Bayesian Inference of Evolutionary Histories under Time-Dependent Substitution Rates

AbstractMany factors complicate the estimation of time scales for phylogenetic histories, requiring increasingly complex evolutionary models and inference procedures. The widespread application of molecular clock dating has led to the insight that evolutionary rate estimates may vary with the time frame of measurement. This is particularly well established for rapidly evolving viruses that can accumulate sequence divergence over years or even months. However, this rapid evolution stands at odds with a relatively high degree of conservation of viruses or endogenous virus elements over much longer time scales. Building on recent insights into time-dependent evolutionary rates, we develop a formal and flexible Bayesian statistical inference approach that accommodates rate variation through time. We evaluate the novel molecular clock model on a foamy virus cospeciation history and a lentivirus evolutionary history and compare the performance to other molecular clock models. For both virus examples, we estimate a similarly strong time-dependent effect that implies rates varying over four orders of magnitude. The application of an analogous codon substitution model does not implicate long-term purifying selection as the cause of this effect. However, selection does appear to affect divergence time estimates for the less deep evolutionary history of the Ebolavirus genus. Finally, we explore the application of our approach on woolly mammoth ancient DNA data, which shows a much weaker, but still important, time-dependent rate effect that has a noticeable impact on node age estimates. Future developments aimed at incorporating more complex evolutionary processes will further add to the broad applicability of our approach.

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Analyses of evolutionary dynamics in viruses are hindered by a time-dependent bias in rate estimates

Proceedings of The Royal Society B Biological Sciences ◽

10.1098/rspb.2014.0732 ◽

2014 ◽

Vol 281 (1786) ◽

pp. 20140732 ◽

Cited By ~ 106

Author(s):

Sebastián Duchêne ◽

Edward C. Holmes ◽

Simon Y. W. Ho

Keyword(s):

Time Scales ◽

Evolutionary Dynamics ◽

Nucleotide Substitution ◽

Viral Evolution ◽

Negative Relationship ◽

Purifying Selection ◽

Time Dependent ◽

Rate Variation ◽

Nucleotide Substitution Rate ◽

Evolutionary Time

Time-scales of viral evolution and emergence have been studied widely, but are often poorly understood. Molecular analyses of viral evolutionary time-scales generally rely on estimates of rates of nucleotide substitution, which vary by several orders of magnitude depending on the timeframe of measurement. We analysed data from all major groups of viruses and found a strong negative relationship between estimates of nucleotide substitution rate and evolutionary timescale. Strikingly, this relationship was upheld both within and among diverse groups of viruses. A detailed case study of primate lentiviruses revealed that the combined effects of sequence saturation and purifying selection can explain this time-dependent pattern of rate variation. Therefore, our analyses show that studies of evolutionary time-scales in viruses require a reconsideration of substitution rates as a dynamic, rather than as a static, feature of molecular evolution. Improved modelling of viral evolutionary rates has the potential to change our understanding of virus origins.

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A63 Quantifying the dynamics of evolutionary rates through time

Virus Evolution ◽

10.1093/ve/vez002.062 ◽

2019 ◽

Vol 5 (Supplement_1) ◽

Author(s):

J V Membrebe ◽

G Baele ◽

M A Suchard ◽

P Lemey

Keyword(s):

Evolutionary History ◽

Nucleotide Substitution ◽

Evolutionary Rate ◽

Evolutionary Rates ◽

Dynamic Feature ◽

Substitution Model ◽

Substitution Rates ◽

Divergence Time Estimates ◽

The Past ◽

Codon Substitution

Abstract The availability of evolutionary rate estimates in recent years led to the observation that they may depend on the time-scale on which they are measured. Specifically, RNA virus evolutionary rates are frequently estimated to be low towards the past and high towards the present. This time-dependent rate phenomenon (TDRP) has important implications for evolutionary studies as it could severely bias divergence time estimates. While recent studies are providing insights into the relationship between viral evolutionary rate and time, formal probabilistic models to draw inference under TDRP scenarios remain lacking. Here, we adopt epoch-modelling to develop a Bayesian model of discrete rate changes through time in an unknown evolutionary history and combine this with a log-linear parameterization of rates as a function of times in the past. We provide an implementation for nucleotide substitution rates as well as for nonsynonymous rates change in a codon substitution model. Using a foamy virus dataset for which internal node calibrations can be applied based on host-virus co-divergence, we estimate a significant decline in evolutionary rates as a function of time into the past for nucleotide substitutions as well as for non-synonymous substitutions in a codon model. We also estimate a deep evolutionary history for primate Lentiviruses by combining an HIV-1 group M node calibration and a biogeographic calibration for viruses in drill monkeys in the TDRP model. Our analyses lead to the conclusion that studies of evolutionary timescales require a reconsideration of substitution rates, in either codon and nucleotide substitution model, as a dynamic feature of molecular evolution.

