Continuous and tractable models for the variation of evolutionary rates

Lepage, Thomas; Lawi, Stephan; Tupper, Paul; Bryant, David

doi:10.1016/j.mbs.2005.11.002

Cited by 49 publications

(51 citation statements)

References 43 publications

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“…Bayesian relaxed clocks include two classes of models, autocorrelated and uncorrelated clocks, which differ in their assumptions about the nature of rate variation among branches. Autocorrelated relaxed clocks assume that neighbouring branches share similar rates (Thorne et al 1998;Lepage et al 2006). In this sense, the motivating principle behind autocorrelated relaxed-clock models is similar to that of local-clock models, but the methods differ in the number of branch-specific rates across the tree.…”

Section: Relaxed Clocks: Parametric and Bayesian Methodsmentioning

confidence: 99%

“…In this way, the rate can be regarded as a quantitative trait that evolves through time, perhaps in correlation with lifehistory characteristics. One problem with these autocorrelated relaxed-clock models is that there is no bound to the potential increase in substitution rate over time (Lepage et al 2006). The more complex Ornstein-Uhlenbeck process (Aris-Brosou & Yang 2002) and Cox-Ingersoll-Ross models (Lepage et al 2006) were implemented with the aim of correcting this nonstationary behaviour, but the Ornstein-Uhlenbeckprocess model involves a systematic decline in the rate over time .…”

Section: Relaxed Clocks: Parametric and Bayesian Methodsmentioning

confidence: 99%

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Molecular‐clock methods for estimating evolutionary rates and timescales

2014

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The molecular clock presents a means of estimating evolutionary rates and timescales using genetic data. These estimates can lead to important insights into evolutionary processes and mechanisms, as well as providing a framework for further biological analyses. To deal with rate variation among genes and among lineages, a diverse range of molecular-clock methods have been developed. These methods have been implemented in various software packages and differ in their statistical properties, ability to handle different models of rate variation, capacity to incorporate various forms of calibrating information and tractability for analysing large data sets. Choosing a suitable molecular-clock model can be a challenging exercise, but a number of model-selection techniques are available. In this review, we describe the different forms of evolutionary rate heterogeneity and explain how they can be accommodated in molecular-clock analyses. We provide an outline of the various clock methods and models that are available, including the strict clock, local clocks, discrete clocks and relaxed clocks. Techniques for calibration and clock-model selection are also described, along with methods for handling multilocus data sets. We conclude our review with some comments about the future of molecular clocks.

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Section: Relaxed Clocks: Parametric and Bayesian Methodsmentioning

confidence: 99%

Section: Relaxed Clocks: Parametric and Bayesian Methodsmentioning

confidence: 99%

Molecular‐clock methods for estimating evolutionary rates and timescales

2014

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“…The density f λ t,λ α is explicitly known ( see for instance [1]). Moreover in [33] or in [36] an explicit expression of the conditional moment generating function of α t λ t,λ s ds is provided as…”

Section: Correlation Expansionmentioning

confidence: 99%

CVA and vulnerable options pricing by correlation expansions

2019

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We consider the problem of computing the Credit Value Adjustment (CVA) of a European option in presence of the Wrong Way Risk (WWR) in a default intensity setting. Namely we model the asset price evolution as solution to a linear equation that might depend on different stochastic factors and we provide an approximate evaluation of the option's price, by exploiting a correlation expansion approach, introduced in [2]. We compare the numerical performance of such a method with that recently proposed by Brigo et al. ([8], [10]) in the case of a call option driven by a GBM correlated with the CIR default intensity. We additionally report some numerical evaluations obtained by other methods.

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“…For both types of branch rate variation, we used a mean rate of 4 × 10 −3 substitutions per site per time unit and a variance parameter of 1.6 × 10 −5 . Branch-rate autocorrelation was simulated with the Cox-Ingersoll-Ross (CIR) process of Lepage et al (2006), using a decorrelation time of 100 time units. The branch lengths and substitution rates were used to simulate sequence evolution of 3000 nucleotides according to the unrestricted empirical codon model of Kosiol et al (2007).…”

Section: Generation Of Data Setsmentioning

confidence: 99%

Bayesian Node Dating based on Probabilities of Fossil Sampling Supports Trans-Atlantic Dispersal of Cichlid Fishes

Matschiner¹,

Musilová

Barth³

et al. 2016

Preprint

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Abstract.-Divergence-time estimation based on molecular phylogenies and the fossil record has provided insights into fundamental questions of evolutionary biology. In 1 . CC-BY 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/038455 doi: bioRxiv preprint first posted online Feb. 2, 2016; Bayesian node dating, phylogenies are commonly time calibrated through the specification of calibration densities on nodes representing clades with known fossil occurrences.Unfortunately, the optimal shape of these calibration densities is usually unknown and they are therefore often chosen arbitrarily, which directly impacts the reliability of the resulting age estimates. As possible solutions to this problem, two non-exclusive alternative approaches have recently been developed, the "fossilized birth-death" model and "total-evidence dating". While these approaches have been shown to perform well under certain conditions, they require including all (or a random subset) of the fossils of each clade in the analysis, rather than just relying on the oldest fossils of clades. In addition, both approaches assume that fossil records of different clades in the phylogeny are all the product of the same underlying fossil sampling rate, even though this rate has been shown to differ strongly between higher-level taxa. We here develop a flexible new approach to Bayesian node dating that combines advantages of traditional node dating and the fossilized birth-death model. In our new approach, calibration densities are defined on the basis of first fossil occurrences and sampling rate estimates that can be specified separately for all clades. We verify our approach with a large number of simulated datasets, and compare its performance to that of the fossilized birth-death model. We find that our approach produces reliable age estimates that are robust to model violation, on par with the fossilized birth-death model. By applying our approach to a large dataset including sequence data from over 1000 species of teleost fishes as well as 147 carefully selected fossil constraints, we recover a timeline of teleost diversification that is incompatible with previously assumed vicariant divergences of freshwater fishes. Our results instead provide strong evidence for trans-oceanic dispersal of cichlids and other groups of teleost fishes.(Keywords: node dating; calibration density; relaxed molecular clock; fossil record; Cichlidae; marine dispersal) 2 . CC-BY 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/038455 doi: bioRxiv preprint first posted online Feb. 2, 2016; In phylogenetic analyses, molecular sequence data are commonly used to infer not only the relationships between species, but also the divergence times between them. The estimation of divergence times in a phyogenetic context is usually ...

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Continuous and tractable models for the variation of evolutionary rates

Cited by 49 publications

References 43 publications

Molecular‐clock methods for estimating evolutionary rates and timescales

Molecular‐clock methods for estimating evolutionary rates and timescales

CVA and vulnerable options pricing by correlation expansions

Bayesian Node Dating based on Probabilities of Fossil Sampling Supports Trans-Atlantic Dispersal of Cichlid Fishes

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