scholarly journals Reliable confidence intervals for RelTime estimates of evolutionary divergence times

2019 ◽  
Author(s):  
Qiqing Tao ◽  
Koichiro Tamura ◽  
Beatriz Mello ◽  
Sudhir Kumar
Keyword(s):  
Confidence Intervals ◽  
Divergence Time ◽  
Simulated Data ◽  
Molecular Dating ◽  
Divergence Times ◽  
Rate Variation ◽  
Evolutionary Divergence ◽  
Posterior Density ◽  
Divergence Time Estimates ◽  
Highest Posterior Density

AbstractConfidence intervals (CIs) depict the statistical uncertainty surrounding evolutionary divergence time estimates. They capture variance contributed by the finite number of sequences and sites used in the alignment, deviations of evolutionary rates from a strict molecular clock in a phylogeny, and uncertainty associated with clock calibrations. Reliable tests of biological hypotheses demand reliable CIs. However, current non-Bayesian methods may produce unreliable CIs because they do not incorporate rate variation among lineages and interactions among clock calibrations properly. Here, we present a new analytical method to calculate CIs of divergence times estimated using the RelTime method, along with an approach to utilize multiple calibration uncertainty densities in these analyses. Empirical data analyses showed that the new methods produce CIs that overlap with Bayesian highest posterior density (HPD) intervals. In the analysis of computer-simulated data, we found that RelTime CIs show excellent average coverage probabilities, i.e., the true time is contained within the CIs with a 95% probability. These developments will encourage broader use of computationally-efficient RelTime approach in molecular dating analyses and biological hypothesis testing.

scholarly journals Reliable Confidence Intervals for RelTime Estimates of Evolutionary Divergence Times

2019 ◽  
Vol 37 (1) ◽  
pp. 280-290 ◽  
Author(s):  
Qiqing Tao ◽  
Koichiro Tamura ◽  
Beatriz Mello ◽  
Sudhir Kumar
Keyword(s):  
Confidence Intervals ◽  
Divergence Time ◽  
Simulated Data ◽  
Molecular Dating ◽  
Divergence Times ◽  
Rate Variation ◽  
Evolutionary Divergence ◽  
Posterior Density ◽  
Divergence Time Estimates ◽  
Highest Posterior Density

Abstract Confidence intervals (CIs) depict the statistical uncertainty surrounding evolutionary divergence time estimates. They capture variance contributed by the finite number of sequences and sites used in the alignment, deviations of evolutionary rates from a strict molecular clock in a phylogeny, and uncertainty associated with clock calibrations. Reliable tests of biological hypotheses demand reliable CIs. However, current non-Bayesian methods may produce unreliable CIs because they do not incorporate rate variation among lineages and interactions among clock calibrations properly. Here, we present a new analytical method to calculate CIs of divergence times estimated using the RelTime method, along with an approach to utilize multiple calibration uncertainty densities in dating analyses. Empirical data analyses showed that the new methods produce CIs that overlap with Bayesian highest posterior density intervals. In the analysis of computer-simulated data, we found that RelTime CIs show excellent average coverage probabilities, that is, the actual time is contained within the CIs with a 94% probability. These developments will encourage broader use of computationally efficient RelTime approaches in molecular dating analyses and biological hypothesis testing.

scholarly journals Using a GTR+Γ substitution model for dating sequence divergence when stationarity and time-reversibility assumptions are violated

2020 ◽  
Vol 36 (Supplement_2) ◽  
pp. i884-i894
Author(s):  
Jose Barba-Montoya ◽  
Qiqing Tao ◽  
Sudhir Kumar
Keyword(s):  
Divergence Time ◽  
Sequence Divergence ◽  
Molecular Dating ◽  
Divergence Times ◽  
Time Reversibility ◽  
Sequence Alignments ◽  
Divergence Time Estimates ◽  
Time Estimates ◽  
Substitution Process ◽  
The Impact

