Accuracy of Rate Estimation Using Relaxed-Clock Models with a Critical Focus on the Early Metazoan Radiation

When sequences evolved under a model of uncorrelated rate change, only Bayesian inference using an exponential rate model performed well.

“When the sequences evolved under a model of uncorrelated rate change, only Bayesian inference using an exponential rate model performed well.”

In a simulation-based case study, high rate estimates in the Cambrian period might be an artifact of the rate estimation method.

“A case study is presented in which we use a simulation-based approach to examine the hypothesis of elevated rates in the Cambrian period, and it is found that these high rate estimates might be an artifact of the rate estimation method.”

In all cases, the spread of rate estimates was much greater than under a molecular clock assumption.

“In all cases, the spread of rate estimates was much greater than under a molecular clock assumption.”

Rates were frequently overestimated under the GD model of rate change, with some rates being overestimated by a factor of three.

“Rates were frequently overestimated under the GD model of rate change, with some rates being overestimated by a factor of three, while the performance of the OUP model was slightly better.”

Three of the four methods performed well when the sequence data evolved according to a molecular clock constraint and were analyzed under a clock assumption.

“Three of the four methods performed well when the sequence data evolved according to a molecular clock constraint and were analyzed under a clock assumption (fig.3a).”

Popular methods for inferring rates from sequence data tend to overestimate rates in the internal branches close to the root of the tree.

“As seen in the case study, as well as in the simulation studies throughout this paper, popular methods for inferring rates from sequence data tend to overestimate rates in the internal branches close to the root of the tree.”

The performance of the OUP model was slightly better than the GD model.

“while the performance of the OUP model was slightly better.”

In Case 3, as in the previous two cases, the OUP model yielded the highest marginal posterior probabilities of the data given the model, even when penalties were imposed for the number of hyperparameters.

“In this case, as with the previous two cases, the OUP model of rate change yielded the highest marginal posterior probabilities of the data given the model (table 1), even when penalties were imposed for the number of hyperparameters involved in each method.”

There does not appear to be a clear relationship between the marginal posterior probability and the accuracy of the rate estimates.

“Nevertheless, there does not appear to be a clear relationship between the marginal posterior probability and the accuracy of the rate estimates.”

Under Case 3, many rates were substantially overestimated under the OUP model of rate change, despite hyperparameters being optimized by comparison of marginal posterior probabilities.

“Furthermore, many rates were substantially overestimated under the OUP model of rate change, despite the hyperparameters being optimized by comparison of marginal posterior probabilities.”

There was a large discrepancy between the levels of estimated uncertainty associated with rate estimates made by multidivtime and PhyBayes using a lognormal model of rate change.

“There was a large discrepancy between the levels of estimated uncertainty associated with rate estimates made by multidivtime and PhyBayes using a lognormal model of rate change.”

The parameter values that produced the most accurate rate estimates were not the ones yielding the highest average marginal probabilities of the data given the model.

“However, the parameter values that produced the most accurate rate estimates were not the ones yielding the highest average (over each group of data sets) marginal probabilities of the data given the model (results not shown).”

In simulation Case 3, where rates in each branch were independently drawn from a uniform distribution U(0.005,0.015), few methods performed well.

“When sequences evolved under a model where the rate in each branch was independently drawn from a uniform distribution U(0.005,0.015),few methods performed well (fig.5).”

An underestimation bias was also seen, to a much lesser extent, in the rate estimates produced under an LND model of rate change by multidivtime and PhyBayes.

“An underestimation bias was also seen, to a much lesser extent, in the rate estimates produced under an LND model of rate change (multidivtime and PhyBayes) (fig.3b).”

Rates estimated by the other methods were close to the true rate of 0.01 average substitutions per site per time unit.

“Rates estimated by the other methods were close to the true rate of 0.01 average substitutions per site per time unit, with the observed variation probably resulting from the stochastic nature of Poisson-distributed nucleotide substitutions.”

When the clock assumption was relaxed, penalized likelihood tended to underestimate rates.

“When the clock assumption was relaxed, penalized likelihood tended to underestimate rates.”

