Estimating the rate of evolution of the rate of molecular evolution

“These models were respectively the lognormal clock model of Thorne and colleagues (Thorne et al., 1998; Thorne and Kishino, 2002), and the uncorrelated gamma multipliers model of Lepage et al.”

“The MULTIDIVTIME program was used to estimate divergence times using both variance – covariance matrices .”

“We applied a Bayesian relaxed molecular clock approach on amino acids for the caviomorph vWF data set via DIVTIME version 5b (Kishino et al., 2001; Thorne et al., 1998).”

“The assumption of the molecular clock was relaxed by allowing rates of molecular evolution to vary along the tree according to a Brownian motion model (Kishino et al., 2001; Thorne et al., 1998).”

“Therefore, we used Thorne and Kishino’ s method (Thorne et al., 1998; Kishino et al., 2001), which takes account of the violation of the clock in estimating divergence times.”

“The 105 Myr ago calibration date was treated as the mean of a prior probability distribution, which was then used in a Bayesian analysis of divergence times (Thorne et al. 1998).”

“At the same time, Bayesian methods were developed with similar modeling assumptions though with different fitting approaches (e.g., Thorne et al., 1998; Thorne and Kishino, 2002).”

“ally accepted that best-fitting models that accommodate these biases are necessary for molecular dating (Arbogast et al, 2002; Welch and Bromham, 2005). Yang and Yo der (2003) examined the effects of partitioning protein coding genes by codon position and estimating dates from these multiple partitions.”

“Molecular clock methodology has been developed to accommodate tree-wide substitution rate heterogeneity [3–6], and precision has increased with the availability of genome-scale datasets (i.”

“…estimating divergence times without a molecular clock (i.e., without requiring a clocklike sequence evolution among lineages) (e.g., Sanderson 1997; Thorne et al. 1998; Huelsenbeck et al. 2000; and Kishino et al. 2001) would be particularly valuable tools for providing estimates of divergence…”

“In a thorough application of model selection, Uyenoyama (1995) investigated the timing of change of function of alleles to produce sporophytic self-incompatibility in Brassica and relatives.”

“A more satisfactory solution to this problem is the recent development of ‘relaxed clock’ models of substitution (Thorne et al., 1998; Huelsenbeck et al., 2000).”

“…residues are considered, it is also evident that different parts of the tree have different substitution rates (Gillespie 1991; Sanderson 1997; Thorne, Kishino, and Painter 1998; Huelsenbeck, Larget, and Swofford 2000; Aris-Brosou and Yang 2002; Sanderson 2002; Aris-Brosou and Yang 2003; Seo,…”

“For example, the higher-level divergence times are very consistent with Teeling et al.’s (2005) estimates from 13 nuclear genes using Bayesian dating methods (Thorne et al. 1998; Kishino et al. 2001).”

“Divergence times were determined using a Bayesian approach that incorporates variation of rates of evolution among genes and among lineages (Thorne et al., 1998; Thorne and Kishino, 2002), which were estimated with MULTIDIVTIME program (available from J.”

“…third category; these are non-parametric rate smoothing (NPRS; Sanderson, 1997), penalized likelihood (PL; Sanderson, 2002), the Bayesian method implemented in the Multidivtime package (Thorne et al., 1998) and Bayesian evolutionary analysis by sampling trees (BEAST; Drummond and Rambaut, 2007).”

“Output branch lengths were then used as priors in MCMC searches in Multidivtime (Thorne and Kishino, 2002), to find the most likely model of rate change given the sequence data, the chosen topology, node constraints, and a Brownian motion parameter nu that determines the permitted rate change between an ancestral and…”

“The algorithm was described in Aris-Brosou and Yang (2002) and is similar to that of Thorne, Kishino, and Painter (1998).”

“Estimation of this parameter requires that the temporal scale of the assumed chronogram is known, either through use of external calibrations (Thorne et al., 1998; Kishino et al., 2001; Thorne and Kishino, 2002; Sanderson, 2002, 2003; Drummond et al., 2006; Drummond and Rambaut, 2007), molecular clock estimates (Zucke…”

“18 and models used to obtain a relaxed molecular clock (i.e., substitution rates vary over the tree) (28, 29).”

