Estimating the rate of evolution of the rate of molecular evolution

“Therefore, we employ the MCMC approach to Bayesian estimation of the ‘‘rate of evolution of the rate of molecular evolution’’ (Thorne and Kishino, 2002; Thorne et al., 1998) using the combined mitochondrial plus nuclear data sets, and assuming the combined data Bayesian tree (Fig.”

“S1, Table 3, and an The multidistribute program (Thorne et al., 1998) was used with four reliable tim constraints within Lepidosauria (lower constraints based on fossil evidence; see Table not shown) presumably because the lower limitation values for these constraints stil 3.”

“Branch lengths and the variance–covariance matrix were then optimized using estbranches (Thorne et al., 1998).”

“6 andMultidivtime, that allow for a relaxed molecular clock (Thorne et al. 1998; Kishino et al. 2001; Thorne and Kishino 2002; Drummond et al. 2006; Drummond and Rambaut 2007).”

“Approximate likelihood computation was used to improve the efficiency of the analysis (Thorne et al. 1998).”

“Given the absence of a constant molecular clock for most of the loci, we employed the relaxed Bayesian methods for multilocus data to obtain the ultrametric trees (Thorne and Kishino, 2002; Thorne et al., 1998).”

“Secondly, we imposed a relaxed clock which allows for a heterogenous substitution rate according to Thorne et al. (1998).”

“These methods are based on different models for the rate of molecular evolution, such as the lognormal distribution and its recent variants (Thorne et al., 1998; Kishino et al., 2001; Thorne and Kishino, 2002), the gamma, the exponential, or the Ornstein-Uhlenbeck processes (Aris-Brosou and Yang, 2002).”

“Analytical methods now try to model change in substitution rates along individual branches of a phylogeny by combining molecular data with multiple simultaneous time constraints, usually from fossils (Thorne et al., 1998; Rambaut and Bromham, 1998; Kishino et al., 2001; Thorne and Kishino, 2002; Aris-Brosou and Yang,…”

“This method allows different rates on different branches (Thorne et al., 1998).”

“There are now statistical methods that estimate divergence times without assuming that all lineages evolve at the same rate (Huelsenbeck et al., 2000; Sanderson, 1997; Thorne et al., 1998).”

“…(sampled every 100 cycles) following a burn-in of 100,000 cycles was then performed using Multidivtime (Thorne and Kishino, 2002) in order to approximate the posterior distribution of substitution rates and divergence times (Thorne et al., 1998; Kishino et al., 2001; Thorne and Kishino, 2002).”

“Nowadays, relaxed molecular clock methods are developed to take these variations of evolutionary rates into account (Thorne et al. 1998; Rannala and Yang 2007).”

“Bayesian divergence dating programs like BEAST [38], Multidivtime [39], and MCMCTree [40] have advantages such as being able to deal with uncertainties in topology and branch length and can allow for different types of prior distributions.”

“Some models assume that the rate of evolution is constant across a phylogeny, while others consider the variation across lineages in rates of evolution to obtain more accurate estimates of divergence times (Thorne et al. 1998).”

“, [62,72,73]), the effect of incomplete sampling and node density [63,64,74], and in some cases active selection on the mitochondrial genome [75-79].”

“Bayesian Markov Chain Monte Carlo (MCMC) methods have become widely used for this purpose [6-8].”

“We concurrently estimate those aspects of phylogeny from molecular data (Zuckerkandl and Pauling 1962; Thorne et al. 1998).”

“, 2005) used the Bayesian rate autocorrelation dating method implemented in MultiDivTime (Kishino et al., 2001; Thorne and Kishino, 2002; Thorne et al., 1998) for the estimation of divergence times.”

“We follow the suggestion of Yang and Rannala (2005) to have different prior means for the s − 3 internal branch lengths and the s external branch lengths.”

“4 (Thorne et al., 1998; Yang, 2007), under the F84 + G model of substitution.”

“This estimation is based on the “relaxed clock” method which is not assuming the constant rate of the molecular clock, and allowing the moderate changes of the evolutionary rate from the parent branches to the daughter branches (Thorne et al., 1998; Hasegawa et al., 2003; Yonezawa et al., 2007).”

“Divergence time estimates were performed using two methods: (i) using linearized trees by re-estimating branch lengths under the assumption of constant rate of evolution (Takezaki et al., 1995) implemented in MEGA 3.1; and (ii) using a Bayesian method described by Thorne et al. (1998) and modified by Kishino et al. (2…”

“In this analysis, we applied the Bayesian method (Kishino et al., 2001; Thorne et al., 1998) to the”

“Divergence dates among the sampled taxa were estimated using the Bayesian relaxed clock method developed by Thorne et al. (1998) and Kishino et al. (2001).”