The resulting rate estimates from the original 18S data set and simulated data sets followed a pattern similar to that seen in Aris-Brosou and Yang (2003), with elevated rates in certain branches, despite the sequence data having been generated under a molecular clock constraint.

“The resulting rate estimates followed a pattern similar to that seen in the study by Aris-Brosou and Yang (2003) (fig.6a), with elevated rates in certain branches, despite the sequence data having been generated under a molecular clock constraint (fig.6b).”

Under Case 3, use of the GD model yielded poor rate estimates, with the majority of rates considerably overestimated, sometimes by a factor of four.

“Use of the GD model also yielded poor rate estimates, with the majority of rates being considerably overestimated, sometimes by a factor of four.”

The values obtained from data simulated under a molecular clock for the intervals 640-420 MYA and 420 MYA-present were 1.24 and 0.87, respectively.

“The values obtained from data simulated under a molecular clock, for these time intervals, were Rate Estimation Using Relaxed-Clock Models 1361 1.24 and 0.87, respectively.”

The OUP model still yields the highest marginal posterior probability even when each method is penalized 1 log unit for each hyperparameter.

“However, the OUP model still yields the highest marginal posterior probability even when each method is penalized 1 log unit for each hyperparameter.”

In Case 3, rate estimates under an ED model of rate change appeared to be the most accurate of all methods tested.

“The rate estimates made under an ED model of rate change appeared to be the most accurate of all the methods that were tested.”

The average across data sets of the sampled marginal probabilities of the data given the model was the highest when the OUP prior was used.

“The average (across data sets) of the sampled marginal probabilities of the data given the model was the highest when the OUP prior was used (table 1), which might simply reflect the fact that the use of this prior involves two hyperparameters.”

Under the GD, ED, and OUP models of rate change, the rate of substitution was often overestimated.

“Under other models of rate change (GD, ED, and OUP), the rate of substitution was often overestimated (fig.3c).”

The Langley-Fitch method implemented in r8s overestimated the rate by about 5% on average.

“The Langley-Fitch method implemented in r8s overestimated the rate by about 5% on average, which suggests that there might be an intrinsic bias (in either the method itself or its current implementation).”

Rates estimated from data that had evolved under a process of LND rate change were recovered with reasonable accuracy when an LND model of rate change was assumed.

“Rates estimated from data that had evolved under a process of LND rate change were recovered with reasonable accuracy when an LND model of rate change was assumed (fig.4).”

In the simulation studies described here, the choice of rate prior has a considerable effect on posterior estimates of substitution rates.

“In the simulation studies described here, the choice of rate prior has a considerable effect on posterior estimates of substitution rates.”

There have been few studies into the accuracy of relaxed-clock models.

“In spite of their increasingly widespread application, there have been few studies into the accuracy of relaxed-clock models (for exceptions, see Kishino, Thorne, and Bruno 2001;Yang and Yoder 2003;Perez-Losada, Hoeg, and Crandall 2004).”

• cites Kishino, Thorne, and Bruno 2001 sourceNot checked — no full text of the source
• cites Yang and Yoder 2003 sourceNot checked — no full text of the source
• cites Perez-Losada, Hoeg, and Crandall 2004Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

If the assumption of rate constancy does not hold across a tree, phylogenetic inference and divergence date estimation can be seriously misled unless rate heterogeneity among lineages is adequately taken into account.

“If the assumption of rate constancy does not hold across a tree, then phylogenetic inference and divergence date estimation can be seriously misled unless this rate heterogeneity among lineages is adequately taken into account (Yoder and Yang 2000).”

• cites Yoder and Yang 2000 sourceNot checked — no full text of the source

A unique rate parameter cannot be assigned to each branch when estimating absolute rates or divergence dates because rate and time are inextricably linked, unless the sequences are noncontemporaneous and have known ages.

“Unfortunately, such an approach cannot be taken when estimating absolute rates or divergence dates because rate and time are inextricably linked, unless the sequences are noncontemporaneous and have known ages (Rambaut 2000;Drummond et al. 2002).”

• cites Rambaut 2000 sourceNot checked — no full text of the source
• cites Drummond et al. 2002 sourceNot checked — no full text of the source

The observed variation in rate estimates probably resulted from the stochastic nature of Poisson-distributed nucleotide substitutions.