Abstract Motivation As the number and diversity of species and genes grow in contemporary datasets, two common assumptions made in all molecular dating methods, namely the time-reversibility and stationarity of the substitution process, become untenable. No software tools for molecular dating allow researchers to relax these two assumptions in their data analyses. Frequently the same General Time Reversible (GTR) model across lineages along with a gamma (+Γ) distributed rates across sites is used in relaxed clock analyses, which assumes time-reversibility and stationarity of the substitution process. Many reports have quantified the impact of violations of these underlying assumptions on molecular phylogeny, but none have systematically analyzed their impact on divergence time estimates. Results We quantified the bias on time estimates that resulted from using the GTR + Γ model for the analysis of computer-simulated nucleotide sequence alignments that were evolved with non-stationary (NS) and non-reversible (NR) substitution models. We tested Bayesian and RelTime approaches that do not require a molecular clock for estimating divergence times. Divergence times obtained using a GTR + Γ model differed only slightly (∼3% on average) from the expected times for NR datasets, but the difference was larger for NS datasets (∼10% on average). The use of only a few calibrations reduced these biases considerably (∼5%). Confidence and credibility intervals from GTR + Γ analysis usually contained correct times. Therefore, the bias introduced by the use of the GTR + Γ model to analyze datasets, in which the time-reversibility and stationarity assumptions are violated, is likely not large and can be reduced by applying multiple calibrations. Availability and implementation All datasets are deposited in Figshare: https://doi.org/10.6084/m9.figshare.12594638.

scholarly journals A Burmese amber fossil of <i>Radula</i> (Porellales, Jungermanniopsida) provides insights into the Cretaceous evolution of epiphytic lineages of leafy liverworts

Fossil Record ◽  
2017 ◽  
Vol 20 (2) ◽  
pp. 201-213 ◽  
Author(s):  
Julia Bechteler ◽  
Alexander R. Schmidt ◽  
Matthew A. M. Renner ◽  
Bo Wang ◽  
Oscar Alejandro Pérez-Escobar ◽  
...  
Keyword(s):  
Divergence Time ◽  
Character State ◽  
Posterior Density ◽  
Crown Group ◽  
Burmese Amber ◽  
Divergence Time Estimates ◽  
Time Estimates ◽  
Leafy Liverwort ◽  
Highest Posterior Density ◽  
Age Estimates

Abstract. DNA-based divergence time estimates suggested major changes in the composition of epiphyte lineages of liverworts during the Cretaceous; however, evidence from the fossil record is scarce. We present the first Cretaceous fossil of the predominantly epiphytic leafy liverwort genus Radula in ca. 100 Myr old Burmese amber. The fossil's exquisite preservation allows first insights into the morphology of early crown group representatives of Radula occurring in gymnosperm-dominated forests. Ancestral character state reconstruction aligns the fossil with the crown group of Radula subg. Odontoradula; however, corresponding divergence time estimates using the software BEAST lead to unrealistically old age estimates. Alternatively, assignment of the fossil to the stem of subg. Odontoradula results in a stem age estimate of Radula of 227.8 Ma (95 % highest posterior density (HPD): 165.7–306.7) and a crown group estimate of 176.3 Ma (135.1–227.4), in agreement with analyses employing standard substitution rates (stem age 235.6 Ma (142.9–368.5), crown group age 183.8 Ma (109.9–289.1)). The fossil likely belongs to the stem lineage of Radula subg. Odontoradula. The fossil's modern morphology suggests that switches from gymnosperm to angiosperm phorophytes occurred without changes in plant body plans in epiphytic liverworts. The fossil provides evidence for striking morphological homoplasy in time. Even conservative node assignments of the fossil support older rather than younger age estimates of the Radula crown group, involving origins for most extant subgenera by the end of the Cretaceous and diversification of their crown groups in the Cenozoic.

scholarly journals The Implications of Lineage-Specific Rates for Divergence Time Estimation

2019 ◽  
Vol 69 (4) ◽  
pp. 660-670 ◽  
Author(s):  
Tom Carruthers ◽  
Michael J Sanderson ◽  
Robert W Scotland
Keyword(s):  
Estimation Error ◽  
Divergence Time ◽  
Time Estimation ◽  
Rate Variation ◽  
Data Set ◽  
Divergence Time Estimation ◽  
Divergence Time Estimates ◽  
Time Estimates ◽  
The Impact ◽  
Highest Posterior Density