“…of DNA substitution at the root node is the same at the beginning and at the end of that branch, and because the method prunes the outgroup from the Bayesian analysis (Kishino et al., 2001; Thorne et al., 1998), we included a tinamou (Tinamus major; NC_002781) as an extra, more external outgroup.”

“Change in the rate of substitution occurs gradually over the tree and closely related lineages have similar rates under the model presented by Thorne et al. (1998) and Kishino et al. (2001).”

“Second, we used the topology obtained with Treefinder and MrBayes and estimated divergence times using the package Multidistribute (Thorne et al., 1998; Thorne and Kishino, 2002).”

“Among several molecular dating methods implementing a relaxed clock (Rutschmann, 2006) the programs Multidivtime (Thorne et al., 1998; Thorne and Kishino, 2002) and r8s (Sanderson, 2002) have been shown to produce reliable results (Smith et al.”

“We also use an internal fossil calibration of the molecular tree and the Bayesian relaxed clock approach developed by Thorne and Kishino (Thorne et al., 1998; Kishino et al., 2001; Thorne and Kishino, 178 B. Stadelmann, D. S. Jacobs, C. Schoeman, and M. Ruedi Downloaded From: https://bioone.org/journals/Acta-Chiropter…”

“This has motivated several developments to relax the strict molecular clock assumption, which can be largely subdivided into models that allow a limited number of discrete rate changes in the phylogeny (“local” molecular clocks, Yoder and Yang (2000); Drummond and Suchard (2010)) and models that allow the rate to chan…”

“A second approach was developed by Thorne et al. (1998), and uses Bayesian statistics to model explicitly the rate of evolution in a fully parametric setting.”

“Bayesian method of Thorne et al. (1998) and Thorne and Kishino (2002), as implemented in the multidivtime package (http://statgen.ncsu.edu/thorne/multidivtime.html), and the likelihood heuristic rate-smoothing algorithm of Yang (1997), as implemented in PAML3.14b3 (Yang, 1997; Yang and Yoder, 2003).”

“, 2001) and the sophistication of molecular dating techniques (e.g., Sanderson, 1997; Thorne et al., 1998; Huelsenbeck et al., 2000), in order to better understand how molecular evolutionary rates vary through time.”

“Divergence times for caniform species and clades were estimated with a Bayesian relaxed molecular-clock method (Thorne et al., 1998; Kishino et al., 2001; Thorne and Kishino, 2002) by using combined information from all sampled genes (Tables 1 and 2) and also two temporal constraints based on the fossil record.”

“Kishino et al. (2001; see also Thorne and Kishino, 2002; Thorne et al., 1998 ) method (KTB).”

“New theoretical developments (e.g. Sanderson 1997, 2002; Near & Sanderson 2004; Thorne et al. 1998; Thorne & Kishino 2002) offer a means of placing a dimension of Phil.”

“, [3-5]), reconstructing ancestral sequences (e.”

“We used three programs: Baseml (PAML, v.3.14; Yang, 1997), to estimate model parameters; Estbranches (v.8/5/03; Thorne et al., 1998), to estimate the maximum likelihood of the branch lengths and a variance–covariance matrix; and Multidivtime (Kishino et al., 2001; Thorne and Kishino, 2002), to perform a MCMC Bayesian…”

“The software described in Thorne et al. (1998) uses the HKY85 1 g; (Hasegawa et al. 1985; Yang 1994) model to estimate branch lengths.”

“Non- or semiparametric (Sanderson 1997; Sanderson 2002) and Bayesian (Thorne et al. 1998; Huelsenbeck et al. 2000; Kishino et al. 2001; Aris-Brosou and Yang 2002; Thorne and Kishino 2002) methods that model rate variation through time are another way to accommodate lineage-specific rate…”

“We used the Bayesian method of Thorne et al. (1998) as implemented in the package multidistribute (available at http://statgen. ncsu.edu/thorne/multidivtime.html) and following the guidelines in Rutschmann (2005).”

“8-5-03; Thorne et al. 1998) and Multidivtime (ver.”

“We improved the efficiency of the analysis using approximate Bayesian computation (Thorne et al., 1998).”

“…previous section, new methods are being developed to account for rate heterogeneity in estimates of divergence time (Sanderson, 1997, 2002, 2003; Thorne et al., 1998; Kishino et al., 2001; Thorne & Kishino, 2002; Drummond et al., 2006) and have been incorporated into the construction of…”

“Divergence times for the nodes on the respective optimal tree (Fig. 1) were estimated for each gene and intergene region separately and for the concatenated data set using the penalized likelihood (PL) method (Sanderson, 2002) and BRMC method ( Thorne et al., 1998; Kishino et al., 2001; Thorne and Kishino, 2002).”

“© 2007 The Authors Journal compilation © 2007 Blackwell Publishing Ltd different lineages (Thorne et al. 1998).”

“Evolutionary divergence times were estimated using the relaxed molecular clock model implemented in the software Multidivtime [56,57].”