“with the observed variation probably resulting from the stochastic nature of Poisson-distributed nucleotide substitutions.”

The Langley-Fitch overestimation suggests that there might be an intrinsic bias in either the method itself or its current implementation.

“which suggests that there might be an intrinsic bias (in either the method itself or its current implementation).”

The impact of overestimation of rates in internal branches on divergence time estimation is likely dependent on whether rate and date estimates are calibrated using the root or using other internal nodes.

“Its impact is likely to be dependent on whether rate and date estimates are calibrated using the root or using other internal nodes.”

If the rate is overestimated in internal branches, then the ages of nodes older than the calibration points will be systematically underestimated.

“This has wide-ranging implications for studies of divergence dates: if the rate is overestimated in internal branches, then the ages of nodes older than the calibration points will be systematically underestimated.”

The consistent overestimation of rates seen in the cases above suggests that the high rate estimates in the Cambrian may be a consequence of the method used.

“However, the consistent overestimation of rates seen in the cases above suggests that the high rate estimates may be a consequence of the method used.”

If sequence data have evolved under clocklike or approximately clocklike conditions, it may be better to assume a molecular clock during phylogenetic analysis to improve the precision, and perhaps accuracy, of substitution rate estimates and inferred divergence dates.

“This suggests that if sequence data have evolved under clocklike (or approximately clocklike) conditions, it may be better to assume a molecular clock during phylogenetic analysis of the sequences to improve the precision, and perhaps accuracy, of substitution rate estimates (and, consequently, of inferred divergence dates).”

Aris-Brosou and Yang (2003) found that the average relative rate in the period from 640 to 420 MYA was 1.37 per site per MYA, compared with 0.62 in the period from 420 MYA to the present.

“Aris-Brosou and Yang (2003) found that the average relative rate in the period from 640 to 420 MYA was 1.37 per site per MYA, compared with 0.62 in the period from 420 MYA to the present.”

• cites Aris-Brosou and Yang (2003)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Penalized likelihood was not expected to accurately recover true rates because its fundamental assumption of minimal rate changes between branches was considerably violated in Case 3.

“Penalized likelihood was not expected to accurately recover the true rates because there was a considerable violation of its fundamental assumption of minimal rate changes between branches.”

Estimates of terminal rates are expected to be more accurate because they are constrained by the calibration points at the internal nodes.

“Estimates of terminal rates are expected to be more accurate because they are constrained by the calibration points at the internal nodes.”

The large difference between the prior range of the birth rate and the prior range of the extinction rate is liable to produce trees with short internal branches.

“The large difference between the prior range of the birth rate and the prior range of the extinction rate is also liable to produce trees with short internal branches.”

The evidence for elevated rates in the Cambrian was at least partly, if not entirely, an artifact of the estimation method.

“This implies that the evidence for elevated rates in the Cambrian was at least partly, if not entirely, an artifact of the estimation method.”

If the molecular clock is rejected, there is currently no method available to determine whether rates are sufficiently autocorrelated to warrant the application of relaxed-clock methods.

“If the clock is rejected, however, there is currently no method available to determine whether rates are sufficiently autocorrelated to warrant the application of relaxed-clock methods.”

If nodes other than the root are used for calibration, then the age of the root might be underestimated.

“If nodes other than the root are used for calibration, however, then the age of the root might be underestimated.”

Our results question the reliability of simplistic (and often inappropriate) model comparison methods, such as using the Akaike Information Criterion, for choosing the model that will most accurately infer molecular rates and divergence dates.

“However, our results also question the reliability of simplistic (and often inappropriate) model comparison methods, such as using the Akaike Information Criterion, for choosing the model that will most accurately infer molecular rates and divergence dates.”

The present study is based on the analysis of alignments comprising only a small number of relatively short sequences.

“The present study, however, is based on the analysis of alignments comprising only a small number of relatively short sequences.”

Our results suggest that careful selection of rate priors is important, especially when the information content of the data set being analyzed is low.

“Our results suggest that careful selection of rate priors is important, especially when the information content of the data set being analyzed is low.”