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Contemporary Distribution, Estimated Age, and Prehistoric Migrations of Old World Monkey Retroviruses

Epidemiologia ◽

10.3390/epidemiologia2010005 ◽

2021 ◽

Vol 2 (1) ◽

pp. 46-67

Author(s):

Antoinette C. van der Kuyl

Keyword(s):

Close Contact ◽

World Monkey ◽

Foamy Virus ◽

Endogenous Retrovirus ◽

Papio Cynocephalus ◽

Endogenous Virus ◽

Simian Foamy Virus ◽

Old World ◽

T Lymphotropic Virus ◽

Type D

Old World monkeys (OWM), simians inhabiting Africa and Asia, are currently affected by at least four infectious retroviruses, namely, simian foamy virus (SFV), simian immunodeficiency virus (SIV), simian T-lymphotropic virus (STLV), and simian type D retrovirus (SRV). OWM also show chromosomal evidence of having been infected in the past with four more retroviral species, baboon endogenous virus (BaEV), Papio cynocephalus endogenous virus (PcEV), simian endogenous retrovirus (SERV), and Rhesus endogenous retrovirus-K (RhERV-K/SERV-K1). For some of the viruses, transmission to other primates still occurs, resulting, for instance, in the HIV pandemic. Retroviruses are intimately connected with their host as they are normally spread by close contact. In this review, an attempt to reconstruct the distribution and history of OWM retroviruses will be made. A literature overview of the species infected by any of the eight retroviruses as well as an age estimation of the pathogens will be given. In addition, primate genomes from databases have been re-analyzed for the presence of endogenous retrovirus integrations. Results suggest that some of the oldest retroviruses, SERV and PcEV, have travelled with their hosts to Asia during the Miocene, when a higher global temperature allowed simian expansions. In contrast, younger viruses, such as SIV and SRV, probably due to the lack of a primate continuum between the continents in later times, have been restricted to Africa and Asia, respectively.

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Reliable confidence intervals for RelTime estimates of evolutionary divergence times

10.1101/677286 ◽

2019 ◽

Cited By ~ 1

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.

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Understanding UCEs: A Comprehensive Primer on Using Ultraconserved Elements for Arthropod Phylogenomics

Insect Systematics and Diversity ◽

10.1093/isd/ixz016 ◽

2019 ◽

Vol 3 (5) ◽

Cited By ~ 9

Author(s):

Y Miles Zhang ◽

Jason L Williams ◽

Andrea Lucky

Keyword(s):

Time Scales ◽

Evolutionary History ◽

Population Level ◽

Tree Of Life ◽

Deep Time ◽

Ultraconserved Elements ◽

Background Theory ◽

Promising Tool ◽

Recent Advances ◽

Targeted Enrichment

Abstract Targeted enrichment of ultraconserved elements (UCEs) has emerged as a promising tool for inferring evolutionary history in many taxa, with utility ranging from phylogenetic and biogeographic questions at deep time scales to population level studies at shallow time scales. However, the methodology can be daunting for beginners. Our goal is to introduce UCE phylogenomics to a wider audience by summarizing recent advances in arthropod research, and to familiarize readers with background theory and steps involved. We define terminology used in association with the UCE approach, evaluate current laboratory and bioinformatic methods and limitations, and, finally, provide a roadmap of steps in the UCE pipeline to assist phylogeneticists in making informed decisions as they employ this powerful tool. By facilitating increased adoption of UCEs in phylogenomics studies that deepen our comprehension of the function of these markers across widely divergent taxa, we aim to ultimately improve understanding of the arthropod tree of life.

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Analyzing Monthly Extreme Sea Levels with a Time-Dependent GEV Model

Journal of Atmospheric and Oceanic Technology ◽

10.1175/jtech2009.1 ◽

2007 ◽

Vol 24 (5) ◽

pp. 894-911 ◽

Cited By ~ 75

Author(s):

Fernando J. Méndez ◽

Melisa Menéndez ◽

Alberto Luceño ◽

Inigo J. Losada

Keyword(s):