“Divergence time estimates were performed using the well-supported optimal topology obtained with the molecular supermatrix (see Section 3), using the Relaxed Molecular Clock approach developed by Thorne et al. (1998) and Kishino et al. (2001).”

“The relaxed molecular clock method implemented in Multidivtime (version 9-25-03) [64–66] was used to estimate divergence”

“…times have employed both traditional molecular clock assumptions (Beverly and Wilson 1984, Powell 1997, Gaunt and Miles 2002, Tamura et al. 2004), and Bayesian methods that allow evolutionary rates to vary across the phylogeny (Thorne et al. 1998, Wiegmann et al. 2003, Winterton et al 2007).”

“…rates is analogous to probabilistic models of the rate of molecular evolution implemented in methods used to estimate divergence times (e.g., Thorne et al., 1998; Huelsenbeck et al., 2000; Kishino et al., 2001). at U niversity of C onnecticut on A pril 29,…”

“The rates can be assumed to be independently and identically distributed, as in uncorrelated relaxed clocks (e.g. Drummond et al., 2006), or related between neighbouring branches, as in autocorrelated relaxed clocks (e.g. Thorne et al., 1998).”

“These analyses are not meant to endorse penalized likelihood over other commonly used strategies such as Bayesian methods to estimate divergence times from molecular phylogenies (Thorne et al. 1998); however, penalized likelihood appears to be the most appropriate method to assess the veracity of individual calibratio…”

“We therefore applied Bayesian molecular dating (Thorne et al. 1998) to species splits.”

“For the divergence time estimation, multidistribute program [41] was used by assuming a topological relationship thus obtained, but without assuming the molecular clock (i.”

“html), a relaxed clock in which the rate of molecular evolution is modeled through time, assuming that different genes may have different substitution rates but share divergence times (Thorne et al. 1998; Kishino et al. 2001; Thorne and Kishino 2002).”

“as minimum and maximum calibration points to estimate, using the method of Thorne–Kishin”

“The field has moved a long way since then, and several sophisticated computer programs that implement Bayesian estimation of divergence times have been developed, such as MULTIDIVTIME (Thorne et al., 1998; Kishino et al., 2001), BEAST (Drummond & Rambaut, 2007), MrBAYES (Ronquist et al., 2012b), MCMCTREE (Yang, 2007),…”

“An obvious extension to our model-averaging technique would be to allow coparameterization of both uncorrelated relaxed clocks and autocorrelated relaxed clocks (Thorne et al. 1998; Aris-Brosou and Yang 2002).”

“Cretaceous Vicariance of Gondwanan Reptiles Our results raise obvious questions regarding the absence of extant B, P, and I from India and Australia.”

“Root Age MRCA Dispersal Into Dispersal Into Back Dispersal Rate of Diversification Sonchus 13.20365.51 8.47565.50 2.71762.15 0.73960.84 NA 0.32339 (0.21472–0.65815) Echium 7.93163.58 3.73362.21 0.28260.36 1.32861.05 NA 0.6168 (0.387–1.51228) Aeonium alliance 18.83361.81 15.26361.95 8.4761.92, 7.1361.89 1.28160.92 2.95…”

“This suggests the importance of research into models that only mildly violate the molecular clock (Thorne, Kishino, and Painter 1998).”

“We then estimated branch lengths and divergence dates on this topology using computer programs (ESTBRANCHES and MULTIDIVTIME) that implement the Bayesian divergence dating method developed by Thorne and coworkers (Thorne et al., 1998; Kishino et al., 2001; Thorne and Kishino, 2002).”

“In other respects, the approaches are quite similar and we use Thorne et al.’s approach (Thorne et al., 1998; Kishino et al., 2001; Thorne and Kishino, 2002) here.”