Abstract Rate variation adds considerable complexity to divergence time estimation in molecular phylogenies. Here, we evaluate the impact of lineage-specific rates—which we define as among-branch-rate-variation that acts consistently across the entire genome. We compare its impact to residual rates—defined as among-branch-rate-variation that shows a different pattern of rate variation at each sampled locus, and gene-specific rates—defined as variation in the average rate across all branches at each sampled locus. We show that lineage-specific rates lead to erroneous divergence time estimates, regardless of how many loci are sampled. Further, we show that stronger lineage-specific rates lead to increasing error. This contrasts to residual rates and gene-specific rates, where sampling more loci significantly reduces error. If divergence times are inferred in a Bayesian framework, we highlight that error caused by lineage-specific rates significantly reduces the probability that the 95% highest posterior density includes the correct value, and leads to sensitivity to the prior. Use of a more complex rate prior—which has recently been proposed to model rate variation more accurately—does not affect these conclusions. Finally, we show that the scale of lineage-specific rates used in our simulation experiments is comparable to that of an empirical data set for the angiosperm genus Ipomoea. Taken together, our findings demonstrate that lineage-specific rates cause error in divergence time estimates, and that this error is not overcome by analyzing genomic scale multilocus data sets. [Divergence time estimation; error; rate variation.]

scholarly journals Using a GTR+Γ substitution model for dating sequence divergence when stationarity and time-reversibility assumptions are violated

2020 ◽  
Author(s):  
Jose Barba-Montoya ◽  
Qiqing Tao ◽  
Sudhir Kumar
Keyword(s):  
Divergence Time ◽  
Sequence Divergence ◽  
Molecular Dating ◽  
Divergence Times ◽  
Time Reversibility ◽  
Sequence Alignments ◽  
Divergence Time Estimates ◽  
Time Estimates ◽  
Substitution Process ◽  
The Impact

AbstractMotivationAs the number and diversity of species and genes grow in contemporary datasets, two common assumptions made in all molecular dating methods, namely the time-reversibility and stationarity of the substitution process, become untenable. No software tools for molecular dating allow researchers to relax these two assumptions in their data analyses. Frequently the same General Time Reversible (GTR) model across lineages along with a gamma (+Γ) distributed rates across sites is used in relaxed clock analyses, which assumes time-reversibility and stationarity of the substitution process. Many reports have quantified the impact of violations of these underlying assumptions on molecular phylogeny, but none have systematically analyzed their impact on divergence time estimates.ResultsWe quantified the bias on time estimates that resulted from using the GTR+Γ model for the analysis of computer-simulated nucleotide sequence alignments that were evolved with non-stationary (NS) and non-reversible (NR) substitution models. We tested Bayesian and RelTime approaches that do not require a molecular clock for estimating divergence times. Divergence times obtained using a GTR+Γ model differed only slightly (∼3% on average) from the expected times for NR datasets, but the difference was larger for NS datasets (∼10% on average). The use of only a few calibrations reduced these biases considerably (∼5%). Confidence and credibility intervals from GTR+Γ analysis usually contained correct times. Therefore, the bias introduced by the use of the GTR+Γ model to analyze datasets, in which the time-reversibility and stationarity assumptions are violated, is likely not large and can be reduced by applying multiple calibrations.AvailabilityAll datasets are deposited in Figshare: https://doi.org/10.6084/[email protected]

scholarly journals A transcriptome-based study on the phylogeny and evolution of the taxonomically controversial subfamily Apioideae (Apiaceae)

2020 ◽  
Vol 125 (6) ◽  
pp. 937-953 ◽  
Author(s):  
Jun Wen ◽  
Yan Yu ◽  
Deng-Feng Xie ◽  
Chang Peng ◽  
Qing Liu ◽  
...  
Keyword(s):  
Evolutionary History ◽  
Incomplete Lineage Sorting ◽  
Morphological Evolution ◽  
Species Tree ◽  
Molecular Dating ◽  
Estimation Methods ◽  
Morphological Evidence ◽  
Evolutionary Divergence ◽  
Posterior Density ◽  
Highest Posterior Density

