Propagating clade and model uncertainty to confidence intervals of divergence times and branch lengths

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.

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Probabilistic divergence time estimation without branch lengths: dating the origins of dinosaurs, avian flight and crown birds

Biology Letters ◽

10.1098/rsbl.2016.0609 ◽

2016 ◽

Vol 12 (11) ◽

pp. 20160609 ◽

Cited By ~ 32

Author(s):

G. T. Lloyd ◽

D. W. Bapst ◽

M. Friedman ◽

K. E. Davis

Keyword(s):

Late Jurassic ◽

Divergence Time ◽

Time Estimation ◽

Divergence Times ◽

Essential Requirement ◽

Divergence Time Estimation ◽

Avian Flight ◽

Time Scaling ◽

Branch Lengths ◽

The Rich

Branch lengths—measured in character changes—are an essential requirement of clock-based divergence estimation, regardless of whether the fossil calibrations used represent nodes or tips. However, a separate set of divergence time approaches are typically used to date palaeontological trees, which may lack such branch lengths. Among these methods, sophisticated probabilistic approaches have recently emerged, in contrast with simpler algorithms relying on minimum node ages. Here, using a novel phylogenetic hypothesis for Mesozoic dinosaurs, we apply two such approaches to estimate divergence times for: (i) Dinosauria, (ii) Avialae (the earliest birds) and (iii) Neornithes (crown birds). We find: (i) the plausibility of a Permian origin for dinosaurs to be dependent on whether Nyasasaurus is the oldest dinosaur, (ii) a Middle to Late Jurassic origin of avian flight regardless of whether Archaeopteryx or Aurornis is considered the first bird and (iii) a Late Cretaceous origin for Neornithes that is broadly congruent with other node- and tip-dating estimates. Demonstrating the feasibility of probabilistic time-scaling further opens up divergence estimation to the rich histories of extinct biodiversity in the fossil record, even in the absence of detailed character data.

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Theoretical foundation of the RelTime method for estimating divergence times from variable evolutionary rates

10.1101/180182 ◽

2017 ◽

Author(s):

Koichiro Tamura ◽

Qiqing Tao ◽

Sudhir Kumar

Keyword(s):

Relative Rate ◽

Molecular Data ◽

Evolutionary Rates ◽

Divergence Times ◽

Computationally Efficient ◽

Molecular Sequence ◽

Branch Lengths ◽

Variable Evolutionary Rates ◽

Relationship Of ◽

The Relationship

AbstractRelTime estimates divergence times by relaxing the assumption of a strict molecular clock in a phylogeny. It showed excellent performance in estimating divergence times for both simulated and empirical molecular sequence datasets in which evolutionary rates varied extensively throughout the tree. RelTime is computationally efficient and scales well with increasing size of datasets. Until now, however, RelTime has not had a formal mathematical foundation. Here, we show that the basis of the RelTime approach is a relative rate framework (RRF) that combines comparisons of evolutionary rates in sister lineages with the principle of minimum rate change between an evolutionary lineage and its descendants. We present analytical solutions for estimating relative lineage rates and divergence times under RRF. We also discuss the relationship of RRF with other approaches, including the Bayesian framework. We conclude that RelTime will be also useful for phylogenies with branch lengths derived not only from molecular data, but also morphological and biochemical traits.

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Reliable Confidence Intervals for RelTime Estimates of Evolutionary Divergence Times

Molecular Biology and Evolution ◽

10.1093/molbev/msz236 ◽

2019 ◽

Vol 37 (1) ◽

pp. 280-290 ◽

Cited By ~ 3

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.

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Molecular and morphological clocks for estimating evolutionary divergence times

BMC Ecology and Evolution ◽

10.1186/s12862-021-01798-6 ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Jose Barba-Montoya ◽

Qiqing Tao ◽

Sudhir Kumar

Keyword(s):