“2006; Rannala and Yang 2007), and the correlated-rates model (Thorne et al. 1998; Rannala and Yang 2007), as long as we use multiple loci and independent priors on locus rates (see also Huelsenbeck et al.”

“and Pauling 1962), autocorrelated through time (Thorne et al. 1998; Sanderson 2002) or uncorrelated (Drum mond et al.”

“…(Hasegawa et al. 1989; Kishino and Hasegawa 1990; Yoder and Yang 2000; Yang and Yoder 2003; Drummond and Suchard 2010), autocorrelated rate models (Thorne et al. 1998; Kishino et al. 2001; Lepage et al. 2006), models accounting for stepwise rate changes along branches (Huelsenbeck et al. 2000),…”

“We used the Bayesian dating method based on a relaxed-clock model to estimate divergence times (Drummond et al., 2006; Thorne et al., 1998; Thorne and Kishino, 2002).”

“The use of molecular data for BIOGEOGRAPHY OF CARPENTER BEES 251 © 2002 The Linnean Society of Sanderson, 1997; Thorne, Kishino & Painter, 1998; Huelsenbeck, Larget & Swofford, 2000; Kishino, Thorne & Bruno, 2001) make it possible to linearize phylogenetic trees, relationships opens the possibility…”

“A Bayesian relaxed molecular clock method with rate autocorrelation along branches (Thorne et al. 1998; Thorne and Kishino 2002; Lepage et al. 2007) was used to estimate divergence dates while accounting for changes in evolutionary rate over time and allowing for mixture models of sequence…”

“A relaxed Bayesian molecular clock [24] dated the coalescence of the cyt b lineages to the late Neogene, 4.”

“To obtain error bars using penalized likelihood, sequence alignments were bootstrapped using Seqboot in PHYLIP and the branch lengths were estimated from each replicate data set using ML in PAUP*. Multidivtime (Thorne et al. 1998) was used for Bayesian inferences of node ages using the na data set, where parameters we…”

“…(Kishino and Hasegawa, 1990; Sanderson, 1997; Rambaut and Bromham, 1998; Yoder and Yang, 2000; Yang and Yoder, 2003) and Bayesian methodologies (Thorne et al., 1998; Huelsenbeck et al., 2000; Kishino et al., 2001; Thorne and Kishino, 2002) have been developed which allow variable rates among…”

“In the latter, the mutation rate is assumed to change independently along different branches of the tree [Thorne, Kishino, and Painter 1998; Huelsenbeck, Larget, and Swofford 2000].)”

“…the recent estimations are based on rich information of fossil records (e.g., Benton 1993; Benton and Donoghue 2007), large sequence data sets from whole mitochondrial genomes, and an method which does not depend on the assumption of constant rate of molecular evolution (Thorne et al. 1998).”

“We used a clock-free and highly parametric Bayesian MCMC approach, as implemented in t3 (Thornian time traveler), a modified version of the software package multidivtime (Thorne et al., 1998; Thorne & Kishino, 2002; Yang & Yoder, 2003).”

“It should also be noted that the lack of a time-calibrated molecular clock makes it difficult, but not impossible, to use nucleotide substitution rates to estimate divergence dates between taxa [119, 140].”

“We furthermore em- ←−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− ployed a Bayesian approach to estimate divergence times with the multidivtime software, included in the multidistribute package (Thorne et al. 1998).”

“Here, we adapt previously proposed Bayesian approaches (Thorne, Kishino, and Painter 1998; Kishino, Thorne, and Bruno 2001; Thorne and Kishino 2002) to a codon model of evolution.”

“population size, generation time, fidelity of DNA replication) may themselves be quite similar among closely related lineages ( Thorne et al. 1998 ).”

“The evolutionary rates are said to be autocorrelated [121–122], and an assumption of autocorrelated rates is included in the smoothing methods introduced by Sanderson [30, 115], as well as in many of the bayesian relaxed-clock models that have been proposed [116–120].”

“…different rates in different clades (Rambaut and Bromham 1998; Yoder and Yang 2000), or on each branch (Drummond et al. 2006), or modeling the instant rate of substitution as a Brownian diffusion (Thorne et al. 1998; Rannala and Yang 2007), or an Ornstein–Uhlenbeck process (Lepage et al. 2007).”

“Thorne, Kishino, and Painter (1998) proposed a different model of rate autocovariance.”

“Under the correlated-rate model, i is the rate at the root of the tree at the locus, from which rates for other nodes or branches evolve according to a stochastic process such as the geometric Brownian motion (Thorne et al. 1998; Thorne and Kishino 2002; Rannala and Yang 2007).”

“However, there is no objective way to define the calibration densities and researchers have used different approaches to define them [19, 37, 38, 40].”

“Rates of evolution (the settings of molecular clocks) often vary among lineages and a ‘global molecular clock’ cannot be applied (Thorne et al. 1998; Ho & Larson, 2006).”