Abstract Background and Aims A long-standing controversy in the subfamily Apioideae concerns relationships among the major lineages, which has prevented a comprehensive study of their fruits and evolutionary history. Here we use single copy genes (SCGs) generated from transcriptome datasets to generate a reliable species tree and explore the evolutionary history of Apioideae. Methods In total, 3351 SCGs were generated from 27 transcriptome datasets and one genome, and further used for phylogenetic analysis using coalescent-based methods. Fruit morphology and anatomy were studied in combination with the species tree. Eleven SCGs were screened out for dating analysis with two fossils selected for calibration. Key Results A well-supported species tree was generated with a topology [Chamaesieae, (Bupleureae, (Pleurospermeae, (Physospermopsis Clade, (Group C, (Group A, Group B)))))] that differed from previous trees. Daucinae and Torilidinae were not in the tribe Scandiceae and existed as sister groups to the Acronema Clade. Five branches (I–V) of the species tree showed low quartet support but strong local posterior probabilities. Dating analysis suggested that Apioideae originated around 56.64 Mya (95 % highest posterior density interval, 45.18–73.53 Mya). Conclusions This study resolves a controversial phylogenetic relationship in Apioideae based on 3351 SCGs and coalescent-based species tree estimation methods. Gene trees that contributed to the species tree may undergoing rapid evolutionary divergence and incomplete lineage sorting. Fruits of Apioideae might have evolved in two directions, anemochorous and hydrochorous, with epizoochorous as a derived mode. Molecular and morphological evidence suggests that Daucinae and Torilidinae should be restored to the tribe level. Our results provide new insights into the morphological evolution of this subfamily, which may contribute to a better understanding of species diversification in Apioideae. Molecular dating analysis suggests that uplift of the Qinghai–Tibetan Plateau (QTP) and climate changes probably drove rapid speciation and diversification of Apioideae in the QTP region.

scholarly journals A posteriori evaluation of molecular divergence dates using empirical estimates of time-heterogeneous fossilization rates

2017 ◽  
Author(s):  
Simon Gunkel ◽  
Jes Rust ◽  
Torsten Wappler ◽  
Christoph Mayer ◽  
Oliver Niehuis ◽  
...  
Keyword(s):  
Fossil Record ◽  
Divergence Time ◽  
Simulated Data ◽  
Divergence Times ◽  
Data Sets ◽  
A Posteriori ◽  
Divergence Time Estimates ◽  
Empirical Estimates ◽  
Time Estimates ◽  
Log Normal

AbstractThe application of molecular clock concepts in phylogenetics permits estimating the divergence times of clades with an incomplete fossil record. However, the reliability of this approach is disputed, because the resulting estimates are often inconsistent with different sets of fossils and other parameters (clock models and prior settings) in the analyses. Here, we present the λ statistic, a likelihood approach for a posteriori evaluating the reliability of estimated divergence times. The λ statistic is based on empirically derived fossilization rates and evaluates the fit of estimated divergence times to the fossil record. We tested the performance of this measure with simulated data sets. Furthermore, we applied it to the estimated divergence times of (i) Clavigeritae beetles of the family Staphylinidae and (ii) all extant insect orders. The reanalyzed beetle data supports the originally published results, but shows that several fossil calibrations used do not increase the reliability of the divergence time estimates. Analyses of estimated inter-ordinal insect divergences indicate that uniform priors with soft bounds marginally outperform log-normal priors on node ages. Furthermore, a posteriori evaluation of the original published analysis indicates that several inter-ordinal divergence estimates might be too young. The λ statistic allows the comparative evaluation of any clade divergence estimate derived from different calibration approaches. Consequently, the application of different algorithms, software tools, and calibration schemes can be empirically assessed.

scholarly journals Insights from Empirical Analyses and Simulations on Using Multiple Fossil Calibrations with Relaxed Clocks to Estimate Divergence Times

2020 ◽  
Vol 37 (5) ◽  
pp. 1508-1529
Author(s):  
Tom Carruthers ◽  
Robert W Scotland
Keyword(s):  
Fossil Record ◽  
Sequence Data ◽  
Divergence Time ◽  
Time Estimation ◽  
Death Process ◽  
Divergence Times ◽  
Rate Variation ◽  
Direct Information ◽  
Divergence Time Estimates ◽  
Calibration Methods