San Francisco ◽

Time Scales ◽

Southern Oscillation ◽

Efficient Estimation ◽

Time Dependent ◽

Seasonal Effects ◽

Complete Analysis ◽

Sea Levels ◽

Data Variability ◽

Extreme Sea Levels

Abstract A statistical model to analyze different time scales of the variability of extreme high sea levels is presented. This model uses a time-dependent generalized extreme value (GEV) distribution to fit monthly maxima series and is applied to a large historical tidal gauge record (San Francisco, California). The model allows the identification and estimation of the effects of several time scales—such as seasonality, interdecadal variability, and secular trends—in the location, scale, and shape parameters of the probability distribution of extreme sea levels. The inclusion of seasonal effects explains a large amount of data variability, thereby allowing a more efficient estimation of the processes involved. Significant correlation with the Southern Oscillation index and the nodal cycle, as well as an increase of about 20% for the secular variability of the scale parameter have been detected for the particular dataset analyzed. Results show that the model is adequate for a complete analysis of seasonal-to-interannual sea level extremes providing time-dependent quantiles and confidence intervals.

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TIME-DEPENDENT SSC COOLING EFFECTS ON BLAZAR EMISSION

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194514601811 ◽

2014 ◽

Vol 28 ◽

pp. 1460181

Author(s):

MICHAEL ZACHARIAS ◽

REINHARD SCHLICKEISER

Keyword(s):

Time Scales ◽

Doubling Time ◽

Spectral Energy Distribution ◽

Nonlinear Behavior ◽

Time Dependent ◽

Spectral Energy ◽

Relativistic Electrons ◽

Linear Approach ◽

Standard Linear ◽

Cooling Effects

Blazars are among the most violent sources in the cosmos exhibiting flaring states with remarkably different variability time scales. Especially rapid flares with flux doubling time scales of the order of minutes have been puzzling for quite some time. Many modeling attempts use the well known linear and steady-state scenario for the cooling and emission processes in the jet, albeit the obvious strongly time-dependent nature of flares. Due to the feedback of the self-produced synchrotron radiation with additional scattering by the relativistic electrons, the synchrotron-self Compton (SSC) effect is inherently time-dependent. Recently, an analytical analysis on the effects of this nonlinear behavior has been presented. Here, we summarize these results concerning the effect of the time-dependent SSC cooling on the spectral energy distribution (SED), and the synchrotron lightcurves of blazars. For that, we calculated analytically the synchrotron, SSC and external Compton (EC) component of the SED, giving remarkably different spectral features compared to the standard linear approach. The resulting fluxes strongly depend on the parameters, and SSC might have a strong effect even in sources with strong external photon fields (such as FSRQs). For the synchrotron lightcurve we considered the effects of retardation, including the geometry of the source. The retardation might smear out some effects of the time-dependent cooling, but since lightcurves and SEDs have to be fitted simultaneously with the same set of parameters, the results give nonetheless important clues about the source. Thus, we argue for a wide utilization of the time-dependent treatment in modeling (especially rapid) blazar flares, since it accounts for features in the SED and the lightcurves that are usually accounted for by introducing several breaks in the electron distribution without any physical justification.

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Time-dependent treatment of scattering: potential referenced and kinetic energy referenced modified Cayley approaches to atom–diatom collisions and time-scale separations

Canadian Journal of Chemistry ◽

10.1139/v92-091 ◽

1992 ◽

Vol 70 (2) ◽

pp. 686-692

Author(s):

Omar A.Sharafeddin ◽

Donald J. Kouri ◽

David K. Hoffman

Keyword(s):

Kinetic Energy ◽

Potential Energy ◽

Time Scales ◽

Quantum Dynamics ◽

Time Dependent ◽

Multiple Time Scales ◽

Binding Potential ◽

Multiple Time ◽

General Reference ◽

Cayley Transformation

The time-dependent Lippmann–Schwinger equation describing atom–diatom collisions is expressed in terms of a general reference Hamiltonian, Hr, whose dynamics are easily solved in one representation, and a corresponding disturbance Hamiltonian, Hd, whose dynamics are easily solved in a different representation. The wavefunction at time t + τ t is then expressed in terms of its value at a previous time t by means of a simple quadrature approximation. The resulting expression for ψ(t + τ) has a form similar to that occurring in earlier numerical unitary solutions to the time-dependent Schrodinger equation via a Cayley transformation. The structure of the new equations is made explicit for (a) the choice where Hr is taken to be the kinetic energy and Hd is the potential energy and (b) the choice where Hr is taken to be the potential energy and Hd is the kinetic energy. In addition, we also deal with several alternatives for treating the binding potential of the diatom. Several alternatives for choosing representations are then explored for reducing the equations to a form amenable to computation. The short time structure of the equations is discussed in terms of a multiple time-scales analysis. Keywords: molecular collisions, multiple time scales, quantum dynamics.

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