“Woodburne et al. (2003) used the estbranches and divtime5b programs of Thorne et al. (1998) and Kishino et al. (2001) with hard constraints and amino acid sequences for two proteins (BRCA1 and IGF2) and obtained point estimates of 182–190 Ma for the split between marsupials and placentals.”

“The Bayesian approach in Multidivtime simultaneously estimates the rate and age for each node of a given tree, assuming a prior distribution of evolutionary rates along branches, and, option- ally, constraints on the age of certain internal nodes.”

“For the sake of comparison, node ages were also estimated with the correlated model of Thorne & Kishino (2002) available in the Multidistribute package (see also Thorne et al., 1998).”

“Bayesian relaxed clock using Markov chain Monte Carlo (MCMC)— Bayesian methods (Thorne et al., 1998; Kishino et al., 2001; Thorne and Kishino, 2002) that relax a strict molecular clock were also used to estimate divergence times using MULTIDIVTIME (available from J. Thorne, North Carolina State…”

“In addition, the geological timing and ecological context of this diversification can be estimated with aculeate fossil-calibrated molecular dating methods (Thorne et al. 1998; Kishino et al. 2001; Thorne & Kishino 2002; Sanderson 2003; Rutschmann et al. 2007); this work is in progress.”

“determine model parameters, and in estbranches (Thorne et al. 1998) to estimate branch lengths.”

“The parametric method proposed by Thorne et al. (1998) uses a probabilistic model based on priors to describe the change in evolutionary rates over time and uses the Markov chain Monte Carlo procedure to derive the posterior distribution of rates and times.”

“More specifically, the rate smoothing methods employed in our dating analyses, based on both Bayesian (Thorne et al., 1998) and penalized likelihood (Sanderson, 2002) approaches, allow rates to change between ancestraldescendant branches, thus creating estimation errors that depend on the number of nodes involved in t…”

“normal rate-autocorrelated model [37] was adopted to relax the molecular clock hypothesis as it has been shown to reasonably fit”

“Bayesian (Thorne et al., 1998; Kishino et al., 2001; Thorne and Kishino, 2002; Yang and Rannala, 2006) and likelihood (Yang and Yoder, 2003; Yang, 2004) methods have been developed and modified such that they can account for violations of the molecular clock and for uncertainties of the fossil record by incorporating…”

“Especially, those methods that relax the assumption of a molecular clock (e.g., Thorne et al., 1998; Kishino et al., 2001; Sanderson, 2002; Britton, 2005) and combine molecular data with time constraints (upper and lower bounds), usually derived from fossils or geological data, have become increasingly popular.”

“Character-based methods are available for correcting rate variation among lineages (Thorne, Kishino, and Painter 1998; Huelsenbeck, Larget, and Swofford 2000), but implementation is still difficult for large matrices.”

“Other Multidivtime parameters were calculated as follows (following Rutschmann 2005): rtrate (mean of prior distribution for the rate at the root node)¼X/rttm, where X is the median amount of evolution from the root to tips; rtratesd (standard deviation of rtrtate) ¼ 0.5 rtrate; brownmean (mean of the prior distributi…”

“We used the lognormal model (Thorne et al. 1998) to describe the change of rates over time and applied a broad gamma-distributed prior to the root of the tree (mean 40, standard deviation 20).”

“In contrast to the study of Hodgson et al. (2009), however, two independent methods were employed to estimate divergence dates: the autocorrelated Bayesian method of Thorne and Kishino (Thorne et al., 1998; Thorne and Kishino, 2002) as implemented with multidivtime from the MULTIDISTRIBUTE package and the uncorrelated…”

“More recently, methods have been developed in a framework of likelihood and Bayesian theory that aim to relax the assumptionof rate constancybymodeling the evolutionof rates between multiple calibration points (Rambaut and Bromham, 1998; Sanderson, 1997; Thorne et al., 1998).”

“Methods exist that allow the dating of divergence times despite unclock-like evolution (Kishino et al., 2001; Sanderson, 1997, 2002; Thorne et al., 1998), and our laboratory is currently investigating molecular clock calibrations for turtles using the R35 intron.”