Abstract Relaxed clock methods account for among-branch-rate-variation when estimating divergence times by inferring different rates for individual branches. In order to infer different rates for individual branches, important assumptions are required. This is because molecular sequence data do not provide direct information about rates but instead provide direct information about the total number of substitutions along any branch, which is a product of the rate and time for that branch. Often, the assumptions required for estimating rates for individual branches depend heavily on the implementation of multiple fossil calibrations in a single phylogeny. Here, we show that the basis of these assumptions is often critically undermined. First, we highlight that the temporal distribution of the fossil record often violates key assumptions of methods that use multiple fossil calibrations with relaxed clocks. With respect to “node calibration” methods, this conclusion is based on our inference that different fossil calibrations are unlikely to reflect the relative ages of different clades. With respect to the fossilized birth–death process, this conclusion is based on our inference that the fossil recovery rate is often highly heterogeneous. We then demonstrate that methods of divergence time estimation that use multiple fossil calibrations are highly sensitive to assumptions about the fossil record and among-branch-rate-variation. Given the problems associated with these assumptions, our results highlight that using multiple fossil calibrations with relaxed clocks often does little to improve the accuracy of divergence time estimates.

scholarly journals Undersampling Taxa Will Underestimate Molecular Divergence Dates: An Example from the South American Lizard Clade Liolaemini

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
James A. Schulte
Keyword(s):  
Divergence Time ◽  
Penalized Likelihood ◽  
Molecular Data ◽  
Molecular Dating ◽  
Taxon Sampling ◽  
South American ◽  
The South ◽  
Divergence Time Estimates ◽  
Time Estimates ◽  
Age Estimates

Methods for estimating divergence times from molecular data have improved dramatically over the past decade, yet there are few studies examining alternative taxon sampling effects on node age estimates. Here, I investigate the effect of undersampling species diversity on node ages of the South American lizard clade Liolaemini using several alternative subsampling strategies for both time calibrations and taxa numbers. Penalized likelihood (PL) and Bayesian molecular dating analyses were conducted on a densely sampled (202 taxa) mtDNA-based phylogenetic hypothesis of Iguanidae, including 92 Liolaemini species. Using all calibrations and penalized likelihood, clades with very low taxon sampling had node age estimates younger than clades with more complete taxon sampling. The effect of Bayesian and PL methods differed when either one or two calibrations only were used with dense taxon sampling. Bayesian node ages were always older when fewer calibrations were used, whereas PL node ages were always younger. This work reinforces two important points: (1) whenever possible, authors should strongly consider adding as many taxa as possible, including numerous outgroups, prior to node age estimation to avoid considerable node age underestimation and (2) using more, critically assessed, and accurate fossil calibrations should yield improved divergence time estimates.

scholarly journals Investigating the reliability of molecular estimates of evolutionary time when substitution rates and speciation rates vary

2021 ◽  
Author(s):  
Andrew M Ritchie ◽  
Xia Hua ◽  
Lindell Bromham
Keyword(s):  
Dna Sequences ◽  
Empirical Studies ◽  
Divergence Time ◽  
Molecular Dating ◽  
Rate Variation ◽  
Substitution Rates ◽  
Molecular Change ◽  
Dna Evidence ◽  
Dating Methods ◽  
Speciation Rates

Background An accurate timescale of evolutionary history is essential to testing hypotheses about the influence of historical events and processes, and the timescale for evolution is increasingly derived from analysis of DNA sequences. But variation in the rate of molecular evolution complicates the inference of time from DNA. Evidence is growing for numerous factors, such as life history and habitat, that are linked both to the molecular processes of mutation and fixation and to rates of macroevolutionary diversification. However, the most widely used models of molecular rate variation, such as the uncorrelated and autocorrelated lognormal clocks, rely on idealised models of rate variation and molecular dating methods are rarely tested against complex models of rate change. One relationship that is not accounted for in molecular dating is the potential for interaction between molecular substitution rates and speciation, a relationship that has been supported by empirical studies in a growing number of taxa. If these relationships are as widespread as evidence indicates, they may have a significant influence on molecular dates. Results We simulate phylogenies and molecular sequences under three different realistic rate variation models - one in which speciation rates and substitution rates both vary but are unlinked, one in which they covary continuously and one punctuated model in which molecular change is concentrated in speciation events, using empirical case studies to parameterise realistic simulations. We test two commonly used "relaxed clock" molecular dating methods against these realistic simulations to explore the degree of error in molecular dates under each model. We find average divergence time inference errors ranging from 12% of node age for the unlinked model when reconstructed under an uncorrelated rate prior, to up to 93% when punctuated simulations are reconstructed under an autocorrelated prior. Conclusions We demonstrate the potential for substantial errors in molecular dates when both speciation rates and substitution rates vary between lineages. This study highlights the need for tests of molecular dating methods against realistic models of rate variation generated from empirical parameters and known relationships.

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