Divergence Time ◽

Morphological Characters ◽

Molecular Data ◽

Morphological Data ◽

Divergence Times ◽

Evolutionary Divergence ◽

Species Divergence ◽

Time Estimates ◽

Branch Lengths ◽

Morphological And Molecular Data

Abstract Background Matrices of morphological characters are frequently used for dating species divergence times in systematics. In some studies, morphological and molecular character data from living taxa are combined, whereas others use morphological characters from extinct taxa as well. We investigated whether morphological data produce time estimates that are concordant with molecular data. If true, it will justify the use of morphological characters alongside molecular data in divergence time inference. Results We systematically analyzed three empirical datasets from different species groups to test the concordance of species divergence dates inferred using molecular and discrete morphological data from extant taxa as test cases. We found a high correlation between their divergence time estimates, despite a poor linear relationship between branch lengths for morphological and molecular data mapped onto the same phylogeny. This was because node-to-tip distances showed a much higher correlation than branch lengths due to an averaging effect over multiple branches. We found that nodes with a large number of taxa often benefit from such averaging. However, considerable discordance between time estimates from molecules and morphology may still occur as some intermediate nodes may show large time differences between these two types of data. Conclusions Our findings suggest that node- and tip-calibration approaches may be better suited for nodes with many taxa. Nevertheless, we highlight the importance of evaluating the concordance of intrinsic time structure in morphological and molecular data before any dating analysis using combined datasets.

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Molecular and morphological clocks for estimating evolutionary divergence times

10.21203/rs.3.rs-29165/v2 ◽

2021 ◽

Author(s):

Jose Barba-Montoya ◽

Qiqing Tao ◽

Sudhir Kumar

Keyword(s):

Divergence Time ◽

Morphological Characters ◽

Molecular Data ◽

Morphological Data ◽

Divergence Times ◽

Evolutionary Divergence ◽

Species Divergence ◽

Time Estimates ◽

Branch Lengths ◽

Morphological And Molecular Data

Abstract Background: Matrices of morphological characters are frequently used for dating species divergence times in systematics. In some studies, morphological and molecular character data from living taxa are combined, whereas others use morphological characters from extinct taxa as well. We investigated whether morphological data produce time estimates that are concordant with molecular data. If true, it will justify the use of morphological characters alongside molecular data in divergence time inference.Results: We systematically analyzed three empirical datasets from different species groups to test the concordance of species divergence dates inferred using molecular and discrete morphological data from extant taxa as test cases. We found a high correlation between their divergence time estimates, despite a poor linear relationship between branch lengths for morphological and molecular data mapped onto the same phylogeny. This was because node-to-tip distances showed a much higher correlation than branch lengths due to an averaging effect over multiple branches. We found that nodes with a large number of taxa often benefit from such averaging. However, considerable discordance between time estimates from molecules and morphology may still occur because some deeper nodes show a large time differences between these two types of data.Conclusions: Our findings suggest that node- and tip-calibration approaches may be better suited for nodes with many taxa. Nevertheless, we highlight the importance of evaluating the concordance of time structure in morphological and molecular data before any dating analysis using combined datasets.

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An enhanced calibration of a recently released megatree for the analysis of phylogenetic diversity

Brazilian Journal of Biology ◽

10.1590/1519-6984.20814 ◽

2016 ◽

Vol 76 (3) ◽

pp. 619-628 ◽

Cited By ~ 21

Author(s):

M. Gastauer ◽

J. A. A. Meira-Neto

Keyword(s):

Community Structure ◽

Vascular Plants ◽

Phylogenetic Trees ◽

Phylogenetic Diversity ◽

Vascular Plant ◽

Divergence Times ◽

Evolutionary Divergence ◽

Phylogenetic Community Structure ◽

Branch Lengths ◽

Age Estimates

Abstract Dated or calibrated phylogenetic trees, in which branch lengths correspond to evolutionary divergence times between nodes, are important requirements for computing measures of phylogenetic diversity or phylogenetic community structure. The increasing knowledge about the diversification and evolutionary divergence times of vascular plants requires a revision of the age estimates used for the calibration of phylogenetic trees by the bladj algorithm of the Phylocom 4.2 package. Comparing the recently released megatree R20120829.new with two calibrated vascular plant phylogenies provided in the literature, we found 242 corresponding nodes. We modified the megatree (R20120829mod.new), inserting names for all corresponding nodes. Furthermore, we provide files containing age estimates from both sources for the updated calibration of R20120829mod.new. Applying these files consistently in analyses of phylogenetic community structure or diversity serves to avoid erroneous measures and ecological misinterpretation.

