Rannala and Yang 2007).”

“The divergence time between clades was estimated under a relaxed molecular clock model (Drummond et al., 2006) using the Bayesian approach implemented in PAML version 4.1 (Yang, 2007) and MULTIDIVTIME (Kishino et al., 2001; Thorne and Kishino, 2002; Thorne et al., 1998).”

“Divergence times were estimated with the multidistribute program [48] by assuming a topological relationship thus obtained but without assuming the strict molecular clock.”

“We illustrate our analysis with the same model for evolution (i.e., time-tree) and variation of substitution rates over edges as in Thorne et al. (1998).”

“The stable model we introduce to phylogenetic evolutionary biology here may find other uses, for example in assigning substitution rates to edges on phylogenetic trees under relaxed clock models [78].”

“This statistical result agrees with the molecular evidence that: 1) the origin of primates, as well as the initial interordinal split within Primates, occurred in the Cretaceous; 2) only a relatively short time gap, ca. 8 Ma, likely separates the divergence between strepsirrhines and haplorhines…”

“Our estimates were younger than those inferred by earlier studies [67,99,100] that used MultiDivtime [102,103], even though the 95% credibility intervals (CI) mostly overlapped.”

“determined by the rate of the parent branch [7,8]; other Bayesian methods relax this assumption of autocorrelation for the co-estimation of phylogeny and divergence times [9].”

“15; Yang, 1997), Estbranches (Thorne et al., 1998), and Multidivtime (Thorne and Kishino, 2002).”

“…has further refined divergence estimates by the use of models that incorporate rate heterogeneity through a lognormal model of rate variation (Thorne et al. 1998) and the extension of this approach to multilocus data appears to represent a significant advance (Thorne and Kishino 2002; but…”

“The divergence times between the major species groups were estimated through the Bayes MCMC package, ''Thornnian Time Traveller, (T3)'' (ftp://abacus.gene.ucl.ac.uk/pub/T3) developed by Thorne et al. (1998), Kishino et al. (2001), Thorne and Kishino (2002), and Yang and Yoder (2003).”

“We performed divergence time estimates using the relaxed clock method of Thorne et al. (1998) and Kishino et al. (2001) as implemented in the MULTIDISTRIBUTE package, which includes the programs MULTIDIVTIME, base2paml and estbranches (http: //statgen.ncsu.edu/thorne/multidivtime.html).”

“Even when imposing a model of rate heterogeneity (Thorne et al. 1998; Drummond et al. 2006), only relative times may be estimated.”

“Previous studies have approximated the likelihood surface of phylogenies using multivariate normal distributions [Thorne et al., 1998, Guindon, 2010], including the use of parameter transformations to account for positivity and skew [Reis and Yang, 2011].”

“…63 (version 4.1c), specifying the site-heterogeneous CAT-GTR + G4 65 substitution model along with an autocorrelated lognormal relaxed clock model 64 (which fi ts and performs well in jawed vertebrate phylogenomics 85 ), and a birth-death prior with soft bounds 103,104 on fossil calibrations.”

“…and to incorporate calibrations in the form of parametric dis- Downloaded from https://academic.oup.com/cz/article-abstract/57/1/116/1803904 by guest on 30 July 2018 120 Current Zoology Vol. 57 No. 1 tributions (Thorne et al., 1998; Sanderson, 2002; Drummond et al., 2006; Britton et al., 2007).”

“To infer the time of north-south divergence of Poecilia butleri ,I used the Bayesian relaxed molecular clock of Thorne et al. (1998) and Kishino et al. (2001) as implemented in the software divtime, version 5b (ftp://statgen.ncsu.edu/pub/ thorne).”

“…and loss of conservation on multiple lineages and also encourages nearby branches to have the same state and substitution rate, which is reasonable for closely related species and branches in a phylogeny and is also a common assumption in phylogenetics (Thorne et al. 1998; Rannala and Yang 2007).”