“The Bayesian method of Thorne et al. (1998) is useful for this purpose, as shown by Nikaido et al. (2000) and Cao et al. (2000), who applied this method to mammalian mt-proteins.”

“…size histories and other population genetic parameters of interest to be inferred alongside increasingly sophisticated phylogenetic tree reconstructions, which, for example, do away with the assumption of a strict molecular clock (Drummond et al., 2006; Sanderson, 2002; Thorne et al., 1998).”

“GTR [10, 12] or evolving rates [15], can easily be incorporated in our method; the model parameters would then be estimated in the MCMC-analysis.”

“Rate variations occur when distantly-related taxa are used to construct phylogenetic trees, but two recent software programs, multidivtime ( Thorne et al. 1998 ) and r8s (Sanderson 2003), were developed to account for these rate variations and allow calculations of divergence times with more confidence.”

“For these data sets, divergence dates were also estimatedHIV-1 group O: A Bayesian coalescent framework was used for the joint estimation of population parameters, under a relaxed molecular clock using the program MULTIDIVTIME (Thorne et al. 1998; Thorne andsubstitution parameters, dates of divergence, and tree topolo…”

“2012), as turtles show both slow rates of miRNA evolution (Thorne et al. 1998) (ESM File”

“Maximum likelihood estimates of the branch lengths and their variance–covariance matrix were then estimated by the program Estbranches for each data set.”

“This is similar to the model used to describe phylogenetic autocorrelation of molecular evolutionary rates along the branches of a phylogenetic tree (Thorne et al. 1998; Drummond et al. 2006).”

“…that molecular date estimates will be improved by the choice of several cross-validated calibration points, by an increase in the number and accuracy of palaeontological data, and by development of new dating methods, allowing variation of evolutionary rates (Sanderson 1997; Thorne et al. 1998).”

“It also uses the Markov chain Monte Carlo (MCMC) procedure to derive the posterior distribution of rates (Thorne et al., 1998; Kishino et al., 2001) and times, and in a multigene data set allows each gene to be analyzed with an independent model (Thorne and Kishino, 2002).”

“Three relaxed clock models, the log–normal autocorrelated clock model (LOG) (Thorne et al., 1998), the ‘CIR’ process (CIR) (Cox et al., 1985; see also Lepage et al., 2006) and uncorrelated gamma multipliers (UGM) (Drummond et al., 2006), were used under a uniform prior on divergence times for…”

“A common framework of many of these models is the assumption that molecular rates are autocorrelated, whereby the rates in daughter lineages are inherited from parent branches (e.g., Sanderson 1997; Thorne et al. 1998; Aris-Brosou and Yang 2002; Drummond and Suchard 2010).”

“Thismethod is similar in spirit to models of rate shifts in molecular evolution (Thorne et al. 1998; Huelsenbeck et al. 2000; Drummond and Suchard 2010).”

“Thorne et al. (1998) have used Markov chain Monte Carlo (MCMC) methods to integrate likelihoods over a phylogeny on which branch lengths can vary among branches, but in the context of an approximate clock.”

“The BRMC method was implemented utilizing the software MULTIDIVTIME (Thorne et al., 1998).”

“The Bayesian approach was performed with PAML/multidivtime (Thorne et al., 1998; Yang, 2007), following the step-by-step manual, version 1.”

“Multidivtime requires a rooted tree topology, only allows for fixed minimum and maximum constraints, assumes autocorrelated rates of molecular evolution among lineages, and estimates branch lengths using the program estbranches (Thorne et al., 1998; Kishino et al., 2001; Thorne and Kishino, 2002).”

“ces. It may be used in a simple model where all characters evolve homogeneously or it may be extended by, e.g., using site-specic rate-multipliers (Yang 1994; 1996), branch-specic rate-multipliers (Thorne et al. 1998), branch-specic substitution rate matrices (Yang and Roberts 1995; Galtier and Gouy 1998) and site-spe…”