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Molecular and morphological clocks for estimating evolutionary divergence times

10.21203/rs.3.rs-29165/v3 ◽

2021 ◽

Author(s):

Jose Barba-Montoya ◽

Qiqing Tao ◽

Sudhir Kumar

Keyword(s):

Divergence Time ◽

Morphological Characters ◽

Molecular Data ◽

Morphological Data ◽

Divergence Times ◽

Evolutionary Divergence ◽

Species Divergence ◽

Time Estimates ◽

Branch Lengths ◽

Morphological And Molecular Data

Abstract Background: Matrices of morphological characters are frequently used for dating species divergence times in systematics. In some studies, morphological and molecular character data from living taxa are combined, whereas others use morphological characters from extinct taxa as well. We investigated whether morphological data produce time estimates that are concordant with molecular data. If true, it will justify the use of morphological characters alongside molecular data in divergence time inference.Results: We systematically analyzed three empirical datasets from different species groups to test the concordance of species divergence dates inferred using molecular and discrete morphological data from extant taxa as test cases. We found a high correlation between their divergence time estimates, despite a poor linear relationship between branch lengths for morphological and molecular data mapped onto the same phylogeny. This was because node-to-tip distances showed a much higher correlation than branch lengths due to an averaging effect over multiple branches. We found that nodes with a large number of taxa often benefit from such averaging. However, considerable discordance between time estimates from molecules and morphology may still occur because some deeper nodes may show large time differences between these two types of data.Conclusions: Our findings suggest that node- and tip-calibration approaches may be better suited for nodes with many taxa. Nevertheless, we highlight the importance of evaluating the concordance of intrinsic time structure in morphological and molecular data before any dating analysis using combined datasets.

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Log Transformation Improves Dating of Phylogenies

Molecular Biology and Evolution ◽

10.1093/molbev/msaa222 ◽

2020 ◽

Author(s):

Uyen Mai ◽

Siavash Mirarab

Keyword(s):

Nonconvex Optimization ◽

Phylogenetic Trees ◽

Optimization Problem ◽

Sequence Data ◽

Real Data ◽

Divergence Times ◽

Expected Number ◽

Require Time ◽

Branch Lengths ◽

Complex Models

Abstract Phylogenetic trees inferred from sequence data often have branch lengths measured in the expected number of substitutions and therefore, do not have divergence times estimated. These trees give an incomplete view of evolutionary histories since many applications of phylogenies require time trees. Many methods have been developed to convert the inferred branch lengths from substitution unit to time unit using calibration points, but none is universally accepted as they are challenged in both scalability and accuracy under complex models. Here, we introduce a new method that formulates dating as a nonconvex optimization problem where the variance of log-transformed rate multipliers is minimized across the tree. On simulated and real data, we show that our method, wLogDate, is often more accurate than alternatives and is more robust to various model assumptions.

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Fitting a non-parametric stock–recruitment model in R that is useful for deriving MSY reference points and accounting for model uncertainty

ICES Journal of Marine Science ◽

10.1093/icesjms/fss183 ◽

2012 ◽

Vol 70 (1) ◽

pp. 56-67 ◽

Cited By ~ 11

Author(s):

Noel G. Cadigan

Keyword(s):

Confidence Intervals ◽

Model Uncertainty ◽

Fishery Management ◽

Reference Points ◽

Parametric Models ◽

Parametric Approach ◽

Stock Size ◽

Stock Recruitment ◽

Recruitment Model ◽

Non Parametric

Abstract Cadigan, N. G. 2013. Fitting a non-parametric stock–recruitment model in R that is useful for deriving MSY reference points and accounting for model uncertainty. – ICES Journal of Marine Science, 70:56–67. Modelling the relationship between parental stock size and subsequent recruitment of fish to a fishery is often required when deriving reference points, which are a fundamental component of fishery management. A non-parametric approach to estimate stock–recruitment relationships is illustrated using a simulated example and nine case studies. The approach preserves compensatory density dependence in which the recruitment rate monotonically decreases as stock size increases, which is a basic assumption of commonly used parametric stock–recruitment models. The implications of the non-parametric estimates on maximum sustainable yield (MSY) reference points are illustrated. The approach is used to provide non-parametric bootstrapped confidence intervals for reference points. The efficacy of the approach is investigated using simulations. The results demonstrate that the non-parametric approach can provide a more realistic estimation of the stock–recruitment relationship when informative data are available compared with common parametric models. Also, bootstrap confidence intervals for MSY reference points based on different parametric stock–recruitment models often do not overlap. The confidence intervals based on the non-parametric approach tend to be much wider, and reflect better uncertainty due to stock–recruit model choice.

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